Page 275 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes 11.1 Introduction to CAPM

William F. Sharpe and John Linter developed the Capital Asset Pricing Model (CAPM). The
model is based on the portfolio theory developed by Harry Markowitz. The model emphasises
the risk factor in portfolio theory is a combination of two risks, systematic risk and unsystematic
risk. The model suggests that a security’s return is directly related to its systematic risk, which
cannot be neutralised through diversification. The combination of both types of risks stated
above provides the total risk. The total variance of returns is equal to market related variance
plus company’s specific variance. CAPM explains the behaviour of security prices and provides
a mechanism whereby investors could assess the impact of a proposed security investment on
the overall portfolio risk and return. CAPM suggests that the prices of securities are determined
in such a way that the risk premium or excess returns are proportional to systematic risk, which
is indicated by the beta coefficient. The model is used for analysing the risk-return implications
of holding securities. CAPM refers to the manner in which securities are valued in line with
their anticipated risks and returns. A risk-averse investor prefers to invest in risk-free securities.
For a small investor having few securities in his portfolio, the risk is greater. To reduce the
unsystematic risk, he must build up well-diversified securities in his portfolio.
The asset return depends on the amount for the asset today. The price paid must ensure that the
market portfolio’s risk/return characteristics improve when the asset is added to it. The CAPM
is a model, which derives the theoretical required return (i.e. discount rate) for an asset in a
market, given the risk-free rate available to investors and the risk of the market as a whole.

The CAPM is usually expressed:
E(R) = R + (E(R ) – R )
i f i m f

Notes (Beta), is the measure of asset sensitivity to a movement in the overall market;
Beta is usually found via regression on historical data. Betas exceeding one signify more
than average “riskiness”; betas below one indicate lower than average.

E(R ) – (R ) is the market premium, the historically observed excess return of the market over
m f
the risk-free rate.
Once the expected return, E(r ), is calculated using CAPM, the future cash flows of the asset can be
i
discounted to their present value using this rate to establish the correct price for the asset. (Here
again, the theory accepts in its assumptions that a parameter based on past data can be combined with a
future expectation.)

A more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive
stocks will have lower betas and be discounted at a lower rate. In theory, an asset is correctly
priced when its observed price is the same as its value calculated using the CAPM derived
discount rate. If the observed price is higher than the valuation, then the asset is overvalued; it
is undervalued for a too low price.
1. Mathematically:
(a) The incremental impact on risk and return when an additional risky asset, a, is
added to the market portfolio, m, follows from the formulae for a two asset portfolio.
These results are used to derive the asset appropriate discount rate.
Risk = ( w 2 m 2 m [w 2 a 2 a 2w w a am a m ])
m
Hence, risk added to portfolio = [w 2 a 2 a 2w m am a m ]

270 LOVELY PROFESSIONAL UNIVERSITY