Not Another Investment Podcast
Understand investing beyond the headlines with Edward Finley, sometime Professor of Finance at the University of Virginia and veteran Wall Street investor.
Not Another Investment Podcast
So What Exactly Are Equities? (S1 E9)
Buckle up for a thrilling foray into the world of equities, where we try to understand the risks we own when we invest in equities.
We dissect the mean-variance theory, which predicts that greater volatility should fetch higher rewards, and we scrutinize the empirical data that puts this financial cornerstone to the test.
We navigate the intricacies of the Capital Asset Pricing Model (CAPM), an alternative framework for evaluating equity investments. However, it's not just a love story; we also cast a critical eye on the CAPM, exposing its shortcomings amidst real-world complexity.
Then, we shift gears to dissect the Arbitrage Pricing Theory (APT), decoding the nuance of factors like size and value in stock returns. As we peel back the layers of these financial models, we reveal how they can both enlighten investors and, at times, lead them astray.
The final act of our financial drama puts passive and active investment strategies center stage. Witness the tug-of-war between the two as we scrutinize Warren Buffett's legendary tactics with Berkshire Hathaway through the lens of APT. Does Buffett's alchemy in outmaneuvering market expectations prove the superiority of active management? Or does it highlight an anomaly in an otherwise efficient market? Join us for a riveting dialogue that not only challenges what you think you know about investing but also aims to elevate your market acumen to the next level.
Notes - https://1drv.ms/p/s!AqjfuX3WVgp8uWo1lG57LUc15OlX?e=jnZf77
Thanks for listening! Please be sure to review the podcast or send your comments to me by email at info@not-another-investment-podcast.com. And tell your friends!
Welcome to the podcast. I'm Edward Finley. Well, we're going to take a pivot now in this podcast and turn our attention to a different aspect of markets. Up until now, we've spent our time thinking about what markets are, why we have them, who are the players in markets, what are their roles. We've talked about how securities trade in markets and we've introduced some notions of finance theory to explain why we think markets do the job well, that we think they do. We've also introduced some probability theory, mainly to set us up for this rest of the podcast.
Speaker 1:What we're going to talk about for the rest of the podcast is now from the perspective, not of those who are seeking capital, but those who are providing capital. That is, we're going to look at the markets as asset classes, as investors who are providing capital to those who need it. We're going to start with not the biggest, as we've discussed before, but probably the most ubiquitous, and that is equities. As we've done in the past, I'll follow the same pattern. I'm going to give definitions. I'll repeat the definition so that it makes sense. I'll break it down into component parts. We'll then talk a little bit about some theory to make sure we understand what's going on. We'll look at the empirical data and if the empirical data lines up, that's great. If it doesn't, we have to go back to our theory and rethink the theory, all right. So what exactly are equities? If you're an investor and you're thinking about buying equities, what exactly are you buying? We're going to define equities as exposure to the productive economy, earning a premium for the uncertainty of the bad times that may lay ahead when the prices of those equities decline. Again, equity is exposure to the productive economy, earning a premium for the uncertainty of the bad times that might lie ahead when the price of those equities will decline. Well, let's take that apart.
Speaker 1:Productive economy well, equity, you'll recall, is a residual claim on the assets of the firm. If the firm is strong and healthy, the equity owners have a residual claim to any cash that's not used to run the firm. Usually that's paid in the form of dividends. If a firm is not well and it's winding itself up, the bondholders get paid first, and only after the bondholders get paid do the equity owners get anything from the firm. So equity is a residual claim on the assets of the firm. You'll remember from our discussion of the players in a capital market, firms are the only part of the economy that engage in the production of income. Firms make stuff, they employ labor, they employ other capital and they make stuff and they sell stuff. And so if you own equity a residual claim on the assets of a firm and firms are the only part of the productive economy that engages in the production of income when you're an equity owner, you have exposure to the productive economy.
Speaker 1:Okay, so equities are exposure to the productive economy, earning a premium. What do we mean by premium? Well, remember, returns are just calculated by changes in price Prices in equity markets. All prices in equity markets are going to change with the time value of money, that is to say inflation. But all prices in equity markets are also going to change in response to changes in the expected growth in the productive economy. If we think the economy is going to grow more, we would expect all equity prices to rise as people price in that information. If we expect the economy to grow more slowly, we would expect equity prices to decline again to price in that information. And so when we say premium, what we mean is the change in price in excess of the change in the time value of money, or in other words, the return on equities over and above inflation, just the part, that's exposure to the productive economy.
Speaker 1:All right. So equities, exposure to the productive economy, because you are a residual claimholder of the only participant that produces income in the economy, you're earning a premium, which is the change in price over and above the rate of inflation, and you earn that for the uncertainty of bad times that might lie ahead. Well, as we've discussed before, markets exist because there is uncertainty. If there were no uncertainty, we wouldn't need capital markets to allocate capital to risky uses. The more uncertainty there is, one could say there is more risk, more uncertainty, there's more risk. And if there's more risk, if you're not clear about what's going to happen, you're going to demand to get paid more for that uncertainty. So you would expect a higher rate of return. And so if we own equities as exposure to the productive economy with a premium, that premium is for what it's? For the uncertainty of knowing whether or not there is going to be good times ahead or bad times ahead.
