11. Percival Hygiene has $10 million invested in long-term corporate bonds. This
ID: 2673002 • Letter: 1
Question
11. Percival Hygiene has $10 million invested in long-term corporate bonds. This bondportfolios expected annual rate of return is 9 percent, and the annual standard deviation
is 10 percent.
Amanda Reckonwith, Percivals financial adviser, recommends that Percival consider
investing in an index fund which closely tracks the Standard and Poors 500 index.
The index has an expected return of 14 percent, and its standard deviation is 16 percent.
a. Suppose Percival puts all his money in a combination of the index fund and Treasury
bills. Can he thereby improve his expected rate of return without changing the
risk of his portfolio? The Treasury bill yield is 6 percent.
b. Could Percival do even better by investing equal amounts in the corporate bond
portfolio and the index fund? The correlation between the bond portfolio and the index
fund is _.1.
Explanation / Answer
We find the portfolio weights first. For a two security portfolio
sP2 = x12s12 + 2x1x2s1s2r12 + x22s22
(0.10)2 = 0 + 0 + x22(0.16)2
x2 = 0.625 Þ x1 = 0.375
Then
rp = x1r1 + x2r2
rp = (0.375 ´ 0.06) + (0.625 ´ 0.14)
= 0.11
= 11.0%
Hence, he can improve the expected rate of return without any change in the risk of
the portfolio.
b. Could Percival do even better by investing equal amounts in the corporate bond
portfolio and the index fund? The correlation between the bond portfolio and the index
fund is _.1.
Solution:
The expected return is:
rp = x1r1 + x2r2
rp = (0.5 ´ 0.09) + (0.5 ´ 0.14) = 0.115 = 11.5%
sP2 = x12s12 + 2x1x2s1s2r12 + x22s22
sP2 = (0.5)2(0.10)2 + 2(0.5)(0.5)(0.10)(0.16)(0.10) + (0.5)2(0.16)2
sP2 = 0.0097
sP = 0.985 = 9.85%
Hence, he can never perform better by investing equal amount in bond portfolio and index fund. The expected return increases to 11.5% and standard deviation decreases to 9.85%.
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