Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets

45 Pages Posted: 5 Oct 2000

See all articles by Aleš Černý

Aleš Černý

Cass Business School, City, University of London

Date Written: November 2002

Abstract

The paper presents an incomplete market pricing methodology generating asset price bounds conditional on the absence of attractive investment opportunities in equilibrium. The paper extends and generalises the seminal article of Cochrane and Saa-Requejo who pioneered option pricing based on the absence of arbitrage and high Sharpe Ratios. Our contribution is threefold:

We base the equilibrium restrictions on an arbitrary utility function, obtaining the Cochrane and Saa-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms of Generalised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide a consistent ranking of investment opportunities even when asset returns are highly non-normal. Last but not least, we demonstrate that for Ito processes the Cochrane and Saa-Requejo price bounds are invariant to the choice of the utility function, and that in the limit they tend to a unique price determined by the minimal martingale measure.

Suggested Citation

Černý, Aleš, Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets (November 2002). AFA 2001 New Orleans Meetings; Cass Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=244731 or http://dx.doi.org/10.2139/ssrn.244731

Aleš Černý (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

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