Speaker 1:The question is how we measure that uncertainty, and I'm going to introduce the first bedrock theory in finance, and that is mean variance theory. So what's the proposition in mean variance theory? Well, the proposition is rather simple. And assets returns are primarily compensation for the volatility of the assets returns. So the higher the volatility would suggest investors will think there's more uncertainty, and the more uncertainty means we would expect to earn higher returns. Well, that makes a lot of sense. And let's remember just back to our basics of probability theory Volatility is just measured by the standard deviation of all the observed returns.
Speaker 1:So if we look at the observed returns, and they are all very tightly gathered around the mean, then we would say there's a fairly low standard deviation, ie not a whole lot of uncertainty. But when there's a lot of uncertainty, we would expect equity prices to swing widely around the mean, making the dispersion much wider, and that dispersion is measured by its standard deviation, which we'll call volatility. Okay, so what's the data tell us? I mean, that's a pretty good theory, but does it stand up to the test of time? Well, there's some data that I've posted on the website which you can take a look at. You don't have to, I'm just going to tell you what it is.
Speaker 1:But from 1971 through the end of last year December 2023, what we observed is that the volatility of US equities was much higher, almost double the volatility of the tenure treasury. Volatility of US equities for that period was a little more than 16% and the volatility for the tenure treasury was 9% and, consistent with mean variance theory, the returns on US equities were much higher, again almost double the returns on the tenure treasury. The geometric mean and you remember, we want to look at that when we're trying to understand how much you would have earned if you owned it, not to predict the future the geometric mean was a little shy of 11% for the US equity market and the tenure treasury market. Over that period it earned a little more than 5%. It results in both US equities and the tenure treasury during that period to have a fairly similar information ratio. And again, just as a refresher, the information ratio is just a ratio of the return to the volatility. It's how much return do you earn per unit of volatility or, as we're now introducing as an idea, per unit of uncertainty? So per unit of uncertainty, how much do you get paid? And in the case of US equities, you got paid 0.67% per unit of volatility and in the case of the tenure treasury, you got paid 0.57%. So roughly, roughly the same, and so that would tell us that higher volatility equities earned more in return than lower volatility treasuries, and that that return, seemingly, is compensation for the higher uncertainty. And the rate of return per unit of uncertainty is about the same for the two of them. All right, well, that seems to stand up. What about looking, though, at just higher volatility equities versus lower volatility equities? If our theory stands up, we should be able to see the same thing at work.
Speaker 1:Well, there's a study produced by Fei-Fei Li called low volatility anomaly. Again, there'll be a link in the website if you're interested in reading this article, but no need, I can explain it. And in this article, she suggests that higher volatility equities did not earn higher returns than lower volatility equities. That is to say, she found an inconsistency in what seemed to be the data regarding mean variance theory. So she looked from 1991 to February 2012. She found that US large cap equities as a whole earned lower nominal returns than US low volatility stocks, but she found that they earned higher volatility adjusted returns, and you'll note in the data we convert what the author had as the sharp ratio to the information ratio. That's just to take into account that we're not subtracting inflation from the rate of return. So, overall, it was not entirely clear that mean variance theory held up for equities in this period that Li was looking at, from 1991 to 2012.
Speaker 1:She broke it down into some subparts and so during the bull market of 1997 to 1999, that was the rising of the tech bubble she found that higher volatility equities earned higher nominal returns and higher volatility adjusted returns than low volatility equities. Great, that's very consistent with mean variance theory. But during all of the other successive bull and bear markets 2000 to 2002, 2003 to 2006, 2007 to 2008, she found the opposite. She found that low volatility stocks outperformed all stocks by both in nominal terms and in volatility adjusted returns. So this casts some doubt on whether mean variance theory really does help us explain the premium that we earn for uncertainty, ie is volatility the right way to measure uncertainty? When we update Li's data so we take from 2012 and we bring it to the end of last year mean variance theory is redeemed. So the S&P 500's nominal return during that period was a little shy of 14% a year and US low volatility S&P 500 stocks earned a lower 10% return and likewise the volatility of the S&P as a whole during that period was a little shy of 15% and the volatility of the low volatility stocks, not surprisingly, was about 12%, and so when we find inconsistency in the data like this, it means that our theory is incomplete, we're missing a piece, and so we have to move beyond mean variance theory to understand, then, what really can we measure in order to help us understand the uncertainty risk that we take when we own equities.
Speaker 1:That brings us to the second model that economists have developed, which is called the capital asset pricing model, and some of you may have heard something referred to as the CAPM. That's this, the capital asset pricing model. All right, well, what's the proposition? Well, the proposition is this mean variance theory got it almost right, which is to say, volatility does play a very important role in explaining to us what uncertainty there is and what risk there is, but it misses a piece, and the piece it misses is the relationship among securities price movements that are friend to the correlation of securities price movements, and so the proposition of the CAPM is that an asset's return is going to be partly compensation for the time value of money that's the same as in mean variance theory and then partly for the degree of systematic risk in an asset, which is sometimes called beta and the systematic risk of the asset is the degree to which that asset represents something different than the market as a whole. Any excess return is attributable to then that excess risk of the market. All right, let's take that thing apart. It's kind of complicated.
