Percival Hygiene has $10 million invested in long-term corporate bonds. The bond

Question

Percival Hygiene has $10 million invested in long-term corporate bonds. The bond portfolio's expected annual rate of return is 9%, and the annual standard deviation is 10%. Amanda Reckonwith, Percival's financial adviser, recommends that Percival consider investing in an index fund that closely tracks the Standard and Poor's 500 index. The index has an expected return of 14%, and its standard deviation is 16%. a. Suppose Percival shifts $4 million from his bond portfolio into the index fund. What would be his expected return and standard deviation? The correlation between the bond portfolio and bond fund is +0.3. b. Suppose, instead, that Percival shifts all of his money into a combination of the index fund and Treasury bills. How much would he invest in Treasury bills and how much in the index fund to match the expected return of the combination of the bond portfolio and index fund described in part a? What is the standard deviation of this portfolio? The Treasury bill yield is 6%. c. Which of these two portfolios, a and b, would you recommend? Why?

Explanation / Answer

a) Expected return = weighted average of the returns of the component portolios.

= 9*0.6 + 14*0.4 = 5.4 + 5.6 = 11.00%

Standard deviation of the portfolio:

(w1^2*sd1^2 + w2^2*sd2^2+2*w1*w2*sd1*sd2*cor12)^1/2

(0.6^2*0.1^2+0.4^2*0.16^2+2*.6*.4*.1*.16*.3) = (0.0036 + 0.004096 + 0.002304 = 0.01^2 = 0.10 = 10%

b) expected return of the 14% and std dev: 16%, treasury bills with yield of 6%.

yield required = 11%.

11 = 14*w + 6*(1-w) = 14w+6-6w; 11 - 6 = 8w; w = 5/8 = 0.625.

So investment in the index fund should be 62.5% and in the treasury bill 37.5%

The expected return would be 14*0.625 + 6*0.375 = 11%.

The portfolio standard deviation will be w1 * sd1 (as the sd of the treasury bill is zero, which shortens the formula)

=16*0.625 = 10%.

C) Both the portfolios have the same return of 11% and standard deviation of 10%. Hence, both are equally acceptable. There is nothing to choose between them.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.