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Equilibrium and Something About Quack Remedies Sold on the Internet
The expected return for the market portfolio should be a function of the level of interest rates. When rates are high, investors require higher returns on all tradable assets.
—JPP
A note to readers: I completed this book shortly before the Covid crisis. No model can predict what might come next in the evolution of the pandemic from a public health perspective. If we take a long-term view, I don’t expect the estimates provided in this and other sections of the book to be too different from those that we could construct in the postcrisis environment. Methodologies are simple and transparent. They can easily be updated with more recent data.
FOR MULTI-ASSET INVESTORS, A BASIC WAY TO ESTIMATE expected returns is to use the capital asset pricing model (CAPM). Despite its shortcomings, the CAPM is more useful than most investors think, because it links expected returns to an objective measure of risk and current interest rate levels. Jack Treynor, Bill Sharpe, John Lintner, and Jan Mossin independently developed this model in the 1960s.1 Anyone who has taken a basic course in finance knows about the CAPM. I was first introduced to the history behind it as an undergraduate. A professor gave me a copy of the book Capital Ideas, by Peter L. Bernstein (1991), a masterfully written account of the beginnings of modern finance. (This book had more influence on my interest in finance and career choices than any other book I’ve ever read.) In his follow-up book, Capital Ideas Evolving, in which he discussed applications of the concepts presented in Capital Ideas, Bernstein (2007) concludes that the CAPM “has turned into the most fascinating and perhaps the most influential of all the theoretical developments described in Capital Ideas.” Similarly, in their ubiquitous textbook Modern Portfolio Theory and Investment Analysis, Edwin Elton and Martin Gruber (1995) describe it as “one of the most important discoveries in the field of finance.”
However, there are issues with the CAPM. Its derivation relies on a long list of questionable assumptions: investors are rational; taxes and transactions costs do not exist; all investors have the same information; etc. Even Harry Markowitz, father of portfolio theory, has expressed misgivings about the widespread use of the CAPM. In a paper titled “Market Efficiency: A Theoretical Distinction and So What?” published in the Financial Analysts Journal in 2005, he writes about the model’s “convenient but unrealistic assumptions.” He focuses on one of the key, yet rarely discussed, building blocks of the model: the (clearly unrealistic) assumption that investors can borrow all they want at the risk-free rate. Like taking away the wrong Jenga piece will make the tower of blocks collapse, if we take away this important theoretical building block, the CAPM edifice crumbles. Markowitz demonstrates that the market portfolio is no longer “efficient,” which means that other portfolios offer a better expected risk-adjusted return, and the key conclusions and applications of the model are no longer valid (an interesting conclusion given the popularity of index funds).
At the Q Group conferences, which bring together academics and investment professionals, we’ve had the chance on a few occasions to hear Markowitz and Sharpe debate these and related issues. I’ve felt lucky to be part of an industry group where Nobel Prize winners engage in intellectual debates and exchange ideas with practitioners. It’s been clear from these discussions that the two intellectual giants have agreed to disagree on a few topics. But they seem to have maintained a longstanding friendship. When Sharpe received news that he, Markowitz, and Merton Miller had won the Nobel Prize, he said he was particularly happy to share the award with Markowitz: “We’re old and very close friends. He was basically my mentor. He so richly deserves it, as did Miller of course.”2
But if I read between the lines, Markowitz’s motivation to critique the CAPM could be that while the model was derived from mean-variance portfolio optimization (which is one of Markowitz’s most important contributions to the field of finance), it also suggests there is no need for it. When taken literally, the model dictates that all investors should buy a combination of cash and the market portfolio, mixed together in proportions consistent with their risk aversion. In his 2005 paper, Markowitz directly questions this conclusion:
Before the CAPM, conventional wisdom was that some investments were suitable for widows and orphans whereas others were suitable only for those prepared to take on “a businessman’s risk.” The CAPM convinced many that this conventional wisdom was wrong; the market portfolio is the proper mix among risky securities for everyone. The portfolios of the widow and businessman should differ only in the amount of cash or leverage used. As we will see, however, an analysis that takes into account limited borrowing capacity implies that the pre-CAPM conventional wisdom is probably correct.
Ultimately, Markowitz acknowledges the theoretical relevance of the model, but with a great analogy from physics, he argues that we should be aware of its limitations in practice:
Despite its drawbacks as illustrated here, the CAPM should be taught. It is like studying the motion of objects on Earth under the assumption that the Earth has no air. The calculations and results are much simpler if this assumption is made. But at some point, the obvious fact that, on Earth, cannonballs and feathers do not fall at the same rate should be noted and explained to some extent. Similarly, at some point, the finance student should be shown the effect of replacing [the model’s assumptions about borrowing at the risk-free rate and shorting] with more realistic constraints.
