Principles of Managerial Finance

228 PART 2 Important Financial Concepts

perfectly positively correlated
Describes two positively
correlated series that have a
correlation coefficientof1.

perfectly negatively correlated
Describes two negatively
correlatedseries that have a
correlation coefficientof 1.

uncorrelated
Describes two series that lack
any interaction and therefore
have a correlation coefficient
close to zero.

Perfectly Positively Correlated Perfectly Negatively Correlated

Return Return

N

M M

N

Time Time

FIGURE 5.5

Correlations
The correlation between
series M and series N

Return Return Return

Asset F Asset G

Portfolio of

Assets F and G

Time Time Time

k k

FIGURE 5.6

Diversification
Combining negatively
correlated assets to diversify
risk

correlation coefficient
A measure of the degree of
correlation between two series.

The degree of correlation is measured by the correlation coefficient,which

ranges from1 for perfectly positively correlatedseries to 1 for perfectly nega-

tively correlatedseries. These two extremes are depicted for series M and N in

Figure 5.5. The perfectly positively correlated series move exactly together; the per-

fectly negatively correlated series move in exactly opposite directions.

Diversification

The concept of correlation is essential to developing an efficient portfolio. To

reduce overall risk, it is best to combine, or add to the portfolio, assets that have

a negative (or a low positive) correlation. Combining negatively correlated assets

can reduce the overall variability of returns. Figure 5.6 shows that a portfolio

containing the negatively correlated assets F and G, both of which have the same

expected return, k,also has that same return kbut has less risk (variability) than

either of the individual assets. Even if assets are not negatively correlated, the

lower the positive correlation between them, the lower the resulting risk.

Some assets areuncorrelated—that is, there is no interaction between their

returns. Combining uncorrelated assets can reduce risk, not so effectively as com-

bining negatively correlated assets, but more effectively than combining positively

correlated assets. The correlation coefficient for uncorrelated assets is close to zero

and acts as the midpoint between perfect positive and perfect negative correlation.