When backtesting a portfolio strategy, you have to decide how far back to look. Should you use all available data, stretching back decades? Or should you just look at the last few years? There are arguments to be made for both options.

There are those who believe that factors are eternal and immutable, and that the farther back you go, the better. If some factors are currently out of favor, they’ll bounce back soon enough.

Others argue that the market has changed so fundamentally that old factors simply don’t apply. In addition, a lot of them have been arbitraged away. People point to the book-to-market factor as a good example: it worked well for decades, and then in 2006 it stopped working altogether. (The graph below charts the cumulative log returns of the upper half of the book-to-market spectrum minus the lower half from 1926 to 2024, assuming an initial investment of $100 and no transaction costs.)

For my entire investing career I’ve been in the latter camp. But something happened lately that caused me to change my mind.

Backtesting and Correlation

Do backtests have any correlation with out-of-sample results? If not, the whole idea of backtesting falls apart.

Let’s say an academic study finds that if you divided stocks into five groups according to how high their X ratio was, the highest group has a much higher Sharpe ratio than the lowest group. The study looks at US stocks over the last fifteen years. Would that be enough evidence to make you invest in stocks in that highest group?

It wouldn’t be enough evidence for me. I would want to know the answer to the following question: if I backtest fifty different strategies and take their Sharpe ratios over a fifteen-year period, would the results have a positive or negative relationship to the performance of those same strategies over the next five years? Perhaps the strategies would all mean revert, or perhaps having a high Sharpe ratio over a fifteen-year period signifies nothing.

In other words, backtests are only useful if their parameters are predictive. And that is something that these academic studies never really study.

So when I started using backtests to design investment strategies back in 2015, I decided to do some correlation studies. I had three major questions:

• Which performance measure is most predictive?
• Which lookback period is most predictive?
• How large a portfolio (or how many stocks out of the tested universe) is most predictive?

The work this took was enormous. First I had to design dozens of different strategies that were more or less untested; then I had to test them in various ways over various periods; and then I had to calculate the correlations between the backtests and a subsequent out-of-sample, untested period.

I was helped enormously in this endeavor by the tools available from Portfolio123, an invaluable source for factor research. And I came to the following conclusions, which I have affirmed by retesting many times:

• Trimmed alpha is the most predictive performance measure.
• A lookback period of nine to twelve years is optimal.
• A backtest that uses a lot more stocks than the final portfolio will hold is best.

The Problem of the Recent Past

As I’ve backtested and retested in order to design ranking systems, I’ve noticed over the years that the weight of value factors in my systems has kept dropping. And it was quite clear why. In general, value factors haven’t worked that well over the last twelve years compared to prior years.

But I have a strong gut feeling that there will be a resurgence (and perhaps there has been in the last few years). So I recently began to question my backtesting methodology.

Portfolio123’s data only goes back to 1999. Doing a twenty-year backtest and comparing the results with a three-year out-of-sample period with a one-year gap between them has only been possible since January 2023. And then you only have one or two out-of-sample periods to go on. Because of this limitation, I tested up to thirteen to fifteen years, never twenty or more. And there was always a drop-off after ten or twelve years. For example, I could set up a test that compared strategy returns through 2014 with an out-of-sample period spanning 2015 through 2017 inclusive, and test various starting dates for the backtested period. I could then move all the dates forward one year and end up with a somewhat wide variety of out-of-sample periods. When I averaged all the correlations over the various periods, it was quite clear that five-year periods were relatively useless and ten-year periods were pretty optimal.

But the out-of-sample periods were all in the last ten years. There were no out-of-sample periods covering the Great Financial Crisis or the Dot-Com Crash. I just didn’t have the data to go that far. (I did, at some point, use out-of-sample periods that were prior to the in-sample periods, but the results were more or less the same; and I’m not sure that this is really proper procedure.)

The Fama-French Solution

Then, a few weeks ago, I decided to backtest using the Fama-French library rather than Portfolio123. This library has returns for various strategies going back decades. At first, I ran the numbers on strategies going back to 1990 and tested up to fifteen years. This gave me a lot more to go on, and the results were very familiar: the performance dropped off after ten years. But then I decided to go farther. Most of the data in the library goes back to 1963. This gave me the ability to backtest far more than twenty years.

So I set up a rather huge test. I took 203 different series of returns from the library, all at one extreme or another. If, for example, the Fama French library tested 25 different combinations of two factors, size and profitability, I took the four most extreme: the quintile with the largest companies and the one with the highest profitability, the smallest and highest, the largest and lowest, and the smallest and lowest. I then measured the alpha of each strategy in the 3-year, 4-year, 5-year, and so on to 24-year periods ending in June 1987. I repeated that for 3-year to 24-year periods ending in December 1989, and so on every 18 months. Now I had tests covering 22 periods of various lengths ending on 22 different dates for 203 series of returns for a total of 98,252 different alphas.

I then calculated the total return of the same strategies for the three-year periods one year subsequent to the end of the alpha tests. Following that, I calculated the correlation between the ranks of the 203 strategies’ alphas during the backtest and the ranks of the subsequent out-of-sample total returns. And I then averaged those correlations over the 22 different out-of-sample periods.

The result confirmed what I’d been testing for the last eight years or so: if you’re choosing between a backtest period of three to fifteen years, a nine-to-twelve-year lookback is optimal.

But take a look at this chart (keep in mind that the out-of-sample tests begin a year after the backtests end, so the optimal lookback would be one year longer than the number of years tested).

The lookback periods after fifteen years begin to show increasing correlation, until you reach 24 years, at which point the correlations exceed those of the nine-to-twelve-year lookback.

In the end, after a great deal of experimentation, I came to the conclusion that the best approach to a backtest is to use the trimmed alpha of the last ten years as well as the trimmed alpha of the last twenty-five or more, emphasizing the latter. This is a very commonsense solution, and perhaps one I might have arrived at without all the correlation studies.

Searching for an Explanation

How might one explain that the optimal lookbacks are 10 and 25 years? Is there something about market and factor cyclicality at work? Or something about the nature of factors?

The reason is actually rather interesting. Below are two charts. The first are the correlations for the first 11 of the 22 periods I tested; the second are for the last 11.

Basically, in the last sixteen years there were quite a few three-year out-of-sample periods that were very much out-of-sync with the previous twenty-five years and more in-sync with the recent past. But in the previous sixteen years, there were almost none.

Let’s break this down a little more. Here’s a chart showing the optimal lookback periods for the 22 different starting dates of the three-year out-of-sample periods.

The biggest outliers here are the four three-year out-of-sample periods that began on June 2002, June 2014, December 2015, and June 2017. These all resembled the more recent past much more than they did the distant past. And those are the periods that really skewed the results. Close on their heels are three other periods: those that began in June 2008, December 2012, and December 2018. Notice that between 2012 and 2017 (the last of these ended in June 2020) we had five of these periods in a row. During that entire eight-year period, factors worked more in line with the last three to ten years than in line with the last twenty-five.

Why?

It could just be chance. I have observed a pretty good correlation between the optimal lookback period for a three-year out-of-sample period and the performance of value stocks during that period, as measured by high book-to-market stocks minus low book-to-market stocks. But that may be coincidental.

There’s another possibility, though. Between the Great Financial Crisis and the COVID crash there were relatively few retail investors actively participating in the US stock market. The GFC scared them away and most of them turned to 60/40 funds; if they invested in stocks, they did so passively, buying ETFs. Institutional investors dominated the market. By 2009 trades by retail investors made up less than 2% of trading volume, and by 2019 daily net flows from retail investors bottomed out at about $200M per day. Things changed dramatically with COVID. Suddenly a huge number of retail investors were actively stockpicking. By mid-2020 daily net flows had risen to $1B and by 2023 to $1.4B. By then, retail trades made up as much as a third of all trading in the US, beating out mutual funds and bank trading, and breaking even with hedge funds.

What does this have to do with factors? One could argue that retail investors are “dumb money” and that they’re more susceptible to behavioral fallacies than institutional investors are, and that therefore when retail investors participate heavily in the market, factor-based investing can rely more on the age-old tried and true factors rather than having to search for the new and different. Factors only work because of investor behavior; the more uninformed the average investor is, the better factors should work in the long run. (The exception might be during extended bubbles.)

What Factors Will Work Best in the Near Future?

We know from numerous studies that factors tend to be arbitraged away once discovered. We also know from numerous studies that factor classes tend to bounce back: if value has been in disfavor for a number of years, it will likely return; the same can be said of size, quality, growth, momentum, and so on. Lastly, we know that there are fundamental changes in the market, e.g. the speed of information dissemination, which quickens arbitrage and makes the discovery of new factors more imperative. All three of these forces tend to push and pull in different directions. The result might well be a complete absence of predictiveness when it comes to factors. People speak of factor momentum and factor reversion, but I have yet to be convinced of any predictability when it comes to what factors will work best in the near future.

Even if the years between the Great Financial Crisis and the COVID crisis were anomolous because of low retail participation, we shouldn’t discard them altogether. There are many valuable lessons to be learned from focusing on that period, which was a difficult one for factor-based investors.

Rather than guessing what factors will work best in the near future, I think it’s far better to concentrate on what factors work well in general. And that’s what the 10-year and 25-year combination tries to emphasize.

My conclusion goes strongly against the way machine-learning has been devised. There’s a strong resemblance between my studies and machine learning: one trains the model on X number of years, there’s a pause, and then there’s an out-of-sample (or holdout) period in which the model runs without further training. Normally the whole thing is then advanced a year or two. The model whose out-of-sample tests do best is the one you choose. But there’s a good deal of difference between my conclusions and machine learning. These models are not designed to take into account the entirety of past data. There is always a set limit, and that’s usually substantially less than the entirety. Machine-learning models trained on the last ten or twelve years of data will likely not favor deep value stocks. The idea behind sequential training periods disfavors the idea that out-of-favor factors can bounce back.

Before I conclude, one caveat to the backtest-as-far-back-as-you-can conclusion is in order. The farther you go back, the less data you have, and the less reliable that data can be. This isn’t necessarily true of fundamental data, but it is of analyst, institutional, insider, short interest, and similar kinds of data, especially outside North America. Even fundamental data has had some shifts due to changing IFRS and GAAP standards. The Fama-French data doesn’t have these limitations: the 25-year-and-more lookback is an idealized case. So when considering how far back to backtest, also take into account how far back you can reliably backtest.

The post How Far Back Should You Backtest? appeared first on Portfolio123 Blog.

Leverage can be a powerful tool in increasing your returns, but it must be used very carefully. This brief guide will attempt to cover margin, hedging, and related issues.

Financing Your Investments

In theory, if your expected returns on an investment are higher than whatever interest you might pay, it makes sense to increase your investments with borrowed money. But there is one important caveat. If your investment has variable returns, that fact can negate the increase.

For example, let’s say your expected return is 10% and you can borrow money at 7%. (These rates match the long-term expected return of the stock market and typical margin borrowing costs.) If you lose lots of money in the first year and then bounce back in the second and third so that your 3-year compound average growth rate (CAGR) is 10%, you still might end up worse off than if you hadn’t borrowed any money at all. This is due to what’s called sequence-of-returns risk. For example, let’s say you have $10,000 to invest and you borrow $5,000 at 7%/year interest. Your portfolio goes down 40% the first year, so you have $15,000 × 60% – 7% × $5,000 = $8,650. Your portfolio goes up 8% the second year, so you have $8,650 × 108% – 7% × $5,000 = $8,992. The third year you bounce back with your portfolio, scoring a 105.4% return for a CAGR of 10%. Your portfolio is now $8,992 × 205.4% – 7% × $5,000 = $18,120. At this point you pay back the $5,000 in debt for a total three-year return of $3,120. If you had invested your $10,000 without using any debt, though, your return would be 1.1³ × $10,000 – $10,000 = $3,310, which is significantly higher.

So financing your investments with debt only makes sense if at least one of the following is true: a) the difference between the expected return and the interest charged is quite large; b) the expected return is relatively steady; c) you minimize your short-term losses by using an effective hedge.

The only two relatively inexpensive ways to finance your investments that I’ve been able to find are cash-back mortgages and margin. The interest on both can be deducted from your taxes. Other loans tend to be far more expensive. Mortgage financing is relatively straightforward and cheap if you get a fixed-interest mortgage. I did this twice and due to compounding effects I made a huge amount of money hereby. Margin, however, is considerably more complicated.

Margin in a Nutshell

If you obtain margin on your portfolio, you borrow money from your broker using the securities you own as collateral. The amount your broker will allow you to borrow will depend on the value of your securities. If you borrow a significant amount and the value of your securities drops, you may face a margin call, asking you to deposit more cash in your account to cover the margin. If you fail to do so, the broker will liquidate your positions in order to settle the debt. This could wipe you out completely. Believe me: this happened to one of my best friends.

There are two basic types of margin: Regulation T margin and portfolio margin. Portfolio margin is significantly more difficult to obtain.

The Basics of Margin

Every position in a margin account has a margin requirement. At most brokers, the margin requirement is 100% for small, illiquid, foreign, and/or OTC stocks, as well as for uncovered options positions. At Fidelity, the margin requirement drops to 30% for very liquid stocks that are not concentrated positions or that are in sectors that comprise less than 20% of your portfolio. Margin requirements will vary between 30% and 60% for positions that are in-between those two extremes. For stocks whose price is between $3 and $10, the margin requirement will often be $3 per share.

Margin requirements are not intuitive, so let me explain their significance.

Below is a snapshot of the positions in my margin account at Fidelity in early October, along with their margin requirements.

The totals of the numbers in the “Position Value” column are the market value of my holdings (around $643,409). The “Dollar requirements” column consists of a) if the percentage requirement is a percentage, the product of that percentage and the position value; or b) if the percentage requirement is a dollar amount, the product of that dollar amount and the number of shares held. The total dollar requirements amount to about $265,404. At this point I had $223,185 in debt (this is not shown on the above chart). So my margin equity was the market value minus the debt, or $420,224. And my surplus was the margin equity minus the dollar requirements, or $154,820.

The surplus is the number you must watch if you’re using margin. As you can see, if the requirement is high (100% or $3 on a $3 stock), your surplus will be low, while if the requirement is low, your surplus will be high.

How much margin was I using at this point? Well, the amount of debt divided by the market value was about 35%, so I was using 1.35X margin. This number has a direct impact on your returns. For every dollar your investments gain you’ll be richer by $1.35; for every dollar your investments lose, you’ll be poorer by $1.35.

I have only faced a margin call once, when I was almost finished depleting a margin account. The key to avoiding calls is to always keep an eye on the surplus. Because margin requirements can go up at any time, I calculate what the surplus might be if all my margin requirements went up by 5% and my securities all went down in value by 20%, and keep that possible future surplus above zero. If the VIX (the CBOE Volatility Index) is high, I increase the 20% in the above sentence to 25% or 30%.

Reg T Margin

It’s not really essential to understand the rules of Regulation T Margin, which are very complicated. Suffice it to note three things.

1. Reg T will effectively cap your margin use at 2X, even if your margin requirements are all 30%.
2. If your securities appreciate, your Reg T surplus can go up, but if your securities depreciate, it won’t go down unless you buy or sell something in your portfolio. In other words, a market crash will not cause a Reg T call.
3. Your broker will very likely stop you from doing anything that would result in a Reg T call.

Portfolio Margin

Portfolio margin allows one to evade Reg T requirements; typically the margin requirements can be as low as 15% to 18%. The entire portfolio behaves as if it has one overall requirement. This allows you to use a positively unhealthy amount of leverage (up to 6X in some cases), and can result in very risky behavior. But it also makes your life considerably easier because you’re much, much less likely to be in danger of a margin call as long as you keep your leverage below 2X or 3X.

Different brokers have very different requirements for portfolio margin. Fidelity rarely grants it; Interactive Brokers grants it frequently but if you’re trading heavily in microcaps or foreign stocks the margin requirements are onerous. StoneX, the broker for my hedge fund (Fieldsong Investments), has allowed me to use portfolio margin, and it’s considerably easier to use than Reg T margin.

Leverage and Hedging

Without a hedge, the use of leverage can be disastrous. Because leverage multiplies one’s losses just as much as one’s gains (or more if you count the interest you pay), the risks one faces when using leverage are enormous. That’s why it’s advantageous to hedge your portfolio when using leverage.

I’ve been using put options on stocks likely to collapse to hedge my long equity positions. I’ve written about this strategy here. This kind of hedge is useless at counteracting small losses, and loses a huge amount of money during periods of market gains. But during significant corrections and bear markets, it tends to increase stratospherically. Below is a chart illustrating the relationship between a put hedge and the returns of a portfolio of the underlying stocks. This is based on the actual returns of my own investments in puts and assumes a portfolio of a dozen or more underlying stocks and a holding period of about 100 days.

You can see that if the portfolio has no gain or loss, the hedge loses between 5% and 10%. If the portfolio gains 20%, the hedge will lose about 40%. If, on the other hand, the portfolio goes down 10%, the hedge will go up between 15% and 20%, and if the portfolio goes down 20%, the hedge will go up about 50%. By the time the portfolio goes down 30%, the hedge will have gone up over 100%. Here’s a rough formula: y = –8.3x³ + 3x² – 2x + 0.07, where y is the put hedge return and x is the portfolio return. (Remember that this is assuming a 100-day period.) This formula was derived from the trendline in the above chart.