Other academics have expressed broader misgivings about the model, from both the theoretical and the empirical perspectives. In a 2004 paper titled “The Capital Asset Pricing Model: Theory and Evidence,” published in the Journal of Economic Perspectives, Eugene Fama and Kenneth French attack the CAPM much more directly than Markowitz:
In the end, we argue that whether the model’s problems reflect weaknesses in the theory or in its empirical implementation, the failure of the CAPM in empirical tests implies that most applications of the model are invalid.
Ouch. For an academic paper, that’s an unusually direct attack. To back it up, Fama and French show that individual stocks’ CAPM expected returns do not line up with subsequent realized returns. Superficially, they show that the average month-to-month returns of portfolios of individual stocks ranked on the basis of their CAPM expected returns do not line up with the model’s predictions. Also, Fama and French explain that other factors add explanatory power to the CAPM, namely book-to-market ratio and size. (However, multi-asset investors should take these tests with a grain of salt, as they are based on a short time horizon and rely on stock-level estimates of the model. These tests say nothing about the validity of CAPM expected returns at the asset class level.)
And then there’s Nassim Nicholas Taleb, who never minces words. In his sometimes bombastic but entertaining book The Black Swan (Taleb, 2010), he expresses disdain for the work of Markowitz and Sharpe. He almost sounds angry when he discusses their Nobel Prize:
The [Nobel] committee has gotten into the habit of handing out Nobel Prizes to those who “bring rigor” to the process with pseudoscience and phony mathematics. After the stock market crash, they rewarded two theoreticians, Harry Markowitz and William Sharpe, who build beautifully Platonic models on a Gaussian Base, contributing to what is called Modern Portfolio Theory. Simply, if you remove their Gaussian assumptions and treat prices as scalable, you are left with hot air. The Nobel Committee could have tested the Sharpe and Markowitz models—they work like quack remedies sold on the internet—but nobody in Stockholm seems to have thought of it.
“Locke’s Madmen, or Bell Curves in the Wrong Places” from The Black Swan: The Impact of the Highly Improbable, with a new section “On Robustness and Fragility” second edition, by Nassim Nicholas Taleb, copyright © 2007, 2010 by Nassim Nicholas Taleb. Used by permission of Random House, an imprint and division of Penguin Random House LLC. All rights reserved.
That’s far from Elton and Gruber’s description of the CAPM as “one of the most important discoveries in the field of finance.” Taleb’s concern is that modern portfolio theory and the CAPM were derived under Gaussian assumptions. Essentially, the models assume that investment risk can be represented by the standard deviation of returns. Hence, we must assume that the underlying return distributions are “normal”; i.e., they have no fat tails. In Part Two of this book I’ll discuss the limitations of Gaussian assumptions, as well as remedies for multi-asset investors, but for now, suffice it to say that extreme returns—in particular on the downside—are more frequent than the normal distribution predicts. Experienced investors know that in the markets, the tails are always fat. Therefore, exposure to loss can be much greater than expected if one relies on the theoretical foundations behind the CAPM.
To be fair to Markowitz, Sharpe, and other academics, I’m sure they would agree that empirical return distributions are often nonnormal. Markowitz, for example, wrote about semivariance to address nonnormal returns as far back as 1959. It doesn’t mean the CAPM and other related models are wrong. To borrow Markowitz’s analogy of the physics experiment that shows a feather and a cannonball falling at the same speed under vacuum, it means that if the assumptions hold, then these models are correct. In this sense, the CAPM is perhaps as close as it gets to a law of motion in finance.
Ultimately, to estimate expected returns is to try to predict the future. It should be hard! In the absence of a crystal ball, any model will have its flaws. In my view, despite the multidecade academic equivocation on its merit, the CAPM is as good as any other starting point for multi-asset investors, because it relates expected returns to risk.
From that perspective, while discussions on expected returns often degenerate into never-ending debates about what the future holds, with the CAPM we can make predictions in a somewhat agnostic, less controversial way. It’s hard to refute the argument that risk should be compensated: asset classes with higher risk should have higher expected returns than those with lower risk, as least over a reasonably long time horizon. There’s an appealing notion of equilibrium behind this approach. But there’s an important subtlety: under the CAPM, risk isn’t defined as the asset’s volatility or exposure to loss. It’s defined as its contribution to a diversified portfolio’s volatility. In other words, expected return on a security or asset class is proportional to its sensitivity (beta) to the world market portfolio.
