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) 17 % 35 % Bond fund (B) 14 18 The correlation between the fund returns is 0.09. a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) a-2. What is the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Answer 1

		Expected return		Standard deviation
Stock fund (S)		17	%	35	%
Bond fund (B)		14	%	18	%
Correlation between funds				0.09
Covariance formula = Correlation between funds * Std. Dev. Of S * Std. Dev. Of B
		0.09*35*18
		56.7
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
			(18)^2   - 56.70
			________________
			(35)^2 + (18)^2 - ( 56.70)
0.186194
So, Weight of Minimum portfolio variance
Bond fund B =			0.1862
weight of Stock fund S =			0.8138
(1-0.173913)
So, Portfolio invested in stock fund S is 0.8138 and Bond fund B is 0.1862
Calculation of Expected return of Minimum Variance portfolio
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)
	(0.8138* 17) + (0.1862*14))
	16.44142
So, expected return of portfolio is 16.4414%
Calculation of standard deviation of Minimum Variance portfolio
Standard deviation formula
(σp) =	√ ( (wS * σS ) ^2 + (wB * σB ) ^2 + 2 * wB* wS*σB *σS* rSB )
	28.97773
So, Standard deviation of portfolio is 28.9777%