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 rate of 8%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		23	%		29	%
Bond fund (B)		14			17

The correlation between the fund returns is 0.12.

  

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

	Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

Answer 1

		Expected return		Standard deviation
Stock fund (S)		23	%	29	%
Bond fund (B)		14	%	17	%
Correlation between funds				0.12
Covariance formula = Correlation between funds * Std. Dev. Of S * Std. Dev. Of B
		0.12*29*17
		59.16
Here Y = Bond fund B, X = Stock fund S
From Minimum Variance portfolio formula, weight of Y (Bond fund B) is calculated, where risk is minimum.
Formula for Minimum Variance Portfolio (weight Y) =     σ2y - CoV xy
(Optimal risky portfolio weight)					________________
					σ2x + σ2y - 2 Cov xy
			(17)^2   - 59.16
			________________
			(29)^2 + (17)^2 - ( 59.16)
0.227186
So, Weight of Minimum portfolio variance
Bond fund B =			0.227186
weight of Stock fund S =			0.772814
(1-0.173913)
So, Portfolio invested in stock fund S is 0.772814 and Bond fund B is 0.227186.
Calculation of Expected return of Optimal risky portfoli0
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)
	(0.772814* 23) + (0.227186*17))
	20.95532
So, expected retun of portolio is 20.96%
Calculation of standard deviation of Optmial risky portfolio
Standard deviation formula
(σp) =	√ ( (wS * σS ) ^2 + (wB * σB ) ^2 + 2 * wB* wS*σB *σS* rSB )
	23.19417
So, Standard deviaiton of portfolio is 23.19%