Let us briefly get into some technical details. To calculate an asset’s beta, we multiply (a) the ratio of its volatility to the market’s volatility by (b) its correlation with the market. So the formula is
Beta = (asset volatility/market volatility) × correlation
where volatility is the standard deviation of returns, and the correlation is calculated between the asset and the market. Then we define expected return as follows:
Expected return = risk-free rate + beta × (market expected return – risk-free rate)
In their 2004 critique of the CAPM, Fama and French show that high-beta stocks can underperform low-beta stocks during long periods of time, which invalidates this equation. On the other hand, in his excellent monograph, titled Expected Returns on Major Asset Classes, Antti Ilmanen (2012) points out that from 1962 to 2009, there is a positive relationship between beta and the relative returns of stocks and bonds. It’s obvious: stocks have a higher beta than bonds, and over time they can deliver a higher return. While simplistic, this example suggests the CAPM may work better across asset classes than for individual stocks.
In addition to beta, expected returns depend on the current risk-free rate and the expected market risk premium (market expected return – risk-free rate). Purists will point out that there’s no such thing as a risk-free rate. That’s correct, as even cash has nonzero volatility, and in theory, there’s default risk associated with even the safest of government bonds. However, practitioners aren’t purists, and US Treasury bonds are generally used as a proxy for the risk-free asset. (As an interesting side note, for liability-focused investors such as defined benefit plan sponsors, cash is far from the risk-free rate. In fact, on a surplus basis, cash is a high-volatility asset compared with a long-duration bond that matches the duration of the liabilities. I’ll discuss liability-driven investing in Part Three of this book.)
To account for the “historical data” critique, our estimate of the risk-free rate must be forward-looking. We can think of the CAPM as a simple building block approach: we start with the current risk-free rate and add a risk premium (scaled by the asset’s beta). Suppose we use the three-month US Treasury bill rate as our risk-free rate, and we want to calculate expected return on an asset class with a beta of 1. Also, suppose we estimate the total market risk premium to be 1.9%, and we assume it doesn’t change over time. (I’ll discuss this total market risk premium estimate in more detail shortly.)
During the first half of the 1980s, the three-month US Treasury bill yield rose above 10%. As of March 23, 2018,3 it was at 1.7%. If we travel back in time and assume we’re in the early 1980s, we’ll have to endure bad music and questionable hairstyles. We’ll also notice high nominal expected returns. I use the term “nominal” because inflation was also very high, and this simple version of the CAPM doesn’t say anything about inflation and real returns. Expected return on our asset class in the early 1980s would have been 11.9%, calculated as follows:
Expected return = risk-free rate + beta × market risk premium
11.9% = 10% + 1 × 1.9%
whereas in the current environment, it’s 3.6%:
3.6% = 1.7% + 1 × 1.9%
Same asset class, same risk level . . . different starting points. In a low-rate environment, investors should expect low returns across the board. The risk-free rate is the anchor, and when it’s low, it holds down expected returns across markets.
Skeptics will say that we’ve been in a low-rate environment, yet realized equity returns have been very high. In March 2018, the S&P 500 was up a staggering 292% over the previous nine years (12.7% annualized4), including dividends. Even when rates are low, it’s still possible to see high realized risk premiums. Valuation may be the missing part of the puzzle: nine years earlier, equities were extremely cheap in the wake of the 2008–2009 financial crisis. My view is that in a CAPM framework, the forecast of the market risk premium (which includes both stocks and bonds) should account for whether financial markets are expensive or cheap in general. We can’t adjust for relative valuations to model each asset class’s expected return individually, but a valuation adjustment to the overall market risk premium should improve our forecasts. Investors sometimes use the expression “A rising tide lifts all boats” to describe market rallies. Do we expect the tide to rise or to come down? For the nine years previous to 2018, price-to-earnings ratios (P/Es) rose, and rates declined—clearly a rising tide.
In March 2018, we faced extended valuations across markets. If we want our estimates to be forward-looking, shouldn’t we calibrate our CAPM expected returns to be lower than historical averages? “When the tide comes down, we’ll see who’s been skinny-dipping” is a quote frequently attributed to Warren Buffett. With apologies for my overuse of the tide analogy, my point is that bear (or even just weak) financial markets are harder to navigate for unskilled investors and can make life difficult for plan sponsors, financial advisors, and individual investors.
