The statistics of capture ratios

Ruihong Jiang; David Saunders; Chengguo Weng

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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.

Abstract

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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