Our findings challenge the dire view of finance research. We find that the majority of factors do replicate, do survive joint modeling of all factors, do hold up out-of-sample, are strengthened (not weakened) by the large number of observed factors, are further strengthened by global evidence, and the number of factors can be understood as multiple versions of a smaller number of themes. At the same time, a non-trivial minority of factors fail to replicate in our data, but the overall evidence is much less disastrous than some people suggest.

Jensen et al., “Is There a Replication Crisis in Finance?”

In this article I’m going to summarize their paper and talk about the various factors that they tested, what factors they didn’t test, their factor classification system, some things about their research that remain vague, and some useful conclusions about the results.

The Difference Between This Paper and Previous Ones

What do these researchers do differently than the authors of the you-can’t-replicate-this papers?

1. They use one-month holding periods rather than six- or twelve-month periods. (This makes sense to me, as it provides an even playing ground for factors that have short and long look-back periods.)
2. They use terciles rather than deciles (earlier papers claimed that a factor didn’t work if the top tenth of stocks ranked by the factor failed to beat the bottom tenth; these authors say that if the top third beats the bottom third, it works; this is a somewhat more forgiving and broader measure).
3. They test in 93 different countries. (This is one of the signal merits of this study.)
4. They use value-weighted (cap-weighted) results, but winsorize at the 80th percentile of the NYSE, so that massive firms don’t overwhelm the rest. (This makes sense especially if you’re designing a system that works for large caps.)
5. They exclude factors that the original researchers found insignificant (or at least they say they do, but they end up including a few anyway).
6. They measure success for a factor by looking at its alpha rather than its raw return. (This is, in my opinion, exactly the way it should be measured.)
7. They use a Bayesian approach to factor evaluation based on the prior assumption that alpha is zero. This, together with considering all factors simultaneously, naturally lowers the p-value threshold for factor success.

As a result, their overall out-of-sample success rate for factors tested in academic papers is a massive 85%. In addition, they find that higher in-sample alphas correspond to higher out-of-sample alphas. Their conclusion: academic research into factors is totally valid.

Why Out-of-Sample Results are Rarely Higher than In-Sample Results

As anyone who does any backtesting can attest, in-sample alpha is always higher than out-of-sample alpha, and this is confirmed by the authors’ testing. The authors don’t explain why, though, so I thought I would.

1. Regression to the mean. One must start with the assumption of zero alpha—the assumption that the market is either quite efficient or quite random. In both cases, betting on a factor will prove unprofitable. A researcher will backtest several factors and publish the results for those that work best. Because of the statistical law of regression to the mean, factors that work best over one period are unlikely to work best over another period.
2. Arbitrage. Once a factor has been published, investors are going to try to use that factor, thus arbitraging away its effect. For example, let’s say I publish an academic paper that touts a new factor, Factor X, that nobody has used before. A number of investors read that paper and decide to go long stocks with high levels of Factor X and short stocks with low levels of Factor X. If enough investors do this, the prices of stocks with high levels of Factor X will rise and the prices of stocks with low levels of Factor X will fall. After a short while, high–Factor X stocks will be, on the whole, quite expensive and low–Factor X stocks will be quite cheap. This will drastically reduce the profitability of the Factor X–based investing strategy. Very widely used factors such as book-to-market, price-to-earnings, price-to-sales, and return on equity may have been mostly arbitraged away.
3. Changes in market structure. There are always going to be fundamental structural changes in market conditions. For example, the elimination of trading commissions has enabled much more frequent placement of small orders. The ready availability of fundamental and aggregate estimate data has enabled a far greater number of people to trade according to factor analysis. The rise of the internet has created huge and fundamental changes in the retail, business-to-business, communications, and technology industries. The creation of new kinds of securities like ETFs and SPACs has fundamentally altered the way people invest. All of these changes create conditions in which replicating the success of past factors will be difficult.
4. Manipulation of data. The more certain factors become important to shareholders, the more financial officers at companies will try to give the shareholders what they want. Companies are given rather broad discretion in reporting various expenses, and there is strong evidence that they manipulate earnings, EBITDA, and free-cash-flow numbers to influence their stock price. This makes it harder to replicate findings based on those numbers.

Classification of Factors

The authors algorithmically classified the hundreds of factors they tested into thirteen “themes,” based on the correlation of their returns. Taken all together, these themes attempt to comprise a rather efficient portrait of market behavior. However, there are, in my opinion, many major logical errors in the classification, and there are several additional “themes” that the authors didn’t test. I’ll talk about each one briefly, in alphabetical order.

1. Accruals. This theme consists of five factors: operating accruals and total accruals, each divided by total assets, and each divided by net income, along with the one-year change in current operating working capital divided by total assets. (Operating accruals is the difference between net income and operating cash flow; total accruals adds net financial assets to the mix; and current operating working capital is simply the portion of net operating assets that are current assets.) What’s missing here is the traditional definition of accruals as the one-year change in net operating assets; that ends up in the “investment” theme.
2. Debt Issuance. While this theme includes three-year growth in debt and changes in liability, it also includes net operating assets to total assets and a factor called “abnormal corporate investment,” which is calculated according to the ratio of capital expenditures to sales. Neither of these have anything to do with new debt issuance or reduction.
3. Investment. This is a real grab bag of factors including balance-sheet accruals (change in net operating assets), inventory changes, capex changes, asset growth, changes in noncurrent operating assets, some long-term mean reversion measures, and sales growth. This category is, simply put, a mess.
4. Leverage. Another grab bag. This includes a few factors that you’d expect in this category, like assets to equity, cash to assets, debt to price, and the Altman Z-score. It also, however, includes two R&D-related factors, earnings volatility, the high-low bid-ask spread, and the age of the firm.
5. Low Risk. Most of these factors are related to market beta, including idiosyncratic volatility and share turnover. Two have to do with the volatility of fundamentals: cash flow volatility and earnings variability. And some of the short-term volatility factors double in a sense as short-term mean reversion factors. But also lumped into this category is free cash flow to price and net total share issuance.
6. Momentum. This comprises eight highly related factors, all having to do with six-to-twelve-month momentum but measured in different ways.
7. Profit growth. This includes some expected factors like the change in sales minus the change in inventory or the change in return on equity. But it also includes earnings surprises and a few leftover momentum factors that I assume didn’t correlate as well to the others.
8. Profitability. This includes Piotroski’s F-score, Ohlson’s O-score, operating cash flow to assets, operating profits to equity, return on equity, profit margin, and so on, along with a couple of completely unrelated factors having to do with the coefficient of variation of share volume.
9. Quality. The difference between quality and profitability factors, as the authors categorize them, is a bit fuzzy for me. This category includes asset turnover, gross profits to assets, ROA, operating ROA, gross margin change minus sales change, the number of consecutive quarters with earnings increases, and a few other things.
10. Seasonality. I confess I had not come across this concept prior to reading this paper; the idea is that stocks tend to go up and down in the same months year after year, so you go long stocks with large upward price moves five or ten years ago in the same month that you open your position, as well as stocks with large downward price moves five or ten years ago in the other eleven months. But for some reason the authors also stick some completely unrelated factors in this category, e.g. net debt issuance, earnings persistence, and change in long-term investments.
11. Size. Interestingly, besides the expected factors—Amihud’s measure, daily dollar volume, market cap, and price per share—R&D expenses to market cap is also included here.
12. Skewness. The authors list various skewness measures along with one-month short-term mean reversion.
13. Value. These are more or less what you’d expect: earnings yield, price to sales, book to market, dividend yield, various versions of buyback yield and shareholder yield, and operating cash flow to market. But this category includes only two enterprise value-based ratios and no free cash flow or R&D-based ratios. And it includes a real weird one: total assets to market cap, which makes no financial sense (total assets have to be compared to enterprise value, not to equity; this factor apparently comes from Fama and French, who I’d think would know better, so something odd is happening here).

As you’ve undoubtedly noticed, I’m quite skeptical about this factor classification. In addition, there are no estimate-based factors, only one short-term mean-reversion factor, only three or four fundamental stability factors (factors that measure the stability of a company’s fundamentals), no industry-specific factors, and no ownership factors (like insider buying, percent held by institutions, short interest, etc.). The debt and leverage-based factors do not include such common measures as debt to cash flow, debt to EBITDA, current ratio, or quick ratio; there’s no mention of post-earnings-announcement drift; and there’s little use of enterprise value-based ratios.

Factor Performance

The authors tested each factor over the 1975 to 2019 period and isolated the post-publication portion of the returns. I’ll give a few of the results below.

The best five factors for the US market over the entire period were:

1. cash-based operating profits to total assets (this is EBITDA plus R&D expenses minus operating accruals all divided by total assets; interestingly, this factor was not found to be significant in the original paper);
2. one-year net operating assets change to total assets;
3. 12-month residual momentum (this is more or less the Fama-French 3-factor alpha over the last twelve months, not including the most recent month);
4. one-year current operating working capital change to total assets; and
5. net operating assets to total assets.

