82 Corporate Finance
where
a = intercept from the regression, and
b = slope = beta of the stock.
The intercept of the regression provides a simple measure of performance during the period of the regres-
sion relative to CAPM.
Rj = Rf + β(RM – Rf)
= Rf (1 – β) + βRm (B)Thus, a comparison of the intercept (a) to Rf (1 – β) provides a measure of performance relative to CAPM
(Jensen’s Alpha).
Ifa > Rf (1 – β), stock did better than expected during the period
a = Rf (1 – β), stock did as well as expected
a < Rf (1 – β), stock did worse than expected.
Jensen’s alpha, thus, measures the difference between the actual returns on an asset and the return expected
from it during the period.
IN CONCLUSION
The CAPM is a forward-looking model although past returns and betas are taken as proxies for future. It
is supposed to give us expected return. In this chapter different asset pricing theories were outlined. The
simple CAPM is intuitive and easy to use. But it might not be the best. An analyst has the liberty to construct
his/her framework for establishing relationship between risk and return. A riskless asset is one whose actual
return equals expected return, i.e., variance is zero. Its covariance, by definition, with other assets is also zero.
No asset is truly risk-free in reality. Since government securities are default risk-free, we take the T-Bond
rate as proxy for risk-free rate. Variance is a measure of total risk. Total risk can be split into two components—
systematic risk and unsystematic risk. The portion of risk which cannot be diversified is called systematic
risk or non diversifiable risk and that which can be diversified is called unsystematic risk.
The portfolio of all risky assets in the economy is called market portfolio. The systematic risk of an asset
is the risk it adds to the market portfolio. Beta is the standard measure of systematic risk. It measures the
sensitivity of stock returns to changes in market returns. Since the market portfolio is unobservable, a broad
stock market index such as the BSE Sensex is used as a proxy. By definition, the beta of the market is 1.0.
Stocks with betas greater than 1 are considered aggressive; those with betas less than 1.0 are considered
defensive.
The risk of a well-diversified portfolio mainly reflects the market risk of individual securities because the
unsystematic risk is diversified. Portfolio beta is simply the weighted average of individual stock betas.
Investing partly in a risk-free asset reduces risk for the same level of return as demonstrated by the
Capital Market Line.