Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:

	Expected Return		Standard Deviation
Stock fund (S)	15	%	32	%
Bond fund (B)	9	%	23	%

The correlation between the fund returns is 0.15.

a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%?

b. Calculate the standard deviation of the portfolio which yields an expected return of 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Part A:

Portfolio Ret = weighted Avg Ret of securities in that portfolio.

Let y be the weight of investment in Stock fund.

1 - y be the weight of investment in Bond fund.

Stock	Weight	Ret	WTd Ret
Stock fund	y	0.1500	0.15y
Bond fund	1 - y	0.0900	0.09 - 0.09y
Portfolio Ret Return		0.0700	0.09 + 0.06y

Given portfolio Ret = 0.12

Thus 0.09 + 0.06y = 0.12

0.06y = 0.03

y = 0.03 / 0.06

= 0.5

Weight in stock fund = 0.5

weight in Bond fund = 0.5

Part B:

Portfolio SD:

It is nothing but volataility of Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual Asset's SD in portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at propoer weights.
If correlation > -1 but <1, We can reduce the SD, n=but it will not become Zero.

Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B

Assume A = Stock fund

B = Bond fund

Particulars	Amount
Weight in A	0.5000
Weight in B	0.5000
SD of A	32.00%
SD of B	23.00%
r(A,B)	0.15

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.5*0.32)^2)+((0.5*0.23)^2)+2*(0.5*0.32)*(0.5*0.23)*0.15]
=SQRT[((0.16)^2)+((0.115)^2)+2*(0.16)*(0.115)*0.15]
=SQRT[0.0443]
= 0.2106
= I.e 21.06 %

Pls comment, if any further assistance is required,