You can easily see, then, that a hedge like this will make it much easier, safer, and more profitable to use margin. There are other hedging options too: you could sell short a portfolio of stocks, or you could invest in an inverse ETF.

Here’s a graphic illustration of what can happen when you combine leverage with a hedge:

You’ll see that in this example the put hedge alone loses money: a lot of money. Between 1999 and today it loses more than 99% of its value. But with regular rebalancing, it shores up the returns during downturns. Here are the numbers:

(CVAR is the conditional value at risk at 10%, which means the average of all monthly returns below the 10th percentile of monthly returns. In my opinion, CVAR at 2%, 5%, 10%, and 15% are the best measures of risk available.)

These are, of course, hypothetical portfolios, and your actual portfolio may differ a great deal from them. I’ve done a huge amount of playing with various scenarios, and I’ve settled on a relatively conservative strategy for my hedge fund: use around 1.3X to 1.4X leverage and hedge that with around 8% to 10% puts. Feel free to try your own backtests, though, to come up with your own levels. Here are some rough guidelines:

1. Don’t be too optimistic. Never backtest a best-case scenario. Even a realistic scenario based on actual out-of-sample returns is probably not bad enough for a good backtest. You’re better off preparing for a worst-case scenario than aiming for realism.
2. Don’t look only at CAGR. Also look at median quarterly returns and CVARs.
3. Backtesting for a high Sharpe ratio will almost never favor the use of leverage, no matter how well you hedge. The same is true for CVARs. That’s why it’s important to balance measures like these with actual returns, whether they’re compounded or median.
4. While I’ve always advocated using alpha as a portfolio return measure, it’s useless when a hedge is involved. A few years ago I came up with a mathematical proof that when the market as a whole is showing positive returns, alpha and beta are inversely correlated. A hedge, whether it’s put-based or short-based, is going to radically decrease your beta, and therefore increase your alpha. If you’re looking for a very high alpha in your backtests, you’ll be favoring a much higher use of your hedge than is healthy for a portfolio.
5. Think of an unlevered unhedged portfolio as a base case. In no event do you want your CVARs or returns to be lower than that.
6. While it’s not very hard to adjust a short-based hedge depending on market conditions, it’s difficult and expensive to do so with a puts-based hedge. When backtesting, take into account that increasing or decreasing a hedge is a slow process. If you’re aiming for, say, a 10% hedge and the market takes a huge downturn, your hedge will balloon and it might take you a while to get back down to 10%; similarly, a huge upswing can cut your hedge percentage in half in a few days, and it’ll take some time to build it back to 10%. Options have a built-in time decay: they lose some of their value every day. This means that buying and selling puts has an opportunity cost that holding them doesn’t incur. Not only that, but their spread costs tend to be huge. That’s why it’s best to buy and sell puts slowly to avoid any unnecessary transactions.

Unhedged Leverage: An Example

In January 2022 I established a private foundation for charitable giving. I decided at the time to maximize my use of leverage by avoiding non-marginable stocks, and I did not use a hedge. To buy and sell stocks I use ranking systems I’ve designed on Portfolio123 (I also use those to determine which stocks to buy puts on). The returns have been very good: a time-weighted annualized return of 37%.

Significantly, however, this is lower than the returns I obtained managing very similar portfolios for my wife and my kids over the last three years, without using any leverage at all.

Part of this is due to the fact that in the Foundation account I only invest in marginable stocks, which excludes some Canadian and European stocks and all US OTC stocks, as well as a number of microcaps. But in addition, leverage is expensive (margin interest is not cheap on a highly levered portfolio), and the increased volatility, as I showed above, can harm overall returns. So at this point I’m planning to add a hedge to my foundation account. We’ll see how that goes . . .

The post How to Use Leverage to Boost Your Returns appeared first on Portfolio123 Blog.

The Nature of Financial Data

Late last year, Marcos M. López de Prado, a hedge fund manager and professor who has pioneered machine learning in finance and who is currently global head of quantitative research and development at one of the world’s largest sovereign wealth funds, published a monograph called Causal Factor Investing: Can Factor Investing Become Scientific? In it, he decries what he calls “rampant backtest overfitting and incorrect specification choices” in the academic literature about factor investing, discussing “spurious claims” and “causal confusion.” He then “proposes solutions with the potential to transform factor investing into a truly scientific discipline.”

López de Prado is at his best when debunking academic approaches to finance, specifically the pretension of financial/economic academics to a truly scientific approach. Much of his work along these lines is rehashed in this monograph. But here he falls into the same trap as the academics he debunks with the claim that factor investing can be “a truly scientific discipline.” I have my doubts.

The main problem is that the data factor investors work with is anything but scientific. Earnings, free cash flow, and other financial items are interpretations by accountants of what happens in firms that they work for. They follow regulatory standards, but have plenty of discretion, as well as a vested interest in presenting these items in a positive light. Nothing could be less scientific than this data, and this data is the foundation for all factor investing. While certain accounting items may be more “scientific” than others—interest expense, for instance, is quite quantifiable—so much depends upon completely discretionary items like depreciation rates, classification of costs and salaries (as CapEx, SG&A, R&D, other costs of goods, and so on), estimation of intangibles, and the timing of recognition of cash inflows and outflows. Despite regulatory frameworks like GAAP (generally accepted accounting principles, the US standard) and IFRS (International Financial Reporting Standards, the European standard) that aim to standardize reporting, there are very few financial items that are not infected with the discretionary practices of company accountants.

Factor investors take a quantitative approach to variables that are extraordinarily unreliable. What does that make us? Certainly not scientists. But neither are we soothsayers or literary interpreters. We take this extremely unreliable data and use established statistical methods and employ advanced testing techniques to get meaning out of it.

The only comparison I can come up with is parimutuel betting. A good gambler will take unreliable data and, using a probabilistic approach, place bets that have a somewhat decent chance of paying off. Nobody would confuse a gambler with a scientist, even though both may use advanced statistical techniques. People do confuse investors and gamblers, and there’s a good reason for that.

Discretionary Accounting

Here are a few specific examples of the kinds of discretion accountants can make.

• When valuing inventory, GAAP allows for all three methods (first in, first out; last in, first out; and weighted average cost).
• IFRS allows flexibility as to how interest and dividends are categorized in the cash flow statement, permitting listing under either operating or financial cash flow.
• IFRS allows revaluation of a broad range of assets.
• For software services, GAAP allows additional flexibility in revenue recognition.

I definitely do not want to suggest that GAAP and/or IFRS are flawed. Without them, things would be a thousand times worse. There’s a cost to overstandardization: the nuances in company accounts are important for investors to take notice of. That’s why 95% of the S&P 500 report both GAAP and non-GAAP earnings.

The key point is that financial reporting was not designed for broad data analysis but for properly illuminating an individual firm’s financial results. The standardization that GAAP and IFRS impose are important for establishing some consistency, but that consistency is geared toward comparison of individual firms and industries rather than toward scientific or statistical analysis. And comparison of individual firms and industries falls prey to a very different form of terribly unscientific data.

Industry Classification

Most factor investing necessitates intraindustry comparisons. Earnings yield is meaningful, but much more meaningful if you compare it to other companies in the same industry. But how do you classify companies into industries? Take, for example, Kewaunee Scientific (KEQU), which is currently one of my top holdings, both in my hedge fund and in my personal accounts. The company makes specialized furniture primarily for health care facilities. So is it a health care company? That’s what Compustat/S&P says it is. Or is it a furniture company? That’s what FactSet says it is. The problem goes beyond quirky businesses like Kewaunee. It makes a big difference whether Amazon (AMZN) is classified as a discretionary (cyclical) or a staples (non-cyclical) retail firm, or whether Visa (V) is in the financial or the technology sector. Different data providers classify these companies differently at different times (Compustat classifies Amazon as “discretionary” while FactSet classifies it as “noncyclical”; Compustat used to classify Visa in the tech sector, then moved it to the financial sector). And this brings us to yet another source of uncertainty.

Data Providers

For the sake of argument, I created a ranking system on Portfolio123 (a subscription-based tool that helps research and build systematic quantitative investing strategies) with thirty factors that I’ve been using quite heavily lately. I then compared how companies fared on this system depending on whether the data came from Compustat or FactSet.

One of the many companies with jaw-dropping discrepancies is eBay (EBAY). On FactSet it ranks 86 out of 100 while on Compustat it ranks 25.

So let’s take this apart a bit.

• The first thing I notice is an issue with special items. These are non-recurring pretax items such as moving expenses, severance payments, write-offs, write-downs, reserves for litigation, and so on. They should be taken into account when calculating a company’s net income. Compustat has this figure as –$206 million for 2023 while FactSet has it as +$1.75 billion for the same year. (Compustat lists a couple of dozen items that together make up special items; FactSet calculates it as the difference between extraordinary charges and extraordinary credits.) With a net income last year of $2.75 billion, whether you add back $206 million or subtract $1.75 billion makes a huge difference. According to FactSet, eBay is experiencing excellent earnings growth, since last year’s income is adjusted so radically. According to Compustat, its earnings growth is not so great.
• The next thing I notice is a big discrepancy in the balance sheet accruals. This is traceable to the fact that FactSet shows more than $3.1 billion in other investments and advances this quarter and $1.2 billion the same quarter last year, meaning that eBay has substantially increased its long-term receivables. Compustat, on the other hand, gives N/A for both. So for FactSet, eBay’s accruals are fine; for Compustat, they’re terribly high given that eBay’s cash on hand has decreased substantially in the last year. (This problem is lessened if you use annual figures. Compustat doesn’t usually list quarterly figures for this particular line item, which explains the N/As.)
• eBay’s earnings yield, based on current fiscal year estimates, is a little over 8%. How good is that? Well, normally one compares earnings yield to other companies in the same industry. For Compustat, the industry is multiline retail, which puts them in 7th place out of 19 companies (I’m limiting my scope to companies with sufficient liquidity to trade large amounts). For FactSet, the industry is general merchandise retail, which puts them in 10th place out of 32 companies. So eBay scores a little better with FactSet than with Compustat on earnings yield.
• I look at a lot of aspects of a company’s subsector, including its momentum and its average free cash flow yield; I also compare the inventory change of the company (which in this case is zero) to the inventory change of the subsector. For FactSet, eBay is in the food and staples retail subsector of the staples sector, while for Compustat, it’s in the consumer discretionary distribution and retail subsector, which is in the discretionary sector. Those two subsectors are very different indeed. The first has stronger momentum, higher free cash flow yield, and higher inventory growth. These make very substantial differences to the company rankings.
• According to FactSet, eBay’s operating income growth, comparing the most recent quarter to the same quarter a year ago, is 31%, while according to Compustat it’s only 7%. FactSet lists eBay’s current operating income as $658 million while Compustat lists it as $552 million; there are discrepancies between the numbers for the same quarter a year ago too. I’m not going to pronounce judgment on which data provider is correct: they simply standardize operating income (also called EBIT) in different ways.

eBay isn’t really an outlier here. 15% of the companies in Portfolio123’s “easy to trade” universe have a discrepancy of 20 or more between their FactSet and Compustat rankings (on this thirty-factor system), and that’s not even mentioning those companies that are covered by only one of the two data providers.

Using Unscientific Data to Assess Companies

How does one proceed, then, with assessing companies given the craziness of financial data? I have a few suggestions.

1. Don’t ever think that what you’re doing is scientific, objective, or truly solid. Suspect every conclusion you come to.
2. Check your data. If you come across major discrepancies, investigate them. Try to figure out what the company is reporting and what your data providers are doing with those numbers.
3. The more data you use, the less these discrepancies will matter. If you base your judgment of a company on just a handful of metrics, you’re bound to run into serious problems. Use ten different measures of earnings growth or earnings yield rather than only one; use a wide variety of measures of company quality, stability, and so on; calculate a company’s value using intrinsic value methods (preferably more than one) as well as relative value methods; use two or three different data providers rather than only one; and so on.
4. Hedge your bets with diversity. Use several different systems or strategies at once, provided you’re agnostic about which is better.
5. Concentrate on probability rather than absolutes in your thinking about investing and in your approach to systematization.

Working with financial data is never easy, and it’s made much more complex by the amount of data out there. Add to that the fact that the data itself is unreliable, fuzzy, capricious, and mutable and you’re liable to drown in data soup. Taking a cut-and-dry approach to data like this, simplifying your strategy to its essence, treating data as if it is sacrosanct, or ignoring it altogether is bound to backfire. Instead you have to learn to swim in the data soup, because the more of it you absorb, the better a picture you’ll be able to paint of the companies you’re investing in.

I have based my entire investing career on using financial data in novel ways. Ever since late 2015, I have been investing using ranking systems based on financial data, concentrating on safe, solid, boring, and under-the-radar companies, and as a result I have a CAGR of 42% during that period, without a single negative calendar year. I generally have little use for the kinds of factors that are standard in the financial services industry, the kinds of simple and well-trodden factors that are, for example, the basis of Seeking Alpha’s quant rankings. I have found that

• low profit margins can be predictive of earnings growth,
• the ratio of gross profit to total assets can be more meaningful than ROA,
• if a company’s receivables vary a great deal from quarter to quarter that usually spells trouble,
• you can base a value ratio on taxes paid,
• a company whose sales are turning around can be a much better investment than a company whose sales are growing steadily,
• low share turnover decreases market risk,
• dividend yield means nothing without considering the payout ratio,
• a simultaneous increase in both inventory and gross plant is a bad sign,
• operating cash flow had better exceed net income, and
• intrinsic value can be roughly estimated algorithmically.

My entire philosophy of investing is based on taking a look at every stock I buy or bet against from as many different angles as possible.

But I’m a quant at heart. I spend a hundred times more time and energy on my algorithmic systems than I do looking up the specifics of one company’s financials. The discretionary decisions I make have nothing to do with whether or not I buy or sell a particular stock on a particular day, but are all about improving my system and incorporating into it financial factors. Data matters to me a lot, and it scares the daylights out of me that it could be all wrong.

But what does “wrong” really mean when it comes to financial data? Nothing. Financial data is a mess of biased interpretations, but it’s all we have to work with. Approaching it in a holistic, individualized, and well-reasoned way is your best bet if you want to beat the market consistently.

The post Drowning in Data Soup: Why Factor Investing Cannot Be Scientific appeared first on Portfolio123 Blog.

The strategy isn’t as complicated as most options strategies. I buy low-priced medium-range out-of-the-money puts on a select group of stocks that I deem worthless. I then hold them until the week prior to expiration, with a few minor exceptions.

In this article I’m going to

1. explain why hedging with put options is preferable to hedging with short positions;
2. explain what put options are and how they work;
3. take you through my process of choosing put options to buy;
4. give you some tips on portfolio management with a put-option hedge.

Why Not Short?

When you short a stock, you borrow shares (sell short) and then close your deal by buying them back (buy to cover). If the price has fallen 50%, you gain 50%; if the price falls 85%, you gain 85%. But if the price rises by 80%, you lose 80%; if the price rises by 250%, you lose 250%. The most you can gain from a short position is 100%. But you can lose an infinite amount of money.

This tremendous imbalance between downside and upside has always prevented me from implementing a short strategy. I have, over the last eight years, repeatedly tried to come up with a short strategy that, when backtested, would not only provide a hedge but also increase my returns. I have, over those years, repeatedly failed to do so.

When you buy a put option, you are placing a bet on a stock’s price. If the price falls more than a certain amount, you’ll break even; if the price falls farther than that, your return will be a rough multiple of what you paid. If a stock’s price falls to close to zero, you could make a return of 1,000% or more. If the stock’s price does not go down to the strike price, then your option will expire worthless and you’ll lose the entirety of your investment. So your gain is unlimited and your loss is limited to 100%.

Why Puts Are Not a Good Stand-Alone Strategy

2022 and 2023 were a favorable environment for puts. First, there was a full-fledged bear market, during which stock prices fell. Then, during the recovery, volatility decreased quite a lot. When volatility is low, options are cheap.

However, I’ve identified other recent two-year periods during which my put strategy would be a complete failure, with a probable loss of 100%.

In addition, put options are extremely volatile instruments, and they are often correlated with each other. The value of my put portfolio can easily drop by 15% in a day and by 80% in a month.

So I view puts as a hedge, not a stand-alone strategy.

The purpose of hedges is to reduce volatility. In my backtesting, put options have served this purpose very well. It’s especially important to have an effective hedge if you’re using leverage. In the hedge fund I’m managing, I’m employing both leverage and a put-option hedge. The combination should allow me to increase returns while reducing market risk.

How I Came Up With This Idea

In 2021 I read Jim Cramer’s Real Money. Despite what Cramer has since become, it’s not a bad book; it was written almost twenty years ago. In it, Cramer writes, “please use puts when you can instead of borrowing and selling short stock. . . . If you are sure something is going to go down but don’t know when, use deep puts going out many, many months. You will never regret paying the extra money.”

