4. 10 points] Consider a portfolio selection problem where the following 2 secur

Question

4. 10 points] Consider a portfolio selection problem where the following 2 securities with uncor- related rates of return are available Stocks 11% 17.5% Bonds 6.2% 10.8% The portfolio with minimum variance that can be constructed, p*, requires a distribution of u stocks-27.58% and u bonds 72.42%, and yields an expected rate of return r p. 7.52%. a) 15 points Find the expected rate of return for a portfolio constructed by allocating 50% of the funds to p, and 50% to a portfolio consisting exclusively of stocks. (b) [5 points] For the portfolio described in part (a), find the rate of return's variance.

Explanation / Answer

Portfolio Expected Return = Ws * Rs + Wb * Rb

Portfolio Variance = (Ws2 * SDs2) + (WB2 * SDB2) + 2 Ws WB SDs SDB* Correlation
As Uncorrealted securities, thus r = 0
Portfolio Variance = (Ws2 * SDs2) + (WB2 * SDB2)

For minimum Variance Portfolio P*,

P* Expected Return = (0.2758 * 0.11) + (0.7242 * 0.062)
P* Expected Return = 7.52%

P* Variance = (0.27582 * 0.1752) + (0.72422 * 0.1082)
P* Variance = 0.845 %

(a)
Portfolio of P* & Stocks --- WP* = 50% & WS = 50%
P* Expected Return, RP* = 7.52%
Stock Expected Return, Rs = 11%

Expected Return = (0.50 * 0.0752) + (0.50 * 0.11)
Expected Return = 9.26%

(b)
Portfolio of P* & Stocks --- WP* = 50% & WS = 50%
P* Variance, SDP*2= 0.845%
Stock Variance, SDs2 = 17.5% 2 = 3.06 %

Portfolio Variance = (0.502 * 0.0306) + (0.502 * 0.00845)
Portfolio Variance = 0.98%

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