In the next chapter, we’ll review methodologies to forecast returns based on valuations. For now, let us focus on the simplest of models. Jeremy Siegel, Wharton professor and author of Stocks for the Long Run (Siegel, 2002), often uses the inverse of the P/E ratio as a back-of-the-envelope forecast of real return for stocks. If we assume a P/E of 20, which is a number Siegel has quoted recently,5 expected real return for equities should be 5% (1/20). For inflation, we can use a market-implied or “breakeven” estimate, as measured by the difference between the yield of a nominal bond and an inflation-linked bond. In March 2018, 10-year inflation breakevens were around 2%. If we add inflation to the real return estimate, we get an expected nominal equity return of 7% (5% + 2%). Not bad.
On the other hand, Robert Shiller, Yale professor and Nobel laureate, uses a P/E ratio that normalizes earnings over the last 10 years and adjusts for inflation (the cyclically adjusted price-earnings ratio, or CAPE). The 10-year period is meant to represent a full business cycle. His approach yields a meager 1% expected real return for US stocks, or 3% nominal if we assume 2% inflation.6 The CAPE is higher than the current P/E in part because earnings have increased significantly over the last 10 years. Another reason for Shiller’s ultralow forecast may be that he doesn’t simply invert the ratio—he adjusts the estimate based on a regression model.
As much as we try to keep it simple, it’s never easy to forecast returns. Markowitz and Sharpe seem to disagree on the theory behind CAPM, even though it’s one of the most important foundations of modern finance. And here, two equally credible thought leaders disagree, this time on the equity risk premium, a key input to the model. I suspect the Shiller and Siegel estimates represent bookends—from one of the most bearish to one of the most bullish forecasts.
Because we want to build an estimate for global equity markets (CAPE ratios are closer to 20 outside the United States versus 30 in the United States),7 and for other reasons that I’ll explain shortly when we revisit the CAPE debate, my recommendation is to tilt the forecast toward Siegel’s estimate. A split of 80% Siegel, 20% Shiller seems reasonable to me, which gives us an expected nominal equity return of
6.2% = 0.8 × 7% + 0.2 × 3%
Some important caveats: This 6.2% forecast doesn’t represent T. Rowe Price’s view (as a firm, we don’t have a “house view”) or the views of our Global Multi-Asset Division. It’s just meant to be a simple and transparent forecast that uses a single factor, the P/E ratio. And the 80–20 blend is clearly my own finger-in-the air estimate—definitely not “robust” from a quantitative perspective. In fact, my colleagues in our Multi-Asset Division’s research team would be embarrassed and worried if I used it anywhere in our investment process. In the next several chapters, I’ll review several other methodologies to forecast returns that include more factors and that incorporate judgment in a more tractable way.
Here I use this estimate as a basic input to the CAPM. Is 6.2% reasonable for the world equity market portfolio? Bond managers tend to have a pessimistic bias on risk assets, so perhaps it’s not surprising that my old employer, PIMCO, expects equity returns to be quite low going forward. In early 2018, my ex-colleagues Ravi Mattu and Vasant Naik published a valuation-informed view that the equity risk premium should be about 2.5%, with an additional warning: “Equities may deliver even lower excess returns than the current ex-ante equity risk premium (ERP) of 2.5%, since a reasonable fair value for the ERP may be slightly higher.”8 (I assume they mean that in order to get a higher ERP, valuations will have to come down.) If we assume a nominal risk-free rate of 2%, we get an expected return of 4.5%. In contrast, BlackRock expects long-term equilibrium returns to be 7.2% for US stocks and 8.1% for international stocks.9 Once again, these forecasts look like bookends. In that context, 6.2% seems reasonable to me. It turns out that it’s close to estimates published by AQR (6.2%), Northern Trust (6.4%), Aon (6.5%), and BNY Mellon (6.2%).10
Is the goal to forecast returns over the next month, year, or longer? The CAPM is a single-period model, so in theory, the question of time horizon is abstracted away. In practice, investors use the model for relatively long time horizons. (I’ve never come across an investor who uses the CAPM for short-term investment decisions.) Plan sponsors and consultants use it for strategic asset allocation studies, for example. For such studies, the time horizon is usually between 3 and 10 years. And for life cycle investing applications, the investment horizon can be as long as 40 or more years. Similarly, Shiller’s and Siegel’s equity return forecasts assume a long time horizon. It’s my view that this relative consistency in time horizon makes them appropriate inputs to the CAPM.
What About Bonds?
