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Measuring portfolio performance using a modified measure of risk

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  • Chris Adcock

Abstract

This paper reports the results of an investigation into the properties of a theoretical modification of beta proposed by Leland (1999) and based on earlier work of Rubinstein (1976). It is shown that when returns are elliptically symmetric, beta is the appropriate measure of risk and that there are other situations in which the modified beta will be similar to the traditional measure based on the capital asset pricing model. For the case where returns have a normal distribution, it is shown that the criterion either does not exist or reduces exactly to the conventional beta. It is therefore conjectured that the modified measure will only be useful for portfolios that have nonstandard return distributions which incorporate skewness. For such situations, it is shown how to estimate the measure using regression and how to compare the resulting statistic with a traditional estimated beta using Hotelling's test. An empirical study based on stocks from the FTSE350 does not find evidence to support the use of the new measure even in the presence of skewness.

Suggested Citation

  • Chris Adcock, 2007. "Measuring portfolio performance using a modified measure of risk," Journal of Asset Management, Palgrave Macmillan, vol. 7(6), pages 388-403, March.
    • Handle: RePEc:pal:assmgt:v:7:y:2007:i:6:d:10.1057_palgrave.jam.2250054
    DOI: 10.1057/palgrave.jam.2250054
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    Cited by:

    1. Alexandros Kostakis, 2009. "Performance measures and incentives: loading negative coskewness to outperform the CAPM," The European Journal of Finance, Taylor & Francis Journals, vol. 15(5-6), pages 463-486.
    2. Jose Soares da Fonseca, 2010. "The performance of the European stock markets: a time-varying Sharpe ratio approach," The European Journal of Finance, Taylor & Francis Journals, vol. 16(7), pages 727-741.
    3. José Soares da Fonseca, 2013. "Innovations in return transmission and performance comparison between the five biggest Euro area stock markets," International Economics and Economic Policy, Springer, vol. 10(3), pages 393-404, September.
    4. José Soares da Fonseca, 2014. "Linkages and Performance Comparison among Eastern Europe Stock Markets," Notas Económicas, Faculty of Economics, University of Coimbra, issue 39, pages 73-83, June.

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