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(^66) Financial Management
that constitute the portfolio, the weights being the proportions of investments in respective
securities.
Measurement of Beta
The systematic relationship between the return on the security or a portfolio and the
return on the market can be described using a simple linear regression, identifying the
return on a security or portfolio as the dependent variable Kj and the return on market
portfolio as the independent variable Km, in the single-index model or market model
developed by William Sharpe.
This can be expressed as:
Kj=aj+bjKm+ej
The Beta parameter bj in the model represents the slope of the above regression
relationship and measures the responsiveness of the security or portfolio to the general
market and indicates how extensively the return of the portfolio or security will vary
with changes in the market return. The Beta coefficient of a security is defined as the
ratio of the security's covariance of return with the market to the variance of the
market. This can be calculated as follows:
Var (K )
Cov (KK )
m
j m
bj=
The Alpha parameter "a" is the intercept of the fitted line and indicates what the return
of the security or portfolio will be when the market return is zero. For example, a
security with an a of +2 per cent would earn 2 percent even when the market return
was zero and would earn an additional 2 percent at all levels of market return. The
converse is true if a security has a of -2 percent. The positive a thus represents a sort
of bonus return and would be a highly desirable aspect of a portfolio or security while a
negative a represents a penalty to the investor.
The third term ej is the unexpected return resulting from influences not identified by
the model. Frequently referred to as random or residual return, it may take on any value
but is generally found to average out to zero.
The Capital Asset Pricing Model (CAPM)
The CAPM developed by William F Sharpe, John Linter and Jan Mossin is one of the
major developments in financial theory. The CAPM establishes a linear relationship
between the required rate of return of a security and its systematic or undiversifiable
risk or beta.
This relationship as defined by CAPM can be used to value an equity share.