Cramer’s entire chapter on options, “Advanced Strategies for Speculators,” is well worth a read, even twenty years later.

The Costs of Put Options and Short Positions

When you short a stock you often pay a borrowing cost. This is a daily percentage of your outlay. Borrowing costs will vary wildly from stock to stock and from broker to broker. With some brokers (e.g. Fidelity), there is no borrowing cost for most stocks; others (e.g. Interactive Brokers) charge for every stock. The borrowing cost depends on how many shares are available to short. So very popular shorts will be far more expensive than unpopular ones. I’ve often seen borrowing costs that are more than 100% a year.

With put options, you pay a substantial commission in addition to the price of the option. In addition, puts can be extremely expensive. Just like shorts, the more popular a put option is, the higher its price will be. It’s also far more complicated to determine a good price for a put option than it is for a short position. Lastly, the bid-ask spreads for put options are far, far wider than those for short positions. For the kinds of stocks I buy options on, the spread will often be 25% of the midpoint.

Shorting stocks is quite expensive, but not as expensive as trading puts. One reason that people prefer shorting to buying put options is that the costs of put options are so high. Another is that it’s a lot easier to buy and sell short than it is to trade in options. I probably spend three times as many hours investing in puts as I would investing in shorts.

Put options have other disadvantages over shorts. You can choose how long to hold a short position, and you don’t have to tie it to a specific price. Put options, on the other hand, expire on a certain date, and while you can exercise them early if you’re in the money and roll them over if you don’t mind paying large commissions, they’re far less flexible.

So if you choose to hedge with put options, it’s extremely important to calculate how much you’re willing to pay, to take commissions into account, and to use limit orders only.

What Are Put Options?

Option markets have been around for hundreds of years; some even date them to ancient Greece. The market for them was developed in the late 1800s by an American entrepreneur named Russell Sage. But it wasn’t until 1973, with the birth of the Chicago Board of Options Exchange (CBOE) and the Options Clearing Corporation, that trading options became standardized and safe. Even then, only call options, most of them relatively illiquid, were available. In 1977, put options were introduced to the CBOE, and liquidity was far better than before. Since then, the growth in options trading has been exponential.

A put option consists of four elements. First, there’s the underlying stock. Second, there’s the strike price: the price which you’ll get for the stock if you’re holding it upon expiration. Third, there’s the expiration date, which is usually the third Friday of a particular month. Fourth, there’s the premium, which is the price you pay for the option.

A few other terms are important. If the current price of the stock is above a put’s strike price, the option is out-of-the-money; if it’s under the strike price, it’s in-the-money. If the expiration date is more than a year from now, it’s a long-term option; if it’s in the next month, it’s short-term; if it’s in-between, it’s a medium-term option. Lastly, an option is always for 100 shares, so a $2.00 option costs $200.

I’ll illustrate how put options work. Let’s say I want to bet against Rivian Automotive (RIVN). The stock is trading at $10.88. I buy 50 December $10.00 RIVN puts for $1.95 apiece. What does that mean?

That means that if I own 5,000 shares of RIVN and the price is less than $10.00, I can sell each of my shares for $10.00 on any date prior to and including December 20 (each option gives you the right to sell 100 shares). If, on the other hand, I’m holding my puts on December 20 and the price of RIVN is greater than $10.00, my options expire worthless.

Essentially, I am betting $1.95 that the price of RIVN will be below $10.00, and my return on that $1.95 is the difference between $10.00 and the price of RIVN. So if the price falls to $8.05 ($10.00 – $1.95), I break even (ignoring commissions), since I’m able to sell my puts for $1.95 or buy the underlying for $8.05 and exercise the puts for $10.00. If the price falls below that, I begin to make money.

The Relationship Between the Price Change of the Underlying and the Value of the Option

As you can see from the foregoing, as a stock’s price falls, the value of the option rises. Below is a chart of my realized returns on the options I’ve bought and sold or exercised against the rise or fall in price of the underlying during the period I’ve held the option.

As you can see, if you use my strategy, you’re unlikely to make any money on puts unless the price of the underlying falls by more than 20%. If the price rises, you’re likely to lose your entire investment. 58% of my puts have lost money, and 22% have expired worthless (a 100% loss). Given that, it seems improbable at first glance that you’d be able to make any money using this strategy.

But those losses are compensated for by the wins, which have at times exceeded 500%. All in all, my average gain was 31%. Now consider my average holding period was 122 days. Annualized, if I’d invested equally in each of these puts, I would have made (1 + 31%)^365/122 – 1 = 142%.

Here’s a rough formula summarizing the relationship of price change to put change. If the price change is x and the put change is y and the holding period is 17 to 18 weeks, y = max (–1, –4.75x – 0.55). A slightly less rough formula is y = max (–1, 3.23x² – 2.7x – 0.51) for x < 40%; for x ≥ 40%, y = –1.

Selecting Stocks Primed to Fail

I use multifactor ranking systems at Portfolio123 for stock picking, whether I’m going long or buying puts. But the factors I concentrate on are quite different. At the moment, I’m looking for puts on stocks with the following characteristics:

• Frequent reductions in earnings over the last few years.
• A ratio of taxes paid to market cap that’s far lower than that of similar companies.
• Unstable sales.
• Poor price momentum over the last nine or ten months (not considering the most recent month).
• Poor subsector or industry group momentum.
• Low asset turnover.
• Low institutional ownership.
• A wide dispersion in analyst estimates.
• Asset instability (lots of big changes over the last few years).
• A recent very unpleasant earnings surprise.
• If the ratio of gross plant to sales is both wildly different from what it’s been for the last few years and wildly different from the industry norm, that’s a good sign that something’s amiss.
• Stocks in industries particularly susceptible to factor-based assessment: capital goods; consumer goods, retail, and services; energy; entertainment; health-care equipment and services; household products and services; industrial services; IT services; software; staples retail.
• Dividend-paying companies who clearly can’t afford to pay dividends. If the sum of net income, preferred and non-preferred dividends, and special items is less than zero, they’re in trouble.
• Low intangible-adjusted EBITDA to assets.
• A major increase in investment (gross plant + inventory) compared to total assets; also if there’s been a lot of instability in this ratio over the last twelve quarters, that’s a good sign.
• High price volatility.
• High accruals.
• Unstable ROA.
• Enormous increases or decreases in cash.

I’m looking at lots of other factors too, but those are a few of the ones that stand out right now.

Pricing and Holding Period

There are five factors that go into determining a fair price to pay for an option.

1. The current price of the underlying stock.
2. The strike price.
3. The expiration date.
4. The volatility of the stock.
5. The risk-free interest rate.

There are two widely established formulas for determining the fair price of an option based on these five inputs. Personally, I don’t use either one. But they’re important and good to know. You can skip the following paragraphs if you feel like they’re too far into the weeds. Pick up again at the paragraph beginning “There’s one other fair-price value.”

The first of these formulas is the Black-Scholes formula. Let’s call the strike price s, the current price p, the years to expiration t, the volatility v, and the risk-free interest rate r. Then the Black-Scholes price for a put is

where Φ is the normal cumulative distribution function.

(It’s important to note how volatility is measured for these formulas. You take the standard deviation of percentage moves in daily price over a certain period, and then multiply that by the square root of 252, since there are approximately 252 trading days in a year. I have found that another indicator of volatility is equally good: the median ratio of the high-low difference to the closing price; again, one has to adjust this so that it approximates the annual volatility. To do so I multiply it by 1375.)

The Black-Scholes formula is quite complex, but at least you can fit it into a line or two in an Excel file. The formula for the binomial price, on the other hand, requires an entire Excel sheet to compute and an explanation of how to do so would be excessive for this article.

There’s one other fair-price value that’s essential, and that’s the intrinsic value. That one is easy to calculate. If the stock’s price is less than the strike price, the intrinsic value is simply the strike price minus the stock price. If it’s more, then the intrinsic value is $0. The intrinsic value is the amount of money you would get if you were to buy the stock and then exercise the option. If the intrinsic value is greater than what you paid for the option, you’ve made a profit.

Now what do I consider a fair price for an option?

For me, both the Black-Scholes and the binomial prices are usually too expensive. The only exception is when t is greater than five or six months and v is relatively low compared to the other stocks I’ve identified as good bets for puts. For such stocks I’ll consider paying a little more than the Black-Scholes or binomial price.

Now you don’t see Black-Scholes or binomial prices in most options screens. Instead you get an indication of the Black-Scholes price by looking at the implied volatility of the stock. Implied volatility is the v in the above formula given a certain price.

I use a complicated spreadsheet to calculate the price I’m willing to pay for an option. And while it’s complicated, it’s also deliberately naïve in that it doesn’t take into account any of the Greeks or other conventional measures most people use in options pricing.

One can extrapolate the future price change of a stock in terms of probabilities based on the stock’s historical volatility and the amount of time that elapses. For a given stock, there’s an X% chance that its price will increase (or decrease) by Y% by time T given its volatility V between now and time T. Because of mean reversion, the stock’s implied volatility V is going to be different from its historical volatility; we also should take into account that the overall market’s volatility is going to be a factor that we have no way of predicting.

Because of this I use only three inputs in determining the price I’m willing to pay for an option: the expiration date, the relationship of the strike price to the current price, and the relationship of the stock’s historical volatility to that of other stocks that I favor for puts. I assume that a stock’s future volatility will be roughly the average of its historical volatility and the average volatility of those stocks.

My spreadsheet takes these inputs and then calculates the amount of money I will make if the option is priced at $0.05, $0.10, $0.15, and so on, given a range of fifty different possibilities for the stock’s price.

Let’s use a concrete example. I have an option on a stock priced at $16.28 with an expiration date 199 days hence and a strike price of $15.00. Its historical volatility is 67.3% and the volatility of similar stocks is 72.33%.

Here’s a graph of the stock’s probabilities between now and expiration, with each dot representing a 2% chance.

Corresponding to that, here’s a graph of the value of the option contract at the time of expiration.

I can then use these figures to calculate what my returns might be if I bet on this option fifty times, spending a nickel on each bet. Obviously, with a bet that cheap, you’re going to have astronomical returns if the contract ends up being worth $2.00 or more. With a bet of $3.00, however, your losses would far outweigh your gains. My spreadsheet calculates the profit or loss for each bet and then settles on the highest price that would probabilistically justify me putting a certain percentage of my money into the option. (In this case, it’s $2.50.)

Based on this spreadsheet, I calculated that out-of-the-money options were more worth my while than investing in in-the-money options; that options with expiration dates in the next two or three months were impossible to find cheaply enough; and that options with expiration dates more than nine months away were too unpredictable to be worth considering. This narrows down my field of put options considerably.

How to Buy and Sell Puts

Given the low prices I demand for put options, they’re very hard to find. But I do have a trick up my sleeve: GTC (good-til-canceled) orders. Because the prices of the underlying stocks are usually extremely volatile, if I place a GTC order at a price significantly lower than the ask, it’ll often get filled later when the stock’s price has a temporary spike. I usually keep my orders on for about a week.

If a stock’s rank goes down quite significantly between the time I buy the stock and the expiration date, I may choose to sell it early. I only do so if the stock’s price is relatively close to or under the strike price. Again, I’ll use GTC orders to maximize my chances of getting filled at a decent price.

It can be quite expensive in the short term to exercise put options, because you have to buy the underlying stocks and wait a day for the trade to clear. So you’re temporarily out of pocket a huge multiple of what you’ll get when you exercise. On the other hand, it’s by far the safest method of profiting from an in-the-money put that is about to expire. Once you own the underlying, it doesn’t matter if the price goes up past the strike and renders the put option worthless. In that case, if you can’t get the strike price for the shares you own, you can sell them for even more.

Managing a Put-Option Hedge

A well-diversified portfolio of underlying stocks is a good idea: I would suggest a minimum of a dozen. It’s also very important to diversify your expiration dates. Both of these will reduce the chances of your hedge going to zero in unfavorable market conditions. I try to buy puts on each of my underlying stocks with at least two different expiration dates. It’s also good to diversify your strike prices on each underlying, but that’s much less important.

I think one should decrease and increase one’s hedge based on the market. If horrible stocks have been doing extremely well lately, it may not be a good time to buy or hold put options. You especially want to watch out for market rebounds after a significant fall, or major contractions in the yield spread once it’s been high (these two usually coincide). All of this is very difficult to predict, of course, and transaction costs of decreasing and increasing your hedge will be huge. So do this in moderation.

Stocks I’ve Hedged and Puts I Own

The biggest gains I’ve made on put options have been on Enviva (EVA) ($553,737) and Peloton Interactive (PTON) ($191,331). I currently own puts on sixteen stocks, and the ones I’m most hopeful for a complete collapse are Cibus (CBUS), Avid Bioservices (CDMO), Enovix (ENVX), Ivanhoe Electric (IE), NextDecade (NEXT), Sunnova Energy (NOVA), and EchoStar (SATS).

Returns of the Put-Option Hedge

Overall, I’ve lost 3% of my investment in put options. My realized trades have made 14.5%, but that isn’t high enough to offset my unrealized losses. However, unrealized losses present an unbalanced picture when it comes to medium-term options: realized returns are a far better indicator of their potential. The other reason for the imbalance is that I’m managing a whole lot more money now than I did in 2022 and 2023, and 2024 has not been a good year for hedging. I’ve seen a lot of unrealized underperformance before, and even a mild market correction will change that completely. The hedge has certainly smoothed my overall returns, which is its main function, and a return to profitability is in the cards as well.

The post How to Profitably Hedge with Put Options appeared first on Portfolio123 Blog.

The Importance of Portfolio Management

I’ve had a successful run as a retail investor, with an eight-year CAGR of 44%. I attribute my success to two things: my ability to find stocks that will outperform and my portfolio management techniques, which may be of equal importance to my returns. Without good portfolio management techniques I’m absolutely sure I wouldn’t have performed as well. So I wanted to share some pointers with you.

Simple Portfolio Management

Here is the simplest way to manage a portfolio from its inception.

1. Create a ranking system that ranks all stocks.
2. Buy the top fifteen stocks in equal amounts.
3. Once or twice a week or month, rerun your ranking system. If one or more of the top five are stocks you don’t own, buy those and sell your lowest-ranked stocks.

(If you already have a portfolio, skip step 2.)

This is, in my opinion, absolutely solid. It requires very little work; it’s easy to understand; and, if your ranking system is pretty good, it’s going to produce reliable results.

(What exactly is a “ranking system”? It can be as simple as a checklist that gives points to each stock according to whether it fulfills various criteria, or it can be as complicated as a machine-learning algorithm that scores stocks on a variety of factors. As far as I know, there’s only one subscription service on the Internet that allows you to create and backtest ranking systems, and it’s the one I use: Portfolio123. There I can create ranking systems that use over a hundred different factors, all weighted as I choose, each factor customized to my liking.)

However, I’m a tinkerer. I’m constantly trying to improve my portfolio management techniques. So I’m going to suggest a number of ways to create what might be an even better portfolio management system, starting with the above basic rules.

The Primacy of Transaction Costs

The first principle is this: the higher your transaction costs, the more stocks you’ll want to hold, and the more equal your portfolio weights should be. If your transaction costs are very low, you can hold few stocks, rebalance frequently, and weight your top-ranked positions much higher than those that don’t rank as high. If your transaction costs are very high, you’ll want to hold lots of positions in more or less equal weights and hold them for a relatively long time, rebalancing infrequently. This should make intuitive sense. The more positions you hold, the smaller they’ll be, which will reduce market impact costs; huge position weights will have tremendous market impact costs; frequent rebalancing may increase your returns if your transaction costs are very low but will decrease them if your transaction costs are very high. Similarly, when assigning weights to the different stocks in your portfolio, you should reduce the weights of stocks whose transaction costs are significantly higher than others.

Calculating Transaction Costs

Let’s get into the weeds a bit. What are your transaction costs? Those depend primarily on five things:

• a) the ratio of the bid-ask spread to the stock’s price;
• b) the daily volatility of the stock, best measured by the standard deviation of the ratio of the high-low difference to the closing price;
• c) the median daily volume traded (in number of shares);
• d) the number of shares of the stock you are going to trade per day;
• e) whether or not you can use a VWAP order.

If we take the above variables and assign them letters a through e (with e being zero if you can’t use a VWAP order and one if you can), a rough estimation of your transaction costs would be:

0.25 × a + 0.5 × b × √ (d / c)× (1.2 – e / 2)

Let’s take, for example, Nature’s Sunshine Products (NATR). The ratio of the bid-ask spread to the stock’s price is 0.18%. The daily volatility is 1.9%. It trades about 32,000 shares per day. I am planning to buy 6,000 shares per day, using VWAP orders. My transaction cost will then be

0.25 × 0.0018 + 0.5 × 0.019 × √ (6,000 / 32,000) × (1.2 – 0.5)

which comes to 0.33%. My round-trip transaction cost (for both buying and selling the stock) would be double that.

