Principles of Managerial Finance

CHAPTER 5 Risk and Return 231

TABLE 5.9 Correlation, Return, and Risk for Various

Two-Asset Portfolio Combinations

Correlation

coefficient Range of return Range of risk

1 (perfect positive) Between returns of two assets Between risk of two assets held

held in isolation in isolation

0 (uncorrelated) Between returns of two assets Between risk of most risky asset

held in isolation and an amount less than risk

of least risky asset but greater

than 0

1 (perfect negative) Between returns of two assets Between risk of most risky asset

held in isolation and 0

(^0567890123456789)
Ranges of Return
Correlation
Coefficient Ranges of Risk
+1 (Perfect Positive)
0 (Uncorrelated)

• 1 (Perfect Negative)

kR kS

Portfolio Return (%)

(kp)

+1

0

• 1

σkR σkS

Portfolio Risk (%)

(σkp)

FIGURE 5.7

Possible Correlations
Range of portfolio return (kp)
and risk (kp) for combina-
tions of assets R and
S for various correlation
coefficients

EXAMPLE A firm has calculated the expected return and the risk for each of two assets—R

and S.

Clearly, asset R is a lower-return, lower-risk asset than asset S.

To evaluate possible combinations, the firm considered three possible corre-

lations—perfect positive, uncorrelated, and perfect negative. The results of the

analysis are shown in Figure 5.7, using the ranges of return and risk noted above.

In all cases, the return will range between the 6% return of R and the 8% return

of S. The risk, on the other hand, ranges between the individual risks of R and S

(from 3% to 8%) in the case of perfect positive correlation, from below 3% (the

risk of R) and greater than 0% to 8% (the risk of S) in the uncorrelated case, and

between 0% and 8% (the risk of S) in the perfectly negatively correlated case.

Asset Expected return, k Risk (standard deviation), 

R6% 3%

S8 8