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 4.4%. The probability distributions of the risky funds are: Standard Deviation Expected Return 14% - 5% Stock fund (S) Bond fund (B) 34% 28% The correlation between the fund returns is 0.0214. 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 olo Standard deviation Standard deviation

Answer 1

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' v . a 1x 9 ENG 00:17 31-03-2020 ... o X : for AT1 |_ AR X A S AT AU AV AW AX AY AZ BA BB BC BD BE - 1 nm 00 Minimum variance Portfolio (66) ² (2) (6A) (08) GA) 2- arom ) 11 12 SD O(A) O (B) 34.0000 28.0000 VARIANCE (0 (A))^2 (0 (B))^2 1156.00 784.00 13 14 0.0214 15 W(A) = [=(AX13) - ((AX14)*(AU12)*(AU13))] [=(AX12) + (AX13) - (2*(AX14)*(AU12)*(AU13))] (784 - (0.0214*34*28)) (784 + 1156 - (2*0.0214*34*28)) 763.6272 = 0.4021 1899.2544 20 WEIGHTS W(A)= W(B) = 0.4021 0.5979 40.21% 59.79% 23 24 R(A) = 14.00% FA001 T ... MIN VAR PORT BEST CAL Sheet9 BINOMIAL 2 TIME SINKING AMORTIZA greta Sheet2 VC | JORDAN INSURANCE Sheet1 Sheet3 Sheet4 ... • : I

+ Ø e - 9 ' W v . a 1x 9 ENG E 00:17 31-03-2020 ... o X AT41 : X fix AS AT AU AV AW AX AY AZ BA BB BC BD BE A 20 WEIGHTS W(A)= W(B) = 0.4021 0.5979 40.21% 59.79% 21 22 23 24 R(A) = R(B) = 14.00% 5.00% 25 26 ANSWER Rp = EXPECTED RETURN = W(A)*R(A) + W(B)*R(B ) = (0.4021)*(14%) + (0.5979) *(5%) = 8.62% 28 34 SDA SDB 28 0.0214 31 32 33 34 PORTFOLIO VARIANCE = (W(A))^2* (SD(A))^2 + (W(B))^2*(SD(B))^2 + 2 W(A)*W(B)* SD(A)*SD(B)* r PORTFOLIO VARIANCE = [(0.4021)^2*(34)^2 + (0.5979)^2* (28)^2 + 2*(0.4021)*(0.5979)*(34)*(28)*(0.0214)] PORTFOLIO VARIANCE = 476.97083 STANDARD DEVIATION = 21.8397 % [SQRT(variance)] 35 36 SDp = 37 38 ANSWER SDp = STANDARD DEVIATION = 21.84% 39 ... MIN VAR PORT BEST CAL Sheet9 BINOMIAL 2 TIME SINKING AMORTIZA greta Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 ... 7