Now let’s compare that with a much less liquid stock, iHuman (IH). The ratio of the bid-ask spread to the stock’s price is 4.2%. The daily volatility is 2.8%. It trades about 6,000 shares a day. I want to buy 14,000 shares per day, but I’m going to have trouble using a VWAP order, so I’m just going to place a few orders throughout the day. What will my transaction cost be for this stock?

0.25 × 0.042 + 0.5 × 0.028 × √ (14,000 / 6,000) × 1.2

which comes to 3.6%. My round-trip transaction cost would be a gigantic 7.2%. It’s rather difficult to justify such a purchase, since the cost would likely exceed the expected return.

You can calculate the transaction costs of your portfolio pretty easily. Calculate the weighted average of the transaction costs of each stock you own using the existing amount you own as variable d above. Double that for the round-trip cost. Then multiply that by your annual turnover. You’ll see that as you reduce or equalize the size of your positions and as you reduce your turnover, your total transaction cost per year will go down.

Diversification

The following discussion is paraphrased from Frederik Vanhaverbeke’s excellent book Excess Returns: A Comparative Study of the Methods of the World’s Greatest Investors.

The conventional wisdom is that you have to diversify to mitigate risk. Great investors reject that idea and instead take large positions in a small number of stocks. Philip Fisher usually had three or four companies that accounted for about 75% of his portfolio. Joel Greenblatt put about 80% of his funds in eight or fewer stocks. Eddie Lampert holds about eight major positions at any one time. Glenn Greenberg won’t buy a stock if he’s not willing to put 5% of his assets in it. Warren Buffett, who has a well-deserved reputation for caution, says that for a small portfolio of less than $200 million, he would put about 80% in five stocks. In his private portfolio he’s willing to risk up to 75% in a single stock.

The reasons behind portfolio concentration are pretty clear. First, by focusing on your best ideas you take full advantage of those and avoid dilution by second-rate ideas. Second, concentration leads to in-depth knowledge, while diversification leads to ignorance.

(Now I’m no longer paraphrasing Vanhaverbeke.) Several studies have found that among active portfolio managers, the more concentrated positions tend to do better than the less concentrated ones.

As for my own practice, as of November 15, I had 12% of my portfolio in Bird Construction (BDT:CA), 12% in Nature’s Sunshine Products (NATR), 7% in Perdoceo Education (PRDO), 7% in Daktronics (DAKT), and 6% in International General Insurance (IGIC). Those are my truly concentrated positions. Altogether I’m holding twenty-four stocks that each make up more than 1% of my portfolio, and fourteen more that are under 1% each. This kind of imbalance isn’t uncommon: Peter Lynch sometimes had more than 1,000 stocks in his portfolio, but still had some very large positions among them.

I do advocate diversification among industries or subsectors. I’m currently overly concentrated in “industrial services” (transportation, infrastructure, delivery, logistics, distribution, facilities, construction), so I’m taking some steps to limit my investment there.

Portfolio Weighting

If you use ranking systems, it makes sense to scale your positions by rank, with the highest-ranked positions having the greatest weight. There are any number of ways to specify this in a formula: if a stock’s rank position is r (i.e. for your top ranked stock, r = 1 and for your second ranked stock, r = 2), some formulas might include 25 – r, 1 / r, e ^{–0.2 r}, ln (25 – r), √ (25 – r), and so on. I advocate taking transaction costs into account when setting a stock’s weight. One way to do this would be to use one of the formulas above and multiply it by (0.06 – x) / 0.06, where x is twice the stock’s transaction cost and 6% is the average expected return of a stock. (You can adjust the expected return to match your own historical returns.)

Buy and Sell Rules

Besides the very basic buy and sell rules outlined above—buy a stock if it ranks in the top X and sell it if you need money to buy another and it ranks lower than other stocks—a few others are worth considering.

1. Sell rules. You might want a minimum holding period, which would mean selling a stock only if it has been held more than X days. You might want to sell companies going through merger proceedings. I would strongly advise against using stop losses. If a stock’s price goes down but its ranking remains the same or goes up, you probably want to buy more of it. Remember that a stock’s prospects have nothing to do with the price you paid for it, since everyone who owns shares paid a different price for them. Using stop losses virtually guarantees that you buy high and sell low. Studies have shown that most active managers sell positions that have either gone way up in price or gone way down in price and hold positions whose price remains the same. Don’t do things like that. Instead base your selling on a) rank and b) what you need in order to buy something else.
2. Buy rules. Instead of buying stocks simply based on their rank in your ranking system, you might want to buy them based on their rank in terms of expected excess returns. (In other words, instead of buying the five top-ranked stocks, buy the five stocks that will give you the highest expected excess returns. The difference between the two comes down to transaction costs per stock.) This gets complicated: first you have to determine how much more money a stock ranked #1 will make versus a stock ranked #5, and then you have to subtract double the transaction costs for each stock to come up with a total expected excess return. Here’s a formula you’re welcome to use. If r is the rank position of the stock and c is the transaction cost in percentage points, your expected return may be approximately 0.1 – 0.025 × ln (r) – 2 × c.

Rebalancing Frequency

I tend to rebalance or reconstitute my own portfolio every day and my kids’ portfolios twice a week. Their portfolios have outperformed mine pretty consistently. On the other hand, theirs have less market impact, being much smaller than mine. Twice a week is probably good enough. More frequent rebalancing gives you the opportunity to take advantage of strong and sudden price moves, but it also increases churn.

Holding Period and Rebalancing Size

I tend to hold positions on average eighty or ninety days, but you might want a longer or shorter holding period. In addition, I’m often adjusting position weights, so that even when I’ve held a position for five hundred days, there are portions that have been held much less and others that I might have already sold. This creates additional transaction costs, and lowers my returns. It’s therefore important to not diminish or increase positions simply because there’s a small difference in rank, but to place strict limits on rebalancing and do it only when the discrepancy is rather extreme (say more than a third of the position).

Hedging

I like to hedge my long positions with put options.

Shorting has a very lopsided return profile: you can never make more than 100% on a short position, but you can lose more than 500%. I wouldn’t recommend taking short positions, and I don’t short stocks myself. But perhaps if done very carefully, it can smooth and even increase returns. That’s still something I’m investigating. So far, I haven’t found a good method of making it work.

Put options have the opposite return profile: you can easily make far more than 100% and you cannot lose more than 100%. I favor three-to-nine-month out-of-the-money put options with a price that’s usually well under the Black-Scholes or binomial price (or, put another way, whose implied volatility is significantly less than the stock’s historical volatility; I’m willing to pay a bit more for stocks with relatively low historical volatility). Cheap puts like these are hard to find; during high volatility periods, you might only buy puts on 5% of the stocks you’re interested in. At any rate, this is by far the best hedge I’ve come across, and has increased my own returns significantly. I’ve only been buying puts for about 21 months, but my annualized return so far is about 840%. As with shorting, you want to choose your stocks carefully: buy puts on the stocks with the greatest odds of underperforming, and use a good ranking system designed for this. As for selling them, I usually wait until the week before expiration, unless my ranking system tells me that they’re no longer likely to fall in price, in which case I sell them for whatever I can get.

To keep your sanity with out-of-the-money options, it’s important to realize that

• a) they’ll often expire worthless;
• b) their value can plunge about ten times faster than stocks; and
• c) when the market is in high-risk mode, their value may all plunge at the same time.

It’s such a rocky ride that you may not want to put more than 25% of your money in them.

Many people like to hedge only under certain market conditions. I have not found any system of reliably predicting market conditions, and have always found market timing and/or tactical asset allocation unrewarding. Almost all such systems are overfitted. Yes, of course, there are certain times when it’s better to be out of the market or refrain from shorting anything. But predicting those is a very tall order, and if you happen to be even slightly wrong you can squander your best opportunities. It’s far easier to use a relatively constant hedge: 75% to 80% long and 20% to 25% short/puts.

Easing into Positions

If you’re facing massive market impact, it’s far better to ease into and out of positions by buying or selling a small amount daily than trying to get into positions all at once. On the other hand, there may be a small cost of delay, especially right after an event or earnings announcement. These are the considerations to weigh when you’re thinking of easing into or out of positions.

Taxes

It’s always best to invest in retirement accounts, where taxes aren’t an issue.

If you have both a cash account and a retirement account, I advise trying to make as many of your yearly losses occur in the cash account as possible and as many of your gains in the retirement account as possible. The following practices may help you avoid paying capital gains taxes.

1. If you can move stock into a retirement account, a business account, a foundation, or as a charitable donation, move the stock that has appreciated the most (in dollar terms, not percentage).
2. If you’re going to sell a portion of a position that’s held in both your cash account and your retirement account, first look to see if the stock has appreciated in the cash account. If it has, sell the portion in your retirement account; if it has lost money, sell the portion in the cash account.

Last year I made 22% on my investments, but because I followed the two rules above, I paid no capital gains tax at all.

Margin

It’s not a bad idea to use margin in your non-retirement accounts, as long as you do so carefully. Here are a few recommendations.

1. Negotiate a good margin interest rate with your broker. Interactive Brokers charges the lowest margin rate, and you can always threaten your broker to leave and use IB instead.
2. Keep track of which stocks are marginable and which are not. Buy the marginable ones in your margin accounts and the non-marginable ones in your retirement accounts.
3. When allocating how much to spend on a stock, take margin into account. It’s better to buy larger amounts of marginable stocks.
4. Watch market volatility. I use CBOE’s RVIX index, which is a lot like VIX except it gauges the Russell 2000. When the VIX or RVIX goes up, decrease your use of margin.
5. Always keep a cushion. When calculating the amount of margin to use, add 5% to your margin requirements for each stock. The idea is to avoid margin calls.

Here’s a quick primer on how I manage margin.

Let V be the market value of all the stocks in your margin account, let R be the weighted average margin requirement of those stocks, and let D be your total debt. Your surplus will then be V – D – R × V, or (1 – R) × V – D.

Next, let’s calculate your worst-case expected future drawdown (this is based on your current assets, not on your high-water mark). I use 0.65% of the VIX minus 1%. So if the VIX is at 20, your expected drawdown is 14%, and if the VIX is at 40, it’s 29%. We’ll call that number dd.

Now recalculate the value of your portfolio if the drawdown happens: V × (1 – dd). Then calculate the margin requirement of your stocks at that lower value if your margin requirements went up by 5% (since some margin accounts will increase margin requirements in the case of high risk): (R + 0.05) × V × (1 – dd). Your new surplus, after the disaster, would be V × (1 – dd) – D – (R + 0.05) × V × (1 – dd), which simplifies to (0.95 – R) × V × (1 – dd) – D. When I’m buying and selling stocks, I try to keep that new surplus above zero at all times.

For example, let’s say the market value of all the stocks in your account is $750,000, your weighted average margin requirement is 36%, and you have $350,000 in margin debt. Your surplus is therefore 0.64 × $750,000 – $350,000 = $130,000.

Now let’s say the VIX is at 20, giving you an expected drawdown of 14%. Your new surplus will be 0.59 × $750,000 × 0.86 – $350,000 = $30,550. You can therefore spend $30,000 on buying new stocks with a margin requirement of 100%, and quite a bit more on new stocks with a lower margin requirement. As long as you do this kind of math, you should never get a margin call. I never have, even during the COVID crash.

Conclusion

All of this can be overwhelmingly complicated. That’s why I began this article with a very simple portfolio management method. I still think that it is an excellent foundation, and everything else is icing on the cake. But many people never even think about portfolio management. They keep a huge amount in cash in case they see a stock they want. They buy on whim, and base the weight of their new buy on things like how much cash they happen to have. They sell when stocks go way up or way down, disregarding their prospects. They get margin calls; they get into and out of hedges on a moment’s notice; they overdiversify; and so on. All of this will diminish their investing success.

Systematic and thoughtful portfolio management should be a key part of your investing process. Don’t let your stock-picking talents go to waste by not managing your portfolio well.

The post How to Manage Your Portfolio to Maximize Your Returns appeared first on Portfolio123 Blog.

I. Getting Defrauded

Not too long ago, an investment research firm exposed a company I had invested in as a massive fraud. Most of this company’s revenue apparently comes from some other companies that they had recently acquired, but it turned out to be practically impossible to verify that any of that revenue actually existed outside of the company’s books.

Based on their most recent financial statements, I gave this company a very high rating. And I put a lot of money behind it.

This hurt. Not only did it hurt financially—I lost over $80,000—but it hurt my credibility as a quantitative investor. In the big picture, I could stomach the loss. But my investing philosophy is founded on the maxim that safer stocks are better investments than risky ones. And yet I put a large bet on a stock that this research firm would shortly and rightly label an easy-to-spot swindle with fictitious financials.

One reason I was caught off-guard is that this company is listed on the NASDAQ as a US company. Listed stocks domiciled in the US are the safest stocks on earth simply because the SEC is better at going after fraudsters in the US stock market than any other government regulatory body.

Stock market history, though, is full of frauds. It’s in the very nature of the beast. We are taught that we should beware of companies engaging in manipulation of their financial statements. Yet every company, by the very nature of financial reporting, has some leeway in constructing financial statements. There are hundreds of gray areas when reporting financials—which is one reason I frequently say that there is absolutely nothing scientific about financial data. What am I doing when I rank stocks based on this discretionary data, then? Well, I’m dealing in probabilities. If a stock’s reported free cash flow is high, that doesn’t mean that it’s a winner: it means that it’s more likely to be a winner than a stock whose reported free cash flow is extremely low.

So what should have tipped me off that this company was a fraud? Is there something quant-based that I should learn here? Is there a screening rule I can apply to my universes to prevent this from happening again?

II. Messod D. Beneish and “The Detection of Earnings Manipulation”

In 1999, a professor of accounting at Indiana University published “The Detection of Earnings Manipulation” in Financial Analysts Journal. (This was a thorough revision of a method he had first published in 1997.) Messod Beneish was not the first nor the last to attempt to use financial statement analysis to detect fraud. But his method has held up better than any other; in a 2020 follow-up paper, “The Cost of Fraud Prediction Errors,” he proved that his method had a lower ratio of false to true positives than any other method besides a machine-learning-based one introduced in 2020.

Beneish arrived at his formula by examining 74 firms that manipulated earnings over a six-year period and comparing those to 2,332 similar firms that did not. He came up with eight factors whose higher values seemed to indicate a greater chance of manipulation, seven of which compare the latest fiscal year’s figure to the previous one’s. Out of those eight, only five were statistically significant (and one of those five, AQI, still had rather high p-values). Using probit regression, he came up with a formula that included all eight factors, but gave a negative coefficient to two of the statistically insignificant ones and a very low coefficient to the third.

The eight factors are as follows:

1. Days Sales in Receivables (DSRI). This compares the ratio of receivables to sales in the most recent fiscal year to the same ratio in the previous fiscal year. The ratio of receivables to sales is basically the percentage of sales for which cash has not yet been received. If that ratio is getting a lot bigger, it’s a sign that the company may be overstating its sales.
2. Gross Margin (GMI). This compares the company’s gross margin in the previous fiscal year to the company’s present gross margin. If a company’s gross margin is markedly deteriorating, that gives it a strong incentive to manipulate its financials.
3. Asset Quality (AQI). This takes the company’s non-current assets that are not in net plant, property, and equipment, divides that by its total assets, and compares that number to that of the previous fiscal year. If this number is going up, the company may be improperly deferring costs (or it may be engaging in substantial acquisitions; but Beneish notes that “sample manipulators undertake few acquisitions and those are primarily stock-for-stock exchanges accounted for using pooling of interests.”) As he says, “An increase in asset realization risk indicates an increased propensity to capitalize and thus defer costs.”
4. Sales Growth (SGI). This is a simple measure of sales growth from the most recent fiscal year to the previous one. High-growth firms are more likely to engage in financial statement fraud.
5. Depreciation (DEPI). Beneish measured depreciation by comparing it to the sum of depreciation and net plant. If this ratio is going down, that’s a sign that the company has been revising upwards the estimates of the useful lives of assets, thus increasing the company’s net income through financial manipulation.
6. Sales, General, and Administrative Expenses (SGAI). This is the ratio of SG&A to sales. In his original paper, Beneish is rather unclear about why he feels that if this ratio is increasing, it’s a sign of financial manipulation. The only justification he gives is that “analysts would interpret a disproportionate increase in sales as a negative signal about firms future prospects. I expect a positive relation between SGAI and the probability of manipulation.” There’s a contradiction between those two sentences. Later writers have suggested that the factor is justified by the idea that if administrative and marketing efficiency decreases, that could motivate managers to manipulate earnings; similarly, if managers are being paid a lot more, that’s another good signal of financial misdeeds.
7. Leverage (LVGI). This compares the ratio of total debt to total assets between the most recent two fiscal years. If debt is rising, there’s more incentive for earnings manipulation, Beneish reasoned.
8. Total Accruals to Total Assets (TATA). This ratio does not compare the most recent two fiscal years, but simply takes accruals and divides by total assets. Beneish at first measured accruals using Richard Sloan’s balance-sheet approach, but later (in 2013) switched to a more widely accepted method based on the cash flow statement, which is simply net income less cash from operations.

