Corporate Finance

Risk and Return 
 65

But the risk of the portfolio is not the sum of individual variances. It would be smaller than that of hold-
ing individual stocks. As illustrated, the investor is assured of return R (the horizontal dotted line)
however volatile individual stocks may be. This happens because of negative correlation between the returns.
The returns from stock exactly counterbalance the returns from the other stock. As the cliché goes, not
putting all eggs in one basket reduces risk. But is it always so? A moment’s reflection tells us that it is not
true. When stock returns are perfectly positively correlated, losses can coincide. So diversification does
not reduce risk in this case.
We established the fact that diversification reduces risk. But you need to know how. To illustrate risk in
a portfolio context, consider two stocks: Bajaj Auto and Bombay Dyeing. Assume that the expected
annual returns are 21.48 percent and 16.56 percent respectively. Suppose you invest 60 percent of your
initial investment in Bajaj Auto and 40 percent in Bombay Dyeing:

Expected portfolio return = (0.6 × 21.48) + (0.4 × 16.56)

= 19.5 percent

The standard deviation of past returns is 18 percent and 27 percent respectively. The portfolio variance is
not the weighted average of individual variances.
Portfolio variance:

σp^2 = X 12 × σ 12 + X 22 *σ 22 + 2X 1 × X 2 × Cov 12 (6)

where
X 1 = Proportion of money invested in stock 1,
X 2 = Proportion of money invested in stock 2,
σ 1 = Standard deviation of returns from stock 1, and
σ 2 = Standard deviation of returns from stock 2.

The portfolio standard deviation is the square root of equation (6). Note the third term in the equation.
Covariance is a measure of the extent to which the two stocks covary. A positive covariance suggests that
the returns (prices) move in the same direction and a negative covariance indicates that prices move in
opposite direction most of the time.

Cov (1, 2) = ρ 12 × σ 1 × σ 2

where ρ 12 is the correlation coefficient, and the three situations suggest themselves.

Situation 1

The stock returns are perfectly positively correlated, i.e., ρ 12 is 1.

σp^2 = (0.6 × 18)^2 + (0.4 × 27)^2 + 2 × 0.6 × 0.4 × 1 × 18 × 27

= 466.56

σp= 21.6 percent