The Ex Ante Physical Distributions of Individual Stock Returns

55 Pages Posted: 2 Dec 2020 Last revised: 16 Feb 2021

Date Written: September 17, 2020


I present a method for deriving the entire physical return distributions of individual stocks directly from option prices. The method is theoretically nested in an equilibrium model, obeys the law-of one-price, and can be implemented in real-time in a forward-looking manner. The method performs well out-of-sample in predicting ex-post distributions of individual stock returns. The physical stock distributions and the co-moments with the market are important for risk-management decisions, portfolio allocation, and can help understand the cross-section of returns. A tradeable long-short portfolio that buys (sells) low (high) co-skewness stocks yields a monthly five-factor alpha of 0.61% (t-stat 3.25). The equity risk factors: value, profitability, investments, momentum, and betting-against-beta can all be used to hedge co-skewness risk.

Keywords: Physical distributions, individual stocks, option implied, physical co-skewness

JEL Classification: G00, G11, G12, G13

Suggested Citation

Jensen, Christian Skov, The Ex Ante Physical Distributions of Individual Stock Returns (September 17, 2020). Available at SSRN: or

Christian Skov Jensen (Contact Author)

Bocconi University ( email )

Via Roentgen 1
Milano, MI 20136

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