The calculation of each of these factors is relatively easy. The first seven are simple quotients: if the compared figures are the same from one year to the other, the result is 1; for most of them you take the most recent fiscal year’s number and divide it by the previous year’s and for GMI and DEPI you do the reverse. Accruals are easily calculated as well. Each of the factors are then Winsorized by the 99th and 1st percentile. (For those unfamiliar with Winsorization, that means that any factor above the 99th percentile is given that value rather than its true value; it helps avoid outliers.) Lastly, if elements of AQI, DEPI, or SGAI are N/A, the value is set to 1.

The final M-score (M stands for manipulation) is then calculated using the following formula, based on an unweighted probit regression:

–4.84 + 0.92*DSR + 0.528*GMI + 0.404*AQI + 0.892*SGI + 0.115*DEPI – 0.172*SGAI – 0.372*LVGI + 4.679*TATA.

In his original paper, Beneish admitted that the three factors with low and negative coefficients (DEPI, SGAI, and LVGI) were not proven to be of value. They all have relatively high p-values. While he gave the above probit regression numbers, he did not propose that the M-score be calculated using them. Nonetheless, that is the way it has been calculated ever since, and Beneish has since touted this formula in both his 2013 and 2020 follow-up papers.

The threshold for whether a company is likely to be a manipulator is an M-score of –1.78 or higher, though he allowed plenty of leeway here. If a company’s M-score is below –2 it is unlikely to be manipulating its financials.

There are a lot of online versions of the Beneish M-score, and many of them take slightly different approaches. Portfolio123 uses trailing-twelve-month or, for balance-sheet items, quarterly figures rather than annual ones, and does not Winsorize. YCharts uses annual numbers and does not Winsorize; for AQI they deduct not only noncurrent assets and PPE, but also long-term investments, and for accruals they use operating income rather than net income. There’s an excellent online calculator from Indiana University’s Kelley School of Business, where Beneish teaches, which breaks down any company’s M-score by factor and gives probabilities and odds. It’s faithful to the original calculation, using annual figures and Winsorizing. Other calculations can be found from GuruFocus, FinBox, MacroAxis, and so on. Seeking Alpha does not offer the M-score—yet.

III. Digging into the M-score

I’m going to look a little more closely at how the M-score functions in practicality, examining each of its factors.

I recently looked at the M-scores and the eight factors for about forty companies that have received damning reports from an investment research firm that specializes in accounting irregularities, undisclosed related-party transactions, and illegal financial reporting practices. Not all of those companies engaged in financial manipulation, but a majority of them seem to have. The conclusions I arrive at below are informed by my examination of those reports.

As concrete examples, I’m going to be looking at five companies. The first four manipulated their financial statements, while the last doesn’t seem suspect in the least. I’m identifying all of them besides Enron using pseudonyms and changing almost all of the details about them, including dates; but the financials I’m giving are not fictional. The companies are:

• The Argonarm Group, which is the company I lost money on. At the time the report came out identifying it as an obvious fraud, the M-score identified it as a possible manipulator. It identified it as a likely manipulator prior to that, but that was before it had acquired the other companies, so it wasn’t really on anybody’s radar.
• Miracle Prospect Machinery. This company was taken over nearly a decade ago by a man who was wanted abroad for running a ponzi scheme and for forgery. A year later, the company pivoted into a new business segment and entered into a joint venture with a firm whose VP was this man’s wife; that firm was then investigated by the SEC, and most of its software contracts did not exist. I’ll be looking at Miracle’s financials, before its stock price collapsed. The M-score identified this company as a safe one.
• Neapolis Charter Tools. The SEC hit this company with subpoenas several years ago and again two years later. Neapolis admitted “weakness” related to its financials, and restated some of them as a result. The company had a long history of questionable business practices; I lost a lot of money on it myself. I’ll be looking at its financials between the year of the original subpoena and the second one. The M-score correctly identified this company as having a high probability of earnings manipulation.
• Enron. Problems with Enron’s financials were beginning to be seen in late 2000, but it wasn’t until October 2001 that they were out in the open. That was when Enron announced that restatements to the last four annual reports (those of 1997 through 2000) were necessary to correct accounting violations. The following month they filed documents with the SEC revising those statements to account for losses of $586 million. Using an earlier version of Beneish’s M-score, Cornell University students identified Enron as having a high probability of earnings manipulation way back in 1998, based on its annual report covering 1997. But if one applies the M-score to the annual reports covering fiscal years 1998 or 1999, it indicates that the company is a safe one; all the while, Enron was moving its operating losses to special purpose entities. The 2000 annual report, issued in 2001, was a different kettle of fish: the M-score rose to –0.55, and people were growing extremely skeptical of what was in those reports. But by that time, the stock had begun its descent. I’ll be looking at the Enron M-scores as of mid-2000 and mid-2001.
• Rebria Services. There is absolutely no evidence of any fraudulent practices or earnings manipulation at Rebria, and nobody seems to have even suggested any such thing. I’ll be looking at its current financials. The M-score identifies this company as having a high probability of earnings manipulation, solely because its DSRI is extremely high (due to the sale of the commercialization rights to one of its technologies to another company).

The chart below gives each of the Beneish M-score factors for these five companies using Compustat data from Portfolio123, with the Winsorization points gleaned from the Kelley School website. I have two lines for Enron for different dates.

For the factors, red shading indicates high scores (above the 90th percentile) and green shading indicates low scores (below the 10th percentile); no shading indicates normal scores (between the 10th and 90th percentiles). For the M-score, red is given to companies above –1.78 (“likely manipulator,” according to the Kelley School website), green to companies below –2 (“not manipulator”), and no shading to companies between (“possible manipulator”).

One of the striking things about this chart is that the three recent companies that have committed earnings manipulations have extreme scores (very high or very low) in most categories. Let’s go through the factors one by one and see if we can explain that.

1. DSRI. If a company has a low score, it means it’s decreasing its receivables compared to sales. That may be a good thing, but it could also be a sign that the company is desperately offering extended credit terms to customers, making sales to customers with weak creditworthiness, channel stuffing (shipping excess inventory to distributors or retailers without demand), or—and this is the prevalent point for the companies I’ve been looking at—recognizing revenue prematurely. In my research I’ve found that companies with very high or very low DSRI scores are suspicious. Argonarm, Miracle, and Neapolis all had abnormally low DSRI scores. Rebria, on the other hand, had an abnormally high DSRI score, greater than the 99th percentile, because of the sale of the commercialization rights to one of its technologies, so it was Winsorized to 3.12.
2. GMI. If a company’s gross margins are wildly increasing—as is the case with Argonarm, whose margins improbably went from 16% to 68%—that’s plenty of cause for concern. One of the things that alerted the research firm to Argonarm’s fraud was its insane margins, which were far higher than that of any other company in its industry. Neapolis also reported an extreme increase in its gross margin, as did a number of the other companies that I examined.
3. AQI. This factor depends on the balance between three things: current assets, net plant, and total assets. If one or two of those change radically from one year to the next, that can be a significant warning sign. Let’s look specifically at Miracle, for example. Their 2013 balance sheet listed only $0.1M in cash and $1.9M in current assets, almost all of which was in receivables. They also had $3M in deposits, so their total assets were $5.7M. In 2014, however, their total assets had grown almost ten times to $53M because they had reportedly increased their cash to $45M. Their PPE remained about the same (from $0.5M to $0.7M). That’s why they received such an absurdly low AQI. Something similar was happening with Argonarm: their cash ballooned from $97M to $500M, their net plant went from $0.7M to $855M, and their total assets grew almost ten-fold, from $177M to $1.68B. Reverse mergers and acquisitions notwithstanding, this kind of thing merits close consideration.
4. SGI. Extremely high reported sales growth is indeed the number-one flag for revenue falsification. Beneish was right on target here.
5. DEPI. Once again, Beneish was on the nose. Argonarm, Miracle, and Neapolis scored very high on this measure. But it’s important to point out that two things can make this ratio work: one is an extreme decrease in depreciation; the other is an extreme increase in net plant. In the case of these three companies, it appears that their new assets either had a much longer useful life or a much lower cost than their old ones did. The likelihood of that does not seem terribly high.
6. SGAI. A huge increase in sales without a corresponding increase in SG&A is a clear warning sign that sales may be overstated, so a low SGAI may be just as bad as a high SGAI. This is actually what Beneish’s original language in the 1999 paper suggested, and corresponds with the negative coefficient given to this factor. In my research on suspect companies, a large number of them had either extremely low or extremely high SGAI scores.
7. LVGI. Beneish supposed that an increase in debt would be a sign of manipulation, but it’s actually the reverse. Companies that are decreasing their ratio of debts to assets might be paying off their debts, but they might also be increasing their equity by selling lots of shares. That’s certainly what Argonarm did: its ratio of debt to assets went down to 9% of what it had been the year before! One of the most prevalent signs of a company engaging in fraudulent activities is that they sell shares. Argonarm wasn’t the only company that did so: so did Miracle and Enron. That’s what makes the fraud pay off!
8. TATA. Coincidentally, all five of the companies in question here have moderate accruals. In my limited research, I didn’t actually find that much of a correspondence between high accruals and a propensity for financial malfeasance. But I trust Beneish on this: he looked at a lot more companies than I did.

IV. Revising the M-score

I have a few minor quibbles with the M-score, so I took it upon myself to make some changes to it, to wit:

1. Averaging. I found the M-score varied wildly from year to year. Each annual statement gave a different picture. I also worried that the M-score wasn’t current. If Argonarm’s “coup”—its acquisition of several kindred companies in the same quarter—had happened between annual reports, its M-score wouldn’t have changed. (In this case, that would have been a good thing, as the previous year’s annual report earned an extremely high M-score of 0.21.) At any rate, I thought it would be better for each factor to average the comparison of this year to last year with a comparison of the current quarter to the same one last year and, for non-balance-sheet items, the trailing twelve-month values with those of a year ago.
2. N/As. Beneish gave values of 1 to three factors if information wasn’t available; I did the same with the other four year-to-year factors, and gave a value of -0.05 if TATA was N/A. This improves coverage, and allows us to include financial stocks (which Beneish excluded), to many of which items like gross margins or current assets don’t apply. In order to best protect oneself from fraud, it’s good to have a number for all companies.
3. Winsorizing. Beneish winsorized at 1% and 99%. That allows one factor to completely dominate, as we saw with Rebria. I think it’s better to Winsorize at 5% and 95%.
4. Bidirectionality. For four of the factors I thought it would be better to give high scores to both huge increases and huge decreases. Those are DSRI, GMI, AQI, and SGAI. To calculate these, I first took the averages, then Winsorized them; after that, if the result was less than one, I used its reciprocal instead.
5. Leverage. I found a slight problem with the way Beneish used this factor. Let’s say a company increased its debt load by 700%. Because of Winsorization, it would get a score of 3.13 (a company that keeps its debt the same gets a score of 1). LVGI has a coefficient of –0.327. So a company that significantly increased its debt would see its M-score go down by (3.13 – 1) x 0.327, or 0.7, making it a much safer bet. That didn’t make sense to me. So I use the reciprocal of the leverage factor (i.e. last year’s debt to assets divided by this year’s) and give it a positive coefficient. Now a company that increases its debt load by 700% gets a score of 0.33, which makes its M-score go down by only (1 – 0.33) x 0.327, or 0.22. As for a company that radically increases its equity by selling a huge number of shares, Argonarm’s debt-to-assets ratio went down by 74% (its value is 0.26). So reversing it gives it a score of 3.85, which would then get Winsorized to 2.63. That raises its M-score by 0.53, which seems more appropriate than having its M-score raised by only 0.24.
6. Share Increase. I added one additional factor, called share increase index (SII), modeled on Beneish’s factors, that compares the fully diluted share count for this year (and the most recent quarter) to that of the previous year (and the same quarter last year). I noticed that a lot of these fraudulent companies issue a lot of new shares or issue additional treasury shares or sell convertible preferreds to make money before they’re caught. And they weren’t always the same companies as those with low LVGI scores, since many of them both issued shares and increased their debt load.
7. Coefficients. Because I changed the way four of these factors worked, I had to change their coefficients too, which I did by comparing the new range (10th percentile to 90th) of the factors to the old range. I gave my new factor (SII) a coefficient that was a range-adjusted average of the eight existing factors; I also changed the two factors with negative coefficients to positive ones due to the way I changed those factors. In the end, I altered five of Beneish’s coefficients somewhat, but kept three of them the same (SGI, DEPI, and TATA).
8. Intercept and Cutoff. Beneish’s formula had an intercept that seemed arbitrary. It’s a bit confusing for novices to have to deal with the fact that most but not all Beneish M-scores are negative. I think that an M-score of zero means that the probability that the company is a manipulator is 50%, but I’m not sure. At any rate, I changed my intercept so that a company with all N/A values would get a score of zero. Some companies still get negative scores, but most of them get positive ones. Since approximately 8.25% of listed companies with reasonable liquidity get a Beneish M-score greater than –1.78, I used the same percentile to come up with a cut-off score of 1.83.

My final formula is as follows:

–5.384 + 1.312*DSRI + 0.585*GMI + 0.663*AQI + 0.892*SGI + 0.115*DEPI + 0.255*SGAI + 4.679*TATA + 0.288*LVGI + 1.508*SII

where the various formulas are altered as described above.

I have not been able to backtest my formula to see whether it works better than Beneish’s in general. Beneish had access to a well-defined dataset of companies that had definitely manipulated their financials. I do not. I was able to backtest it to see whether imposing limits based on the revised M-score improved returns when used in conjunction with a ranking system to pick stocks. The results were mixed: most backtests improved, but a few did not. Using it, my own returns would have been better and I would have avoided buying Argonarm.

Perhaps my formula is not an improvement on Beneish’s. Certainly it’s much more difficult to calculate, requiring inputs from eight quarterly reports rather than two annual ones, and some more complex calculations with a few of his factors.

Here are the revised scores for the five companies I examined earlier. Note that due to the changes I made, DSRI, GMI, AQI, and SGAI never go below 1.

My revised formula does perform better than the original one for three out of these five companies (Argonarm, Miracle, and Rebria) but worse for Enron and about the same for Neapolis. There’s selection bias at work here too: I chose these companies to illustrate my points.

I have made a public screen on Portfolio123 so that you can see exactly how all of the factors for both the Beneish M-score and the revised version are calculated; you can also input tickers to see their scores.

V. How to Use the M-score

There are two options that seem logical to me. The first is to simply subject companies with high M-scores to further scrutiny on a case-by-case, discretionary basis. The second is to simply exclude companies whose M-score is high.

Some of the companies I’m invested in have quite high M-scores too (both Beneish and revised). I may reconsider those investments. On the other hand, it’s comforting that two of the companies I’ve taken a strong position against (by buying puts) also have very high M-scores.

There is no simple method for catching financial fraud, just as there is no simple method for picking winning stocks. However, paying attention to certain signs of fraud would have helped me avoid the Argonarm fiasco. I hope that using the M-score will help me—and you—avoid others in the future.

The post Detecting Financial Fraud: A Close Look at the Beneish M-Score appeared first on Portfolio123 Blog.

But more important than how much I earned is how much I learned. Was this a better year than most? I don’t know. I learn a lot every year. But with every lesson I learn, I realize how stupid I was the year before.

So here are some things I learned in 2022, in no particular order at all.

1. Buy in Batches to Reduce Market Impact.

I studied market impact a lot in 2022, and learned that the market impact cost of a trade is approximately

where m is a constant (approximately 1.0), σ is the daily volatility of the stock, S is the number of shares you want to trade, and V is the daily volume. Besides reading a lot on the subject, I also measured the market impact of my own trades, comparing the price of my fills to the price of the stock immediately before I placed the order. (I use VWAP orders a lot; if I used straight limit or market orders, m would likely be significantly higher.)

Before 2022, I had been placing my entire order for a stock on one day and paying the market impact cost accordingly because there’s a price you pay for delaying an order. But this year, I decided to do the math.

Let’s talk about the daily cost of delaying an order, which I signify as y in the equations below. I’m assuming that it has a linear relationship to the daily volatility of the stock.

If you place 100% of your order today, there’s no delay cost, and if you place none of it today and all of it tomorrow, the delay cost is y. If you place half today and half tomorrow, your delay cost is 0.5y. If you place a third today, a third tomorrow, and a third the next day, your delay cost is y (0 today, a third y tomorrow, and two-thirds y the next day). If you place a quarter today, a quarter tomorrow, a quarter the next day, and a quarter the day after that, your delay cost is 1.5y. So the delay cost can be expressed as

where S is the total number of shares you want to trade and a is the actual order size.

Now let’s let c be the total cost of the trade. We want to minimize our cost and figure out what the best order size is to do so. In mathematical language, our object is to minimize c as a function of a. And the best way to do that is to use differential calculus.

So here’s the equation for the total cost of a trade, assuming that placing an order one day has no effect on the price the next day (a tenuous assumption, yes, but we have to simplify this somehow):

Since y and σ have a linear relationship, we can substitute nσ for y above, where n, like m, is another constant.

To minimize c we take the derivative of the right side and set it equal to zero, treating all variables as constants except a.