To estimate the total market risk premium, we also need to forecast bond returns. (In theory, we need to forecast returns on all assets, including illiquid investments, but for practical reasons I’ll focus on liquid markets.) In fixed income markets, yield to maturity is a reasonably good predictor of future returns . . . better than most people think. In fact, by definition, yield to maturity is a perfect predictor of the buy-and-hold return of a single default-free bond. However, with the CAPM we need a return forecast for the total bond market, which includes credit exposures and is better represented as a constant maturity portfolio, rather than buy and hold.
Nonetheless, ultimately, it’s easier to forecast bond returns than equity returns, and the math behind forecasting bond returns is fascinating, at least to a geek like me.
First, the key takeaway is that higher reinvestment rates offset interest rate shocks over time. Suppose a bond portfolio has a duration (interest rate sensitivity) of five years. If rates unexpectedly spike by +0.5%, the portfolio should go down about –2.5% (5 × –0.5%). However, we now earn +0.5% more on the portfolio than we did before the rate shock. If we ignore several less important subtleties, such as yield curve effects and the timing of the rate shock, we can expect to recover the 2.5% over roughly five years (5 × +0.5%). This offset effect works no matter the size of the rate shock. It explains why, historically, the initial yield to maturity has been a remarkably good predictor of forward return for bonds, and the sweet spot of our ability to forecast, or close enough, is when the investment horizon matches the portfolio’s duration.
Bond investors tend to worry about rising rates because of the short-term losses that occur when the rate hikes aren’t already priced into the forward curve. However, contrary to conventional wisdom, this example illustrates how rising rates are good for bonds: higher rates mean higher reinvestment rates and, ultimately, higher expected returns. In an excellent paper titled “Bond Investing in a Rising Rate Environment” (2014), my former colleagues Helen Guo and Niels Pedersen go beyond this simple example. They account for the timing of the rate shock(s), and they model nonparallel yield curve shifts. They find that if rates rise gradually, or if the increase occurs later in the investment horizon, then it takes longer for the reinvestment effect to heal the price shock(s). They derive rules of thumb to predict when the convergence will occur for these special cases. Their results are remarkably intuitive, simple, and quite interesting (again, if you’re into geeky bond math). The bottom line is that the impact of rising rates on bonds is both bad (in the short run) and good (in the long run).
In a related empirical study published in 2014, Marty Leibowitz, Anthony Bova, and Stanley Kogelman show that returns for the Barclays U.S. Government/Credit Index have consistently converged toward the initial yield to maturity on the index. Over their study period, the index has had a relatively constant duration of about six years—consistent with the time horizon they used to measure convergence. Therefore, historically, the simplest rule of thumb seems to have prevailed: returns have converged to the initial yield to maturity at a time horizon that matches duration. This result holds across a variety of rate paths. It begets the question, why are bond investors and financial commentators in the media so worried about rising rates? If the horizon is long enough, it doesn’t matter whether rates go up, down, or sideways. The starting yield is what matters. As a predictor of the return on bonds, the accuracy of this single, publicly available number is much higher than that of any model we could ever build to forecast equity returns, at least out-of-sample.
As I write these thoughts on the impact of rising rates, the yield to maturity on the Barclays Global Aggregate is a meager 1.9% (yield to worst, as of April 3, 2018),11 and its duration is about seven years. Therefore, 1.9% is a reasonable long-term estimate of expected return for the bond market portfolio. Earlier I mentioned that stocks appear expensive after a nine-year bull market. But as we stare down the barrel of a 30-year bull market in bonds, bonds appear even more expensive. Some multi-asset investment firms (not my firm), primarily in Europe, have seduced investors with promises of “stock-like returns for bond-like volatility.” Until recently, several of them had been able to deliver on this promise. But from 2000 to 2016, guess what had delivered stock-like returns for bond-like volatility? Bonds.12 Again, the tired expression “A rising tide lifts all boats” applies. Going forward, it might be more difficult to deliver a stock-like return for bond-like volatility. It certainly was in 2017, as stock markets significantly outperformed bonds, such that any unlevered allocation that was not 100% invested in stocks did not deliver “stock-like returns.”
Yields are especially low outside the United States, due to unprecedented monetary easing in Europe, Japan, China, and the United Kingdom. Globally, not only have many central banks driven rates toward zero, but they’ve also pumped more than USD 20 trillion of liquidity into financial markets, through quantitative easing (QE).13 Meanwhile, the Fed has started normalizing. As an illustration of the impact of QE and divergence in policies, two-year US Treasuries currently yield more than two-year Greek government bonds (2.3% versus 1.3%, as of April 3, 2018). Yet, clearly, Greek bonds are much riskier.