The best five factors for the non-US developed market over the entire period were:

1. 12-month residual momentum;
2. 12-month net equity payout (this is the log of the 12-month increase in price minus the log of the 12-month increase in market cap);
3. 21-day idiosyncratic volatility (based on 4-factor alpha);
4. six-to-ten-year lagged returns, non-annual (this is the returns of the stock in the other eleven months besides the one you’re in, six to ten years ago, with worse returns being better); and
5. 12-month adjusted change in share count (which is essentially the same as the second factor on this list, but measured differently).

This is just a small sample of the hundreds of factors that had positive alpha. 

A number of the best-performing factors that the authors tested are variations on one central concept: that net operating assets, cash-based accruals, and net operating working capital (which are all closely related) should be low in comparison to total assets. I wrote an article about this years ago, and it’s been a constantly useful factor for me ever since; it’s nice to see how many variations of this concept there are.

Interestingly, not a single value factor ranks highly. Of the various value factors that were tested, the best was free cash flow to market cap, followed closely by operating cash flow to market cap and shareholder yield (which they call “equity net payout to market cap”). The next two value factors are EBITDA to EV and earnings yield. But they’re all pretty close to each other. The reason they don’t rank highly, I suspect, is twofold: first, in testing them, the authors, I believe, compared their values to the entire universe of companies they were testing rather than to the company industry; second, the value factor has had a very high beta lately, which lowers its alpha.

Putting the Authors’ Conclusions into Practice

If we were to put together a multifactor ranking system according to the authors’ conclusions in this paper, in theory it would probably be best to do the following:

• include one factor from each category, since the categories are relatively uncorrelated;
• include the factors with the highest overall alpha, since out-of-sample alpha varies a great deal from factor to factor in terms of what years are covered; and
• weight the factors according to their overall alpha.

I have therefore designed a ranking system that does exactly this, based on the factor alphas in the US. The thirteen factors are, in order of highest to lowest alpha, the five in the above list followed by:

1. change in sales minus change in inventory;
2. operating cash flow to assets;
3. highest five days of return scaled by volatility (this is the average of the five highest out of the last 21 days’ return divided by the volatility of the stock over the last year), lower values better;
4. free cash flow to price
5. net payout yield (dividends paid plus equity purchased minus equity issued, all divided by market cap)
6. years 6 to 10 lagged return, nonannual (see above description);
7. R&D to market cap; and
8. asset tangibility (a complex measure of how tangible the total assets are; this factor’s alpha is very low, but is the highest in its category, which is “Leverage”).

If you are a Portfolio123 member, you can find the ranking system here. This is what it looks like:

(Two of the above formulas need a little further explanation. First, in the paper, residual momentum is the Fama-French three-factor alpha; I used a simpler version of alpha here since calculating Fama-French beta isn’t possible using Portfolio123. Second, the “highest 5 days of return” required a custom formula, which I called “$21medmed,” which is LoopMedian (“Eval (Close (Ctr) / Close (Ctr + 1) > $21med, Close (Ctr) / Close (Ctr + 1), NA)”, 21) where $21med is another custom formula, LoopMedian (“Close (Ctr) / Close (Ctr + 1)”, 21).)

The authors tested their factors on a universe that excluded any stocks with a market cap less than the 20th percentile of the NYSE (currently about $800 million). I was able to approximate this limitation and ran a 20-bucket test using Compustat data with four-week rebalancing covering the years 1999 to 2021. This was the result:

If I run the test to cover only the last ten years, the results aren’t quite as good, but they’re still nothing to sneeze at:

This strikes me as a decent ranking system for mid-caps and large-caps going forward, though there are a large number of improvements I would make.

Currently, the top ten stocks that this system recommends are Medifast (MED), Myovant Sciences (MYOV), Smith & Wesson (SWBI), Evertz Technologies (EVTZF), Sonos (SONO), Translate Bio (TBIO), Overstock (OSTK), Internet Initiative Japan (IIJIY), Tupperware (TUP), and Michaels (MIK). 

Conclusions

I found the authors’ conclusions intensely gratifying. Factor-based investing works! I was also immensely pleased that the authors refrained from calling these factors “anomalies,” as is so often done in academic literature.

But I was dismayed by the numerous flaws in the authors’ paper:

• The factor results are presented in a terribly difficult-to-parse manner. The authors use “posterior” and “out-of-sample” seemingly interchangeably, yet some of these papers were published very recently and at one point they make it clear that some of the out-of-sample period was prior to the in-sample period (i.e. in the original paper, the testing period began after 1975 and the authors used the pre-1975 data). In general, the presentation of the results is terribly confusing. The world posterior results are included as a bar chart with labels that are almost too tiny to read and nearly impossible to match to the bars. It took me many hours to figure out which factors worked best, how they were constructed, what category they were in, and what sample period was being used.
• The classification of factors is more or less a joke. It’s an ambitious endeavor and the authors are to be commended for the attempt, but about half of the categories include factors that by no stretch of the imagination belong there, other categories are missing important factors, and a number of factors remain uncategorized. The fact that the best performing (out-of-sample) value factor, free cash flow to market cap, isn’t even classified as a value factor, while its close cousin operating cash flow to market cap is, indicates the problems here.
• A huge number of the factors are simply variations of each other, and a huge number of factors (especially those involving analyst and ownership data) went untested.
• There is no indication whether any of these factors were tested against similar companies. Certainly similar-company testing (testing against other companies in the same industry or sector) has long been a valid approach, and I find it hard to believe that none of the original papers used it. But there’s no sign of this distinction in the authors’ work. I would guess that the value factors would show far better results if they were tested against other companies in the same industry or sector rather than against the universe of stocks as a whole.

It almost goes without saying that a multi-factor approach to investing, in which every stock is subjected to a number of factor tests and those that rank the highest are purchased, makes good sense, and this paper, while neither affirming or condoning the approach, goes a long way toward validating its various inputs. Despite its flaws, it’s a major contribution to the literature.

The post The “Factor Zoo”: Some Thoughts on “Is There a Replication Crisis in Finance?” appeared first on Portfolio123 Blog.

1. Expenditures on R&D that amount to 15% or more of market cap
2. Less than 5% short interest as a percentage of shares outstanding

Since I created the screen on October 4, 2019, it has returned 66%, which is 105% annualized, entirely out of sample. It invested in approximately 30 stocks, rebalancing monthly with 0.25% slippage. With only those two rules, the same backtest invests in an average of over 60 stocks, while the return increases to 76%. If you backtest this two-rule system all the way back to 1999, you get a nice annualized return of 19% (compared to 6.35% for the S&P 500), and backtesting only ten years back gets you 28% (compared to 12.88% for the S&P). If you limit yourself to the 25 companies with the highest percentage of market cap spent on R&D, your ten-year annualized return goes up to 32%. Clearly, considering R&D expenditures when choosing stocks can make you quite wealthy.

Now for real-life investing, I don’t believe in simple stock-picking formulas with only two rules. At the same time as I created the R&D screen I created four other screens, all of which backtested well and all of which I had some real faith in. Only two of the five have performed well since October 4, 2019, and one has been a total disaster. We just happen to be in an environment in which R&D outperforms. How long will that last? It’s anyone’s guess.

I do, however, think that taking R&D expenses into account when picking stocks is a good idea. This article explores some things to consider.

I. R&D Expenses by Industry

What industries spend the most and the least on R&D?

Here are the industries that spend the most (in alphabetical order): automobile manufacturers, biopharma, computers (hardware and software), consumer electronics, consumer finance, entertainment, interactive media, manufacturing equipment, and telecommunications.

Here are the industries that spend the least: agriculture, banks, construction, distribution, energy, food and drink, freight, health-care providers, hotels and restaurants, insurance, mining, REITs, retail, tobacco, utilities, and waste management.

II. The Difference Between CapEx and R&D.

Now here’s the rub. When a biopharmaceutical company spends money researching and developing a new drug, that’s R&D. When an energy company spends money researching and developing a new place to drill or a mining company spends money researching and developing a new place to dig, that’s a capital expenditure. The FASB (Financial Accounting Standards Board) has made a generalized exception for extractive industries so that all activities unique to those industries are capitalized rather than being treated as R&D.

And when it comes to non-extractive industries, not all R&D is classified as R&D. If you build a data center, that can be capitalized. If you build a laboratory, that can be capitalized. Labor costs for running (as opposed to building) the data center and laboratory can’t be capitalized, though, so most R&D expenditures are actually salaries.

What is the difference between R&D and a capital expenditure? The FASB is clear: “At the time most research and development costs are incurred, the future benefits are at best uncertain. In other words, there is no indication that an economic resource has been created.” A capital expenditure leads pretty directly to sales while an R&D expense is entirely speculative. Therefore they are treated entirely differently by accounting rules. R&D expenses are deducted from income all at once, at the time that they are spent; capital expenditures are depreciated so that the cost is deducted little by little over a period of years.

