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 21 percent, respectively. Joi, Inc., stock has an annual return mean and standard deviation of 12 percent and 34 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. 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

Stock Prob. Annual return Standard Deviation Raybrooks Co. 50.00% 10.00% 21.00% Joi,Inc 50.00% 12.00% 34.00% Portfolio Expected 1 month Return Stock Prob. Annual return Expected Return Raybrooks Co. 50.00% 10.00% 5.00% Joi,Inc 50.00% 12.00% 6.00% Annual Return 11.00% Monthly Return = 11%/12 0.92% Portfolio Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cov(RA, RB) Portfolio Variance = .50^2 x 21%^2 + .50^2 x 34% + 2 x .50 x .50 x 0 x 10% x12% Annual Portfolio Variance = 0.039925 Monthly Portfolio SD = sqrt(.039925/12) 5.77% Prob(R< 0.92% - 1.96 x 5.77%) = 2.5% Prob(R< -.1039) = 2.5% Smallest expected loss -10.39%

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