Speaker 1:Well, the CAPM is an equilibrium model based on supply and demand in the capital markets, and so, remember, the concept of diversification tells us that when we combine two assets with different returns and different volatilities together but that don't co-move perfectly, the combinations of those securities are not going to form a straight line. That is, if I have a security with a 10% return and a 10% volatility, I have another security with a 5% return and a 5% volatility. I can't figure out what the return and volatility of a combination of the two assets is by just multiplying the proportion of each times the return and adding it up, and the proportion of each times the volatility and adding it up. That would be a linear relationship. The only time I can do that is if those assets perfectly co-move. But in the real world assets don't perfectly co-move, and so what CAPM tells us is when we begin to combine assets that have different co-movements, that do not perfectly co-move, then the relationship, if I made a graph of, it would not be linear but it would be parabolic. The more of the second asset that I add to the first will have the effect of. Let's say, in my first example, the more of the first asset that I add to the second will have the result of increasing the return and reducing the volatility up to a point, and then, past that point, the more I add of that first asset will have the result of modestly increasing the return and increasing the volatility. So if you can picture in your mind a sort of Buddha's belly parabola, that is, it arcs with its point to the left.
Speaker 1:Well, if we extend this concept to a fictional version of equity markets where we say, right, it's the version of equity markets, we have all equities, every one of them in combination with each other, then we can have, in theory, a really large parabola where we can add securities continually, to add securities so long as they don't perfectly co-move with the market, and that results in a single combination of all equities that will earn the maximum return for any given level of volatility. That's the theory behind the cap image. We start with just two equities and we build up this model theoretically to all equities. We would imagine that there would be a set of combinations of all equities which will have different returns at different points in volatility, but no point off that line would be efficient. If I had a mix of equities that was below the line, I should change it in order to either increase the return and not change the volatility, or I should change it to decrease the volatility and keep the return the same. Well, since adding a security to a portfolio, if that security perfectly co-moves, we'll have no value.
Speaker 1:Why would anybody that already owns the market want that security? So let's use an example. Let's say I already own the whole equity market and long you come and you say I've got a new equity for you. It's terrific, it's expected to earn 14% return with 14% volatility. Would you like some? My first question is going to be does it co-move with the market? And if the answer is yes, it co-moves perfectly with the market, for every increase in the market return, that security will return the same. Then my answer is great. I'll pay you a price, not that will result in a 14% return, but I'll pay you a price that results in the same return as the equity market as a whole. It's of no value to me to add that security to my portfolio of all equities. Because why? Because it already does the same thing that all equities do it moves with the same systematic risk. The fact that it pays 14% is irrelevant, because it just means that I won't be willing to pay its current price. I'd pay something more than its current price so that its return to me as a percentage of the price I pay will be exactly the same as the market.
Speaker 1:So if we assume efficient markets and we understand the world through a CAPM lens, what does it tell us? It tells us that the expected return of any security is linear, related to its beta, to the degree to which the security co-moves with the market. If the security has a beta of 1.0, it perfectly co-moves with the market. We should expect to earn exactly the same return as the market, regardless of what its cash flow will be. Its cash flow is only going to be return relative to the price we pay. If the security has a beta of 2.0, we should expect to earn two times the rate of return of the market, and you could make the same argument in the inverse. So the CAPM suggests that higher beta is a kind of form of leverage. It's just like borrowing money, adding it to my portfolio and then investing, like we saw earlier, with margin. So the CAPM tells me that if I have a security with a 2x beta to the market, it's just like my borrowing $100, adding it to my own $100, and investing the $200 in the market as a whole, not buying that security at all. My return will be two times the gains and losses of the market. Right, that's a lot to understand.
Speaker 1:So let's take a very concrete example to illustrate. Let's look at Apple, just like we did earlier when we were talking about some of the basics of probability theory. In order to compute the beta of a security, what we do is something called a linear regression. We regress its returns against the returns of the market as a whole. Linear regression is not as fancy as it sounds. What's involved is simply plotting the return pairs for each month of the security and the market, in our case of Apple and the S&P 500.
Speaker 1:So in January, what was the return of Apple? And we sort of find that on the x-axis. What was the return of the S&P? We find that on the y-axis and we put a dot. We do that for every month of our period all the way through 2023, and we have a scatter graph of all of the different pairs. Regression is just then, drawing the line that best fits all of those dots. Drawing the line that best fits all of those dots.
Speaker 1:That's why it's called a linear regression. We are regressing those very noisy, messy data points into a single line to see if we can understand what's going on. The equation of that line follows the equation of any line. Think back to high school algebra y equals mx plus b, where m is the slope of the line, b is the intercept where the line crosses the y-axis. So in a CAPM world, the slope of the linear regression is the beta of that security to the market. How much should we expect its return to change for a given change in the market's returns? In other words, we can say that tells us something about how much market risk is exposed in that security.
Speaker 1:The intercept of the linear regression represents how much of the return is explained by risks other than the market risk. One example is it could be just that firm's idiosyncratic risk. So when we regress Apple against the S&P 500 from 1997 to 2023, we can observe a few things based on the CAPM. First, apple is a high beta stock. The slope of the line is 1.29. In other words, for any 1% change in market returns we would expect to see a 1.29% change in Apple's returns. Since the S&P earned a little more than 9% a year during that period, we would expect Apple to have earned about 11% just from its exposure to market risk. But Apple has a lot of idiosyncratic risk. The intercept of that line is 1.89%, but remember, those are monthly returns so we have to multiply that times 12. That's 22% annually. So 80% of Apple's total return is compensation for idiosyncratic risk, not market risk. Only 11% of that return was a function of market risk.
