Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 1, pp. 108--121

CAPITAL ASSET PRICING MODEL WHEN DATA IS SKEWED

By

DIGANTA MUKHERJEE,

and

SAMIK METIA, *Indian Statistical Institute, Calcutta, India*

SUMMARY. Capital Asset Pricing Models (CAPM) describe how the expected return of an asset is determined in a securities market. We assume that the individual investors are risk averse. An often observed but usually ignored feature of the distribution of security returns is its skewness. To modify the usual CAPM to allow for skewness, we attempt to change the mean-variance set up and try to work with a different metric. We explore the theoretical implications of the model and study its optimality properties. We apply our methodology on Toronto stock exchange data.

*AMS (1991) subject classification.* Primary 62P05;
secondary 62P20, 62P25.

*Key words and phrases. *CAPM, portfolio frontier, median, mean absolute
deviation, skewness.