Capm vs. Apt: an Empirical Analysis

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Yurop Shrestha
Economics Thesis
CAPM vs. APT: An Empirical Analysis
The Capital Asset Pricing Model (CAPM), was first developed by William Sharpe (1964), and later extended and clarified by John Lintner (1965) and Fischer Black (1972). Four decades after the birth of this model, CAPM is still accepted as an appropriate technique for evaluating financial assets and retains an important place in both academic scholars and finance practitioners. It is used to estimate cost of capital for firms, evaluating the performance of managed portfolios and also to determine asset prices. Since the inception of this model there have been numerous researches and empirical testing to assess the strength and the validity of the model. Several variations of the models have been developed since then (Wei 1988, Stein, Fama & French 1993, Merton 1973). The Arbitrage Pricing Theory of Capital Asset Pricing formulated by Stephen Ross (1976) and Richard Roll (1980) offers a testable alternative to the CAPM. Both of these asset pricing theories have gone through intense empirical and theoretical scrutiny with multiple researches supporting or refuting both the models. The purpose of this paper is to empirically investigate the two competing theories in light of the US Stock Market in relatively stable economic times. The first section will look at the logic and theoretical aspects of the competing asset pricing models. The second section analyses and discusses the existing literature and empirical analyses on both the theories. In the third section I explain the data and the testing methods employed to empirically examine the theories. The fourth section explains the results derived from the tests. The last section includes the conclusion and discusses the limits and implications of my research. SECTION I: CAPM and APT

Sharpe’s (1964) CAPM is built upon the model of portfolio choice by Harry Markowitz (1959). According to his theory, investors choose “mean-variance-efficient” portfolio. This basically means that they choose portfolios that minimize the variance of portfolio return, given expected return, and maximize expected return, given variance. In addition to these assumptions, the CAPM makes several other key assumptions. They assume that (1) all investors are risk averse and looking to maximize wealth in a single period and can choose portfolios solely on the basis of mean and variance, (2) taxes and transaction costs do not exist, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a riskless rate of interest (Black et al. 1972).

The CAPM is an equilibrium model that explains why each different security has its own distinct expected returns. It provides a method to quantify the risk associated with each asset. One key assumption of the CAPM is that it assumes that all the diversifiable risk can be and is eliminated in an efficient ‘market’ portfolio. An individual security’s idiosyncratic risk will be compensated for by another stock. So the risk associated with each security is its systemic risk with the market. This is measured in the CAPM by its beta (its sensitivity to the movements in the market). There is a linear relationship between the security’s beta and its expected returns. Formally the CAPM equation can be written as follows ERi= Rf+βi(ERm- Rf) (1)

ERi = Expected return on the capital asset
Rf = Risk Free Rate (Usually of 6 month Treasury bill)
βi = beta which is the sensitivity of the expected excess asset returns to the expected excess market returns. Formally, the market beta of an asset i is the covariance of its return with the market return divided by the variance of the market return. βi = Cov(Ri, Rm)σ2(Rm) (2)

Rm = Expected return of the market
A zero beta...
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