Tuesday, March 8, 2011

Beta Isn't Risk: A look at CAPM and APT - Ari Paul

In this issue:
1) The Capital Asset Pricing Model (CAPM)
2) Beta Isn't Risk
3) Arbitrage Pricing Theory (APT)
4) "It is better to be roughly right than precisely wrong."

For a PDF version of this newsletter, please look here:

The Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) are financial paradigms that shape portfolio construction and the way professionals think about the market, but they provide a very dangerous conception of risk. I'll provide a basic introduction to the theories before exploring their most serious flaw.

1) The Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model (CAPM) is a cornerstone of the way financial professionals think about the market . While CAPM is a great academic theory, it’s dangerous to rely on it for investment decisions or to judge a portfolio’s performance. CAPM assumes that market participants can expect to earn returns in excess of the risk-free rate only by taking on systematic (non-diversifiable) risk. With this assumption, the expected return of any asset is entirely dependent on its Beta to the market portfolio.

There's a lot of jargon in this description, so let me try to state it more plainly. Investors shouldn't care about company specific risk (like the death of a CEO), because they can completely diversify that risk away by holding a portfolio with a bunch of companies. Since they can effectively get rid of company specific (non-systematic) risk, the market won't reward investors for taking it on. CAPM suggests that the market will only reward you for taking on risk that is impossible to diversify away; that's the risk that's left over when you build a portfolio with hundreds of companies and it's called systematic risk, AKA Beta.
Beta is just a measure of how a security generally moves with the market. A slight oversimplification: if a stock has a Beta of 2, we’d expect that if the market is up 1% on a given day, the stock will be up 2%. Buying a lower Beta security will add less risk to your portfolio than a higher Beta security.

Alpha is the leftover return after we account for Beta. If the market is up 1% and that stock is up 3%, CAPM suggests that 2% of the stock’s return came from systematic risk and 1% was “extra”. That extra return is frequently thought to be a portfolio manager’s skill. This is a valuable framework because it demonstrates that a manager can always juice their returns in an up market by simply increasing their Beta. If the stock market is up 8% in a year, a manager who uses leverage or buys high beta stocks will very likely produce a better than 8% return. However, if they double their returns with this method, they are also doubling the risk to their investors. A manager should not be rewarded for simply using leverage. If instead, a portfolio has a beta of 1 and produces double the returns of the market, CAPM suggests that the manager is exceptionally skilled.

E(R) = expected return on the security
E(Rm) = expected return on the market
Rf = risk-free rate
= alpha
B = Beta

2) Beta Isn't Risk
The problem with CAPM is that it’s entirely based on old data. Beta is used as a proxy for risk, but it’s not; it’s a measure of how the equity moved relative to the market in the past. Much of the time a company with a volatile past has a risky future, but we’re not investing blind. We have the opportunity to analyze a potential investment and judge its future riskiness for ourselves. Sometimes the factors that made a company risky in the past, like a specific lawsuit or labor dispute, are no longer applicable. This logical fact is backed up by extensive research.

The economists Eugene Fama and Kenneth French performed exhaustive statistical analysis from 1963 to 1990 that demonstrated that Beta (i.e. historical volatility) was not a predictor of future performance ("The Cross-Section of Expected Stock Returns" Journal of Finance 67, 1992, pp 427-465). Fama stated, “over the last 50 years, knowing the volatility of an equity doesn't tell you much about the stock's return." If Beta is risk, than this means there is no consistent relationship between risk and reward. I think the better explanation is that Beta is simply a poor measure of risk.

The emphasis on Alpha and Beta confuses historical regression for actual risk and return. Perhaps even more perniciously, it assumes the market portfolio as the benchmark. Imagine a hedge fund manager who bought a collection of tech stocks in 1999. Over the next 3 years, the Nasdaq collapsed more than 80%. If his portfolio only fell 60%, he might claim that the loss was entirely due to Beta, and that he was actually a skilled Alpha generator since his portfolio outperformed the market. However, he made the decision to buy a collection of overvalued stocks. CAPM implicitly excuses the fund manager from having to judge whether the market as a whole is overvalued.

Some fund managers have a specific market mandate - for example, a manager of a tech mutual fund is always supposed to be roughly 100% long technology stocks. For that manager, alpha and beta are a decent measure of performance since the manager has little discretion over his general market exposure. Most fund managers, however, can choose to be 100% long equities today and flat equities tomorrow. They are responsible for both the general positioning of their portfolios as well as the performance of their individual stock picks. A big part of their jobs is choosing the benchmark.

3) Arbitrage Pricing Theory (APT)
Arbitrage Pricing Theory (APT) is another popular measure for forecasting equity returns. APT defines an equity’s expected return by its exposure to a series of factors. The specific factors are left open for discussion, but generally include macroeconomic data like GDP, inflation, and yield curve changes.

E(r) = expected return on the security
Rf = risk-free rate
B = Beta
RP = risk factor premium

This equation formalizes the idea that a company’s return comes from its exposure to specific risks. The theory’s name comes from the assumption that asset prices must obey the equation, otherwise, investors would buy the asset and sell short a synthetic portfolio with the same exposure to the specific risks and gain an arbitrage profit...so the theory goes. Like in CAPM, the higher the risk, the higher the expected return. The difference is that where CAPM defines the only risk as being the Beta to the market, APT let’s the user define just about any risk they want. Unfortunately, this added freedom isn’t all that helpful.

Every input into this equation (except maybe the risk-free rate) will always be subjective. The very concept of a risk premium for a stocks’ sensitivity to inflation is debatable. APT practitioners generally data mine the last 30 years to identify key factors, but the importance of factors is always changing. Second, we’re stuck with the same problem as in CAPM - we’re using historical Betas that will likely be inaccurate going forward. A company may have had little sensitivity to GDP in the past when it solely produced fast food, but now that it has grown into a conglomerate, it may be far more sensitive.

4) "It is better to be roughly right than precisely wrong."
- John Maynard Keynes

No one ever got a Nobel Prize for saying, "it's complicated." Economists are incentivized to produce elegant equations. Financial professionals seek formulas to simplify their chaotic world and convince their risk managers and investors that they know what they're doing. A theme of the "Risk over Reward" team for the last 2 years has been that a great source of risk is the oversimplification of risk.

In pursuing elegant simplicity, both CAPM and APT ignore economic reality when calculating risk. They confuse the volatility of historic stock returns with future business risk. For short-term traders, CAPM and APT are valuable tools in predicting how the market will act. The theories identify past patterns and have additional predictive power simply because they are so widely accepted. However, for investors and economists, they are misleading and harmful metrics.

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