After some simplification, we come to

If I use a new constant, k = (n/m)^2/3,then

From my calculations, based on the returns I’m getting, k ≈ 0.42. It would be significantly smaller if my alpha were lower, because my delay cost would be lower.

So let’s say I want to buy $66,000 worth of IBEX (IBEX), which trades $500,000 a day. Can I buy the whole amount in one day? Well, let’s do the math.

0.42*66,000^2/3*500,000^1/3=54,442. So I should buy only about $54,000 the first day and the rest on the second.

2. Free Cash Flow Yield Is the Best Value Ratio

This was the subject of a recent article I wrote. I’m not going to repeat it here. I’ve been using free cash flow yield in the form of unlevered free cash flow to enterprise value ever since 2016. But it was only in 2022 that I realized that it beats all other value ratios, and that net free cash flow to market cap can be an equally productive factor.

3. The Ins and Outs of VWAP Orders with Fidelity.

2022 was the year I started using VWAP orders, and it has not only improved my life no end, it has made a huge impact on my trading practices. I’ll discuss this some more in a future article, but for now, I want to share what I’ve learned about placing VWAP orders with Fidelity and Interactive Brokers.

In order to place a VWAP order with Fidelity, you use an application called Fidelity Active Trader Pro. From the main menu choose “Trade & Orders,” then “Directed Trade & Extended Hours.” If the market is open, you can then place a VWAP order by selecting “VWAP” in the “Route” box. If the market is not open yet, you’re out of luck. There are two other very important restrictions on VWAP orders with Fidelity: you have to order at least 1,000 shares, and the stock has to be listed on a major exchange. Because a lot of my daily trades are for fewer than 1,000 shares or are for Canadian F shares, I use limit orders for those and crudely simulate a VWAP order by breaking up the trades into four or five equal amounts and placing them throughout the trading day.

The way Fidelity actually trades its VWAP orders is pretty commonsensical. Orders are broken into small chunks and submitted throughout the day, but the chunks are larger and more frequent when trading is heaviest (the end of the day). By the end of the day, as long as your limit hasn’t been exceeded, your order will have been completely filled.

4. The Ins and Outs of VWAP Orders with Interactive Brokers.

The major advantages of placing VWAP orders with Interactive Brokers rather than with Fidelity is that you don’t have to worry about the above restrictions. VWAP orders can be placed prior to market open, can be placed for practically any stock (though not on all exchanges—for trades on the Warsaw and Stockholm exchanges, for instance, you can’t use VWAP), and can be used with orders of less than 1,000 shares. The major disadvantage is that VWAP orders for thinly traded shares are executed haphazardly if at all. I can’t count the number of times I’ve placed a VWAP order and watched in vain for a trade to actually occur, even when other people are trading the stock. Moreover, there’s no guarantee of a complete fill even if the stock is trading under your limit. Interactive Brokers’ algorithms seem to be trying to get good prices for all their tiny orders, so if there’s a wide spread and no hidden orders in the book, a trade simply won’t be placed. Or perhaps their algorithm places small trades between the bid and the ask and when they go unfilled they don’t submit the trades at the bid or ask—they don’t “take liquidity,” as the jargon has it. But these are just guesses. All I know is that VWAP orders on Interactive Brokers for thinly traded stocks are about as dependable as a 1967 Volkswagen that hasn’t had a tune-up in twenty years. Sometimes they work extremely well, and sometimes they don’t.

5. Factor momentum doesn’t work.

Factor momentum is the idea that groups of factors go in and out of favor and that there’s enough lag time in those shifts for investors to take advantage of them. For example, if, in the last month or two or three, value has done really well and stability has done really badly, you can invest in value stocks and short stable stocks for the next few weeks until another shift occurs.

This idea, like many, presents two problems. First, how does one measure whether it actually happens? Second, if it does, how can we best take advantage of it?

Last summer, I thought I had the answer: it does actually happen, and I can take advantage of it. So I switched my strategy so that my multifactor ranking system placed heavier weights on factor groups that had done well in the last three months and less weight on factor groups that had done badly.

The result was insane turnover. From week to week the factor groups would shift and I ended up doing so much buying and selling that I lost a lot of money. After two or three months I gave up.

But for the purposes of this article, I’d like to start from scratch.

Portfolio123, a company that allows you to create, backtest, and invest in your own rule-based strategies, and the only service that allows you to both rank stocks and backtest your ideas, has created what they call “Core” ranking systems that each focus on one group of factors. (To give credit where credit is due, these ranking systems were created by Marc Gerstein and subsequently modified by Gerstein, Riccardo Tambara, and myself.) There are six such systems, focusing on growth, low volatility, momentum, quality, sentiment, and value. While I have some issues with some of the factors in these systems, they’re generally sensible. I’ve taken the liberty of adding a seventh, focusing on size (favoring small stocks), for the purposes of this experiment.

Here is how I propose to measure factor momentum.

First, I will use a bucket test for each ranking system and determine its slope. A bucket test is a measurement of the performance of the worst ten percent of companies, the next worst, and so on, until the best ten percent. I call it a bucket test because at every rebalance period (monthly), every stock is put into one of ten buckets according to its percentile rank on the factor group in question. So if I’m testing the value factors, the cheapest stocks are in the first bucket and the most expensive ones are in the tenth. The slope is the result of a linear regression of the ten-bucket annualized returns, regressed to the series 0.1, 0.2, 0.3, 0.4, . . . 1.0. It approximates the difference between the tenth bucket and the first and adjusts for the various buckets in-between.

I’ll do this for the last three months, since the one-month values are crazily variable, and I’ll also do it for the last eight years, to give me something to compare the last three months to. The final measure of factor momentum is the three-month slope minus the eight-year slope. Because I only have data going back to 1999, that means I can’t actually start the monthly measure until 2007, since that’s the first point at which I’ll have eight years of data to use as a benchmark.

I’ll be measuring performance using a group of US stocks that Portfolio123 has labeled “easy-to-trade.” These are listed stocks with a price greater than $3 and a median daily dollar volume greater than $50,000, excluding MLPs.

This is the result (click to enlarge).

As you can see, there’s not much persistence. You don’t see one factor outperforming over a years-long period. (The percentage numbers on the left represent the outperformance of the top bucket over the bottom bucket over the last three months, annualized, minus that same outperformance over the last eight years, annualized, and adjusted for how smoothly the in-between buckets rank.)

Now let’s say that every month you invested in the top bucket of stocks according to the factor that performed the best over the previous three months and shorted the bottom bucket of stocks according to the factor that performed the worst over the previous three months.

The result would be absolutely disastrous. You’d lose almost 4% per annum. You’d do far better investing in all of the top ten buckets and shorting all of the bottom ten than choosing just one based on factor momentum.

In short, if factor momentum actually works, I haven’t been able to verify it.

6. European stocks are easier to evaluate than US stocks.

This is the subject of an article I wrote last year, and I still stand by it. Unfortunately, they’re harder to trade . . .

7. If you think you’ve got a talent for getting good fills, you’re probably fooling yourself.

Sorry for the second person—I’m talking about myself here. Until 2022 I thought I was able to get better fills than most other investors by placing my limit orders at the right point and at the right time and adjusting them using a pretty smart method.

But I don’t think so anymore.

If it were even remotely possible to get better fills by placing limit orders at certain points and certain times, everyone would do it. 97% of day traders lose money, but that wouldn’t be the case if they could consistently get good fills. Identical pair trading—buying a stock in one account and selling it in another—would be a great way to make money if you could identify when a stock was likely to be at its low and high point for the day. The arbitrage opportunities would be unbelievable. But it’s not happening.

If you’re not worried about market impact or spread costs, it doesn’t matter when you place your order. Spreads tend to be narrower at the end of the day, so that’s a good time to place orders if you want to minimize those costs. VWAP orders (small orders automatically placed throughout the trading day) minimize market impact, so that’s the route you want to take if market impact is a concern. Orders placed before open below the previous close for a buy or above the previous close for a sell are more likely to be filled than the same orders placed shortly after open because of the way opening prices are calculated and the high price volatility in the first few minutes of trading. On the other hand, those prices might not be as good as what you’d get later in the day if the price moves in your favor.

What I do now is this. If I can place a VWAP limit order, I’ll do so shortly before or after market open. If I can’t—if I’m trading too few shares or if I’m trading an over-the-counter stock—I’ll place a limit order prior to market open not too far from yesterday’s close for a portion of the shares I want to buy, and then place further orders throughout the day. And if the price moves drastically away from me, I’ll abandon the order.

This isn’t brilliant or foolproof, and I’m sure there are plenty of other good ways to place orders. One investor I know swears by the Fox River VWAP algorithm at Interactive Brokers, and says that it has dramatically reduced his trading costs.

8. Persistence of growth is chimerical.

Verdad Capital published an excellent piece this year that proved that companies that have grown in the past are not much more likely to grow in the future than companies that haven’t. Past growth is not really indicative of future growth. If you want to estimate future growth, using past numbers is often going to give you garbage.

There are other ways to predict growth besides looking at past numbers. I’ve written about this before, but I had never seen such a good outside study about it until 2022.

9. Volatility matters when measuring market impact.

I have made many attempts to measure market impact over the years, and it was only late last year that I started taking volatility into account. Before that I was relying primarily on the amount you trade divided by the typical daily volume, which has a nice correlation to market impact. Volatility alone has a significantly lower correlation than that measure. But if you couple the two measures, you get a much better model for market impact than if you leave volatility out. I experimented extensively with this, comparing my fills with the price before placing the order, and was pleasantly surprised by how much volatility matters.

If σ is volatility, a is the amount you trade, and v is the daily volume, then the general formula for market impact is pσ^q(a/d)^r, where p, q, and r are constants. In my experience, q is pretty close to 1 and r is pretty close to 0.5; p depends on how you measure σ, but I use about 1.0.

10. Call options, as a form of leverage, are very undependable.

When I started buying calls and puts near the beginning of 2022, doing so made sense to me. I got the idea from reading Jim Cramer’s Real Money. (It’s not a bad book, despite what Cramer has since become; it was written way back in 2005.) In it, Cramer writes,

I used both puts and calls to tremendous effect when I first started out as a little investor and ultimately at my multi-million-dollar hedge fund. Over the years I found that options were a fantastic way to make a little money into a lot of money. As I am a constant risk-reward hunter, I loved the idea that I could risk some money on calls to make much bigger money than I could make buying common stock. I also loved the idea that I could bet against a stock using puts without worrying about a short squeeze. . . .

This appealed to me. Certainly buying puts seemed a lot better than shorting because the upside of shorting is limited to 100% per stock and the downside is unlimited. And buying calls made sense because it struck me as similar to using much greater leverage than simply going long.

But I didn’t pay enough attention to something Cramer wrote later in that chapter:

When you know that you have something big, either way, the best way to play it is in puts or calls. But if it isn’t big—and about 99 percent of the situations I hear daily aren’t big—it is better to use the common stock.

I bought too many call options on stocks that I wasn’t actually terribly certain about. As a result, I did quite poorly. Overall, over the course of a year I invested about $300,000 in call options and only got back about half of that. That hurt.

Put options, on the other hand, required more conviction, in part because they’re so damn expensive. Fewer than 5% of the puts I wanted to buy struck me as cheap enough for me to actually purchase. Also I had no alternative for these stocks. If I wanted to bet against Peloton (PTON), buying puts was far safer than shorting the stock. So I invested $240,000 in puts and made $216,000 in profits for a 90% return. (And indeed, a large chunk of that was from Peloton puts.)

I realize that 2022 was an unusual year, and that in most other years I would have done much better with call options than I did and much worse with puts. Nonetheless, I’ve decided to only buy puts in the future, simply as an alternative to shorting, and to simply go long on the stocks I believe will appreciate.

11. Subtract preferred dividend payments when considering earnings.

When a company calculates its earnings, it deducts all of its interest expenses—except one. It does not subtract its preferred dividend payments.

Preferred stock functions a lot like debt. When a company needs more money, it can borrow it from a bank, sell bonds, sell preferred shares, or issue more equity; selling bonds and selling preferred shares are quite similar. Just like bonds, preferreds have contractual dividends, have par value, can be redeemed early, and sometimes have a fixed maturity date. If the company liquidates, preferred stock owners, just like debt holders, get seniority over stockholders (though bondholders have seniority over preferred stockholders).

But because of the peculiarities of generally accepted accounting principles (GAAP), in their financial statements, companies deduct payments to preferred stockholders only after calculating their earnings attributable to the company. (They must do so in order to arrive at earnings attributable to common shareholders.)

In order to get a true picture of a company’s income, then, preferred dividend payments should be deducted. And these can be substantial. For example, General Electric’s (GE) preferred dividend payments amounted to more than a third of its net income last year.

FactSet and Compustat both subtract preferred dividends when they calculate EPS. FactSet also subtracts them when they calculate net income, return on assets, profit margin, and so on, but Compustat does not. In this regard, FactSet’s figures give investors a better picture of how much a company is actually earning than do those from Compustat, at least in my opinion.

But analyst estimates rarely take preferred dividends into account. That’s why you’ll find a huge discrepancy among companies that pay preferred dividends between the analyst actuals for the most recent quarter and the EPS adjusted by data providers for the most recent quarter, with analyst actuals almost always higher.

Before I discovered this in 2022, I was relying a great deal on earnings estimates and unadjusted Compustat numbers for vital earnings data. Now I’ve revised my formulae to take preferred dividends into account.

12. You end up paying about half of the bid-ask spread on each trade.

Before last year, I was quite uncertain about this number. But I then did a massive study comparing my fills to the most recent price prior to placing my order. This study included straight limit orders, some modified after placement; VWAP orders; and relative peg orders. It included extremely large and extremely small orders, on many of which I got some price improvement by my brokers (Fidelity and Interactive Brokers). The only kinds of orders I excluded were those placed prior to market open and those for which there were no fills on the day of the order prior to my placing it. The data was a mess, but after some smoothing, the relationship in the heading above was pretty clear.

13. Why DCF analysis is so unreliable, and why a simplistic version might actually work better.

Discounted cash flow analysis depends primarily upon the following variables: a company’s unlevered free cash flow over the next ten years, its cost of equity, its cost of debt, and its “permanent” growth rate in the distant future. A company’s cost of debt isn’t that hard to figure out, and most analysts peg the permanent growth rate to historical GDP growth. But future cash flows and cost of equity tend to be wild guesses at best. This is true whether one bases future cash flows on a fixed growth rate or something else; basing that fixed growth rate on past growth is a terrible idea, as growth in free cash flow tends to mean revert.

A simplified version might work better. We want to arrive at an intrinsic value that we can compare to the company’s enterprise value. We assume that the company’s free cash flow, cost of equity, and cost of debt will be constant in perpetuity, setting its growth rate at zero. The intrinsic value of the company will then be its free cash flow divided by its cost of capital, where the cost of capital is the weighted average of the cost of debt and cost of equity according to how much debt and equity the company has.

For free cash flow, we can use current and future estimates plus the taxable portion of the most recent annual interest expense or, if we want to be more careful, an average of the company’s unlevered free cash flow over the last five years, adjusting for inflation and trimming outliers, and weighting more recent figures higher.

For cost of debt, we can use the average of the interest expense divided by the company’s debt over the last five years, again trimming for outliers.

We can set the cost of equity between 7% and 13% depending on the company’s historical share turnover and price variability (decent proxies for risk), but since the cost of equity should never be lower than the cost of debt, there has to be some flexibility with that 13% maximum.

Finally, in calculating the cost of capital, we should cap the weight of the cost of debt at 30%; a company with a huge amount of debt should not have a lower cost of capital than a company with very little debt.

(I’m indebted for these ideas to the second edition of Value Investing by Bruce Greenwald, Judd Kahn, et al.)

We end up with an intrinsic value that’s almost always between five and fifteen times the company’s unlevered free cash flow.

For banks, insurance companies, and other financial companies that use debt as a source of income, you’d want to compare their intrinsic value to their market cap rather than to their enterprise value. So you’d ignore interest expense and cost of debt and simply use free cash flow and cost of equity.

Not long ago I wrote an article on the best value ratios, of which unlevered free cash flow to enterprise value and free cash flow to price are two. The performance seems to improve to some degree if you use the above calculations to take into account cost of capital or cost of equity.

14. Your number of positions should be proportional to your transaction costs, not your assets under management.

Before 2022, I believed that as your assets under management go up, you need to have more positions in order to keep your transaction costs down. I still believe that, but the AUM shouldn’t drive your position count. Instead your transaction costs should. If you can reduce transaction costs without increasing position count, then there’s no reason to increase the latter.

Transaction costs can be attributed to two factors: market impact and the bid-ask spread. The amount traded has nothing to do with the bid-ask spread, but it certainly affects market impact. Let’s say you’re trading Espey Manufacturing & Electronics (ESP). The spread is about 1.66% of the price, the daily dollar volume is about $53,000, and the daily volatility is about 2.2%. If you were paying only spread costs, you’d expect to pay about 0.8% per trade. If you were paying only market impact costs, those are approximately the daily volatility times the square root of amount traded divided by the daily dollar volume. So if you were trading $53,000 worth, you’d be paying 2.2% and if you were trading only $10,000 worth you’d be paying about 0.96%. You’d then average the spread costs and the market impact costs for the total cost per trade, and then multiply by two to get the round-trip costs.

