Diversification and Asset Allocation 11-7
Is the decision to invest 100 percent in the bond fund a wise one, even for a very
risk-averse investor? The answer is no; in fact, it is a bad decision for any
investor. To see why, Table 11.11 shows expected returns and standard
deviations available from different combinations of the two mutual funds. In
constructing the table, we begin with 100 percent in the stock fund and work our
way down to 100 percent in the bond fund by reducing the percentage in the
stock fund in increments of .05.
Beginning on the first row in Table 11.11, we have 100 percent in the stock fund,
so our expected return is 12 percent, and our standard deviation is 15 percent.
As we begin to move out of the stock fund and into the bond fund, we are not
surprised to see both the expected return and the standard deviation decline.
However, the standard deviation falls only so far and then begins to rise again. In
other words, beyond a point, adding more of the lower risk bond fund actually
increases your risk!
Figure 11.5 plots the various combinations of expected returns and standard
deviations. Note that the returns plot on a smooth curve (in fact, for the
geometrically inclined, it’s a hyperbola—if we were plotting returns versus
variance, the curve would be a parabola).
Now we see clearly why a 100 percent bonds strategy is a poor one. With a 10
percent standard deviation, the bond fund offers an expected return of 6 percent.
However, Table 11.11 shows us that a combination of about 60 percent stocks
and 40 percent bonds has almost the same standard deviation, but a return of
about 9.6 percent. Comparing 9.6 percent to 6 percent, we see that this portfolio
has a return that is fully 60 percent greater (6% × 1.6 = 9.6%) with approximately
the same risk. Our conclusion? Asset allocation matters.
D. More on Correlation and the Risk-Return Trade-Off
Figure 11.5 shows how the shape of the investment opportunity set is a
hyperbola. The shape of this curve changes as the correlation changes. Figure
11.6 shows how the shape of this curve varies. The extremes occur at Corr =
+1.0 and Corr = -1.0. At a correlation of +1.0 the portfolios lie on a straight line
between the two stocks. At a correlation of -1.0 the portfolios lie on two straight
lines; one connecting Stock A to a return with zero standard deviation (Y axis),
and another connecting Stock B to the same point with zero standard deviation
(Y axis). This shows how two securities with a correlation of -1.0 can be
combined to give a portfolio with zero risk. To calculate the weight of asset A in
the minimum variance portfolio:
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