Raybrooks Co. stock has an annual return mean and standard deviation of 10 perce

Question

Raybrooks Co. stock has an annual return mean and standard deviation of 10 percent and 27 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 0.4. 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

R1 Mean return of Paybrooks Stock 10 percent R2 MeanReturn ofJoi Inc stock 16 percent S1 Standard Deviation of Paybrooks Stock 27 percent S2 Standad Deviation ofJoi Inc stock 32 percent w1 Weight of Paybrooks Stock in the portfolio 0.5 w2 Weight ofJoi Inc stock in the portfolio 0.5 Cor(1,2) Correlation between Paybrooks and Joi inc 0.4 Cov(1,2)=Cor(1,2)*S1*S2 Covariance between Paybrooks and Joistock 345.6 Rp=w1*R1+w2*R2 Mean return of the Portfolio 13 Vp Variance of the portfolio Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2w1*w2*Cov(1,2) Vp Variance of the portfolio=(0.5^2)*(27^2)+(0.5^2)*(32^2)+2*0.5*0.5*345.6 611.05 Portfolio Standard deviation=Square root of Variance Sp=Square root(Vp) Portfolio Standard deviation=(611.05^(1/2)) 24.72 percent Z value=(Portfolio return-13)/24.72 From Standard Normal Table , for N(d)=0.0250 Z value=-1.96 Hence for 2.5% probability, Z=-1.96 (Portfolio Return -13)/24.72=-1.96 13-PortfolioReturn=1.96*24.72= 48.45 percent Portfolio Return=13-48.45= -35.45 percent Smallest expected loss inpercentage with probability 2.5% 35.45 percent

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