Butterfly Implied Returns

Abstract

For each S&P 500 stock, we calculate the rolling correlation between the Cboe Volatility Index (VIX) and the prices of butterfly options at different strikes. The butterfly that co-moves most positively with the VIX reveals the expectation of the stock’s return in a future market crash and is called the butterfly implied return (BIR). A long-short strategy based on BIR hedges the market downturn while earning an annualized alpha of 3.4% to 4.7%. Using the demand system approach, we find that hedge funds tilt their portfolios towards stocks with a high BIR, whereas households typically take the other side, as the strategy realizes negative returns at the bottom of a crash and hence strongly correlates with the pricing kernel of a representative household. The value-weighted average BIR is the butterfly implied return of the market (BIRM), which measures the severity of a future market crash. BIRM strongly affects both the theory-based equity risk premium (negatively) and the survey-based expectation of return (positively).

Keywords: Predictability of stock returns; Cross-section of stock returns; Downside risk

JEL Classification: G11;G12