# Three Factor Asset Pricing Model

**Topics:**Capital asset pricing model, Investment, Stock market

**Pages:**5 (1445 words)

**Published:**August 2, 2012

Student name: Umar Abdullaev

Proposed research topic:

The implication of conditional betas on the Fama-French three factor model

Introduction

CAPM has been an active area of research over the past half century since the introduction of Sharpe development of the capital asset pricing model. Much progress has been made in the early years on the linear relationship between expected return and beta(Black, Jensen and Scholes 1972 and Fama and MacBeth 1973). Later studies however show weak empirical evidence on these relationships. Since then, although extended versions of CAMP have been introduced such as CAPM with higher-order co-moments and CAPM conditional on time-varying volatility little research has been done in the effect of up and downside risk on the three factor model proposed by Fama and French in 1993 and 1996.

The research aims to make a contribution to the understanding of the complicated version of CAPM through adding up and down betas to the three factor model for two main reasons. First, this area of study is little researched and second the single beta value is rarely accepted by many academics and practitioners to explain portfolio returns, suggesting that downside or upside risk may be more appropriate measure of portfolio risk than the single beta.

Since the three factor model is important to estimate the cost of equity capital and now widely used in empirical research, the study will primary be concerned with the examination of three factor model that incorporates conditional betas and test weather these factors are priced. Although there is published evidence on the significantly positive (negative) beta-return relationship in the up(down) markets(Pettengill, Sundaram and Mathur, 1995) and on the usefulness of two non-market risk factors SMB(the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks) and HML(the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to-market stocks), all of which explain cross-section of equity returns, no study work has been made on the implication of upside and downside risk to the three factor model. And therefore the potential of this research is to fill this space in the literature.

Also another contribution of this study is to compare the Fama-French cross sectional return-risk relations under single beta model and those obtained when the estimated betas are based on downside or upside markets.

Research Method

The data is two sets of 25 formed portfolios on the three major European Market Indices, the first of which is based on size and book-to-market factors and the second is formed on industry. The period under consideration is from January 1988 to January 2008. Time series tests and cross-sectional tests on two models are conducted over two different portfolio sets. Similar to Fama and Macbeth we run monthly cross-sectional regressions of excess return of portfolios on the estimated betas, SMB an HML. Factor loadings for the estimated beta, SMB and HML are taken from the time series regression of the excess portfolios return on the excess market return, SMB and HML.

Generally to test empirical data we go through the three main steps. The first step is to identify factors. In case of Fama-French three factor model, they are market factor (Rm-Rf), or the market risk premium, size factor (the returns of small portfolio stocks minus the returns of large portfolio stocks) and book-to market factor(the returns on high B/P portfolio stocks minus the returns on low B/P portfolio stocks). And the second step is using historical statistics to estimate the return on the market factor, size factor and book-to market factor. And the final step is to estimate factor sensitivities in order to identify how two sets of portfolio returns are affected when there are changes in...

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