Speaker 1:Okay, so that's the CAPM. It says mean variance theory wasn't wrong. Volatility is a very good measure of uncertainty, but it's not complete. That makes it complete. The CAPM tells us correlation. We have to take into account the degree to which securities co-move and when we do that we can compute for any security or any portfolio of securities, the beta or the degree of market risk that that security has. And that will help us to know what should we expect the return of that security to be? Okay, did it stand up to time? Has the data that we just suggest make sense and have economists agree that it works. Not quite.
Speaker 1:The observed premium of equities in markets really doesn't let the CAPM hold up. Two very famous economists, merra and Prescott, built an economic model to predict what equity risk premiums should be using a CAPM model, and they concluded that under the CAPM, equities should earn a premium. Remember that's the return in excess of the risk-free rate that equity should earn a premium of about 1%. However, the empirical data Dimson and others have measured this and it's all very consistent. Us equity premiums over a very long period of time, say 1900 to 2010, were more like 7.4%. So, at least in terms of the observed data, the CAPM isn't doing a terribly good job of helping us understand what the expected premium for equities should be. It's not a good measure of that uncertainty. Moreover, just like we did with volatility, we could take a look at high beta equities and make sure that they're earning higher returns per unit of risk than low beta equities. Capm tells us that high beta stocks move much more extremely than the market as a whole and therefore we should expect to earn higher returns for a given unit of volatility.
Speaker 1:I just want to make a note first, not to confuse beta with volatility. They're related but they're different and I'll give you a good illustration. But first just a little theory. Beta is the correlation of two securities or the security and the market times the ratio of the securities' volatility to the market volatility, and so it is definitely volatility related. But we multiply it times the correlation and that means that high beta can be the result of normal volatility, but very high correlation or normal correlations let's say, perfect correlation and very high volatility, or some combination of the two. So don't confuse beta and volatility. They sound awfully similar but they're importantly different.
Speaker 1:The illustration of that is a public company called Duke Energy. When we look at the returns of Duke Energy from 1993 to 2020, it had an annual volatility of 20%. That's way higher than the market's volatility. So you would say, ah, high volatility, it must be a high beta stock, but in fact its beta to the S&P was 0.3, very low beta. So take great care, not the same thing. Okay, back to our test.
Speaker 1:How about high volatility and low volatility stocks? In a study done from 1970 to 2011, low beta stocks, it were found, earned higher nominal returns 10.6% in this study and had higher risk adjusted returns an information ratio of 0.85, than all equities, and the same was roughly true for global equities as well, and so measured in terms of whether we see this difference in beta. Describing the uncertainty and therefore expected returns fails also when we look at high beta stocks versus low beta stocks. Finally, there's another study that suggests that the CAPM is not capturing the right measure of uncertainty.
Speaker 1:This economist named Bessem Binder, found that the bulk of equity returns seems to be due to the returns of a very small number of stocks. He found that the mean monthly stock return in the US was a little more than 1% compared to the Treasury bill mean return of 0.37. But the median return that is, if we line them all up from lowest to highest and divided the group in half, the median return for stocks was zero. That tells us that a lot of the return is the function of a smaller number of stocks that are earning very high positive returns. He found that 48% of stocks earn higher monthly returns than T-bills. Only 48%, in other words, 52%, earned lower monthly returns than T-bills. You would have been better off owning a Treasury during that period.
Speaker 1:He looked over decade-long horizons and he found that stocks earned higher average returns than T-bills. Fine, but median stocks returned lower returns than T-bills and only 50% of stocks earned higher returns than T-bills. Taking it all together, what did he find? Over the long run? That over the entire time horizon, 50 stocks 50 stocks were responsible for 40% of all equity returns. That is enormous.
Speaker 1:When we pull it all together the Merah and Prescott study that found that the CAPM didn't accurately predict equity premiums when we looked at high beta stocks versus low beta stocks and we didn't find the consistent relationship we expect. And Bessem-Binder study telling us that only a very small number of stocks, relatively, were responsible for more than a third of equity returns. It tells us that there probably isn't a single market risk that drives equity returns, but there may be other risks at work. That takes us, then, to what is today probably the most current, let's say, state of the art although that's a little flattering to it way in which economists study equity risks and try to understand the uncertainties involved in owning equities and what we should expect returns to be, and that's something called arbitrage pricing theory. What's the proposition here? The proposition is simple. It's sort of like the CAPM's proposition in that it doesn't say the CAPM is wrong, it just says that the CAPM was incomplete because a single market risk was just way too broad to capture the various risks that drive equity returns. Equity returns are too widely dispersed and they time vary among a number of systematic risk factors, and so any single systematic risk is going to fail to predict market returns. Instead, we have to come up with a more granular understanding of the kinds of risks that can predict the uncertainty in markets.
Speaker 1:Over time, economists have identified five systematic risks that they believe explain the majority of equity returns Market risk that's our old friend, the CAPM. Market risk, size, risk, value risk, momentum, risk and quality risk, market size, value, momentum and quality. There are many, many other factors in the literature. In fact, some have called it a factor zoo, because there are just so many economists that write paper saying I found a new factor. These five have garnered a kind of rough consensus among economists to be pretty good at explaining most of the cross-section of equity returns, but I'm not suggesting that they're the only five.
