Question

Percival Hygiene has $10 million invested in long-term corporate bonds. This 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 & Poor's 500 Index. The index has an expected return of 14%, and its standard deviation is 16%. The Treasury bill yield is 6%. 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 measured as the standard deviation?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.

Answer 1

Step-by-step explanation:

a)We find the portfolio weights first. For a two security portfolio

`sP^2 = x_1^2s_1^2 + 2x_1x_2s_1s_2r_1_2 + x_2^2s_2^2`

`(0.10)^2 = 0 + 0 + x_2^2(0.16)^2`

x2 = 0.625 and 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)

The expected return is:

rp = x1r1 + x2r2

rp = (0.5 *´ 0.09) + (0.5 ´* 0.14)

= 0.115 = 11.5%

`sP^2 = x_1^2s_1^2 + 2x_1x_2s_1s_2r_1_2 + x_2^2s_2^2`

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%.