III. R&D Ratios

I like to look at R&D to market cap as a kind of alternative value ratio. The kinds of companies this ratio favors are tiny ones, mostly in biopharma. But other people use R&D to sales or R&D to assets as alternative measures. In backtesting over the last ten years, R&D to market cap performs the best of these three measures, and R&D to sales performs the worst. The advantage of using market cap is that you’re taking into account the company’s price; the disadvantage of using sales in your denominator is that you’re punishing companies with strong sales and rewarding companies with weak sales.

IV. Capitalizating R&D Expenses

Aswath Damodaran, whose valuation methods and deep thinking about accounting have been tremendously influential, has long advocated capitalizing R&D expenses when valuing a company. His argument is as follows. One can classify all expenses as either operating expenses (which are deducted in full at the time they are incurred), financing expenses, or capital expenses (which can be capitalized and thus deducted over a longer period). Damodaran takes a very different approach to this distinction than does the FASB. “Capital expenditures are defined as those expenditures that are likely to create benefits over multiple periods,” he argues, while operating expenses, “at least in theory, provide benefits only for the current period.” R&D should therefore be classified as a capital expenditure and should be capitalized, whether or not an economic resource or asset has been created thereby.

Damodaran points out that prior to 1975, companies were allowed to capitalize R&D expenditures, and that outside the US, development costs are still allowed to be capitalized, though most companies do not do so.

There are strong arguments to be made both in favor of Damodaran’s position and in favor of the FASB’s. I tend to agree with the FASB. How many projects funded by R&D actually become commercially successful? Evidence suggests that it’s well under fifty percent. In addition, most R&D expenses are labor costs, and those are only capitalized if the labor is directly involved in the creation of a capital asset. Lastly, the FASB is always issuing “invitations to comment” and is concerned about keeping current with business standards, and they have not changed this particular accounting standard in 45 years. If there were a good reason to change it one would think they would.

On the other hand, it’s worthwhile considering how capitalizing R&D expenses would affect your valuation of a company.

Here’s what I do when I want to capitalize R&D expenses; you can adapt this depending on your estimation of the length of time by which to depreciate them.

First, take one-fifth of each of the R&D expenses over the four years prior to the most recent year and add those together. We’ll call this number R&D amortization.

In order to get adjusted net income, take the most recent year’s net income, add back this year’s R&D expenditures, then subtract R&D amortization.

In order to get income growth, you’d need to make this adjustment for each year’s net income, and calculate that accordingly.

You then have to add to total assets the amortized R&D. Add the entirety of the current year’s R&D expenditures, 80% of last year’s, 60% of the year before’s, and so on. For calculating adjusted ROA, asset turnover, and other asset-based ratios, this addition to total assets will be important.

V. What Companies Pass the Screen Today?

What companies in the Russell 3000 with less than 5% short interest are spending more than 15% of their market cap on R&D? As of the weekend of 6/28, there were 77 of them, 49 of which were healthcare stocks. The ten biggest are Ford (F), Western Digital (WDC), Hewlitt Packard (HPE), CommScope (COMM), Akebia (AKBA), Akcea (AKCA), Theravance (TBPH), Calix (CALX), Amneal (AMRX), and Hyster-Yale (HY). And the ten that are spending the largest percentage of their market cap on R&D are Solid Biosciences (SLDB), Xeris (XERS), Cooper-Standard (CPS), Cyclerion (CYCN), Commscope (COMM), Extreme Networks (EXTR), Five Prime (FPRX), Arbutus (ABUS), Eastman Kodak (KODK), and Fortress Biotech (FBIO).

Now not all of these are good investments. Personally, of all the stocks that pass the screen, I’d recommend Ribbon Communications (RBBN), Telenav (TNAV), and Checkpoint (CKPT) for the short term, and Endurance (EIGI), Hyster-Yale (HY), and Amneal (AMRX) for the long term. If—and this is a big if—R&D-powered stocks keep on outperforming like they have been lately, these companies may be a good starting point for an R&D-based value strategy.

Disclosure: I am long Ribbon Communications (RBBN).

The post How R&D Expenses Can Help You Pick Outperforming Stocks appeared first on Portfolio123 Blog.

Thanks to the suggestions of some of my readers (especially Marc Gerstein and Hans Koolschijn), I decided to look into whether variability in fundamentals correlates with variability in prices, and if so, whether that variability also inversely correlates with performance. The consistency of my findings, which I present in the table below, astonished me.

The coefficient of variation is the standard deviation divided by the mean. So the coefficient of variation of a stock’s weekly prices over the last three years is simply the standard deviation of those prices divided by the average price. Similarly, the coefficient of variation of a company’s assets over the last three years is the standard deviation of the total assets of the company over the last twelve quarters divided by the average assets over the same period. A company whose assets have changed dramatically from quarter to quarter will show a much higher coefficient of variation than a company whose asset base is stable. Thus, when it comes to assets, FiServ (FISV) has a coefficient of variation of 1.16 over the last three years because its assets have varied so greatly while Regency Centers (REG) has a coefficient of variation of 0.01 because its assets have stayed almost exactly the same.

Using Portfolio123, I took the Russell 3000 and measured the quarterly coefficient of variation of twenty-three fundamental items over the last three years. I then calculated the correlation between that coefficient and the coefficient of variation of weekly prices for those stocks over the same time period. The correlations for fifteen of those items were so low as to be nonexistent. But the correlations for eight of them were quite high. I repeated this experiment five times in all, for three-year periods ending in 2020, 2015, 2010, 2005, and 2000. In each case I got more or less the same results.

Companies with high quarterly variability in assets, liabilities, sales, accounts receivables, asset turnover, total investment (gross plant plus inventory), R&D expenditures, or dividends paid tend to have high variability in prices. On the other hand, companies with high variability in income, cash flow, margins, or profitability show no more nor less variability in prices than companies with low variability in those things.

I then measured what would have happened if you had taken stocks in the Russell 3000 and divided them up into quintiles based on the coefficient of variation of each of these factors, rebalancing monthly since January 1999. Companies with low variability in those factors that correlate with variability in prices tend to massively outperform companies with high variability, with the exception of dividends paid, where the outperformance is more modest. (In addition, companies with low variability in SG&A expenses, gross profit, capital expenditures, and gross margin also strongly outperformed.) On the other hand, companies with high variability in income and cash flow outperformed those with low variability, as did companies with high variability in ratios (profitability and margin) based on income and cash flow.

The explanation for the performance here is relatively simple. Investors prefer companies whose income and cash flow are growing (thus exhibiting variability). But they also like companies with stable fundamentals. The ideal company for an investor is one whose earnings and cash flow are growing while everything else remains more or less the same. (Investors love to give lip service to companies with large growth in sales. But they don’t put their money where their mouth is. The performance of stocks ranked by decile on sales growth looks like a bell curve, with the highest performance smack in the middle and the lowest performance on the tippy ends. This is the case no matter how far back you go in time, as James O’Shaughnessy made clear in What Works on Wall Street.)

The explanation for the correlations is similar. Companies with stable fundamentals have stable prices. Price variability serves as a proxy for variability in fundamentals. Importantly, it reflects only the variability in certain fundamentals, variability which correlates negatively with price performance.

So a much more profitable strategy than investing in stocks with low variability in prices is to invest in stocks with low variability in fundamentals, as long as those fundamentals don’t include income, cash flow, or ratios based on those.

Below is the performance of going long the bottom quintile of stocks in price variability in the Russell 3000 and shorting the top quintile between January 1999 and today, with monthly rebalancing. You can see that this strategy works well in bull markets and badly in bear markets.

I’ve created a ranking system, which you can view here. It equally weights variability in assets, liabilities, receivables, sales, investments, and R&D expenditures. Here’s the bottom-minus-top quintile performance of that system:

This system, as you can see, doesn’t suffer as much during bear markets and makes three or four times the return. It also handily beats the S&P 500, which returned only 250% during this time period. Its CAGR is 8.87%, compared to 5.99% for the S&P 500. (The system also works very well using S&P 500 stocks, but the total return is 351% rather than 614% when using the Russell 3000.) Not many long/short strategies outperformed the S&P 500 over the last two decades.

On the other hand, this is just a backtest. Was there any way to know, back in 1999, that low variability in non-income-related fundamentals would be a ticket to high returns? Not only that, but it would be very hard to short some of the tiny biopharmaceuticals in the top quintile.

And the system’s outperformance really comes from the short side. The bottom seven deciles have slightly above average returns, but the stocks in the top decile—those with the most variability, those you’d want to short—lose 5% a year (this is the compounded figure, not the average).

In short, this is not a complete investment system, and I wouldn’t advise anyone to use low variability as their sole investment criterion. But if you’re interested in a low-volatility portfolio that outperforms, I’d advise you to look at stocks with low variability in fundamentals rather than low variability in prices; and if you’re interested in hedging, shorting a widely diversified portfolio of stocks with high variability in fundamentals is not a bad choice at all. Lastly, if you use a multi-factor system for stock investing, as I do, low variability in fundamentals should be a part of your factor arsenal.

The post Why Low-Variability Investing Works appeared first on Portfolio123 Blog.

