Corporate Finance

Risk and Return 
 71

securities). So the investor can take any position on the line Rf – M (Exhibit 3.13). Note that the line is
tangential to the efficient frontier meaning that the portfolio M gives the highest return per unit of risk.

Exhibit 3.13 Capital market line

E(r)

Variance

M

Rf

B

All the points on the line RfM are combinations of investment in a risk-free asset and M. You might be
wondering how or why this risk-free asset is significant. Going back to the case of the two-stock portfolio:

σp^2 = X 12 * σ 12 + X 22 * σ 22 + 2X 1 * X 2 * Cov 12 (7)

where
X 1 = Proportion of money invested in risk-free asset,
X 2 = Proportion of money invested in portfolio M,
σ 1 = Standard deviation of returns from risk-free asset, and
σ 2 = Standard deviation of returns from M.

By definition, the variance of returns from a riskless asset is 0, and the returns do not covary with the re-
turns from other assets. So the first and the last terms become 0:

σp^2 = X 22 × σ 22

= (1 – X 1 )^2 × σ 22

As is evident, by investing partly in a risk-free asset, the investor can reduce the risk further. Given
a chance to invest in a riskless asset, an investor would always hold a combination of Rf and M and not
an efficient portfolio alone. The combinations yield higher returns for the same level of risk (Exhibit 3.13).
In short, the efficient frontier has been transformed into a straight line.
What could be the composition of M? If the investor has superior information vis-à-vis other investors
in the market, then M is that portfolio which offers superior returns for its risk level (that is, the portfolio
is undervalued). Otherwise, it is that portfolio which any other investor can hold. The logical limit is to
include all risky assets in the economy. The portfolio of all risky assets is called the market portfolio. Since
the market portfolio is unobservable, a market index such as the BSE 30 index is taken as a proxy. The line
joining Rf and M is called Capital Market Line.