Speaker 1:What we do in order to measure the amount of risks in a portfolio of securities using arbitrage pricing theory or APT, is sort of like what we did with CAPM, just a little more complicated, is that we want to instead regress a security or a portfolio of securities against the factors, all of the factors. This is called a multivariate regression instead of a single univariate, linear regression. That can give us a sense for the risks that drive that security or that portfolio's returns. Let's take them apart and just have a quick look at what risks APT tells us are what we own when we own equities. First, simple, the market risk. That's the proportion of returns explained by exposure to equity markets. That's the nature of the return. That is just a function of being a stock. In the case of Apple, that was about, you'll recall, 11% of the return. Next, size and value. They sort of go together.
Speaker 1:In the paper published in 1993, nobel Prize winners Jean Fama and Ken French observed that two factors in addition to the market factor did a better job of explaining the cross-section of equity returns than just a single market factor size and value. Size, they observed, is that small stocks earned a premium over the market. Small stocks earned a premium over the market. How do we measure that? How do we break that, apart from just the market risk as a whole? What Fama and French did, and what economists today do, is they measure the premium just for size, by constructing a factor that is long small stocks and short big stocks.
Speaker 1:So my factor is long small stocks Means I buy all the long stocks. Well, why wouldn't I stop there? Well, if you stop there and I own all the small stocks, I'm getting a premium for small, it's true, but I'm also getting a premium for market. And how do I measure that? But if I short large stocks, what's common to both small stocks and large stocks? What's common is that they're both stocks. So the idea is, if I'm long small stocks and short large stocks, I subtract the short from the long, the market exposure cancels out and what I'm left with is exposure to the small. Now I hope those of you who are listening said hang on, you're not left with small, you're left with small minus large. Yeah, the market cancels out, but you're still minus large. And you'd be exactly right.
Speaker 1:That's one of the weaknesses of APT, which we'll discuss when we sort of wrap it up, is this notion that the construction of the factor is not a pure measure of the risk. But it's pretty good, so we're going to stick with it. All right. So we construct this factor. We say long the small stocks, short the big stocks. That's what gives it the acronym SMB small minus big. We're just going to say sometimes you'll hear me say SMB, sometimes you'll hear me just say size what did Fama and Friends observe?
Speaker 1:They observed that that factor, the small factor, earned a positive premium over time. That was rather stable. Now we might wonder why. Why do small stocks earn a premium over all other stocks? I can tell you that the economic literature is replete with attempts at trying to explain it. Some explanations are risk-based. For example, we could say small companies earn excess returns because, on average, they're more highly levered than other US companies, and this is true. The median net debt to earnings ratio is about 3.8 for the Russell 2000. That's an index of small stocks. The S&P 500 net debt to earnings is 2.3. We might say that if they're more levered than we would expect to earn a premium. Why? Because if they're more levered, that will make the returns more volatile and more risky.
Speaker 1:It's unclear whether size itself is a risk In looking at it. It might just be the result of preferences or behaviors. It might just be that people perceive a risk in small stocks and they demand a higher return than they would if they owned large stocks. It's very, very unclear. What I can tell you is that Fama and Fringe did a follow-up paper to their 1993 paper and they found that the majority of the premium earned by small stocks is really the result of small stocks becoming big stocks. That's it Small stocks becoming big stocks is what earns the premium in excess of the market. But surprisingly, that might lead some people to doubt whether size is really a risk or whether size is a premium earned for perceived risk.
Speaker 1:Remember, fama and Fringe wrote their paper in 1993. They were using data through 1990. If we compute the returns on factors since 1990, what we find is that the original premium that they observed for size has largely evaporated. From 1990 to 2023, the average return for the size factor was 0.07%, even though the volatility was 10%. So once again, that's more proof that mean variance theory. Volatility alone doesn't tell us what the risks are. Here. We had risk of 10% but over a long period of time earned basically zero returns.
Speaker 1:It's interesting to note that the size factor during the global financial crisis lost only a little bit. Lost only 1.2%. That's not terribly much. During the expansion after the global financial crisis lost 0.06% of 1% the premium, while it seems to be unrelated to the market premium. There's a correlation of only 28% there. There's very little to suggest in the data that the size factor is really risk-based.
Speaker 1:Okay, how about the value factor, the second original Fama-French factor, the value factor? Well, they noticed that value stocks earned a premium over the market. Well, what in the world are value stocks? They define value as those stocks that trade at a lower price, multiple to the firm's book value. Value stocks are lower price, multiple to the firm's book value. Book value is simple. Book value is just how much would the firm be worth if it closed its doors and sold all of its assets. That's the book value of the firm and the price is the price. And so Fama and French set about observing all of the ratios of price to book value and they organized the stocks then from lowest price to book value to highest price to book value. And then they observed the third of stocks that had the lowest and they had those with the highest, and they came up with an expectation of what the returns would be. And what they found is that the stocks that had a lower price to book value earned a premium over the market as a whole. All right, well, again, it begs the question why would those stocks earn a higher premium?
Speaker 1:Again, it could be the result of an actual risk. These firms represent an actual risk, what's sometimes called a value trap. If a firm is trading at a price that's very low relative to its value, if it wound up its assets, you could look at that and say what a deal, what a bargain. But it also could be that that's a firm that's about to go out of business because they are no longer relevant. The example that I love to use is you might imagine that when the automobile was introduced, there were a bunch of public stocks of companies that made buggy whips. I bet their price to book value was really low at the time, but that's not because they were a good deal. It's because no one would want buggy whips anymore. These companies were going to go out of business, and so it might be that it's compensation for risk. Why? Because we don't know in advance which company is going to be out of business.
