Corporate Finance

72
Corporate Finance

Deriving the Capital Market Line

The expected return of a portfolio consisting of the risk-free asset and M:

Rp= X 1 Rf + X 2 E(RM)(8)
That is
Rp= (1 – X 2 )Rf + X 2 E(RM)
= Rf + X 2 E (RM) – Rf

We know that

σp^2 = X 22 * σM^2
Or, σp= X 2 × σM
i.e., X 2 = σp / σM

Inserting these values in equation (9):

= Rf + σp / σM [E(RM) – Rf]

This is the equation for the CML. The slope of the line is given by:

[E(RM) – Rf] / σM

This is the market risk premium. Earlier, it was pointed out that the total risk consists of two components:
systematic and unsystematic risk. Unsystematic risk can be diversified away by holding a portfolio of
securities; what remains is the systematic risk. As well-diversified investors are exposed to only systematic
risk, the relevant risk in a Capital Asset Pricing Model (CAPM) universe is the systematic risk. Beta (β) is
the standard measure of systematic risk. It measures the tendency of the returns of a security to move in line
with the stock market as a whole. Beta gauges the sensitivity of security returns vis-à-vis market returns. A
stock with a beta of 1.0 rises and falls at the same percentage as the market. Stocks with a beta greater than
1.0 (aggressive stocks) tend to rise and fall by a greater percentage than the market. That is they are very
sensitive to market swings. Stocks with beta less than 1.0 (defensive stocks) are less sensitive to market
swings. The market, by definition, has a beta of 1.0.

Beta = [Cov Rj, Rm]/σM^2

Estimates of beta for the Sensex stocks are presented in Exhibit 3.14.

Security Market Line

The CAPM establishes the relationship between risk and expected return. In a CAPM world, securities are
priced such that

Exhibit 3.14 Beta estimates for some Sensex stocks

Company Beta

ACC 1.31
BSES 0.69

Exhibit 3.14 contd.