Butterfly Implied Returns

38 Pages Posted: 14 Jul 2021 Last revised: 21 Mar 2023

See all articles by Di Wu

Di Wu

City University of Hong Kong

Lihai Yang

affiliation not provided to SSRN

Date Written: February 23, 2023


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

Suggested Citation

Wu, Di and Yang, Lihai, Butterfly Implied Returns (February 23, 2023). Available at SSRN: https://ssrn.com/abstract=3880815 or http://dx.doi.org/10.2139/ssrn.3880815

Di Wu (Contact Author)

City University of Hong Kong ( email )

83 Tat Chee Avenue
Hong Kong

Lihai Yang

affiliation not provided to SSRN

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