Inferring Expectation of Return in the Crash State with Option Data

Description

The holy grail of asset pricing research is predicting future returns. In the proposed project, I will develop an innovative procedure that uses option data to infer the expectation of return of an individual stock during the market crash state. For example, consider the butterfly strategy. A butterfly strategy pays off only when the stock price falls into a particular range. Naturally, the premium increases when investors consider this range to be more likely. On the other hand, VIX, dubbed as the “fear index”, increases as market crash becomes more likely. For each S&P 500 stock, I calculate the rolling correlation between the VIX and the premium of butterfly at different strikes. The butterfly that co-moves most positively with VIX reveals the expectation of the stock’s return in the future market crash. I call this return the Butterfly Implied Return (BIR). I construct a new strategy by shorting the vulnerable stocks with low BIR and longing the resilient stocks with high BIR. This cross-sectional strategy, which I call Betting with Butterfly, is a bet that the crash will happen. It is highly implementable, as it only involves liquid S&P 500 stocks. Over the 1996 to 2019 sample period, it earns a statistically significant alpha, ranging from 0.25% to 0.36% per month relative to various factor models. Building on BIR, I construct an value weighted average called the Butterfly Implied Return of the Market (BIRM) which is shown to explain 26% to 40% of the variation of SVIX (Martin, 2017) across different horizons. In the proposed project, the first task will be to improve the existing strategy by using the extrapolated digital options instead of the butterfly. This step is feasible but computationally intensive. It will produce a cleaner measure of the expectation of return of individual stocks, which can then be aggregated into a measure of investors' expectation of the market return during a crash. Therefore, the proposed project will contribute to the literature on aggregate predictability, and the literature on cross-sectional stock returns.