Speaker 1:So it could be that, but it could also be the result of behaviors like loss aversion and overconfidence. Investors tend to undervalue the growth prospects of stable, boring businesses, and they tend to overvalue the growth prospects of sexy, sizzly businesses. So a company like Colgate Palmolive makes lots of household products. It's a very profitable company, it's been around for a very long time and it has very stable earnings. And so the behavior theory says well right, that stock might be a value stock, just because people undervalue what the growth prospects will really be, because it's boring, whereas a company like Amazon is sexy and sizzly and therefore investors overestimate what the growth prospects will be.
Speaker 1:It also could be an accounting problem because, as a funny quirk in the accounting rules, what we find is that when a company invests its excess earnings in research and development, typically it can't capitalize those expenses, that is to say it can't add them to the value of the firm. But obviously they have value. If I invest in research and development and I come up with a great new software, great new trademark, a great new product that's going to be patented, that has real economic value, but in the accounting world that asset has no value. All the money I spent on research and development is just a simple expense. And so one might argue that, as the economy has changed since Fama and French's first observation in 1991, as the economy has changed in the 90s to a much more technologically advanced economy. It may be that lots more companies spend money on research and development and that money is not being counted in book value and it's making the fraction, the ratio, look different than it ought to.
Speaker 1:Well, whatever the reason might be, they constructed a factor just as I described for size. They constructed a factor for value, in which they were long the stocks with low price to book value and short the stocks with high price to book value, and what they observed is that the factor earned a positive premium over time, but it was prone to long periods of underperformance and short periods of outperformance, and so that is a very different bird. It's a very, very different thing than the size premium. It exists on average, but you have to experience some long periods of underperformance in order to get the juice out of that. Well, if we extend the data from Fama and French's original paper and we go from 1990 to 2023, we see a similar story with the size factor.
Speaker 1:The return for the value factor was less than 1%, about 0.7%, with volatility of about 17%. So that sort of stands up to the idea that most of this return has largely gone away, but, consistent with what Fama and French originally observed, the kurtosis. The outliers in this distribution were quite high. The kurtosis was 7.59% and, as I say, the volatility was 17%. It also had a reasonably high auto correlation and you will recall, auto correlation can be thought of as measuring either the illiquidity of a security or it might even be measuring its momentum. More on that in a minute. In either case, the value factor has a fairly high auto correlation, which suggests that the factor is really not necessarily producing risk results in the way that the original model has described. It's interesting to note that during the global financial crisis, the value factor lost a lot. It lost 23%, not nearly as much as the market, which was almost 50% decline. But in the post-global financial crisis expansion the value factor lost 2% a year. So again, it casts some doubt on whether the value factor is indeed measuring something that we want to own or that is a risk.
Speaker 1:I'm going to pass through the remaining two arbitrage pricing theory factors rather quickly, just because I think they're a little more esoteric. The next is momentum. The economist Mason Carhart observed that stocks that were rising tended to keep rising and stocks that were falling tended to keep falling. He found that if he constructed a factor that was, long the stocks that were up the most over the last six months and short the stocks that were down the most over the last six months. He earned a positive premium that was persistent over time but subject to periodic crashes. So earned a premium over time but was subject to periodic crashes, not stable at all. When he added momentum to market size and value, he found that now these four factors did a better job of explaining the cross-section of US equity returns.
Speaker 1:There's no clear explanation for why momentum is a risk. The only explanation for momentum is behavioral and many economists, including Fama and French, don't view momentum as a systematic risk. But the data is rather compelling. Remember, if you're long the stocks that were up the most over the prior six months and short the stocks down the most over the prior six months, you construct that factor. You're going to have very nearly no equity market exposure. It will have canceled out on both sides. Yet the factor from 1990 to 2023, earned on average a 5% return, albeit with 18% volatility, so not much more volatile than the market as a whole, and its adjusted information ratio is rather low. But the factor has negative correlation with the market return. That should be obvious. But it also has negative correlation with size and negative correlation with value. And so in a portfolio, momentum stocks that are momentum stocks might serve a very interesting purpose if, in the aggregate, they earn something like 5%, but with negative correlation to your other equity exposures. It's also true that, as Carhart observed, the kurtosis here is quite high. It's about 11. So much, much higher than markets, which, on average, are about two. During the global financial crisis, the momentum factor earned almost 20%, when the market lost almost 50%, and during the expansion after the global financial crisis, it earned about 4% a year, far less than its average. And so momentum is a very, very interesting thing. That's hard to pin down, it's hard to really understand it as a risk, but it's rather persuasive when we look at the data.
Speaker 1:And last is quality. This might be the most obvious sounding of all of them. The economist Robert Novy-Marx observed that quality stocks, those that have the most robust profits, revenues, dividends, etc. Earn a premium to all other equities. It seems rather obvious, doesn't it? But nobody had really thought to put that risk factor into the mix. There was market, there was size, there was value, there's momentum, but nobody thought to consider well, aren't there just good stocks and bad stocks. And so what if we took a look at that and Robert Novy-Marx found that good stocks high profit, high revenue, high dividend stocks earned more than the market as a whole, presumably because the companies with higher profits and higher cash flows are going to be worth more and investors tend to be slow to update their beliefs when they're confronted with new information. The most quality companies aren't more risky. They're less risky if you think about it. But the problem is, how do you know ex ante which are going to be the quality companies? Well, he found that if he constructed a factor that was long quality stocks and short junk stocks what he called them, and so the acronym is sometimes QMJ it earned a positive premium that was persistent, and he found that by adding that factor to the other four factors, he was better able to explain the cross-section in equity returns.