One approach to determine how many positions to hold, therefore, is to do some math to optimize the total portfolio return given that each additional position will probably lower your return but also reduce your transaction costs. That’s what I was doing before 2022, and believe me, it was mathematically pretty complex.

But there were too many variables for it to really work. Another approach to reducing transaction costs is to increase your holding period. You can also reduce transaction costs by buying and selling over several days rather than all at once. Placing VWAP orders cuts your market impact by almost 50%. Moving from high-volatility to low-volatility stocks will decrease your transaction costs, as will buying stocks with higher volume.

In 2022, I realized something. If I were to run backtests to optimize the number of positions in a strategy given a certain amount of slippage per transaction, I would get a very different answer if I were to use a high slippage or a low slippage. With very little slippage, it would make sense to buy the top five stocks in terms of rank and sell them if they went down in rank past twenty-five. With very high slippage, it would make much more sense to buy the top twenty stocks and sell them when they went down to 120 or 150 in rank. A whole different portfolio management approach was optimal, all depending on slippage costs. And I could run simulations to determine the appropriate buy and sell rules, which would then determine my number of positions.

15. Industry momentum doesn’t work like individual stock momentum.

For individual stocks, the tendency to mean revert predominates over periods less than one month and more than two years. Momentum predominates for periods between three months and one year, and the factor is most effective when you exclude the most recent month. For sectors, subsectors (industry groups), industries, and subindustries, on the other hand, momentum is effective even for the most recent month. I have no idea why and how industry momentum works; not only does it contradict the law of reversion to the mean, but it does so consistently and much more strongly than individual stock momentum. Obviously, sometimes there are dramatic turnarounds, but in general it’s a very useful factor. I’ve found a six-month to nine-month measure to be most effective, but for catching turnarounds, even a one-month measure can work.

16. Companies that have never had positive operating income are best avoided when going long.

Peter Lynch suggests avoiding what he calls “Whisper Stocks” in One Up on Wall Street. He doesn’t define them precisely, but he does mention that “usually there are no earnings.”

Most of the firms that have never reported positive operating income are biopharmaceuticals and SPACs, but this rule also excludes companies like Uber Technologies (UBER), Snowflake (SNOW), Cloudflare (NET), Palantir Technologies (PLTR), and NIO (NIO). Every backtest I’ve run for going long works better if you exclude companies like these, which are practically impossible to price. On the other hand, shorting some of these, or buying puts on them, can be profitable. (I’m currently holding puts on two such companies, Aspen Aerogels (ASPN) and Enovix (ENVX), and my Aspen puts have almost doubled in value.)

The post What I Learned About Investing in 2022 appeared first on Portfolio123 Blog.

Method

I conducted the study using a web-based stock research company called Portfolio123. Here’s my methodology. (This gets a bit technical; feel free to skip to the next paragraph if you’re not interested in the details.) First, I used a universe of all US and Canadian stocks with a price greater than $3, a median daily dollar volume greater than $50,000, and excluded unlisted stocks and MLPs. I then tested the decile performance ranks of each factor both over the last ten years and since 1999, assuming slippage-free monthly rebalancing. (What does that mean? It means I formed ten portfolios according to the rank of each stock on the value ratio in question, so that if a stock ranked in the top 10% it was in the first portfolio, if it ranked in the second 10% it was in the second, and so on. These portfolios were reconstituted every four weeks according to each stock’s rank at that time. The performance of these portfolios was measured and annualized.) I then took these decile performances and measured the slope of their linear regression. (What does that mean? I lined up all the decile performances and used those as my y values, my x values being 0.1, 0.2, 0.3, . . . 1.0. I then calculated the linear regression—in other words the line that best fit these performance numbers—and calculated the slope. If all the decile performances are each one higher than the last, this slope approximates the difference between the performances of the bottom 10% and the top 10%; if they’re more variable, the slope diminishes.) The top performers had not only the greatest differences between the top and bottom decile, but the smoothest slope in-between. I also considered only the top decile in terms of performance, since most people use value ratios to go long, as well as the Sharpe ratio of that top decile. Lastly, I performed this exercise using both Compustat’s and FactSet’s data.

In this article, I want to discuss the value factors that really consistently outperform. They performed well in the last ten years and in the last 23. They have steep bottom-to-top slopes and the top decile is not only a strong performer but has a high Sharpe ratio. They did well both with Compustat and with FactSet data. These are factors that I think are difficult to go wrong with.

The Metrics of Value Ratios

Before we start with those, I want to talk a little about what numbers we should rely on for value ratios. Should we just look at the most recent quarter? The trailing twelve months? The last three years? The last five? Or should we look at analyst estimates instead? And if so, for the current fiscal year, or for the next twelve months, or the next fiscal year?

While there are no wrong answers, I would suggest that the most important values are, in order of importance, the current fiscal year’s estimate, the next twelve months’ estimate, the trailing twelve months’ GAAP figures, and the most recent quarter’s GAAP figures. But a lot depends on your holding period. If you’re a buy-and-hold investor, looking at the most recent quarter will simply result in a lot of churn. If you tend to rebalance more frequently, as I do (I rarely hold a stock more than a year), then the most recent quarter can provide some good guidance.

Ratios all consist of a numerator and a denominator. If market cap, price, or enterprise value is in the numerator, you get a valuation ratio where lower numbers are better. The classic example is P/E (price to earnings), but I’m sure you’re familiar with price to sales, price to free cash flow, and EV to EBITDA. If market cap, price, or enterprise value is in the denominator, you get a valuation ratio that’s called a yield, where higher numbers are better. The two appear to be equivalent, but they’re not. A company with a high P/E may be overpriced, but not as overpriced as a company with a negative earnings yield. Let’s compare three companies, each selling for $20 a share. One has a trailing twelve-month (TTM) EPS of $4.00, one has an EPS of $0.50, and one has an EPS of –$1.00. The first has a P/E of 5, the second has a P/E of 40, and third doesn’t have a P/E at all. Which is a better buy, the second or third company? P/E doesn’t really tell you, in a strict mathematical sense. Earnings yield, however, allows you to rank companies with negative earnings lower than companies with low but positive earnings, and allows you to compare two companies with negative earnings. In fact, companies with barely negative earnings yields significantly outperform companies with extremely negative earnings yields.

Capital Structure and Value Ratios

Why do we compare a company’s earnings to its price but its EBITDA to its EV? Why do we have two different versions of free cash flow, depending on whether we compare it to market cap or enterprise value?

Let’s take an analogy. You buy a house for $500,000, paying $100,000 down and getting a loan for $400,000. You collect $50,000 a year for renting the house, and you pay $20,000 a year in mortgage costs.

There are four possible ways you can look at your earnings. You can simply ignore the debt entirely and divide $50,000 by $100,000 and say you’re getting a 50% yield on your investment. Of course, this is garbage: you’re definitely not. You can deduct the mortgage costs from your $50,000 but also base your yield on the $500,000 the house is worth and say you’re getting a 6% yield on your investment. This is also garbage: you’re deducting your debt twice, once for the interest expense, and once for the $400,000 you owe. Your actual yield is far higher than that.

Here are the other ways to calculate your yield. The first is comparable to earnings yield: you subtract your mortgage costs from the rent you earn and divide by your cash outlay, $100,000, for a 30% yield. The second is comparable to EBIT/EV: you don’t subtract your mortgage costs and divide the $50,000 rent by the entire $500,000, for a 10% yield.

Are those at all commensurate? Indeed, they are. You’re getting a 30% yield on your cash, but a negative 5% yield on your debt. And you have four times as much debt as you have cash. So if you deduct four times 5% from your 30%, you come up with 10%—exactly the same as your EBIT/EV–based yield.

(I probably should have used after-tax numbers in this example, but I wanted to keep it simple.)

The lesson here is that if you’re comparing something to a company’s price or market cap, that “something” has to be an after-debt-related-expenses number. Operating income, EBIT, or EBITDA are not allowed. And if you’re comparing something to a company’s enterprise value, that “something” has to have the interest expense added back to it if it was deducted earlier. That’s why we add the taxable portion of interest expense back to free cash flow if we want to compare it to enterprise value. (Technically, we should also take into account debt issued and debt repaid if the company issues or repays debt regularly.)

As for which to use, it depends on what you’re looking for. If you’re just interested in knowing how expensive your shares are, then don’t bother with enterprise value, since the value of your shares is an equity value and has nothing to do with a company’s debt. But if you’re interested in how valuable the company is, then enterprise value is the way to go.

A warning: never use enterprise value–based ratios for companies in the financial sector. For a good number of those companies, the more debt they issue, the higher their revenue.

As an investor, I’m interested in looking at a company from as many angles as possible. I therefore pay attention to both price-based ratios and EV-based ratios.

Free Cash Flow Yield

The best value factors I found are all variations of free cash flow yield. (I’m not the only one to reach this conclusion: another blogger, Harry Turner, arrived at this result using entirely different methods.)

A few years ago I wrote an article about free cash flow, which you can read here. I suggest you follow that link before continuing with this section. It’s a good guide to free cash flow’s history and the various ways of measuring it. A much more comprehensive guide is Aswath Damodaran’s, which he published recently here.

Free cash flow yield is simply free cash flow divided by market cap, or free cash flow per share divided by price. But there are a number of variations that work equally well or better, and they’re all worth discussing.

1. Measuring free cash flow. The standard measure is operating cash flow minus capital expenditures. (In P123 language, that’s simply FCF.) But there are several good alternatives. Many, including Warren Buffet, maintain that you should only subtract the capital expenditures spent on maintenance, not growth-related capital expenditures. Most companies don’t separate out these two, so it takes some digging—and estimation—to get to the right number. Others go to the opposite extreme and say that you should subtract not only capital expenditures but all other investing-related cash flow, which includes acquisitions. (In P123 language, that’s OperCashFl + CashFrInvest.) Complicating this is that many companies will list major asset purchases as capital expenditures, yet when they sell those same assets they don’t deduct them from capital expenditures but instead list them as other items in the investing portion of the cash flow statement. Yet another way to measure free cash flow is EBITDA (or EBIT) minus capital expenditures (Michael Mauboussin favors a variation of this method; in P123 language, that’s EBIT - CapEx or EBITDA - CapEx). This measure cannot be used with market cap or price, and must be used instead with enterprise value. Many others believe that you should deduct not only capital expenditures but also dividends paid, since that is a better measure of what’s left over to fund a company’s growth. (In P123 language that’s NetFCF.) Lastly, as I stated above, you have a wide choice between estimates and GAAP figures over various time periods. Taken all together, there are more than twenty different ways to measure free cash flow. I don’t have any strong preference between them, and find them all quite valuable measures. But below I’ll tell you which specific measures performed the best. (There is some debate over whether free cash flow ratios are effective for companies in the financial sector. From my research, they definitely are, and sometimes will function even better than earnings yield.)
2. Market cap or EV. It’s generally a little more useful, in my opinion and experience, to compare free cash flow to enterprise value than to compare it to price or market cap. But in order to do so, you have to add back the company’s interest expense. (If you’re using EBITDA or EBIT minus capital expenditures, you don’t have to worry about this because these are pre–interest expense numbers.) Because free cash flow is an after-tax measure, you only want to add back interest expense after taxes, or interest expense times one minus the company’s tax rate (or the industry’s tax rate, or some measure of the effective tax rate of the country’s companies, depending on your preference). (My preferred measure, in P123 language, is IntExpA * (1 - TaxRate%TTMInd/100)). And, once again, never use EV-based ratios for companies in the financial sector.

The Best Variations of Free Cash Flow Yield

Below are the variations of free cash flow yield that performed the best in my tests. I’m listing them from the simplest to the most complicated, with the market-cap-based ratios first, followed by the enterprise-value-based ratios.

1. Free cash flow yield. This is simply free cash flow divided by market cap, using TTM values. FCFTTM / MktCap
2. Estimated free cash flow yield. Here you use analyst estimates for the current fiscal year in place of TTM GAAP values. But if those aren’t available, use the TTM values. IsNA (FCFEstCY, FCFTTM) / MktCap
3. Net free cash flow yield. Here you subtract the dividends paid from the TTM free cash flow. NetFCFTTM / MktCap
4. Net free cash flow yield minus equity costs. Here you take the net free cash flow and subtract the cost of equity times the invested equity. There are a lot of different ways to measure cost of equity. The simplest is the risk-free rate plus the company’s beta times an equity risk premium. (I use the ten-year treasury yield as the risk-free rate and 10% minus that yield as the equity risk premium.) A much more complicated method is the subject of another article I wrote. By “invested equity” I mean book value less cash and equivalents. (NetFCFTTM - (Close (0, ##UST10Yr) / 100 + (0.1 - Close(0, ##UST10Yr) / 100) * Beta3Y) * Max (0, AstTotQ - IsNA (CashEquivQ, 0) - IsNA (LiabTotQ, DbtTotQ))) / MktCap
5. Unlevered free cash flow to enterprise value. Unlevered free cash flow is free cash flow plus the taxable portion of interest expense. I use TTM GAAP values. Enterprise value is market cap plus total debt minus cash and equivalents. (FCFTTM + IntExpTTM * (1 - TaxRate%TTMInd/100)) / EV
6. Estimated unlevered free cash flow to enterprise value. Here you use the current fiscal year’s estimate instead of the TTM GAAP value when it’s available. (IsNA (FCFEstCY, FCFTTM) + IntExpTTM * (1 - TaxRate%TTMInd/100)) / EV
7. Either of the above minus cost of capital. Here you calculate the weighted average cost of capital as follows. Take the cost of equity (as outlined in #4 above) and multiply that by the market cap; add to that the cost of debt, which is the average yearly interest expense; then divide that sum by the sum of market cap and debt. This is the WACC, which you should multiply by invested capital. Invested capital is total assets minus cash and equivalents and minus non-debt current liabilities. (FCFTTM + IntExpTTM * (1 - TaxRate%TTMInd/100) - (((Close (0, ##UST10Yr) / 100 + (0.1 - Close(0, ##UST10Yr) / 100) * Beta3Y) * MktCap + IntExp5YAvg) / (MktCap + DbtTotQ)) * (AstTotQ - CashEquivQ - IsNA (LiabCurQ - DbtSTQ, 0))) / EV

Which of these seven had the absolute best performance? Well, they’re all very close, but if I had to choose just one, it would be #6, with #3 in second place.

A Word About Deducting Costs of Equity and Capital

I’ve devoted a lot of my writing to Michael Mauboussin, one of the most perceptive investor/analysts working today. He and Dan Callahan recently published a paper called “Return on Invested Capital: How to Calculate ROIC and Handle Common Issues,” which I suggest you read. It’s a terrific introduction to his thought on one of his key measures, return on invested capital.

Near the beginning of the paper, Mauboussin and Callahan point out that there’s a very strong correlation between a) the difference between return on invested capital (ROIC) and the weighted average cost of capital (WACC) and b) enterprise value (EV) divided by invested capital (IC). See Exhibit 1, the chart on page 2 of the paper, which I take the liberty of reproducing below.

My idea was: why not use this correlation as the basis of a value ratio? If ROIC – WACC is proportional to EV / IC, then EV is proportional to IC × (ROIC – WACC). And since ROIC = NOPAT / IC (where NOPAT is net operating profit after taxes), then EV is proportional to NOPAT – WACC × IC.

If, instead of NOPAT, we use free cash flow, then a good value ratio would be FCF – WACC × IC. So I tried that. The results were very encouraging, and were, in fact, significantly better than using NOPAT. That’s why I deducted the costs of capital and equity in formulas number 4 and 7 above.

Conclusion

I think it’s very telling that the value ratio that seems to work the best, according to my methods of testing, is the one most deeply rooted in valuation methodology.

In fact, it works better than any automated intrinsic value method that I’ve tried. I have a theory about why that is.

Projecting growth rates based on past growth is almost impossible. Verdad, an asset management firm, publishes frequent research notes, and they recently found that persistence of growth is entirely chimerical.

In addition, cost of equity is notoriously difficult to calculate or estimate, as I have discussed at length.

If companies have utterly unpredictable growth trajectories and if cost of equity is more or less chimerical, we could assign all companies the same growth and the same cost of equity. Then intrinsic value calculation becomes extremely simple, and uses only one or two variable inputs: free cash flow and, for EV-based calculations, cost of debt.

That, I believe, is why free-cash-flow-based valuation ratios work so well.