The Market Portfolio: It’s Not What It Used to Be
Now that we have return forecasts for stocks (6.2%) and bonds (1.9%), we must estimate their relative weights within the market portfolio. I exclude private markets for simplicity, but as I mentioned earlier, in theory the CAPM market portfolio should include them. In fact, it should be a weighted sum of all assets in the world. Forbes contributor Phil deMuth explains that the market portfolio should include “your human capital, your family business, your wife’s jewelry, your house, and the Renoir on your fireplace,”14 another good example of when theory doesn’t work in practice.
Importantly, because I exclude private markets, their correlation with the market portfolio—and ipso facto their CAPM betas—will be biased down. For this and other reasons, such as the smoothing bias, their betas will require separate adjustments. In Chapter 9, I’ll discuss methodologies to build risk models for private assets.
Asset weights within the market portfolio should be based on their relative market capitalizations. Theory says these weights represent the aggregate allocation of all investors, a market consensus of sorts. Interestingly, most CAPM research and applications focus on equity-only examples. The stock market is almost always used as the market portfolio, as if other asset classes didn’t exist. It puzzles me that so many academic papers gloss over the multiasset nature of the theoretical foundations of the model, including the paper by Fama and French (2004) I mentioned earlier, as well as most of the prior studies they reference. This omission seems meaningful to me. It raises the question, should stocks be priced based on their beta to the stock market or to the total market portfolio?
In practice, it makes a significant difference. In a 2018 paper titled “Yes, the Composition of the Market Portfolio Matters,” Avraham Kamara and Lance Young use 75 years of monthly data on 30 equity industry portfolios. They show that adding bonds to the market portfolio “produces economically large differences in estimated [returns].” It changes the average level of return estimates across industry portfolios, through the combined effect of lower betas and a lower market risk premium. It also changes the relative expected returns, as some high-dividend industries are more bond-like and therefore more sensitive to interest rates (utilities and telecoms), while others have negative duration (financials). From an asset allocator’s perspective, clearly we should use the multi-asset market portfolio, not just equities.
Unfortunately, it’s difficult to estimate the relative weights of asset classes within the multi-asset market portfolio, due to a lack of reliable data. Overlaps across indexes are also an issue. For example, real estate investment trusts (REITs) are part of most equity indexes, but they invest in real estate, not stocks. Ronald Doeswijk, Trevin Lam, and Laurens Swinkels, in their 2014 paper titled “The Global Multi-Asset Market Portfolio, 1959–2012,” make a valiant effort to scrub the best available data, untangle the Russian nesting dolls of asset class exposures, and create a history of asset class weights within the market portfolio. Their analysis reveals that these weights have changed over time. In 2000, the market portfolio was close to 60% stocks, 40% bonds. Good old 60–40. Nowadays, these weights have flipped to about 40% stocks, 60% bonds.15 The shift has occurred in relatively slow motion. Since 2000, bonds have performed well, and net supply has increased, despite central bank purchases. Meanwhile the supply of publicly traded stocks has shrunk due to corporate buybacks, a reduction in IPOs, and the privatization of an increasing number of companies.
For CAPM purists who believe the capitalization-weighted market portfolio is always optimal, this significant change in its risk level must be a bit of a head-scratcher. To forecast returns, current weights are what matter. After all, we want to be forward-looking. (Or perhaps we should try to forecast the average weights over our time horizon, but that would be difficult, because so many supply and demand factors are unpredictable.)
If we assume the market portfolio is composed of 40% stocks and 60% bonds, our expected total market return is 3.6%, calculated as follows:
Expected total market return = 40% × expected stock market return + 60% × expected bond market return
3.6% = 40% × 6.2% + 60% × 1.9%
If we subtract the current three-month US Treasury bill rate of 1.7% (as of March 23, 2018), we get a market risk premium of 1.9% (3.6% – 1.7%). It’s not clear to me whether cash rates are the appropriate risk-free rate for long-term investors. Over a relatively long investment horizon, the cash return depends on rate changes, due to reinvestment effects (i.e., the three-month yield resets many times before the end of the horizon). From that perspective, cash is riskier than a zero-coupon bond that matches the investment horizon. An investor’s base currency is another consideration. Here I assume a US investor, but cash rates differ across countries. If they’re high, investors should expect high nominal returns on local assets. However, high cash returns usually coincide with high expected inflation.
