# What I Learned About Investing in 2022

2022 was an excellent year for me. OK, I didn’t make as much from my investments as I did in 2020 or 2021—who did?—but a 22% return isn’t bad.

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

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

## 1.Buy in Batches to Reduce Market Impact.

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

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

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

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

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

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

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

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

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

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

After some simplification, we come to

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

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

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

0.42*66,0002/3*500,0001/3=54,442. So I should buy only about \$54,000 the first day and the rest on the second.

## 2.Free Cash Flow Yield Is the Best Value Ratio

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

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

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

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

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

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

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

## 5. Factor momentum doesn’t work.

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

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

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

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

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

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

Here is how I propose to measure factor momentum.

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

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

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

This is the result (click to enlarge).

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

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

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

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

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

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

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

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

But I don’t think so anymore.

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

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

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

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

## 8.Persistence of growth is chimerical.

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

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

## 9. Volatility matters when measuring market impact.

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

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

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

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

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

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

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

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

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

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

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

## 11. Subtract preferred dividend payments when considering earnings.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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