CAPM, Risk, and Return: Why the Relationship Is Broken

In an earlier post we illustrated the fundamental breakdown of the risk-vs-return relationship as proposed by CAPM:   when test empirically, we find surprisingly that higher-risk stocks enjoy lower returns.  In this post we’ll review the suggested rationales.

Before diving in, we’ll first summarize the anomaly:

1. CAPM posits that risk is measured by systematic volatility (“beta”) of an asset; and that the relationship between risk and expected return is positive and linear.  This relationship is one of the most widely cited in finance fields ranging from investment management to cost-of-capital calculations.
2. Almost since the creation of the CAPM framework, empirical tests of its validity revealed problems:  the relationship between risk and realized return wasn’t as strong and as positive as declared by the theory.  In fact, for the past several decades the correlation has been negative:  low-volatility stocks have seen higher returns.
   • This effect is apparent whether we measure just systematic volatility, or total volatility
   • Although the focus of these studies have been on CAPM and its (admittedly unrealistic) proxy for risk, the finding is frankly quite troubling regardless of one’s preferred measure of risk, since most commonly discussed risk measures are highly correlated.  For example, high-beta stocks also usually exhibit higher tail risk (likelihood of extreme price falls)
   • Rebalancing costs, usually excluded by these studies, may in fact exacerbate these effects
3. Investors can benefit from this mismatch by investing in low-volatility stocks, which (based on historical results) will appreciate in value faster, and with lower price volatility in the process.

Recent attempts to explain the anomaly focus on behavior of individual investors and fund managers.

1. Investor Limitations

As early as 1972 we find investigators attributing the anomaly to investor limitations.  We assume that investors wish to construct asset portfolios with a desired risk profile.  They face a choice of constructing a portfolio of high-volatility stocks, or they can choose low-volatility stocks but use leverage to magnify risk and return.  If some investors are leverage-constrained, they will drive up the demand for high-volatility stocks.  The concomitant overpricing reduces the realized return of the riskier stocks.

Wurgler, Bradley, and Baker appeal to various behavioral explanations behind investors’ preference for high-volatility assets, including lottery preference, representativeness, and overconfidence.

The simple observation that on average markets tend to rise suggests a naïve strategy of buying higher-beta assets.  Though the excess demand reduces returns, the expected value of the portfolio (ignoring risk) may still benefit.

2. Fund Manager Incentives

Several considerations related to the success of portfolio fund managers may explain the anomaly.   Many funds exhibit the same leverage constraint as individual investors, or one even more severe:  most mutual funds, for example, use no leverage at all.

A different category of explanations concentrates on the widespread practice of evaluating fund managers against a benchmark.  The risk-reward relationship may impart less influence because the manager isn’t rewarded for absolute return (whether risk-adjusted or not), but for deviations from the benchmark over time.  If the manager is rewarded for her fund’s information ratio (the ratio of return deviation from the benchmark to volatility of return deviation), then Wurgler et al. show that it is easy to demonstrate that managers would not exploit apparent mispricings (for example, an underpriced low-beta, high-alpha asset) because of the depressing effect on her IR.

The explanation from a recent paper by Buffa, Vayanos, and Wolley tracks hypothetical FM actions in light of market swings; if their theory is correct, then managers don’t just respond suboptimally to asset mispricings, they may in fact exacerbate the risk/return anomaly by driving up the beta of overpriced assets through their trading behavior.  See also Curse of the Benchmarks.

These explanations aren’t just theoretical; as shown by Christoffersen and Simutin, the excessive holding of high-risk assets by fund managers can be directly explained by the stringent benchmark-based evaluations by pension-plan clients.  They show that such managers offset the impact to their portfolios’ total volatilities by increasing holdings in low-idiosyncratic-risk stocks.  In comparing these benchmark-driven fund practices, they note that sadly such funds offer no better performance than those with deemed lower pressure to track benchmarks.