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Introduction
(1.2) by the square root of the number of observations per year. Equation
(1.3) shows the standard deviation for monthly data:
(1.3)
Assuming the returns of two assets are normally distributed, the sum
of risk of owning two assets is determined by the risk of the two assets and
the covariance between the two assets. The standard deviation of a two-as-
set portfolio is shown in equation (1.4):
(1.4)
Suppose an investor can invest in asset A, which has an expected return
of 10 percent, or asset B, which has an expected return of 9 percent. How-
ever, both assets are equally risky, having a standard deviation of return equal
to 15 percent. The correlation between the returns of the two assets is 50 per-
cent. The covariance is calculated from the correlation in equation (1.5):
(1.5)
Table 1.1 is created by applying equation (1.4). The risk reduction is clear
on a graphical view of Table 1.1, as shown in Figure 1.5.
WA |
WB |
rA,B |
δPortfolio |
100% |
0% |
10.00% |
15.00% |
90% |
10% |
9.90% |
14.31% |
.4(1",. |
20% |
9.80% |
13.75% |
70% |
30% |
9.70% |
13.33% |
60% |
40% |
9.60% |
13.08% |
50% |
50% |
9.50% |
12.99% |
40% |
60% |
9.40% |
13.08% |
In",. |
70% |
9.30% |
13.33% |
20% |
80% |
9.20% |
13.75% |
10% |
90% |
9.10% |
14.31% |
0% |
100% |
9.00% |
15.00% |
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