# The Capital Asset Pricing Model (CAPM)

Introduction

The Capital Asset Pricing Model (CAPM) was originally developed by Harry Markowitz in 1959 and further published by others, including William Sharpe, over a decade later. CAPM describes the relationship between risk and expected return, and serves as a model for the pricing of risky securities. It says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat our required return then the investment should not be undertaken. The commonly used formula to describe the CAPM relationship is as follows:

E(R) = Rf +[E(Rm) – E(Rf)]

where E(R) is the expected return on an asset or portfolio uncorrelated with the market and 1 is defined as Cov(R, Rm) /2(Rm). Beta measures the volatility of the security, relative to the asset class. The formula can be thinking as predicting a security’s behaviour as a function of beta: CAPM says that if investors know a security’s beta then investors know the value of r that expects it to have.

CAPM decomposes a portfolio’s risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique to an individual asset. It represents the component of an asset’s return which is  with general market moves. According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be  away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio.

The figure below describes portfolio opportunities.

The horizontal axis shows portfolio risk, measured by the standard deviation of portfolio return; the vertical axis shows expected return. The curve abc, which is called the minimum variance frontier, traces combinations of expected return and risk for portfolios of risky assets that minimize return variance at different levels of expected return. The tradeoff between risk and expected return for minimum variance portfolios is apparent. For example, an investor who wants a high expected return, perhaps at point a, must accept high volatility. At point T, the investor can have an intermediate expected return with lower volatility. If there is no risk-free borrowing or lending, only portfolios above b along abc are mean-variance-efficient, since these portfolios also maximize expected return, given their return variances.

The assumptions under CAPM

The CAPM is important as it quantifies and prices systematic risk and expresses it relative to the market portfolio. Thus CAPM provides us with the expected return of any asset or portfolio based on its risk as measured by beta, the risk premium of the market, and the risk free rate. This model is constructed in a hypothetical world based on several rigorous assumptions, but like in any economic model, these simplifications are essential in developing a workable model in a complex and diverse financial world. The assumptions of CAPM and deriving the CAPM through a simple proof, as pointed out in Elton and Gruber are as follows. The first of all assumption to take is there are no transaction costs. This assumption implies frictionless markets; however in reality transaction costs play a varied part in investment decisions. If transaction costs were present, the return from any asset would be a function of whether or not the investor owned it before the decision period. Thus transaction costs play an important role in reality as in most cases as it is not instantaneous shifting one portfolio of assets to another, and also the delivery costs may dissuade an investor even though it might be an included to form an optimum portfolio.

The second assumption behind the CAPM is that assets are infinitely divisible. This implies that an investor can buy any portion of an investment regardless of its size. In reality this is a highly unrealistic assumption as nearly all assets have a unit price.

The third one is the absence of personal income tax. Under this assumption, taxes such as Capital Gains Taxes are absent. Thus the derivation of CAPM is based on a simplified real world based on numerous assumptions.

The fourth assumption is unlimited lending and borrowing at a risk free rate. This implies ...