Speaker 1:The explanation of the factor seems rather obvious. What's confounding is why a market that efficiently allocates capital to risky uses wouldn't have already incorporated that information into price. When we look at the data from 1990 to 2023, we see that the quality factor earned, on average, about 5%. That's lower than the market as a whole. So there's some doubt then about the continued probity of the quality factor. It earned about a 5% return and the factor, while unrelated to all of the other factors, it had negative correlation to market, negative correlation to size, negative correlation to value. It was only moderately correlated to momentum. Nevertheless, it still had reasonably modest skew, really zero skew in fact and reasonably modest kurtosis. So very modest tails, tails consistent with capital markets more broadly.
Speaker 1:All right, what are the issues with the arbitrage pricing theory? It's a useful construct, it's a construct that we're going to use for the rest of these podcasts, but I don't want you to imagine that somehow it's a deep, insightful, correct answer to any kind of analysis. First, there's the problem of construction. As I mentioned, although constructing the factors that are long and short effectively neutralizes the market exposure, it's not purely a measure of the factor we're trying to measure. It's short, the opposite factor, and that has some noise involved with it. Second, the factors are not exclusive. Though we said the five common factors, there's rough consensus around they don't explain all of the cross-section of equity returns. There is still a portion of equity returns unexplained by these factors and that suggests there are other risks that help explain equity returns. That's why we have the factor zoo. It also means that these five factors shouldn't be relied on exclusively to tell us what equity risk there is. Third and last, the factors are overlapping. You might have noticed that we talked about, say, size and value and momentum, but we never really talked about a stock that is small, value and momentum, all three, and that's because these factors absolutely overlap. But the analysis that we do doesn't really permit evaluation of its overlapping. While the factors each earn premiums, it's not clear whether those premiums are only for the factor in hand or maybe some other mix of factors. A good example of that is when we talked about the follow-up paper on size premium that Fama and French did and they found that most of it had to do with small stocks becoming large stocks, and that was almost exclusively small growth stocks, not small value stocks.
Speaker 1:A word here about the active, passive debate, and then I'd like to do a case study to help put to work arbitrage pricing theory. But first a word about the passive and active debate. When we talk about these factor premiums, we talk about market and size and so on, and sometimes I use indices like the S&P 500. That's what's called passive investing, that's a capitalization weighted index, where the securities are chosen by an index provider and the index is computed using a certain percentage based on the weight of the capitalization of each of the constituents. Active is where the portfolio of securities takes different weights on maybe the same exact securities, but does so depending on their conviction about the expected returns.
Speaker 1:Both investors that are passive investors, who only buy the S&P 500 for large or only buy the Russell 2000 for small Active investors and active investors. Both believe in the efficient markets hypothesis. In the long run price will incorporate all known, accurate information and in the short run there's mispricing as market participants engage in price discovery. The difference is that active managers believe that they can identify the mispricings themselves and earn a premium for identifying those mispricings. That's why they own things in different weights to the index. There are different kinds of active managers. There are fundamental managers who try to identify those mispricings based on a fundamental analysis of a company, usually its earnings or its profits. There are also quantitative managers. They think they can identify patterns in the price data and then trade on short-term price movements that are not consistent with the patterns. Active managers, unlike active managers, believe that it's difficult, costly or both to consistently capture the premiums of mispricings in the short run, and so they avoid it altogether in favor of just owning the index.
Speaker 1:That doesn't mean that passive investors have very little activity. We often equate the word passive with its English meaning and we import that into the finance meaning, and that's not fair to do Passive investors. It's not that they have very little activity. Likewise, it's not the case that active investors have lots of activity. Warren Buffett, a very famous active investor, buys and holds companies for 20-plus years. There is very little activity, but he is an active investor In the S&P 500, which is a passive index of US large cap stocks. In order to maintain the price of the S&P 500, a portfolio would have to be traded constantly, all day, to maintain that very low tracking error to the index. So there's lots and lots and lots of activity in keeping that portfolio matched to the index. But we call it passive investing. We want to think instead of passive versus active in terms of the efficient markets hypothesis. Passive investors think that in the short run it's too difficult or too costly, or both, to consistently predict and capture premiums of mispricings in the short run, so they don't try. They just own an index of those securities, where active investors, whether they're fundamental or quantitative, think that they can successfully exploit those mispricings, and so they try to do so in the short run.
Speaker 1:Let's take a look, then, at probably one of the most successful active investors, warren Buffett, and in particular, his portfolio, which is Berkshire Hathaway. Berkshire Hathaway is a public company and it has two share classes class A and class B. We're going to look at the class A shares. They're the more expensive shares and they were the original shares, but we'll just stay with those. There's not much of a difference. I've done the analysis on both the A and the B shares. It's very, very similar.
Speaker 1:What we're going to do is we're going to use arbitrage pricing theory. We're going to use APT to try to decompose Berkshire Hathaway to get a sense for the kinds of risks that Warren Buffett owns in his portfolio. Why? Well, because if we can identify the kinds of risks he owns, we can then tell what the expected returns would have been for owning those risks, and we can compare it to what he did earn If he earned more than the expected return for his risks. Wow, he's a good active manager who's managed somehow to exploit the changes in the short run, if he doesn't earn more than what the expected return is for those risks. Maybe something else is at work. We're going to look at Berkshire's data from 1996 through 2023.
