230 PART 2 Important Financial Concepts
- Identical return streams are used in this example to permit clear illustration of the concepts, but it is notneces-
sary for return streams to be identical for them to be perfectly positively correlated. Any return streams that move
(i.e., vary) exactly together—regardless of the relative magnitude of the returns—are perfectly positively correlated. - For illustrative purposes it has been assumed that each of the assets—X, Y, and Z—can be divided up and com-
bined with other assets to create portfolios. This assumption is made only to permit clear illustration of the concepts.
The assets are not actually divisible.
Hint Remember, low
correlation between two series
of numbers is less positive and
more negative—indicating
greater dissimilarity of behavior
of the two series.
deviation of 3.16%. The assets therefore have equal return and equal risk. The
return patterns of assets X and Y are perfectly negatively correlated. They move
in exactly opposite directions over time. The returns of assets X and Z are per-
fectly positively correlated. They move in precisely the same direction. (Note:The
returns for X and Z are identical.)^14Portfolio XY Portfolio XY (shown in Table 5.8) is created by combining equal
portions of assets X and Y, the perfectly negatively correlated assets.^15 (Calcula-
tion of portfolio XY’s annual expected returns, their expected value, and the
standard deviation of expected portfolio returns was demonstrated in Table 5.7.)
The risk in this portfolio, as reflected by its standard deviation, is reduced to 0%,
whereas the expected return remains at 12%. Thus the combination results in the
complete elimination of risk. Whenever assets are perfectly negatively correlated,
an optimal combination (similar to the 50–50 mix in the case of assets X and Y)
exists for which the resulting standard deviation will equal 0.Portfolio XZ Portfolio XZ (shown in Table 5.8) is created by combining equal
portions of assets X and Z, the perfectly positively correlated assets. The risk in
this portfolio, as reflected by its standard deviation, is unaffected by this combi-
nation. Risk remains at 3.16%, and the expected return value remains at 12%.
Because assets X and Z have the same standard deviation, the minimum and
maximum standard deviations are the same (3.16%).Correlation, Diversification,
Risk, and Return
In general, the lower the correlation between asset returns, the greater the poten-
tial diversification of risk. (This should be clear from the behaviors illustrated in
Table 5.8.) For each pair of assets, there is a combination that will result in the
lowest risk (standard deviation) possible. How much risk can be reduced by this
combination depends on the degree of correlation. Many potential combinations
(assuming divisibility) could be made, but only one combination of the infinite
number of possibilities will minimize risk.
Three possible correlations—perfect positive, uncorrelated, and perfect nega-
tive—illustrate the effect of correlation on the diversification of risk and return.
Table 5.9 summarizes the impact of correlation on the range of return and risk
for various two-asset portfolio combinations. The table shows that as we move
from perfect positive correlation to uncorrelated assets to perfect negative corre-
lation, the ability to reduce risk is improved. Note that in no case will a portfolio
of assets be riskier than the riskiest asset included in the portfolio.