When we as investors talk about volatility, we’re usually talking about variability in price returns. If an investment goes up and down 5% to 10% per day, that’s high volatility; if it goes up and down 0.05% to 0.1% per day, that’s low volatility. It’s a relatively simple concept, and is traditionally measured using standard deviation.

But when we compare investments to each other, we start talking not only about variability in price returns, but also about beta. And the implicit assumption is that beta measures something very different from variability. Beta is market-related risk; variability is unrelated to the market. For example, one writer, whom I won’t name because of my respect for him, wrote recently, “Beta is magnificent in theory but unstable and erratic in practice. . . . Imagine a debt-heavy gold mine whose stock soars in a dull market because of news of a big find. Beta is low or maybe negative, because the move is out of sync with the market, but risk is still massive!”

There’s one major problem with this kind of thinking. Even if the gold mine’s stock was almost completely uncorrelated to the market, its beta would be lower if its price variability was lower. This article will explain why.

Why Beta and Variability Are Interdependent.

It can be observed empirically that the lower the beta of a stock’s returns is, the lower is the standard deviation of its price returns. Below is the three-year beta of the S&P 500 graphed on the x-axis and the three-year percentage deviation of the weekly price returns on the y-axis. (All figures are obtained from Portfolio123; beta is here calculated by comparing the weekly returns over the last 150 weeks to those of the S&P 500 without subtracting a risk-free rate from either one and percentage deviation is calculated by taking the standard deviation of the weekly returns over the last 150 weeks.) The relationship is very clear.

The reason for this is simple. Beta is the slope of the linear regression of a stock’s returns to a benchmark’s returns. The equation of the slope of a linear regression is

or, in plain English, the correlation of returns times the standard deviation of the stock’s returns divided by the standard deviation of the benchmark’s returns. Since the standard deviation of the benchmark’s returns is fixed (it’s the same for all stocks), the slope has a largely positive relationship with both the correlation and the standard deviation of the stock’s returns.

As beta goes to zero, two things could be happening: either the correlation goes to zero, or the standard deviation of the returns goes to zero. A stock whose price never changes has a beta of zero, just like a stock whose price changes in a manner that’s completely uncorrelated to the benchmark.

Now notice there’s a huge amount of white space at the bottom right of the graph. Why, for instance, are there no stock returns with a standard deviation of 5% and a beta of 2?

It’s because r­_x,y (the correlation between the market’s returns and the stock’s returns) cannot be greater than one. So how small can σ_y (the standard deviation of a stock’s returns) go? If we rearrange the above equation, we get

The higher the correlation, the lower σ_y can get, but the lowest it can ever get is σ_xβ, and since σ_x= 2.56% (the percentage deviation of the S&P 500), a stock with a beta of 2 can never have a standard deviation of less than 5.12%.

What About Negative Betas?

If we introduce short ETFs to the picture, we will get negative betas, and that’s because we’ll have negative correlations. With negative correlations, the higher the standard deviation of the ETF, the lower the beta. In other words, the relationship between beta and standard deviation is V-shaped with the lowest point at zero. After all, standard deviation, being the sum of squares, can never be negative.

This chart shows a sample of the betas and percentage deviations, measured exactly like in the above S&P 500 chart, of 1,600 ETFs, many of them leveraged and short.

Note the slopes of the edge of the plots, which are ± 2.56%—the percentage deviation of the S&P 500.

What Does All This Imply for Low-Volatility Investing?

Judging from empirical data, low-beta and low-variability equity portfolios have both historically outperformed high-beta and high-variability equity portfolios. Portfolios based on beta and on variability are quite similar in constitution because of the interrelationship of these factors. The scale of their outperformance is consequently similar. With monthly rebalancing and no slippage costs, the lowest 20% of the Russell 3000 in terms of variability outperformed the highest 20% by 616.32% over the last twenty years (10.35% annualized); the lowest 20% in terms of beta outperformed the highest 20% by 540.28% (9.73% annualized). There’s not much difference there. The numbers for the S&P 500 are similar: 9.34% annual outperformance for low variability; 10.57% annual outperformance for low beta. Many studies have gone back close to a hundred years and have also looked at non-US markets. The results are strong.

There is a mathematical reason why low-beta equity portfolios outperform: as I have proven, in markets in which returns tend to be positive, alpha and beta are inversely correlated by their very nature. As far as I can tell, there is no mathematical reason why low-variability equity portfolios would outperform high-variability ones.

This outperformance goes against modern portfolio theory, which posits that investors demand greater return for greater risk. By any measure, low-volatility portfolios are less risky than high-volatility portfolios. Why should they outperform?

One theory is that investors tend to overpay for “exciting” stocks and ignore “boring” stocks, and “exciting” stocks clearly have more price variability than “boring” ones. But there seems to be no correlation between value stocks and low-volatility stocks, and this theory depends on one. There are a number of other theories out there, including a “stocks as lotteries” hypothesis. I haven’t found any of them very convincing—certainly not convincing enough to explain outperformance of such magnitude.

It’s possible that low-variability equity portfolios outperform simply because they tend to have low betas. But in that case, the outperformance of low-beta portfolios should be more apparent than the outperformance of low-variability portfolios, and that is not what we see. So there’s probably another reason as well. It merits further investigation.

The post A Tale of Two Volatilities appeared first on Portfolio123 Blog.

1. Low price volatility. This is simply the standard deviation of daily (or weekly) returns. Stocks that are stable and steady in terms of price volatility tend to remain that way.

2. Low volume volatility. Once again, choose stocks with low standard deviation of volume to be really safe.

3. Beta. Beta is a rough measurement of how closely a stock’s movements resemble those of the market as a whole. Alpha is a measurement of excess returns after beta is taken into account. Beta is the slope of the linear regression between the stock’s weekly or monthly price movements and those of the market, and alpha is the y-intercept. If a stock’s beta is 1, then one should expect that when the market goes up or down 2%, the stock will go up or down 2% plus its alpha. If its beta is 2, when the market goes up or down 2%, the stock will go up or down 4% plus its alpha. If its beta is close to 0, the stock will act completely independently of the market. And if the stock’s beta is –1, when the market goes up 2%, the stock will, on average, go down 2% plus its alpha. The lower the beta, the more uncorrelated the stock is to the market, and portfolios with low correlations between stocks have much less variance than those with high correlation. As a bonus, beta and alpha are negatively correlated (I’ve written a mathematical proof of this), so low-beta approaches tend to produce high alpha.

4. Low share turnover. This is the number of shares traded divided by the number of shares outstanding. I have written on this factor at length, but if you don’t want to read my article, here’s a nutshell version.

Older, established, and somewhat boring companies (widows and orphans), often with high-priced shares and low short interest, have low share turnover; and cutting-edge, exciting, controversial, highly hyped, turnaround, high-momentum, and/or heavily shorted companies have high share turnover. Stocks with lower share turnover are less subject to market shocks, and the higher their turnover, the more they’ll be moved by the market. In other words, low-turnover stocks have lower beta and high-turnover stocks have higher beta.

Why? Prices and quantities traded are driven by the same forces. And it almost goes without saying that without a large increase in volume, you simply can’t have a large increase or decrease in price.

If you multiply both the top and bottom of the share turnover formula by the price per share, in the numerator you get dollar volume—the amount of money actually exchanging hands—while in the denominator you get market cap. Put everything together and you can see how the price movements in the cap-weighted market as a whole are going to be much more heavily reflected in stocks that experience a high dollar volume compared to their market cap than in stocks that experience a low dollar volume, simply because volume amplifies market-related price movements. Share turnover—average dollar volume divided by market cap—is essentially a measure of investor participation in a company. And higher investor participation will be associated with a larger amount of capital responding to common shocks. Thus, other things being equal, a larger amount of capital responding to a common shock will result in a stronger price movement.

5. Low fundamentals volatility. I have found that a number of measures of stability can help reduce volatility and increase returns. In particular, look for stocks with stable accounts receivables, assets, cash conversion cycle, cash flow, employees, income, margins, sales, and so on.

6. Large size. Large companies tend to be far more stable than small companies. The measure of size with the lowest negative correlation to volatility is market cap, with sales coming a close second, so companies with large market caps and high sales are good low-volatility investments.

I’ve designed a relatively simple ranking system that combines all these factors for a comprehensive low-volatility approach. If you’re a Portfolio123 subscriber, you can link to it here. If you’re not, a screenshot of it is below.

I’ve put in two fundamental factors as examples of how to minimize fundamentals variance, but feel free to add others. I haven’t assigned weights to any of the factors: please feel free to copy this system and assign weights as you see fit. You can backtest the system with this screen. You’ll see that a 50-stock portfolio of Russell 1000 stocks gets solid excess returns over the last five, ten, and fifteen years, with much higher Sharpe ratios and much lower beta and standard deviation than the S&P 500. I’m sure you can improve these results by adding screening rules and varying the weights of the ranking system.

