Journal of Risk

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The statistics of capture ratios

Ruihong Jiang, David Saunders and Chengguo Weng

  • The authors derive the asymptotic multivariate normal distributions of two capture ratios under the independence and a serial dependence assumption, respectively, for the underlying asset return process.
  • For the small sample sizes used in practice and the literature, the authors find that there are serious concerns regarding the statistical estimates of the capture ratio.
  • This study using a real-world hedge fund return data set indicates that the estimates of capture ratios from monthly and daily data can be significantly different. The estimates from a small sample are rather volatile through time and deviate significantly from the long-term capture ratio.
  • The authors’ observations raise questions about the practical use of the capture ratio e.g., using capture ratios for fund ranking.

The capture ratio is a widely used investment performance measure. We study the statistical problem of estimating the capture ratio based on a finite number of observations of a fund’s returns. We derive the asymptotic distribution of the estimator and use it for testing whether one fund has a capture ratio that is statistically significantly higher than another’s. We also perform hypothesis tests with real-world hedge fund data. Our analysis raises concerns regarding the models and sample sizes used for estimating capture ratios in practice.

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