Using a dynamically hedged trading strategy, the authors are able to develop a new method for measuring risk premiums by attributing them to the risks exposed in specific moments of the distribution—namely, skew and variance. They demonstrate that the two premiums are related and that the variance premium trade strategy is potentially profitable. The skew strategy is not profitable when the variance strategy is hedged away.
What’s Inside?
The authors provide empirical evidence for—and a deeper understanding of—the coexistence of skew and variance risk premiums (or persistent expected excess returns) in the equity index market. Strategies that use the variance risk premium and strategies that use the skew risk premium are both profitable. But the skew strategy and the variance strategy are exposed to each other, and attempts to hedge away variance risk would significantly diminish the skew risk premium, and vice versa.
How Is This Research Useful to Practitioners?
To explore the risk premiums associated with the return distribution and to measure the skew risk premium of US S&P 500 Index options, the authors develop a trading strategy. The strategy involves buying low-strike puts and writing high-strike calls along with trading options and forwards on the underlying, thereby replicating a skew swap. They use dynamic hedging to maintain constant risk exposure and find a significant skew risk premium.
The results indicate that the profit from buying skew swaps is highly correlated with the profit from writing variance swaps. The writer of the variance swap loses money when implied variance increases. The increase in implied variance causes an increase in covariance between variance and returns, thereby causing the buyer of skew swaps to lose money. The authors suggest that variance swaps and skew swaps create similar kinds of risk exposure.
In addition, they demonstrate that the strategy of buying skew swaps and hedging by buying variance swaps does not generate significant excess return. Both skew and variance risk premiums display time variation, and the same combination of risk factors drives both risk premiums.
There is strong evidence that both variance and skew risk premiums exist in the equity index market. The authors’ scale is sufficiently large to be reflected in an asset pricing model. Premiums do not seem to be explained by the equity risk premium, but there is enough empirical evidence to suggest that a single risk factor is sufficient to explain both premiums.
How Did the Authors Conduct This Research?
The authors develop a method to measure the risk premium in any desired moment of returns. It is a trading strategy that allows for the direct interpretation of the expected return as a risk premium, and the marked-to-market value of the strategy perfectly hedges for changes in the implied moment. Therefore, the average profit can be identified as the risk premium for being exposed to the risk in that moment.
For accuracy, the authors maintain the stability of the same risk exposures by dynamically rebalancing the option portfolio. They use the European options written on the S&P 500 spot index traded on the CBOE. The period covered is from January 1996 to January 2012, and the data are from OptionMetrics. The dataset includes closing bid–ask quotes for all corresponding strike prices, the implied volatility, the zero-yield curve, and closing spot prices of the underlying.
More than 40% of the implied skew in the index option prices with one month to expiry can be explained by the risk premium. The authors find that skew risk is closely related to variance risk, and the excess returns on skew swaps and variance swaps exhibit a correlation of nearly 0.9. They also find that the relationship between skew and variance risk is concealed when the positions are not rebalanced; with the corresponding buy-and-hold strategies, the correlation between the excess returns on skew and variance swaps drops to 0.3.
Abstractor’s Viewpoint
The authors provide a new methodology for understanding and measuring risk premiums in any moment of returns. They show the significance of the skew risk premium in the S&P 500 Index and also demonstrate that there is a strong correlation between the skew and variance risk premium when dynamic hedging is used. This result is very useful when hedging the portfolios for variance and skewness.
I agree with the authors that their constant maturity moment swaps provide a more direct exposure to moment risks and are more effective than static or infrequently balanced portfolios in response to significant risks.