What kind of stocks does this system recommend? Right now, the top five stocks are Republic Services (RSG), CNA Financial (CNA), Kimberly-Clark (KMB), Ecolab (ECL), and Procter & Gamble (PG). Boring companies all. And safe, too.

Academics have long puzzled over the fact that low-volatility stocks have higher returns than high-volatility stocks. It goes completely against their theory that higher risk should be compensated with higher returns.

But in fact, high risk does not correlate with high returns. Risk and return do have a relationship, but it’s not linear, and is shaped more like the top of a right-facing baseball cap. If you’d like to read more about this, I’ve written a short article here. By using a low-volatility approach, you can both reduce your risk and increase your returns.

The post Low-Volatility Stock Picking for High-Volatility Markets: A Multifactor Approach appeared first on Portfolio123 Blog.

If you’re a quantitative investor or trader, you build a model and then backtest it to see if it has worked in the past; if you’re like most people, you try to improve your model with repeated backtests. You’re operating under the assumption that there will be at least some modest resemblance between what has worked in the past and what will work in the future. (If you didn’t assume that, you wouldn’t backtest at all.)

But what few backtesters do after building their model is to try to break it by subjecting it to stress tests. A truly robust model should withstand every moderate attempt to break it. Only then should it be put into practice.

This article will outline some techniques for stress testing quantitative models. I use Portfolio123 to build and backtest my models. If you model using a different platform, most of what follows won’t apply, but I’ll try to explain my techniques in language that can be adapted to other platforms.

General Guidelines for Stress Tests

Each model that one designs on Portfolio123 essentially consists of a ranking system and a universe to which it applies. One can add a lot of complexity to the model, but those are perhaps the two most important foundations. The universe consists of a root universe and then incorporates a variety of screening rules to eliminate stocks with low liquidity, high risk, low growth, high price, or whatever else you want to put in there. In order to do these tests, you must put as many of your screening and buy rules into your universe as you can. Each model then buys the top-ranked stocks according to its ranking system, and sells them when their ranking falls to a certain point, buying new stocks to replace them. The number of holdings and the sell rules are some of the things we’re going to vary to see if the models will break.

Portfolio123 offers four very different ways of testing a particular ranking system and universe. We can use:

• a screen backtest, which rebalances to equal weight every rebalance period;
• a rolling screen backtest, which holds stocks for a certain period, and one can see overlapping returns that way;
• ranking system performance, which separates the universe into quantiles according to the ranking and shows how each would have performed; and
• an actual simulation of the model, with buy and sell rules.

To try to break a model, we should try all four of these tests, varying parameters. We should vary the number of stocks held at one time; we should vary the universe rules, testing on subsets of the universe or on an altogether different root universe; we should vary the factor weights in our ranking system; and we should vary the time period tested, including, if possible, testing it on a time period that hasn’t been tested before.

A test can be said to fail if the results have a negative alpha or a negative excess return when compared to a benchmark that consists of all of the stocks in the root universe of the one that’s being tested (or if, in a rank performance test, the top bucket is lower than the middle buckets).

So let’s take a closer look at these stress tests.

Four Sets of Variations

• First, vary the number of stocks being held. Test it on the top ten, top twenty, top fifty, and top one hundred.
• Second, vary the root universe. Test it on the S&P 500, the Russell 1000, the S&P 1500, the Russell 3000, Canadian stocks, international stocks only, and universes consisting of only certain sectors. Be sure to adjust the slippage accordingly: testing on the Russell 3000 will require higher transaction costs than testing on the S&P 500. Change your screening rules by varying your hard limits by 10% or 15%.
• Third, vary the factor weights in your ranking system to a moderate degree. Add, say, 3% to five factors and subtract 3% from another five factors, or add 3% to five factors and normalize them all. Then go back to your original weights and do that again.
• Fourth, vary the time period. Test it on the last ten years, fifteen years, and three years; go back and test it on other discrete time periods as well.

If you do all this using a screen backtest, a rolling screen backtest, a ranking system performance test, and a simulation, you’ll be doing thousands of stress tests. This is obviously impractical, so it’s best to design a subset of a dozen or so stress tests that will help you try to break your system.

Practical Stress Tests

For the purposes of this article, I designed five very different systems that backtested quite well, and then put them through a dozen stress tests. I won’t describe all these in detail, as it would be tedious in the extreme. Suffice it to say that three out of the five systems I tested failed a test. The two toughest tests were as follows:

I ran a ten-bucket rank performance test on one variation of my ranking systems over the last fifteen years with a rebalance period that matched my actual average holding period and my root universe being the S&P 1500. I then compared the top bucket to the middle buckets. In one case, the top bucket was lower than the average of the two middle buckets.

I ran a rolling screen backtest of the top 100 stocks, using the Russell 3000 as my base universe, over the last four years only, using another variation of my ranking systems, with a holding period that matched my actual average. In two cases, my backtest failed to exceed that of the benchmark, in part because of realistic slippage costs and in part because the last four years have been pretty terrible for small-cap value stocks.

Conclusion

The natural impulse for a quantitative investor or trader is to try to create a system by tweaking various inputs so that when backtested it shows excellent returns. But unless the system is subjected to stress tests such as the ones I’ve discussed, it has a higher chance of breaking down when actually implemented with real money. Backtesting for failure may be just as important as backtesting for success.

The post Break Your Strategy: How to Stress Test Your Quantitative Models appeared first on Portfolio123 Blog.

As a factor, momentum—the idea that a stock’s relative returns over the past six to twelve months have a tendency to persist over the next six to twelve months—has proved remarkably resilient. Academics first recognized this factor in the early 1990s, and its return premium has since been verified over the past 220 years (no, this is not a typo) of US equity data. As Clifford Asness and his colleagues documented in a 2014 paper entitled “Fact, Fiction, and Momentum Investing,” there have been over 25 years of out-of-sample evidence of momentum, in forty countries, and even in a dozen other asset classes.

Using Portfolio123, I looked at the performance of the Russell 3000 since 1999 if divided into deciles according to momentum over various lookback periods, with monthly rebalancing. I then calculated the slope of those deciles (with the lowest decile getting an x value of 1% and the highest 10%), and also looked at the difference between the top decile and the bottom decile. Here are the results:

It’s pretty clear that over short periods (4 weeks or less) and long periods (5 years or more), price returns revert to the mean; over six- and twelve-month periods, momentum prevails.

(I should add that when looking at momentum decile returns, the difference between the top three deciles is minimal but the difference between the bottom three is huge. Momentum, like many factors, is more effective at identifying losing stocks than winning ones.)

The Explanations So Far

Yet there has been no general agreement on why momentum works. As Asness and his colleagues write, most of the theories fall into two categories: risk-based and behavioral. I’ll outline these theories briefly.

Behavioral explanations explain momentum as either an underreaction or a delayed overreaction. In other words, either momentum happens because new information filters into the market and then the market takes some time to catch up with it, or because investors chase returns, providing a feedback loop that chases prices higher.

These explanations, of course, contradict each other. The second might explain momentum well if it were a two-to-four-week phenomenon, but price returns tend to revert over such a short period. As for the first explanation, why would it take six months for information to filter into the market? Why wouldn’t it take two weeks? The only explanation for momentum that can make sense has to be one that explains why momentum works well if using a six-to-twelve-month lookback and does not work well for shorter or longer periods.

The risk-based explanations are, first, that high-momentum stocks face greater cash-flow risk because of their growth prospects, and second, that they face greater discount risk because of their investment opportunities. Both would give them a higher cost of capital. These explanations make more sense to me than the behavioral ones, but not much. At least they conform with the six-to-twelve-month outlook. But they seem like a stretch. And the second explanation is incompatible with the risk-based explanation for the value factor. In general, I don’t like risk-based explanations for factors because I don’t believe that risk and return have a linear relationship, and because many factors work because they reduce risk.

I think there are some alternative explanations that are quite a bit simpler. The first is regulatory; the second is just common-sense.

Alternative Explanations

1. Tax law encourages investors to sell losing positions.
2. Companies that outperform are more likely to continue to outperform than companies that underperform, and companies that underperform are more likely to continue to underperform than companies that outperform. Since companies that outperform tend to increase in price and companies that underperform tend to fall in price, momentum is a natural consequence of the persistence of performance.

Both these reasons make sense with the six-to-twelve-month optimal lookback period for momentum strategies, and are compatible with long- and short-term price reversal.

Let’s drill down a little deeper into each one.

The Taxation Explanation

Tax law currently encourages investors to sell losing positions and to hold winning positions, thus contributing to momentum. Taxation of capital gains has been a constant in the United States for over one hundred years, and is imposed in a large majority of other countries as well. A capital gain is the result of selling a winning position; a capital loss reduces capital gains. So there has been some tacit governmental encouragement to sell losing positions and hold onto winning ones.

Let’s look at how this works. You invest in two stocks, A and B. After a while, A posts a gain and B posts a loss. Now let’s say you want to sell A. Without capital gains taxes, your decision to sell A would be completely independent of your decision to sell or hold onto B. But given capital gains, it makes much more sense to sell B at the same time as you sell A. Thus capital gains taxation contributes significantly to negative stock momentum.

