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.