Estimating mean-standard deviation ratios of financial data

Abstract

This article treats the problem of linking the relation between excess return and risk of financial assets when the returns follow a factor structure. The authors propose three different estimators and their consistencies are established in cases when the number of assets in the cross-section (n) and the number of observations over time (T) are of comparable size. An empirical investigation is conducted on the Stockholm stock exchange market where the mean-standard deviation ratio is calculated for small- mid- and large cap segments, respectively.

Keywords:

• return-risk ratio
• increasing dimension asymptotics
• coefficient of variation
• Arbitrage Pricing Theory model

Acknowledgements

The authors are thankful to the referees for their valuable and constructive suggestions which improved the presentation and quality of the paper.