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 correlation between the funds returns us 0.25. The optimal risky portfolio for stock fund is 40.94% of the risky portfolio. The probability distributions of the risky funds are: 1. what are the expected return and standard deviation of the optimal risky portfolio? = = Expected Return Stock fund (S) Bond fund (B) The mean and standard deviation of the optimal risky portfolio are: E (r) WB x E (TB) Ws x E (rs) (0.4094 x 11) + (0.5906 17) 14.54% = Standard Deviatio 17% 11% n 32% 23% SD (r) = [W20 + W20 + 2WSWB Cov (rs, B) ] /2 [ (0.59062 x 322) + (0.40942 232) + (2x 0.5906 0.4094 184.0) ] 1/2 = 23.13%. 2. What are the expected return and standard deviation of whole portfolio is the expected return for the whole portfolio must be 10%? 10% = Y*14.54%+(1-Y)*5.5%, Y=?, Standard Deviation: Y*23.13% =?

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 correlation between the funds returns us 0.25 . The optimal risky portfolio for stock fund is 40.94% of the risky portfolio. The probability distributions of the risky funds are: 1. what are the expected return and standard deviation of the optimal risky portfolio? The mean and standard deviation of the optimal risky portfolio are: E(r)=wBE(rB)wsE(rs)=(0.409411)+(0.590617)=14.548SD(r)=[ws2s2+ws2B2+2wswCov(rs,rB)]12=[(0.59062322)+(0.40942232)+(20.59060.4094184.0)]1/2=23.135. 2. What are the expected return and standard deviation of whole portfolio is the expected return for the whole portfolio must be 10% ? 10%=Y14.54%+(1Y)5.5%,Y=?. Standard Deviation: Y23.13%=