Some of my colleagues can effortlessly move between nominal and real returns, local and foreign returns, etc. They mentally account for spot and forward rates, interest rate differentials, and inflation differentials on the fly. I’ve been involved in global macro investing for many years, and I used to oversee a currency overlay business, but I’m embarrassed to say that I still struggle with these problems. I always need to pause and think through them. To make it easy, let’s focus on a US investor who wants to forecast nominal returns.
Betas and Depressingly Low Expected Returns
Now that we have estimates for the risk-free rate (1.7%) and the market risk premium (1.9%), all we need are the asset class betas. In Table 1.1, I show betas for 21 asset classes, based on monthly data from February 2002 to January 2017.16 Also, I show each asset class’s CAPM expected return, which I calculate as explained earlier: risk-free rate + beta × market risk premium. For the market portfolio, I use a blend of 40% world equities (MSCI All Country World Index), 60% world bonds (Barclays Global Aggregate).
TABLE 1.1 CAPM Expected Returns
The return forecasts shown in the table are depressingly low. Yet this shouldn’t be a surprise, given the low level of rates and the low expected market risk premium due to high valuations. Following the 2020 pandemic crisis, as panic runs high, valuations have become more attractive, and the equity risk premium has likely increased. US rates have hit their zero bound. As I’m about to submit my manuscript for this book, it remains difficult to assess the impact of the economic heart attack. But it’s reasonable to expect that as we recover, risk assets will deliver relatively high returns.
A more surprising outcome may be that the numbers aren’t entirely consistent with the return expectations I put in the model for the world equity market (6.2%) and for the world bond market (1.9%). Equity markets have CAPM expected returns in the 4–5% range across US and non-US markets. These numbers can’t add up to my initial 6.2% world equity estimate, even after we include emerging markets. Also, US bond returns are lower than expected, given their current yield to maturity. On the other hand, non-US bonds have higher expected returns than their current yield to maturity suggests.
What explains these inconsistencies? The main reason is that I use a valuation approach to determine the market risk premium, while the CAPM is a statistical, risk-pricing approach. In a sense, because it relies on beta as the main driver of relative expected returns across asset classes, the CAPM is valuation-agnostic. As our director of research, Stefan Hubrich, would say: “These are ‘unconditional’ expected returns. If you were air-dropped into the US and you didn’t know what decade it was, how would you invest?”
Consider the example of non-US bonds. Relative to US bonds, they have higher volatility and higher correlation to the world portfolio. Therefore, they should have a higher expected return, without regard to their artificially low yield. (Central bank interventions create an artificially low yield.) The same intuition holds for stocks. To the CAPM purist, it doesn’t matter whether equity asset classes have a high or low price-to-earnings ratio. Their betas are all that matter.17
From that perspective, CAPM forecasts are most relevant for long investment horizons, say, over 10 years. They’re useful as inputs for life cycle investing applications, for example. Also, CAPM results can indicate whether valuation spreads, relative to long-term averages or between asset classes, may be transitory or permanent. All else being equal, the further away valuations are from their risk-return “CAPM equilibrium,” the greater the gravitational pull of mean reversion.
But there’s another issue I should emphasize: the betas are just statistical estimates produced by a risk model. They’re not very forward-looking. In Table 1.1, non-US small caps have a lower beta than non-US large caps. I did not expect this result. It could be due to idiosyncratic factors that prevailed from February 2002 to January 2017. Over that same period, growth stocks dominated market returns, which could explain why they have a higher beta than value stocks. However, in the current environment, value stocks are more levered to economic growth and cyclical factors in general. Hence, their forward-looking beta to the economy and to the world portfolio should be higher, perhaps even higher than growth stocks’ beta.
There are many extensions to the CAPM. Perhaps the most important extensions are Fama and French’s 2012 three-factor model (market beta, value, and size), as well as Carhart’s 1997 four-factor model (market beta, value, size, and momentum). I’ll discuss these and other factor models in Chapters 9, 11, and 12. Most of them focus on the cross section of equity returns; they are more appropriate for equity risk models and stock-picking strategies than for cross-asset expected returns.