Because capital gains taxes are calculated on a year-to-year basis, and because most institutions tend to hold stocks for about a year, this explanation conforms pretty well with the six-to-twelve-month optimal lookback period for the momentum factor.

The flaw in this explanation is that it only covers the last hundred years or so, and some studies show that momentum was a factor even before then.

The Performance Explanation

What’s a good measurement for performance? Clearly, one that correlates well with future price increases but actually is independent from price.

I’ve chosen free cash return on assets, measured quarterly to avoid any data infiltration. Companies with a high ratio of free cash flow to total assets tend to perform well; companies with a low ratio tend to perform poorly. There are plenty of other performance measures that one could choose instead. But please note that I didn’t test a bunch of factors and then choose one that I thought would persist. I chose this factor because it correlates well with future price increases and therefore, in my opinion, signifies something about company performance.

Indeed, this ratio measured at one point in time and measured again 12 months later has a correlation ranging from 0.6 to 0.9, which is astonishingly high for a ratio based solely on one quarter’s data. But measured over a five-year period, the correlation range drops to 0.2 to 0.4, depending on what that five-year period is.

According to my second explanation, momentum is a proxy for company performance. If a company’s performance is strong, its price is going to rise. If its performance continues to be strong, its price will continue to rise. Therefore, a company whose price is rising now is likely to have a rising price a year from now, and a company whose price has risen over the last year is likely to experience a continued rise in price simply due to the momentum of its performance. And the exact reverse is true for companies with poor performance.

The flaw in this explanation is that it doesn’t account for mean reversion after five years—or after four weeks.

But there’s a solution to this. Price returns in general tend to revert to the mean because their movements often appear to be random, and mean reversion is a characteristic of all random variables. (The farther a random variable is from the mean, the more probable it is that it will reverse course.) Price returns are not random, strictly speaking, but they do have many of the characteristics of random variables.

The momentum of company performance is so strong in the six-to-twelve-month period, however, that it overrides that mean-reversion tendency. Performance momentum in a four-week period is meaningless since one usually measures performance by looking at quarterly statements; performance momentum over five years is simply not strong enough to overcome the natural tendency of price returns to mean revert.

Implications of the Quality Theory of Momentum

The quality theory of momentum, stated in different words, is: If returns are, in part, a sign of company performance, and if relative company performance tends to persist over a certain period—i.e., there is a positive correlation between company performance in two different periods—then the returns over those two different periods will show a stronger resistance to their natural tendency to revert to the mean than over two periods for which the correlation of company performance is weak or difficult to measure.

I admit, that’s a mouthful. But it seems logical.

Momentum, then, is a proxy for company performance. If one can find good measures of company performance that are independent of stock prices but correlate well with future returns, then those measures are preferable to momentum measures. And thankfully, there are dozens of such measures.

One can break down factors into six main types.

1. Value: the ratio of something in a company’s financial statements to its price.
2. Quality: the ratio of something in a company’s financial statements to another thing in a company’s financial statements (this group of factors includes many growth measures).
3. Size: a measure of how big or small a company is.
4. Momentum: a measure of the relative returns of a stock over a certain period of time.
5. Sentiment: factors that indicate the feelings of investors about a company.
6. Volatility: factors that measure deviation and beta, along with other measures of price and volume that have to do with risk.

There are, of course, a few factors that don’t fit into any of those categories, but not many.

My takeaway from the Quality Theory of Momentum is that one should emphasize quality factors over momentum factors because the latter are secondary in nature and the former are primary. In the systems I use to choose stocks, value factors have a combined weight of 15% to 20%, quality factors have a combined weight of 45% to 50%, while momentum factors only have a combined weight of between 5% and 10%. (Size and volatility factors also each have combined weights of between 5% and 10%, while sentiment factors have a combined weight of between 10% and 15%.)

There are, however, certain elements of a company’s quality that are impossible to measure. Financial statements go a long way in outlining to investors how a company is doing, but not all the way. There are always some pesky unquantifiable factors. And that’s why momentum can be so useful as a proxy for quality. One ignores momentum—especially negative momentum—at one’s peril.

The post Why Momentum Works appeared first on Portfolio123 Blog.

The conventional method of finding out whether or not a factor works is to look at the performance of the top (or bottom) ten or twenty percent of stocks ranked according to that factor and then subtract the bottom (or top) ten or twenty percent. One should then buy stocks that rank highly on that factor and sell (or short) stocks that rank near the bottom.

But there are a lot of factors for which it makes more sense for middling values to be best. You have to think each factor through logically.

Change in profit margin (net income divided by revenue/sales) is one such factor. The companies whose margin has risen the most over the last year have decreasing sales and increasing income; companies whose margin has fallen the most have decreasing income and increasing sales. Neither of those is a good thing. If your income is increasing but your sales are falling, your income increase will be unsustainable and you’ll be setting yourself up for a fall (or maybe you’re cooking the books). If your sales are increasing but your income is falling, you’re likely using your revenue inefficiently.

Using the S&P 1500 and monthly rebalancing, I created, using Portfolio123, a decile-by-decile graph of how stocks have fared on this factor over the last twenty years:

Sales growth is another such factor. Companies with unsustainable sales growth are usually punished by the market. Here’s a chart using the same parameters as the previous one, except looking at sales growth rather than margin growth. I bet you could look at a hundred years of data and see this play out well.

These are what I like to think of as “misbehaving factors.” They’re giving you the middle finger, challenging you to deal with them.

It’s absolutely vital to think every factor through. Ask yourself: Are stocks that have super high (or super low) factor X really more likely to outperform than stocks that have middling factor X? You’ll often find yourself answering: Well, not necessarily.

But what should we do with factors like this? Should we simply ignore them? Should we combine them with other factors to see if the pattern will change? Or should we favor middling values?

When I started evaluating stocks back in 2015, I decided to concentrate on factors that had the most impact, that made the most difference. Here was my thinking.

I wanted to evaluate every stock I bought from as many angles as possible. Obviously, I couldn’t hope to evaluate stocks on absolutely everything—there were certain factors I tried for which it made little sense to evaluate a stock. I wanted to look at the factors that showed the largest discrepancies between high and low forward performance, no matter where those discrepancies showed up on the chart—at one end or in the middle. And while it may be “data-mining” to estimate an optimal rank or value for a factor, that still may be more logical than settling on the highest/lowest value or ignoring the factor altogether.

So that’s what I did. I created ranking systems in which I favored low values for some factors, high values for others, and middling values for yet others. Since nobody else at the time was favoring middling values for anything, that gave me an edge. And I went on to triple my money in less than three years. Of course, there may be absolutely no relationship between using middling rankings and tripling my money. But both in backtests and out of sample, this technique seems to improve results.

Just because some factors “misbehave,” don’t count them out. If you want to really evaluate every stock you buy from every major angle, leaving out a factor with a large significance (a big difference between the highest and lowest decile performance) can have a worse effect on your returns than including a factor that, it turns out, doesn’t “work.” Feel free to leave out factors that honestly don’t make much difference. But if you see a factor with a huge variation in returns between deciles, you probably want to avoid stocks in the top and bottom deciles and favor stocks in the middle few. That will help make every stock you pick a real treasure.

The post Misbehaving Factors appeared first on Portfolio123 Blog.

Alpha has, over the last fifty years, become the standard way to measure the active return of a portfolio: how much the portfolio outperformed the benchmark.

Technically, however, it’s a point on a line, specifically the point where the line crosses the y axis.

And that line is the linear regression line between the portfolio’s returns minus the risk-free rate (on the y axis) and the benchmark’s returns minus the risk-free rate (on the x axis). In other words, you make a graph out of a lot of dots. Each dot has the benchmark’s return minus the risk-free rate as its x value and your return minus the risk-free rate as its y value. You then find the straight line that best fits all the dots, and that’s your linear regression line. Where it crosses the y axis is your alpha, and the slope of the line is your beta.

When beta is high (above one), the portfolio’s returns vary a great deal proportionally to those of the benchmark. When beta is low (below one), either the portfolio’s returns and the benchmark’s are relatively uncorrelated, or the variation in the portfolio’s returns is significantly less than that of the market’s. When beta is negative, the portfolio’s returns move opposite to those of the benchmark.

As for alpha, to put it plainly, it’s the expected return of the portfolio when the benchmark’s return equals the risk-free rate.

Why Use Alpha as a Performance Measure?

The most obvious performance measure is simple return: the amount in the portfolio at the end of a certain time period divided by the amount at the beginning, minus one. However, this measure doesn’t take into account what the rest of the market is doing, and it’s entirely dependent on the beginning and ending dates. It’s a more or less meaningless measure.

A more meaningful measure would be less dependent on beginning and ending dates and would take into account the movements of the market. There are various such measures besides alpha. Average excess return, median excess return, and the information ratio are three of them. All of them rely on simple subtraction: one subtracts the monthly (or weekly) market returns from the portfolio returns to obtain the excess returns. You then take either the average, the median, or the average divided by the deviation from the average for these respective measures.

