An investor’s portfolio currently consists of 100% of stocks that have a mean return of 16.5% and an expected variance of 0. 0324. The investor plans to diversify slightly by replacing 20% of her portfolio with U. S. Treasury bills that earn 4.75%. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio ERP σP （）①A. 14.15% 14.40%②B. 10.63% 2.59%③C. 10.63% 14.40%
A. ①
B. ②
C. ③
参考答案：A
解析：
Since Treasury bills (T-bills) are considered risk-free, we know that the standard deviation of this asset and the correlation between T-bills and the other stocks is 0. Thus, we can calculate the portfolio expected return and standard deviation.
ERP=(WT-bills×ERT-bills)+(WStocks×ERStocks)=0.20×0.0475+(1.00-0.20)×0.165=14.15%.
When combining a risk-free asset and a risky asset (or portfolio or risky assets), σ1，2=(w12σ12 +w22σ22+2w1w2σ1σ2ρ1,2)1/2 reduces to: σ1,2=[(WStocks)(σStocks)]1/2=0.80×0.03241/2=14.40%. (Remember to convert variance to standard deviation).