Higher returns compensate for tail risk in US and non-US equity mutual funds. In contrast, volatility is not compensated on a risk-adjusted basis in either market. The authors introduce a new left-tail risk measure called “excess conditional value at risk.” The tail risk premium is estimated by using regressions that account for Carhart’s four factors and that are validated by Fama–MacBeth regressions on volatility and tail risk.
What’s Inside?
Economic theory suggests that investors demand a premium to hold riskier assets that pose the potential for higher losses. But such risk measures as volatility and beta treat downside returns and upside returns equally. To tackle this issue, the authors define a new left-tail risk measure, called “excess conditional value at risk” (ECVaR), and they study whether tail risk is rewarded with higher risk-adjusted returns. Investors tend to be more concerned with systematic risk than with diversifiable, idiosyncratic risk. To capture systematic risk and account for transaction costs, the authors use equity mutual funds and analyze whether volatility and the tail risk premium are compensated in US and non-US markets.
How Is This Research Useful to Practitioners?
The authors document three main findings. First, volatility, as measured by the standard deviation of returns, is not compensated on a risk-adjusted basis in US or non-US equity funds. Second, tail risks are rewarded on a risk-adjusted basis, and funds with higher tail risks generate higher returns for US and non-US markets. Third, using their ECVaR measure, they estimate the tail risk premium to be about 2.7% annually for US equity funds and about 2.5% annually for non-US equity funds. Tail risk premiums are statistically significant even after they control for size, value, momentum, and fund beta factors.
The low-volatility anomaly—the empirical observation that lower volatility portfolios earn higher returns than high-risk, high-volatility portfolios—is well-documented. Economics dictates that higher risk yields higher returns, so the authors investigate whether another risk measure, such as tail risk, would better capture the expected risk premium.
Increasing correlations, especially during crises, have brought tail risk strategies into focus for risk management and hedging, and this study could serve as a resource for risk managers and investment managers. Other applications may include products seeking to gain from the identified tail risk premium. Actuarial and insurance applications, in which risk and dispersion quantification are essential, may also prove fruitful.
How Did the Authors Conduct This Research?
The dataset contains 3,400 US and 1,100 non-US equity mutual funds from Morningstar’s databases, including dead funds to reduce survivorship bias. Using fund returns covering the 1980–2011 time period, the authors evaluate three risk measures: (1) volatility measured by standard deviation of returns; (2) skewness, calculated as the third central moment; and (3) ECVaR, a newly introduced left-tail measure. Value at risk (VaR) provides an estimate of the lower bound of loss to be exceeded for a specified time period and confidence level. Conditional VaR (CVaR) provides an estimate of the tail loss conditional on the VaR level being reached and is approximately the probability weighted average of losses equal to or higher than VaR. ECVaR is defined as the CVaR of the equity fund (returns non-normally distributed) minus the CVaR assuming normality. ECVaR thus controls for fund volatility.
The authors sort funds into quintiles based on volatility and ECVaR. They analyze risk-adjusted returns of low- and high-volatility quintiles and find that volatility is not compensated. But when they analyze risk-adjusted returns of the low- and high-ECVaR quintiles, they find a significant tail risk premium.
Long–short portfolios of high minus low ECVaR and volatility quintiles are regressed against the Carhart model factors of size, value, beta, and momentum. The authors find that alpha is not statistically significant for volatility but is statistically significant for ECVaR. Fama–MacBeth cross-sectional regressions of future returns on volatility and tail risk show that the regression coefficient for volatility is not significant, whereas the tail risk coefficients are significant.
Abstractor’s Viewpoint
The authors provide an accessible analysis of tail risk and introduce a left-tail risk measure (assuming long positions) based on CVaR. Although VaR is widely used, CVaR has better mathematical properties. Directions for future research may include out-of-sample analysis to further explore the robustness, predictive ability, and potential applications of the authors’ findings.