Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets

AFA 2001 New Orleans Meetings

Review of Finance, 2003, 7(2), 191-233

45 Pages Posted: 5 Oct 2000 Last revised: 22 Jun 2020

See all articles by Aleš Černý

Aleš Černý

Bayes Business School (formerly Cass), City, University of London

Date Written: November 1, 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 1, 2002). AFA 2001 New Orleans Meetings, Review of Finance, 2003, 7(2), 191-233, Available at SSRN: https://ssrn.com/abstract=244731 or http://dx.doi.org/10.2139/ssrn.244731

Aleš Černý (Contact Author)

Bayes Business School (formerly Cass), City, University of London

Northampton Square
London, EC1V 0HB
United Kingdom

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