Is there a unique stock risk factor associated with expectations of a bear market? In the November 2016 version of their paper entitled “Bear Beta”, Zhongjin Lu and Scott Murray relate a put option-based indicator of the risk that the U.S. equity market will enter a bear state to individual stock returns. This indicator is based on two near-term out-of-the-money S&P 500 Index put options: a short position in a put option with strike price 1.5 standard deviations (based on S&P 500 implied volatility, VIX) below a zero excess (relative to the risk-free rate) index return; and, a long position in a put option 1.0 standard deviation below a zero excess index return. Using S&P 500 Index option prices, S&P 500 Index levels, VIX levels, risk-free rates, returns for a broad sample of U.S. stocks and various factor returns during January 1996 through August 2015, they find that:
- Regression analyses show a strong negative relationship between a stock’s bear market expectation beta and its future return that is independent of factors used in prevalent models (market, size, book-to-market, momentum, profitability, investment).
- Over the sample period, a value-weighted portfolio of all stocks that is each month long (short) the tenth of stocks with the lowest (highest) bear market expectation betas generates:
- Average gross monthly return 1.13%.
- Gross monthly market alpha 1.48%.
- Gross monthly three-factor (market, size, book-to-market) alpha 1.33%.
- Gross monthly four-factor (adding momentum) alpha 1.25%.
- Gross monthly five-factor (adding profitability and investment instead of momentum) alpha 0.71%.
- Results are robust:
- For a subsample comprised of either the 2,000 most liquid stocks or the 1,000 largest stocks by market capitalization.
- After controlling for several downside risk measures found in prior research and for other known predictors of stock returns.
In summary, evidence indicates that an equity bear market expectation risk factor has a negative premium that importantly and uniquely determines the cross-section of future stock returns.
Cautions regarding findings include:
- Return calculations are gross, not net. Accounting for monthly portfolio reformation frictions and shorting costs would lower returns. Shorting may not be feasible as specified.
- The bear market expectation indicator is fairly complex and therefore susceptible to snooping bias associated with selection of several parameters.
- As noted in the paper, the large negative return associated directly with the bear market expectation indicator are not exploitable due to bid-ask spreads an order of magnitude larger than average return.
- Cross-sectional stock return factors based on U.S. data arguably involve aggregate/cumulative snooping bias as addressed in “Taming the Factor Zoo”, thereby overstating statistical significance.
