A portfolio consists of 35 percent of Stock S and 65 percent of Stock T.Stock S is expected to return 15 percent if the economy booms,10 percent if it is normal,and lose 19 percent if it is recessionary.Stock T will return 26 percent in a boom,15 percent in a normal economy,and lose 40 percent in a recession.The probability of a boom is 5 percent and probability of a recession is 10 percent.What is the portfolio standard deviation?

Question

Quizplus · Accepted Answer

E(r)_Boom = (0.35 × 0.15)+ (0.65 × 0.26)= 0.2215 E(r)_Normal = (0.35 × 0.10)+ (0.65 × 0.15)= 0.1325 E(r)_Recession = 0.35(−0.19)+ 0.65(−0.40)= −0.3265 E(r)_Portfolio = 0.05(0.2215)+ 0.85(0.1325)+ 0.10(−0.3265)= 0.09105 σ_Portfolio = {0.05[(0.2215 − 0.09105)²] + 0.85[(0.1325 − 0.09105)²] + 0.10[(−0.3265 − 0.09105)²]}^0.5 = 0.1405,or 14.05%

A Portfolio Consists of 35 Percent of Stock S and 65