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Sharpe Ratios and Alphas in Continuous Time

Published online by Cambridge University Press:  06 April 2009

Lars Tyge Nielsen  and
Maria Vassalou
Lars Tyge Nielsen
Affiliation:
lars.nielsen@morganstanley.com, Morgan Stanley, 750 7th Avenue, New York, NY 10019
Maria Vassalou
Affiliation:
vassalou@columbia.edu, Graduate School of Business, Columbia University, 3022 Broadway, New York, NY 10027.
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Abstract

This paper proposes modified versions of the Sharpe ratio and Jensen's alpha, which are appropriate in a simple continuous-time model. Both are derived from optimal portfolio selection. The modified Sharpe ratio equals the ordinary Sharpe ratio plus half of the volatility of the fund. The modified alpha also differs from the ordinary alpha by a second-moment adjustment. The modified and the ordinary Sharpe ratios may rank funds differently. In particular, if two funds have the same ordinary Sharpe ratio, then the one with the higher volatility will rank higher according to the modified Sharpe ratio. This is justified by the underlying dynamic portfolio theory. Unlike their discrete-time versions, the continuous-time performance measures take into account that it is optimal for investors to change the fractions of their wealth held in the fund vs. the riskless asset over time.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 39 , Issue 1 , March 2004 , pp. 103 - 114
Copyright
Copyright © School of Business Administration, University of Washington 2004

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