Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T05:36:29.131Z Has data issue: false hasContentIssue false
  • English
  • Français

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:
[email protected], Morgan Stanley, 750 7th Avenue, New York, NY 10019
Maria Vassalou
Affiliation:
[email protected], Graduate School of Business, Columbia University, 3022 Broadway, New York, NY 10027.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Goetzman, W.Ingersoll, J. E.Spiegel, M. I. and Welch, I.. “Sharpening Sharpe Ratios.” Working Paper 02–08, Yale IFC (02 2002).CrossRefGoogle Scholar
Huang, C and Litzenberger, R.. Foundations for Financial Economics. Amsterdam: North-Holland (1988).Google Scholar
Jensen, M. C. “The Performance of Mutual Funds in the Period 1945–1964” Journal of Finance, 23 (1968), 389–415.Google Scholar
Goetzman, W.Ingersoll, J. E.Spiegel, M. I. and Welch, I.. “Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios.” Journal of Business, 42 (1969), 167–242.Google Scholar
Lo, A. W. “The Statistics of Sharpe Ratios.” Financial Analysts Journal, 58 (2002), 36–52.CrossRefGoogle Scholar
Merton, R. C. “Optimum Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory, 3 (1971), 373–413.CrossRefGoogle Scholar
Nielsen, L. T. Pricing and Hedging of Derivative Securities. Oxford, U.K.: Oxford Univ. Press (1999).CrossRefGoogle Scholar
Nielsen, L. T and Vassalou, M.. “Portfolio Selection with Randomly Time-Varying Moments: The Role of the Instantaneous Capital Market Line.” http://www.gsb.columbia.edu/faculty/mvassalou/. Working Paper, Columbia Univ. (1997).Google Scholar
Sharpe, W. F. “Mutual Fund Performance.” Journal of Business, 34 (1966), 119–138.CrossRefGoogle Scholar