Question

Check my work 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 4.5%. The probability distributions of the risky funds are: Expected Return 15% Standard Deviation Stock fund (S) Bond fund (B) 35% 6% 29% The correlation between the fund returns is 0.0517. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return Standard deviation %

Answer 1

Given:

Expected return(Bonds), E(B) = 6%

Expected return(Stocks), E(S) = 15%

Standard deviation of bonds, $\sigma$ (B) = 29%

Standard deviation of stocks, $\sigma$ (S) = 35%

$\rho$ , Correlation = 0.0517

	Return	SD	variance
S	15%	35%	0.1225
B	6%	29%	0.0841

Min Risk Portfolio is given by:

Wrin (s) = 6 6 - Cor (B, 5) +62 – 2 Cor (6,5)

also, Cov (B,S) = $\rho$ * $\sigma$(S) *$\sigma$(B)

Putting in values,

Wmin(S) = [ (0.29)^² - ( 0.0517 * 0.29 * 0.35) ] / [ (0.12)^2 + (0.08)^2 - 2 * ( 0.0517 * 0.29 * 0.35) ]

Wmin(S) = 0.07885245 / 0.1961049

Wmin(S) = 40%

Hence

Wmin(B) = 60%

Formula to be used

Reported quturom postfoto - We # Els & wet. E(B). Std. deviator of Portpales (se) = sqrt (62)

SUMIF fx =(E19*$F$8)+(F19*$F$9) Return SD 15% 6% variance 35% 0.1225 29% 0.0841 0.2066 0.0104951 Check fromula h- 0.1961049 0.00524755 Ws min Wb min 40% 60% 18 % in A (s) % in B 40%] Expected Return Variance 60%!=(E19* $F$8 )+(F19 * $F$9)

Painter SUMIF fx =(B19*$H$8)+(C19*$H$9) н Return SD 15% 6% variance 35% 35% 0.1225 29% 0.0841 0.2066 0.0104951 Check fromula here 0.1961049 0.00524755 0.07885245 Ws min Wb min 40% 60% 18 19 % in A (s) % in B 40% Expected Return Variance Standard Deviation 9.60% =( B19 * $H$8 )+(C19* $H$9) 60%

X fx SUMIE E =SQRT(H19) G A F H Return SD 7 8 S 15% % B 6 variance 35% 0.1225 29% 0.0841 0.2066 0.0104951 Check fromula here 0.1961049 0.00524755 0.07885245 Ws min Wb min 40% 60% 18 19 % in A (s) % in B 40% Expected Return 9.60% Variance Standard Deviation 0.049876 =SQRT(H19) 60%

18 % in A (s) % in B 19 40% Expected Return Variance 9.60% 0.049876 Standard Deviation 0.22 60% Goonil OOOO nT