Asset pricing models imply that equity portfolios’ time-varying exposure to the market risk and uncertainty factors carries with it positive risk premiums. Turan Bali and Hao Zhou contribute to the body of literature on this topic through the study “Risk, Uncertainty, and Expected Returns,” which appeared in the June 2016 issue of the Journal of Financial and Quantitative Analysis.
Their study seeks to investigate whether the market price of risk and the market price of uncertainty are significantly positive, and whether they may help explain the cross-sectional and time-series variation in stock returns. According to the authors’ model, the premium on equity is made up of two separate terms. The first term compensates for standard market risk. The second term represents an additional premium for variance risk.
Measures Of Uncertainty
Economic uncertainty is proxied by the variance risk premium (the price of volatility insurance as implied in options prices) in the U.S. equity market. The second set of uncertainty measures that they use is based on the extreme downside risk of financial institutions and is obtained from the left tail of the time-series and cross-sectional distribution of financial firms' returns.
The third uncertainty variable is related to the general health of the financial sector, and is proxied by the credit default swap index. The final uncertainty variable originates from the aggregate measure of investors' disagreement about the individual stocks trading at the NYSE, AMEX and Nasdaq. The dispersion in analysts' earnings forecasts acts as a proxy for the divergence of opinion.
Bali and Zhou’s study covers the period January 1990 to December 2012. Following is a summary of their findings, all of which are intuitive:
- The variance risk premium (VRP) is strongly and positively correlated with all the measures of uncertainty considered.
- The results indicate a significantly positive market price of uncertainty.
- Equity portfolios (individual stocks) that are highly correlated with uncertainty, as proxied by the VRP, carry a significant premium (8% annualized) relative to portfolios (individual stocks) that are either uncorrelated or minimally correlated with VRP.
- The results indicate that the VRP can be viewed as a proxy for financial and economic uncertainty.
- The results from testing the equality of conditional alphas for the high-return and low-return portfolios provide no evidence of significant alpha for small/big and value/growth portfolios, indicating that the two-factor model proposed in the paper delivers both statistical and economic success in explaining stock market anomalies.
Bali and Zhou found that the difference between the implied and expected variances not only positively covaries with stock returns, but it covaries negatively with future growth rates in GDP.
They explain: “Intuitively, when VRP is high (low), it generally signals a high (low) degree of aggregate economic uncertainty. Consequently agents tend to simultaneously cut (increase) their consumption and investment expenditures and shift their portfolios from more (less) to less (more) risky assets. This in turn results in a rise (decrease) in expected excess returns for stock portfolios that covaries more (less) with the macroeconomic uncertainty, as proxied by VRP.”
Having intuitive explanations for why a premium exists gives us greater confidence that results are not just random outcomes or the result of data mining exercises.
Bali and Zhou’s findings also provide further support for risk-based explanations for the size and value premiums, as small and value firms are more exposed to uncertainty risks, which in turn can lead investors to flee to the stocks of less risky large and growth companies.
Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.