Monotonicity of the Stochastic Discount Factor and Expected Option Returns

76 Pages Posted: 19 Feb 2009 Last revised: 11 Feb 2015

See all articles by Ranadeb Chaudhuri

Ranadeb Chaudhuri

Oakland University

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management

Date Written: September 24, 2013

Abstract

Empirical evidence shows that the pricing kernel, or stochastic discount factor (SDF), is not always downward sloping when estimated using S&P 500 data. On the other hand, we show that individual stock SDFs are in general downward sloping. We show that a simple jump diffusion returns model can reconcile these empirical findings. The same model also implies a steeper implied volatility curve for the index compared to the typical stock, a well-known empirical fact from the options literature. Both the SDF results and the implied-smile results can be explained by a common source of jump risk among stocks together with diversification of Brownian risk in the index. SDF violations arise when the per-unit-return compensation for Brownian risk exceeds that for jump risk. Diversification increases the former compensation more than the latter, making SDF violations more likely in the index than the typical stock. We also devise novel empirical tests of overall SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the density functions of returns.

Keywords: SDF, Risk Premium, Derivatives, Expected Returns

JEL Classification: G12, G13, C8, C50

Suggested Citation

Chaudhuri, Ranadeb and Schroder, Mark D., Monotonicity of the Stochastic Discount Factor and Expected Option Returns (September 24, 2013). Available at SSRN: https://ssrn.com/abstract=1344061 or http://dx.doi.org/10.2139/ssrn.1344061

Ranadeb Chaudhuri (Contact Author)

Oakland University ( email )

320 Eliott Hall
Rochester, MI 48309
United States

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management ( email )

323 Eppley Center
East Lansing, MI 48824-1121
United States
517-432-0622 (Phone)
517-432-1080 (Fax)

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