The capital asset pricing model (CAPM), the foundation of modern portfolio theory, calculates the expected return of an asset as a function of its covariance with the return on broad market movements. Developed in the 1960s, the CAPM implies that the market compensates investors for market risk but not for the risk of individual assets, since investors can eliminate idiosyncratic risk by holding a balanced portfolio.
In 1973, Robert Merton extended this theory to reflect the fact that the set of available investment opportunities changes over time. According to his Inter-temporal CAPM, an asset earns additional risk premiums if it performs poorly when variables driving the overall economic outlook turn sour.
Over time, researchers noticed that the CAPM tends to misprice certain types of stocks, suggesting that market risk is not the only risk factor at work. Eugene Fama and Kenneth French found that small stocks and stocks with high book value to market value ratios have abnormally high average returns. In 1993, they incorporated their findings into a statistical risk-adjustment model known as the Fama-French three-factor model.
While the Fama-French model predicts asset returns more accurately than previous models, it still doesn’t fully explain why some stocks have returns that are above or below average. Professors Andrew Ang and Robert Hodrick of Columbia suspected that changes in market volatility might account for some of these residual anomalies.
Evidence from the late 1990s showed that investors demand higher rates of return for holding illiquid stocks. But while August 1998 — the month of the Russian financial crisis — was an illiquid period, it was also a highly volatile period. Ang and Hodrick posited that if investors dislike increases in volatility, they might demand less of a risk premium for stocks that pay off when market volatility increases. Thus stocks with different exposures to changes in market variance should have different expected rates of return.
To test this hypothesis, Ang and Hodrick sorted U.S. stocks into portfolios based on a stock’s sensitivity to market variance and then analyzed the returns of each portfolio. They found that significant correlation between the market variance and the returns of individual stocks implied lower expected stock returns. These results confirmed that market variance is a unique risk factor that is separate from the three Fama-French factors and the liquidity effect.
Through additional analysis, Ang and Hodrick demonstrated that stocks with high idiosyncratic volatility relative to the Fama-French model have very low average returns. While this evidence supported their hypothesis, they were surprised by the extremely low returns, which are inconsistent with all existing risk-adjustment models. In a follow-up research project, they are attempting to find a conclusive explanation for the idiosyncratic volatility effect and to determine whether it also exists in international markets.
Andrew Ang is the Roger F. Murray Associate Professor of Finance and Robert Hodrick is the Nomura Professor of International Finance at Columbia Business School.