Some Exceptionally Cheap Companies

Using these ratios, here are the cheapest companies right now (as of 12/17/22) in Portfolio123’s “Easy to Trade North America” universe (listed stocks whose primary listing is in the US or Canada with a minimum price of $3 and a minimum daily dollar volume of $50,000, excluding MLPs), using a combination of FactSet’s and Compustat’s data: Friedman Industries (FRD), Vir Biotechnology (VIR), PBF Energy (PBF), Zim Integrated Shipping Services (ZIM), and Insignia Systems (ISIG). All of these have free cash flow yields above 40%. Now some of these may be cheap for good reasons. I believe that you should look at a lot more than just value factors when you’re choosing investments. So here are some other stocks with very high free cash flow yields (above 10%) that I consider especially safe investments (I own shares in all of these): Genie Energy (GNE), Limbach (LMB), Hammond Power Solutions (HPS.A:CAN/HMDPF), PrimeEnergy Resources (PNRG), and RCM Technologies (RCMT). All ten of these stocks are certainly underpriced by the measures I’ve discussed, and may well be worth your attention.

And if you want to short some stocks with extremely negative free cash flow yields (all below -40%), check out Kodiak Sciences (KOD), Groupon (GRPN), Aspen Aerogels (ASPN), Hippo (HIPO), and bluebird bio (BLUE). These aren’t the absolutely worst stocks in terms of free cash flow yield, but they’re companies with almost nothing else going for them either.

Disclosure: I have a beneficial long position in the shares of GNE, LMB, HMDPF, PNRG, and RCMT through stock ownership.

The post What Are the Best Value Ratios? appeared first on Portfolio123 Blog.

First, I’ll classify them into four types:

1. market impact costs;
2. spread costs;
3. getting bad fills; and
4. commissions and taxes.

Market Impact

The market impact cost of a transaction depends on the number of shares you trade divided by the number of shares traded in a typical day. (An equivalent way to think about this is the amount invested divided by the daily dollar volume.)

Some studies have proposed that the relationship between market impact cost and this quotient is linear; others have proposed that the market impact cost has a linear relationship with the square root of that quotient. The results of my own research make me lean toward the latter.

Methodology

If you’d rather skip over my methods, which are a bit involved, don’t read the rest of this section and just go to the next one for the results.

I recently did a study of my own transactions. These ranged from very small (several hundred dollars) to very large (over $100,000), and the stocks involved ranged from nanocaps to mid caps. For some of the trades I used Fidelity, for others I used Interactive Brokers. Some of the trades were VWAP (volume-weighted average price: an algorithm that trades small amounts during the course of the day), some were limit orders placed at the ask for a buy and at the bid for a sell (for these I sometimes got some price improvement), and some were pegged to the NBBO (National Best Bid and Offer). Some were for US stocks, some for Canadian F-shares, and some for stocks traded on European exchanges.

I measured the transaction cost by looking at the price of the stock immediately prior to placement of the order and comparing it to the weighted average price at which the order was filled. (I did not include orders placed before market open or for which there was no fill that day prior to my order.) Please note that this reflects only a limited number of trades and makes no pretense to be an accurate guideline for all investors or traders: it’s simply my personal experience.

The data I came up with was a huge mess. Why? Because

a) the price of a stock immediately prior to placement of an order can vary greatly between the bid and the ask at the time;

b) the price of a stock might well rise and/or fall after order placement completely independently of the trade one’s placing; and

c) whether an order gets filled at the bid, at the ask, or in-between depends on a huge number of factors.

To make sense of this mess, I sorted my orders by the x variable (in this case, dollar amount traded divided by average daily dollar volume), divided it into equal-sized chunks, took the median of the x and y values of each chunk, and plotted the result. I did this again for larger and smaller equal-sized chunks just to be sure that chunk size wasn’t having too much influence on my results.

After smoothing the data like this and modifying it so that it was based on the square root of the percentage of volume traded, I was able to chart the data so that it made sense to me:

There are a number of possible regressions one can create using charts like these. I tried several and measured the median absolute distance of each formula to the actual trading costs. The formula with the lowest median absolute distance is the one I went with; this happened to coincide with the regression line with the highest R².

Results

The cost of a trade will be about 2.5% of the square root of the percentage of daily volume traded.

How do you find the daily volume traded? You probably want to take the median volume over the last few months’ of trading days. Portfolio123 is one service that offers this data; some brokers will offer average (rather than median) daily volume, but averages can be misleading since most stocks trade far, far more heavily on certain days than others. Moreover, the formula above relies on median daily dollar volume, not average.

Let’s say I want to buy $200,000 worth of shares in LSI Industries (LYTS). The median daily dollar volume is $250,000. I’m buying 80% of the daily dollar volume. The square root of 80% is 89%, so I can expect to pay $200,000 × 89% × 2.5%. That’s over 2% of my purchase, a rather hefty price to pay. Now let’s say I’m only buying $10,000 worth of shares. That’s 4% of the daily dollar volume, and the square root of 4% is 20%. Now I’m paying $10,000 × 20% × 2.5% = 0.5% of my purchase.

The Bid-Ask Spread

I used the same methodology as outlined above to measure the trading cost of the bid-ask spread. (The rank correlation between spread as a percentage of price and trading cost is about the same as that between percentage of volume traded and trading cost.) To get the spread, I calculated the median of the last few weeks’ closing bid-ask spread divided by the price. This data is not easy to come by. Portfolio123 offers it, but only for stocks listed in the US. For over-the-counter, Canadian, and European stocks, I use Fidelity’s Active Trader Pro to look up time and sales information, and then calculate it myself after writing down the spread over the last ten trading days.

Once again, the charts were a mess—even worse than the charts for the amount traded versus the trading cost. But after some effort, using the same method as I outlined above, I came up with an exceedingly simple formula for the market impact of the bid-ask spread as a fraction of the stock’s price: the cost of a trade will be about one-half of the median spread.

Considering Both Market Impact and Spread Costs

There isn’t an easy way to put together the cost of a trade based on market impact and the cost based on the spread. Using multilinear regression on data as messy as this is a fool’s game. Personally, I just average the two to estimate the total cost of a buy or sell.

To minimize both market impact and spread costs, I think a VWAP order is ideal, as do most professional investors. If you’re unable to place a VWAP order, then placing small portions of your order over the course of a day or a week is far better than placing it all at once. An order of $200,000 worth of LYTS placed in one single batch might well have a market impact cost significantly higher than 2%. The large majority of the trades I’ve placed and measured are a bit smarter than that.

If you have a different way to minimize market impact or spread costs, I would be grateful for feedback.

Lastly, I should point out that transaction costs are extremely variable. The same order for the same stock placed an hour apart might have completely different transaction costs. I have, on occasion, been able to buy more than the daily dollar volume of a stock in one day with hardly a whimper. I’ve also been slammed doing so.

Getting Bad Fills

For many years I thought I was getting better execution by cleverly placing limit orders and timing their placement to maximize my chance of catching the lowest (for buys) or highest (for sells) prices of the day.

But if that were true, then you could buy a security at its lowest price and sell it at its highest price every day, and day trading wouldn’t be a loser’s game. (Only about 1% of day traders make enough to live on from it; 97% of them lose money.) If it were possible to get better fills than the day’s average, practically everyone would.

In avoiding bad fills, what might matter to some degree is how you place your order. Do you use a market order, a conditional order, a straight limit order, a VWAP order, a pegged NBBO order? The results vary from broker to broker.

I also make a practice of letting a trade go if the price moves away from me by a huge amount. I sometimes place the order again the next day. But I don’t think this is a wise move if you’re not going to reconsider making the trade in the first place. If you’re totally committed to the trade, then go ahead and trade even if the price moves away from you dramatically, because it’s likely to continue that move the next day, and the next. On the other hand, if the price move is going to make you reconsider the trade, then perhaps you should hold off.

In short, I believe that getting good fills is more a matter of luck than skill. But I’d be grateful for tips if anyone can show that they can consistently get good fills.

The question then arises: is it possible to get consistently lousy fills? Your chances of doing so are likely higher with market orders, and your transaction costs will also likely be higher.

Lastly, some studies have suggested that buy orders should be placed near the end of the trading day and sell orders near the beginning. I have not come to a firm conclusion about this, but given that overnight returns dwarf the returns during the trading day, it makes sense to me.

Commissions and Taxes

Very few brokers charge a commission these days, and there are no taxes on trades. (Capital gains taxes are not transaction costs.) But if you’re trading international stocks or using certain brokers, you’ll be racking up additional transaction costs.

1. Commissions. Very few brokers allow you to place an international order without paying some commission. Some charge a commission per order, others per share, and others as a percentage of the trade. In addition, a few brokers still charge commissions for domestic stock trades as well. From my experience, you can expect to pay about 0.2% to 0.25% in commissions if you use Interactive Brokers Pro, and either $33 or $83 per order if you use Fidelity to place international trades, depending on whether you place them online or over the phone (the latter is your only option for retirement accounts).
2. Currency exchange costs. These can range from 0.02% to 1%, depending on your broker.
3. Stamp taxes. These are transaction taxes that some countries charge for stock purchases (but not for stock sales). Ireland charges 1%, the UK charges 0.5%, and a few other European countries significantly less than that.
4. Dividend taxes. If you have a cash account, you can deduct foreign taxes on dividends from your US tax, but if you’re investing in a retirement account, they’re a complete loss. Why do I view this as a transaction cost? Because the price of a stock is adjusted for dividends. Here’s an example. Torpol (TOR:POL) pays a yearly dividend: this year it was 3 zlotys. So the stock’s price fell from 18 zlotys at the close of July 13 to 15 zlotys at the next open since July 14 was the ex-dividend date. If you had bought the stock prior to July 14, your shares would be worth 3 zlotys less, but you would be getting those 3 zlotys back in cash. However, because of the tax on dividends, you wouldn’t be getting the entire 3 zlotys back, you’d only be getting 2.47 zlotys since Poland charges a tax of 19% on dividends. So to express this tax as a transaction cost, you would multiply the dividend yield, which is 16.67% (3 divided by 18), by the 19% tax rate to arrive at 3.17%. This cost only applies a) when you buy the stock, not when you sell it; b) if you buy it before the ex-dividend date and plan not to sell it until after that date; and c) if you’re using a retirement account for your trading.

Why It’s Important to Get a Grip on Transaction Costs

In order to maximize your return on a portfolio, you would, in an ideal world, calculate your expected return on each security in that portfolio and weight more heavily those securities with higher returns. Given that some securities have inherently higher transaction costs than others—because of lower volume, wider spread, or higher commissions and taxes—it’s important to take transaction costs into account when building your portfolio.

Here’s an example. YOC AG, a German company, has a typical bid-ask spread of 2.66% of its price and a daily dollar volume of $29,000. So if I want to buy $60,000 worth of YOC in one day, I can expect to pay about 2.5% in spread and market impact costs and an additional 0.25% in commissions to IB. My round-trip cost—of buying and selling this stock—will then be about 5.5%. Now I figure my expected excess return on an average stock is 4.17% after transaction costs. Why? Because my real-time alpha over the last seven years is 33% per annum and my average holding period is 52 days, and 1.33^52/365 – 1 = 4.17%. If I add back typical round-trip slippage (probably less than 1%, since my market impact costs used to be far lower) to 4.17%, I have a base that I can use from which I can subtract my transaction costs to decide if it’s worthwhile buying a stock. In this case, I would definitely not buy $60,000 worth of YOC in one day unless I had reason to believe it would far outperform my average stock. On the other hand, buying a much smaller amount would be cheaper, and might be worth my while.

Transaction costs affect every single aspect of portfolio management. The number of positions you hold should take transaction costs into account: the more positions you hold, the smaller your trades will be and the longer your holding times will be, so diversification significantly reduces trading costs. Choosing what stocks to exclude from your universe should ideally take into account their trading costs. Increasing turnover will increase your trading costs.

Because backtested returns and trading costs pull in opposite directions—backtests favor small stocks, large positions, high turnover, and few holdings, while minimizing trading costs favors large stocks, small positions, low turnover, and lots of holdings—finding the sweet spot can be an overwhelming task. Personally, I’ve been using differential calculus to do so, but not everyone is as insane as that. I certainly can’t claim to have found the right balance, but I’m working on it.

Disclosure: I/we have a beneficial long position in the shares of LYTS, TOR:POL, and YOC:DEU.

The post The Transaction Costs of Trading Stocks: A Primer for Retail Investors appeared first on Portfolio123 Blog.

That seems counterintuitive, doesn’t it? Information about them seems hard to find. Most stock-oriented websites don’t cover them: European stocks are only listed if they have ADR tickers, and frequently there’s nothing written about them. Many brokers don’t offer them. Not only that, but you have to convert currency, take stamp taxes into account, and keep track of different hours for different exchanges.

So what’s easier about European stocks?

Picking the winners.

Part One: Why It’s Hard to Pick Winners in the US

Perhaps, like me, you believe that stock-picking can be rewarding. But stock-picking has gotten a bad rap lately because the US market is so well-trawled. It often seems that arbitrage opportunities no longer exist, and that if a stock seems seriously underpriced, there’s usually a very good reason for that.

Back in 2011, Portfolio123, a website devoted to helping investors create profitable trading strategies primarily based on fundamental data, created a series of ranking systems based on five categories of factors: growth, momentum, quality, sentiment, and value. Eight years later, three of the analysts at Portfolio123—Marc Gerstein, Riccardo Tambara, and myself—revised those ranking systems to a small degree, added one more category—low volatility—and combined them to create what we called the Core Combination ranking system. This ranking system was by no means optimized through extensive backtesting. It was meant as a starting point for investors, and contained all the usual factors—nothing esoteric or recherché. For example, the growth system was simply EPS growth, sales growth, and operating income growth, with 1/3 weight each; each of those was broken down into basic growth and acceleration, and those were then subdivided by time period. The low volatility ranking system was half beta and half price volatility, with each of those given 1-year, 3-year, and 5-year lookback periods.

Unfortunately, this system was really too simple to work very well on large US stocks. If you bought the top 50 stocks out of the S&P 500 every four weeks over the last ten years, your performance would be no better than the S&P 500 index (I’m using 0.25% slippage). The same is true for the S&P 1500, the Russell 1000, the Russell 2000, and the Russell 3000.

You could, of course, create a better ranking system through extensive research and backtesting, including a lot of more esoteric factors like share turnover, net operating assets to total assets, and accruals; adding size factors to the mix; and modifying a number of other measures. That’s what I’ve done for my own personal ranking systems, and I’ve made a lot of money using them on North American stocks. But it hasn’t been easy. I’ve been spending tons of time tweaking my systems and placing trades on low-liquidity stocks.

Part Two: Why It’s Easy to Pick Winners in Europe

So what happens when we use the Core Combination to pick the top 50 stocks in Europe?

First, let’s exclude a few countries. Turkey, Romania, and Hungary all rank high on corruption indexes. And forget about Russia (which isn’t even included as part of Europe in Portfolio123’s coverage).

Next, let’s start with only the 500 largest companies, like we did in the US. And this time I’ll use higher slippage—0.5% per trade—to compensate for currency exchange, commissions, and stamp taxes. Results are poor. But if you expand your universe to the top 1000 companies, you’ll get an excess return over the MSCI Europe index of 3% per annum. The top 1500 companies? 6.5% per annum. The top 3000 companies? 13.5% per annum.

Here’s a more visual example. Here is the performance of the Core Combination system on the 3000 largest public companies in the US and Canada, in 20 “buckets,” over the last ten years, with monthly rebalancing. If you bought the stocks ranked 95 to 100 you would get 15.5%; if you bought the stocks ranked 0 to 5 you would lose 2.7%.

Now here is that same ranking system’s performance on the top 3000 European stocks. The top 5% make an astonishing 25.5% annually.

What makes this better is that these results are truly out of sample. When we designed the core combination system, we relied to some degree on our experience backtesting US stocks. We didn’t actually backtest the ranking system very much—we didn’t want to overoptimize—but most of the factors had been backtested individually. On the other hand, we did absolutely no testing on European stocks, for which we only added the data recently. This is an entirely new dataset which we’d never tested at all.

So you can see that it’s a lot easier to pick winning stocks in Europe. You can use all the factors that seem to have been arbitraged away in the US to create winning ranking systems and screens.

Part Three: Trading Costs

Trading costs are not to be taken lightly. Currency conversion fees will range from 0.02% to a whopping 1%, depending on your broker and your currency. Commissions can be significantly larger than those for US stocks. Stamp taxes can be expensive: the UK charges 0.5% for all stock purchases, France charges 0.3%, Spain 0.2%, Italy 0.1%, and Ireland beats them all, charging 1% (note that these taxes are only charged when you purchase a stock, not when you sell it). There are some stocks and some exchanges that are difficult or impossible to trade from the US. And while some brokers allow European trades in retirement accounts, others don’t, and one (Fidelity) makes you place them over the phone.

Part Four: Some European Stocks to Buy

I currently hold shares in 18 European companies. My largest holdings are in EdiliziAcrobatica (EDAC:ITA), a Genoese construction company; Arctic Paper (ATC:POL), a Polish paper manufacturer; Anglo-Eastern Plantations (AEP:GBR), a British company that owns rubber and palm oil plantations in Indonesia and Malaysia; Torpol (TOR:POL), a Polish railway infrastructure construction company; and Western Bulk Chartering (WEST:NOR), a Norwegian shipping company. (I take Peter Lynch’s dictum to heart: the more boring a company sounds, the better investment it’s likely to be.) But I’m sure you can find plenty of other gems if you look hard enough.

Or maybe not even that hard.

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