The CAPM Is Useful
One of my finance professors used to say that “there’s nothing more practical than a good theory” and then chuckle to himself. It takes a high level of nerdiness to find that funny, especially toward the end of a three-hour lecture on asset pricing. I never heard any student laugh at that one. Yet there’s something profound about the statement. Peter Bernstein (2007) recognizes the issues with the CAPM, but he also points out that it has influenced how we think about indexing, how we evaluate managers, and how we separate alpha from beta. In his words, “It frames the marching orders and responsibilities involved in the whole investment process.” He concludes that the “CAPM is no longer a toy or theoretical curiosity with dubious empirical credentials. It has become a centerpiece of sophisticated institutional portfolio management.” It’s also one of the theoretical building blocks of a popular portfolio optimization technique used to avoid counterintuitive optimal weights, called the Black-Litterman model. I’ll discuss this model in Chapter 14.
For multi-asset investors, the CAPM is one tool in the return forecasting toolset. Based on a risk model, it gives us an estimate of risk-proportional expected returns, where the only risk that matters is the asset’s contribution to a broadly diversified portfolio’s volatility. At equilibrium, these agnostic estimates make sense, provided we use a good risk model and calibrate the risk-free rate and market risk premium carefully.
Still, like a financial law of motion, the model only works in a world without friction. In the real world, markets deviate from equilibrium, sometimes over long periods of time. The effect of central bank policy on global bond yields provides a good example. As I showed earlier, in the current environment, many central banks have pushed rates down toward zero, such that non-US bond yields are much lower than would be expected given their beta risk. Ultimately, investors should use the CAPM as a reference, a first step toward return forecasting that we can use to test our assumptions about fundamentals and valuations.
Notes
1. See Jack Treynor (1961), Bill Sharpe (1964), John Lintner (1965), and Jan Mossin (1966).
2. “Professor William Sharpe Shares Nobel Prize for Economics,” gsb.stanford .edu.
3. As I finalize this book at the end of March 2020, equity markets have suffered one of their worst and fastest sell-offs in history due to the coronavirus pandemic, combined with a major oil shock. The Federal Reserve has aggressively lowered rates, and the three-month US Treasury bill is at zero. These are unusual circumstances. In this context, expected returns across asset classes should be about 1–2% lower due to lower rates, compared with those of 2018. But on the other hand, valuations are more attractive than they were back in 2018, in a way that may offset lower rates.
4. For the nine years ending March 23, 2018.
5. Robert Huebscher, “Jeremy Siegel’s Predictions for 2018,” Advisor Perspectives, February 5, 2018.
6. Robert Huebscher, “Jeremy Siegel Versus Robert Shiller on Equity Valuations,” Advisor Perspectives, February 23, 2017. As of Q1 2018, the CAPE ratio was still relatively close to where it was when this article was published, hovering around 30. With the CAPE at 30, a simple earnings yield calculation would imply a 3.3% real return. It’s not clear how Shiller arrives at 1%, but I suspect he’s using a regression between the CAPE and subsequent returns to account for the fact that the relationship is not one-to-one.
7. http://shiller.barclays.com/SM/12/en/indices/welcome.app. The average of 24 major countries, excluding the United States, as of February 28, 2018, was 20.01.
8. https://www.pimco.com/en-us/insights/economic-and-market-commentary/global-markets/asset-allocation-outlook/singles-and-doubles.
9. https://www.blackrockblog.com/blackrock-capital-markets-assumptions/.
10. https://www.aqr.com/Insights/Research/Alternative-Thinking/2018-Capital-Market-Assumptions-for-Major-Asset-Classes; https://www.northerntrust.com/documents/white-papers/asset-management/cma-five-year-outlook-2017.pdf; http://www.aon.com/attachments/human-capital-consulting/capital-market-assumptions-2017-q1.pdf; https://www.bnymellonwealth.com/assets/pdfs-strategy/thought_capital-market-return-assumptions.pdf. All forecasts are for US equities, except for Northern Trust’s forecast, which is for developed markets equities. In general, non-US equities forecasts are similar, or slightly higher in some cases.
11. This yield was 1.06% as of May 12, 2020, as monetary authorities lowered rates even further to respond to the COVID-19 crisis. Using data from Bloomberg Finance L.P.
12. Using data from Bloomberg Finance L.P., on the Barclays Global Aggregate and the MSCI ACWI (total return indexes).
13. https://www.telegraph.co.uk/business/2018/01/30/qe-set-27-trillion-last -hurrah/.
14. https://www.forbes.com/sites/phildemuth/2014/07/30/meet-the-global-market-portfolio-the-optimal-portfolio-for-the-average-investor/#5956a39970d1. This comment was made in reference to Roll’s critique (1977).
15. As of 2012, which is the last year in their study.
16. Windham Portfolio Advisor.
17. Again, with the exception that the market risk premium can be calibrated with valuation models, as I’ve shown in my example.