Speaker 1:I didn't pick it randomly. The reason I chose it is because, in case any of you is interested in Berkshire Class B, that's the lower price version of the security same security, but it trades at a lower price. That only was launched in 1996. To keep it apples to apples for those of you who like to do your own number crunching, I thought I would keep it the same.
Speaker 1:Let's just look at the summary statistics. What did Berkshire Hathaway Class A stock earn during that period? What was its volatility, and what do we know about the shape of the dispersion and whether there were more tails, more outliers, in those returns than in markets generally? Berkshire delivered about a 12% return per year during that period, which, on its face, would suggest that Berkshire earned a better return than the S&P 500 during that period. It did so, though, with a 21% volatility. That's much more volatile than the S&P 500. We might say if we were mean variance thinkers, we might say ah well, maybe he's just earning more return for higher volatility. But we know better, right? We know that volatility alone doesn't explain returns. It's volatility plus co-movement. We saw that the skew and the kurtosis for Berkshire Class A suggest that it's not particularly skewed and it doesn't have particularly fat tails relative to the market as a whole.
Speaker 1:What I did was I regressed Berkshire Hathaway Class A share prices against the five factors that we've discussed sort of the market, size, value, momentum and quality. What did I find? Well, so the first thing I would say is that Berkshire earned for that period, on average, about 2% a year more than the returns that it would have earned owning those risks. On its face, it would seem that Berkshire earns returns in excess of its risk exposures. What were those risk exposures? The risk exposures that were the most meaningful was obviously exposure to equity market risk, in addition exposure to size, exposure to value and exposure to quality. Now, what's interesting is that the exposure to size was negative, which is to say Berkshire was short small stocks, or to put it in other words, long, large stocks. So Berkshire had exposure to large, not small, and Berkshire had exposure to quality. And Berkshire had exposure to the market.
Speaker 1:And for those of you that know anything about Warren Buffett and what he says publicly, about what he does. It's rather interesting because that's kind of what he says he does. He buys big companies that he thinks are high-quality companies, but he thinks that they're high-quality companies that are going to grow faster than the market seems to think they're going to be. So it's exposure to the market because they're stocks, and it's exposure to large because these are large companies. It's exposure to value because they're trading at a price that's lower than what he thinks or that people think it should be worth, and it's going to be exposure to quality. So what's the source of that excess return for Berkshire? Well, it could be skill, that's for sure. It could be that Warren Buffett is just really good at picking stocks. It's not so clear, though, whether it's only subject to, it's only the result of skill.
Speaker 1:One other thing that we can do we can look at the variation over time in his exposure to these different factors, and what we find is that it is anything but constant. The only constant is the market factor. The market factor tends to be rather high, near, near to One, near to a hundred percent exposure to market, which makes sense, except that during the period 2005 through 2015, berkshire had half the usual market exposure that it has, and so that suggests that one of the things that Berkshire does is it Dynamically allocates to market risk. It doesn't just own market risk, it sometimes owns less and it sometimes owns more. Likewise, the other factor that changed in some very meaningful ways is we saw a lot of change in the exposure to size. Remember, we said that he tends to be exposed to large cap stocks, but what's interesting is that that was definitely true in the 90s, during the tech market boom, and that's Definitely been true over the last four years, from 2020 through 2023. That it's Really exposure to large companies, but during all the other periods in the early 90s, 2000 to 2014 so really, after the tech bubble bursts, berkshire doesn't have nearly as much of a tilt to large as we, as we would have expected To see.
Speaker 1:The other thing that's, I think, rather interesting is that quality, which is a big Berkshire Stomping point. This is what they do they buy quality for a reasonable price. When we look at the quality factor exposure, it also pretty meaningfully, time varies. In the early 90s, berkshire had negative exposure to quality, that is to say, it had exposure to some stocks that might be considered junk stocks. The same was true in the last four years, from 2020 to 2023.
Speaker 1:The same was true in 2005 through 2009, during the global financial crisis, and so what that suggests is that the Quality that Berkshire Hathaway is talking about may not just be the way we're measuring it in the factor. That quality may be very specific to Warren Buffett's view about the quality of the stock and, last but not least, value. In the case of value, I would say that is a much more consistent exposure over time. In the 90s Up until 2000, the value exposure was fairly modest, but beginning in 2000 and still running through today, there's a pretty significant Heft to value. It would really seem that Buffett is true to his statements when he says that he favors companies that are at a reasonable price, which is to say that their value stocks. So it would seem that one possible explanation for Berkshire's excess return is just the Skill that Berkshire brings to picking stocks.
Speaker 1:But it seems another explanation Maybe that Berkshire times exposures to these risks in different ways that, in the aggregate, produces excess returns. We can't know for sure which it is, but what we can know is that by using something like APT, we get a better idea of what it is we own when we buy equities. What risks do we own and, importantly, what compensation do we expect to get paid for it? That's it for equities. Thanks, and I look forward to seeing you next time. You've been listening to not another investment podcast hosted by me, edward Finland. You can find research links and charts at not another investment podcast, calm, and don't forget to follow us on your favorite platform and leave comments. Thanks for listening.
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