Raybrooks Co. stock has an annual return mean and standard deviation of 10 perce
ID: 2799335 • Letter: R
Question
Raybrooks Co. stock has an annual return mean and standard deviation of 10 percent and 22 percent, respectively. Joi, Inc., stock has an annual return mean and standard deviation of 16 percent and 32 percent, respectively. Your portfolio allocates equal funds to the Raybrooks Co.and Joi, Inc., stocks. The return correlation between Raybrooks Co. and Joi, Inc., is 0.5. What is the smallest expected loss, in percentages, for your portfolio in the coming month with a probability of 2.5 percent? (Note: Use 1.96 as the multiple in your probability statement.)
Explanation / Answer
Solution.
To find smallest expected loss of the portolio when the portfolio allocates equal funds to both Raybrooks Co. and Joi Inc. stock when the correlation between Raybrooks Co. and Joi Inc. is +0.5 :
standard deviation of portfolio = square root of (sd1*w1)2+ (sd2*w2)2+2*sd1*sd2*w1*w2*correlation
= square root of (22*0.5)2+(32*0.5)2 + 2*22*32*0.5*0.5*0.5
= 23.52%
return of the portfolio = R1*W1 + R2*W2
= 10*0.5 + 16*0.5
= 13 %
smallest expected loss = portfolio return - 1.96* Standard deviation of portfolio
= 13-1.96*23.52
= -33.1%
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