Subtraction, however, is less sophisticated and less accurate a tool than regression. A regression line has the form y = α + βx, while subtraction is simply y = x + e (where y is the portfolio return, x is the market return, and e is the excess return). Subtraction is essentially the same as regression except that β is always equal to one. If you actually look at the data, β often does not come close to one.

Let’s look, for example, at a scatter plot of the last five years of monthly returns of XES (SPDR S&P Oil & Gas Equipment & Services ETF) compared to the returns of the S&P 500. (Please note that from now on, for the purposes of keeping this article relatively simple, I will not be subtracting the risk-free rate from monthly returns.) The percentage returns of XES are plotted along the y axis while the returns of the S&P 500 are plotted along the x axis. The orange dotted line is the line y = x, or β = 1.

Using only excess returns would mean either using the orange line to describe the data or moving it wholesale up or down, keeping its slope the same. You wouldn’t be able to tilt that line at all. In other words, the line doesn’t fit the data very well, even if you move it down a few percentages.

That’s why alpha and beta, for many money managers, are the ideal numbers for characterizing portfolio returns. Those two numbers capture the relationship of the portfolio to the benchmark better than any others I’ve come across.

Alpha, Beta, and Risk

Shortly after alpha and beta were introduced to the investment world in the 1960s, it was discovered that alpha and beta were inversely correlated, no matter what asset class you looked at.

The inverse correlation of alpha and beta is inherent in the mathematical relationship of the two variables as long as the market’s returns are more likely to be positive than negative. Remember that the equation y = α + βx can be rewritten as α = y ­– βx. It’s clear from this that if you have two strategies with the same return (x and y are the same), and if the adjusted market return (x) is greater than zero, the strategy with the higher beta will have the lower alpha; it’s also clear that most investable asset classes have market returns which are greater than zero more frequently than they are less than zero. In fact, I have proven mathematically that alpha and beta are indeed inversely correlated when market returns are usually greater than zero. But this idea did not occur to the scholars who came up with the ideas of applying linear regression to finance, and instead they have spent close to fifty years trying to come up with behavioral reasons for the inverse correlation.

Portfolio returns tend to correlate with alpha far better than they correlate with beta. Look again at the equation y = α + βx. Because x (the market’s return) is sometimes negative or zero, a positive correlation of y and α is going to be far more frequent than a positive correlation of y and β. In fact, if you look at any random fifty portfolios, the probability that their returns will be better correlated with their alphas than with their betas is likely greater than 90%.

Now even though alpha and beta tend to be inversely correlated and portfolio returns tend to correlate better with alpha than with beta, this does not mean (in a mathematical sense) that portfolio returns and beta are necessarily negatively correlated. That depends on the degrees of correlation. But evidence shows that high-beta securities tend to underperform low-beta securities within the same asset class.

Beta was rightly proposed as a proxy for risk; indeed, the higher the beta, the more market-related risk the investor is taking on. But many people in the 1960s believed that the higher the risk, the greater the return, which presented them with a paradox. William Sharpe, one of the scholars who came up with the ideas of alpha and beta, put his faith in high-beta securities because of this belief. Because the sum of all alphas of all portfolios has to be zero, and because he believed in an efficient market, he and his colleagues effectively rewrote y = α + βx as y = βx. The idea that one can get better returns by avoiding risk was not taken seriously back then.

At any rate, one of the nice things about alpha is that it takes returns and adjusts them for market-related volatility. It is just as much of a risk-adjusted return measure as the Sharpe or information ratios.

What Is Theil-Sen Estimation?

In 1968, Pranab Kumar Sen published a groundbreaking paper in the Journal of the American Statistical Association called “Estimates of the Regression Coefficient Based on Kendall’s Tau.” In it, he proposed measuring beta, or the regression coefficient (slope), in a new way, building upon a method proposed by Henri Theil (pronounced like the English word tile) in 1950, and drawing parallels to Maurice Kendall’s 1938 method of determining correlation. Theil’s method was, in Sen’s words, “very simple”—he simply took the median of all the slopes determined by all pairs of points.

Beta is ordinarily computed by performing least-squares regression. Here’s a relatively simple example which I’ll use to illustrate the two methods.

In this chart, there are fifteen blue points, and the blue line is the conventional linear regression. The x-axis corresponds to the benchmark; the y-axis corresponds to my monthly returns. So the highest point shows that during one month the benchmark lost 2.5% while my portfolio gained 7.9%, and the lowest point shows that during one month the benchmark lost 10.3% while my portfolio lost 6.1%. This blue line gets as close to the fifteen points as possible if you measure closeness by the square of the vertical distance between the line and each point and add them all together. This regression method is thus called “ordinary least squares,” or OLS for short, and it’s been in use for over two hundred years. Beta is the slope of the line (in this case 0.46) and alpha is where the line crosses the y axis (in this case 1.3% monthly, or 16.3% annualized).

The orange line is the alternative regression line calculated by Theil and Sen’s method. Notice that there are six points above the OLS line and nine points below it. But the TS line (Theil and Sen line) leaves seven points above it and seven points below it, and it intersects one point. TS regression lines, which are calculated by using medians, always leave just as many points above and below them. Neither line fits the data very well, but to my eyes, at least, the orange line seems like a better fit.

To get this line, you go through two steps. First, you calculate beta by taking all possible slopes between pairs of points and getting the median. With fifteen points, that means calculating 105 different slopes. The median of all of them turns out to be 0.41. Second, you calculate alpha, or the y-intercept, by taking the y values, subtracting beta times the x values, and taking the median of all of those. Here, the TS alpha is only 0.6% annualized.

Advantages of TS Regression

Among the few who have examined the subject, the scientific consensus appears to be that no matter what the data is, TS regression is superior to OLS regression. There’s an excellent paper about this called “Linear Valuation Without OLS: The Theil-Sen Estimation Approach.” In it, the authors cite studies that prove that TS regression not only gets rid of outliers, which tend to have an outsize effect on OLS regression, but also take care of the problem of heteroscedasticity. (Homoscedasticity means that the variance of the data is evenly distributed over the independent variables and heteroscedasticity means that it isn’t.) Basically, OLS regression only works well when the data is more or less homoscedastic, and if you’ve ever looked at a typical scatter chart for monthly returns, you’ll see that the dots tend to coalesce around the middle (see the first chart in this article for a good example).

The authors don’t apply TS regression to the calculation of alpha in this paper, instead applying it to valuation multiples, with striking results. As far as I know, nobody has yet proposed using TS regression to calculate alpha. But it can be done.

OLS vs TS

A large majority of the time, OLS and TS alpha and beta are very close. But there are some significant exceptions.

Let’s look at some ETFs as examples. The chart below shows the last three years’ performance of EWZS (iShares MSCI Brazil Small-Cap ETF) compared to VTI (Vanguard Total Stock Market ETF). As before, the blue line is the OLS regression line and the orange line is the TS regression line.

EWZS’s total return was 27% compared to VTI’s 14%. Its annualized TS alpha is 17% while its annualized OLS alpha is 27%. Its TS beta is 0.45 while its OLS beta is 0.07. The OLS beta is so low due to one outlier (-5.6, 21.6). Without that piece of data, the two lines would be almost exactly the same.

Now let’s take a look at the actual chart.

Does this look like a stock with a beta close to 0, a stock with absolutely no correlation to the market? If you look at the last year alone, its OLS beta is 0.79, and if you look at the first of the three years, its OLS beta is 0.75. Why should its performance in 2018 (in particular, one month in 2018) give it a three-year beta of 0.07? Does EWZS look like it deserves an annualized alpha of 27%?

Now let’s compare this with another ETF, SOXX (iShares PHLX Semiconductor ETF).

SOXX’s annualized return over the last three years is 28%, quite close to that of EWZS. Here, the annualized TS alpha is 18% while the annualized OLS alpha is only 7%. The TS beta is 1.26 while the OLS beta is 1.37. Once again, an outlier (-3.6, -14.6) makes all the difference—take that outlier away, and the lines are almost the same.

Here’s the chart:

Looking at the charts of EWZS and SOXX, it looks like they deserve about the same alpha. And indeed, by the TS measure, they have the same alpha. By OLS measures, however, EWZS has an alpha of 27% while SOXX has an alpha of only 7%.

Application and Calculation of TS Alpha

Because I view alpha as a superior performance measure to CAGR, to measures based on average returns (e.g. the Sharpe ratio), and to measures based on excess returns, I use alpha when I backtest portfolio strategies (I use Portfolio123 for all my data and backtesting needs). And because I view TS alpha as superior to OLS alpha, I’ve been relying primarily on that measure to tell me when one strategy is superior to another.

You can easily calculate the Theil-Sen slope (beta) in R, MATLAB, and Python (in Excel, it’s significantly more difficult). After you get TS beta, you take each of the portfolio returns and subtract the product of the TS slope and the benchmark return; you then calculate the median of those numbers. That is TS alpha.

