Downside Beta and Downside Gamma: In Search for a Better Capital Asset Pricing Model

Madiha Kazmi,Imran Abbas Jadoon,Attayah Shafique,Umara Noreen

doi:10.3390/risks9120223

Madiha Kazmi, Imran Abbas Jadoon + Show 2 more

Open Access

https://doi.org/10.3390/risks9120223

Copy DOI

Abstract

In the financial world, the importance of “downside risk” and “higher moments” has been emphasized, predominantly in developing countries such as Pakistan, for a substantial period. Consequently, this study tests four models for a suitable capital asset pricing model. These models are CAPM’s beta, beta replaced by skewness (gamma), CAPM’s beta with gamma, downside beta CAPM (DCAPM), downside beta replaced by downside gamma, and CAPM with downside gamma. The problems of the high correlation between the beta and downside beta models from a regressand point of view is resolved by constructing a double-sorted portfolio of each factor loading. The problem of the high correlation between the beta and gamma, and, similarly, between the downside beta and downside gamma, is resolved by orthogonalizing each risk measure in a two-factor setting. Standard two-pass regression is applied, and the results are reported and analyzed in terms of R2, the significance of the factor loadings, and the risk–return relationship in each model. The risk proxies of the downside beta/gamma are based on Hogan and Warren, Harlow and Rao, and Estrada. The results indicate that the single factor models based on the beta/downside beta or even gamma/downside gamma are not a better choice among all the risk proxies. However, the beta and gamma factors are rejected at a 5% and 1% significance level for different risk proxies. The obvious choice based on the results is an asset pricing model with two risk measures.

Highlights

Asset pricing models are used to estimate the cost of capital for firms and evaluate the performance of managed portfolios
The first two tables report the results for the single-factor asset pricing models of Capital Asset Pricing Model (CAPM) and downside beta CAPM (DCAPM) with risk proxies, namely, Sharpe’s beta, Hogan and Warren (1974); Harlow and Rao (1989); Estrada (2002) downside betas and the proxies of risk as the third moment, i.e., skewness and downside skewness
The results show that the Sharpe–Lintner CAPM is inadequate for the equity market of Pakistan by explaining the economically and statistically significant role of the market risk for the determination of the expected return

Summary

Introduction

Asset pricing models are used to estimate the cost of capital for firms and evaluate the performance of managed portfolios. They are based on the risk–return relationship, which is long established as the backbone of portfolio management. An asset pricing model offers a unique risk–return relationship where an investor tries to optimize an investment decision. One of the earliest and most widely used models comes in the form of the Capital Asset Pricing Model (CAPM). It marks the birth of asset pricing theory, and its simplicity makes it the most widely used in applications. The validity of the CAPM is tested, and the outcome reveals a weak risk–return relationship

Objectives

Results

Conclusion