If you’d rather use Excel than R, MATLAB, or Python, I’ve created an Excel file here that calculates TS alpha and beta from forty returns. You can see pretty easily how it’s done, and then adapt it for the number of returns you have.

No matter which program you use, the number of calculations required will be about half the square of the number of returns. So if you have thousands of returns, I recommend taking a sample of the slopes rather than calculating all of them.

Conclusion

Admittedly, I picked some rather extreme examples above. In the majority of cases, OLS and TS alpha aren’t terribly different from one another. In the examples, TS alpha was closer to the excess returns than OLS alpha, but this is not representative; TS alpha is very often farther. Both can be valuable measures of portfolio performance. Theoretically, however, TS alpha is a more reliable measure and tends to fit the data better.

OLS measures dominate the world of finance. Standard deviation is an OLS measure, which makes the Sharpe ratio and the information ratio OLS measures as well. T-tests and p-tests are OLS measures, and so is R-squared. Some statisticians have been appalled by the proclivity of the world of finance to apply OLS measures to financial and economic data, with its heteroscedasticity and its fat tails. But these measures have persisted because they’re easy to work with and have been used for centuries.

James Ohlson and Seil Kim, the authors of “Linear Valuation without OLS,” wrote, “consider the following counter-factual scenario. Suppose the history of empirical accounting [or financial] research had never been aware of OLS and instead had picked up on TS and used it as a standard paradigm. Now suppose that someone suddenly discovers OLS and tries to sell this new approach to the research community. Would that be an easy sell with plenty of takers? Not likely. What would be the arguments?”

It would be nice if we could slowly replace OLS measures with measures that are not dependent on normally distributed data, measures that are insensitive to outliers. Perhaps using Theil-Sen estimation for alpha and beta—and using Kendall’s tau, a very closely related measure, for correlation—would be a good start. But I don’t expect to see it happening any time soon.

The post Why Alpha Works—and a New Way of Calculating It appeared first on Portfolio123 Blog.

The Netflix Prize was a competition begun in 2006 to predict user ratings for films. Competitors were given ratings scrubbed of information about the users, and were challenged to find, using machine-learning methods, an algorithm based only on the raw data.

Netflix provided each team with about a hundred million ratings that half a million users had given to eighteen thousand movies. Each rating was a set of four numbers: the user number, the movie number, the date of the rating, and the rating itself (one to five stars). This was the training data; there were out-of-sample groups of data that, if correctly predicted, would then determine the winner of the competition.

It took almost three years before two teams passed the threshold Netflix had set for winning the competition. And the secret to their success was their ability to combine a large number of poorly performing algorithms into one that really worked. As Wire magazine wrote at the time, “The secret sauce . . . was collaboration between diverse ideas. . . . The top two teams beat the challenge by combining teams and their algorithms into more complex algorithms incorporating everybody’s work. The more people joined, the more the resulting team’s score would increase.”

This was especially true near the end of the contest. At that point the teams incorporated insights that were marginal and produced poor results. They even incorporated the idea that people tended to rate movies slightly differently depending on what day of the week it was. To quote Wire again, “Taken on its own, the fact that a viewer rated a given movie on a Monday is a horrible indicator of what other movies they’ll want to rent. . . . But combined with hundreds of other algorithms from other minds, each weighted with precision, and combined and recombined, that otherwise inconsequential fact takes on huge importance.”

Application of the Netflix Prize to Investing

When we’re designing a stock-picking strategy, we’re trying to predict stock prices, just as the competitors for the Netflix prize were trying to predict movie ratings. We’re given limited information, but we can glean some principles about how stocks work from that information. And the best way to predict stock prices is to take into account as much information and as many insights about stock prices as possible. We need to study what factors move stock prices and, rather than relying on just one or two of those, combine as many as we can, especially if they’re outliers.

I’m going to illustrate this with a concrete example.

Combining Stock Strategies

I’ve developed four very different stock strategies on Portfolio123. Each strategy is based on a ranking system with four equally weighted factors. Each strategy simply buys the top-ranked 25 companies out of the Russell 3000 (excluding REITs, MLPs, BDCs, and stocks with very low liquidity) every four weeks, rebalancing to equal weight.

Strategy #1 focuses on turnaround companies. It looks for underfollowed and undervalued companies with relatively low earnings that have nonetheless recently surprised analysts, who are now more bullish on them. Good examples of these companies right now are Parker Drilling (PKD), Information Services Group (III), Ambac Financial Group (AMBC), Eidos Therapeutics (EIDX), and BBX Capital (BBX), which are the five top-ranked stocks according to the four factors that I’ve chosen for this strategy. With 0.2% transaction costs, a backtest of this strategy returns a CAGR of 14.44% over the last ten years (compared to 13.19% for the Russell 3000), and 14.89% over the last twenty (compared to 6.23%).

Strategy #2 focuses on stocks whose dividends are growing; it also uses four factors. The top five companies in this strategy are Chemours (CC), Santander Consumer USA (SC), Zions Bancorporation (ZION), Hawaiian Holdings (HA), and Arch Coal (ARCH). This strategy also performs well on backtests, returning 14.91% per year over the last ten years and 13.81% over the last twenty.

Strategy #3 focuses on high-growth stocks with high R&D expenditures, primarily health-care and technology companies. The top five stocks here are Dell (DELL), Ribbon Communications (RBBN), ChannelAdvisor (ECOM), Checkpoint Therapeutics (CKPT), and Chimerix (CMRX). This strategy has stellar backtested returns: 25.41% over the last ten years and 22.44% over the last twenty.

Strategy #4 focuses on high-quality stocks—stocks with steady sales, low accruals, strong free cash flow, and excellent gross margins. It’s the only one of the four strategies that doesn’t take into account the stock’s price. The top five stocks here are Collegium Pharmaceutical (COLL), AbbVie (ABBV), National Research (NRC), Deluxe (DLX), and Verisign (VRSN). This strategy would have earned 14.26% over the last ten years and 12.84% over the last twenty.

Now the conventional thing to do is to put a quarter of your money into each strategy. You would have owned one hundred stocks at any one time, and if you didn’t move any of your money between the four strategies, your ten-year CAGR would have been 18.19% and your twenty-year CAGR would have been 16.60%.

But what would happen if you combined all four systems into one sixteen-factor system and just bought the top 25 stocks? You’d expect the returns to be similar to the returns of buying all four systems separately. Maybe they’d even be lower than that, since dividend-paying stocks and high-growth R&D companies don’t have a lot in common, and stocks with recent low earnings are usually not very high in the quality category.

Well, in fact, this system gets a backtested annualized return of 29.02% over the last ten years and 28.14% over the last twenty, which is significantly higher than any of the other strategies. And it invests in truly well-rounded companies. The top five now are AbbVie (ABBV), Information Services Group (III), ChannelAdvisor (ECOM), Merck (MRK), and Johnson & Johnson (JNJ).

Of course, what we’re looking for when we’re designing an investment strategy is not necessarily the one with the highest backtests, but the one with the greatest potential for future returns. Everything in my experience leads me to believe that combining strategies not only improves backtested results, but improves out-of-sample results too. It certainly worked that way for the competitors for the Netflix Prize.

How It Works

How does combining seemingly incompatible strategies into one big mess actually produce better results than keeping them separate? After all, this isn’t the strategy one would employ to produce good food, good music, good art, or good writing. Why does it produce good investing?

There are two reasons.

The first lies in the power of ranking. Unlike screening, ranking provides a great deal of flexibility. Let’s take a look at those top five stocks in the composite strategy, ABBV, III, ECOM, MRK, and JNJ. Of these, only ABBV has had strong dividend growth, while III and ECOM don’t pay dividends at all. III doesn’t report any R&D spending either. ABBV is clearly not an underfollowed turnaround stock—it fails miserably on three of the four factors in that system.

These are the rankings of each stock on the four factors I used in each system. (In my ranking system, a company that pays no dividend or is in an industry that reports no R&D expenses gets ranked in the middle, between 30 and 70, above companies with poor dividend growth or high payout ratios or low R&D-to-market-cap numbers.) You see, when you are ranking on sixteen different factors, a company can fail miserably on a few factors and still come out near the top if it scores well enough on the others. The average scores of these top five companies on these sixteen factors are not terribly high, in part because the factors vary so widely from each other. But the averages are higher than those of the other 2,600 stocks under consideration here.

The second reason that combining incompatible strategies produces good results is that the secret to getting high returns is to look at every stock from as many angles as possible. Buying a stock, as I’ve written many times, is like buying a used car. You want to look under the hood (or get a mechanic you trust to do so), get an expert opinion, take it for a test drive, read about the make and model, compare the price you’re getting to the listings of similar cars, and so on. Similarly, it pays to check every stock in terms of its value ratios, its quality ratios, its growth ratios, and its sentiment indicators. And employing combined ranking systems is perhaps the best way to do so.

I am long BBX, ECOM, III, and NRC.

The post The Magic of Combination: How Mixing Strategies Can Improve Results appeared first on Portfolio123 Blog.