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You plan to invest in Stock X, Stock Y, or some combination of the two
You plan to invest in Stock X, Stock Y, or some combination of the two. The expected return for X is 10 percent and sX = 5 percent. The expected return for Y is 12 percent and sY = 6 percent. The correlation coefficient, rXY is 0.75.
Calculate rp and sp for 100 percent, 75 percent, 50 percent, 25 percent, and 0 percent in Stock X.
Expert Solution
Expected Return of a 2 stock portfolio is a weighted average of individual returns. It is calculated as (w1*r1)+(w2*r2)
Standard deviation of a 2 stock portfolio is calculated as sqrt((w1^2*sd1^2)+(w2^2*sd2^2)+(2*w1*w2*c*sd1*sd2)); where w is weight of the stock, sd is standard deviation of the stock and c is the correlation between the stocks.
100% in Stock X:
rp= (100%*10%)+(0%*12%)= 10%
sp= ((100%^2*5%^2)+(0%^2*6%^2)+(2*100%*0%*0.75*5%*6%)= 5%
75% in Stock X:
rp= (75%*10%)+(25%*12%)= 10.5%
sp= ((75%^2*5%^2)+(25%^2*6%^2)+(2*75%*25%*0.75*5%*6%)= 4.97%
50% in Stock X:
rp= (50%*10%)+(50%*12%)= 11%
sp= ((50%^2*5%^2)+(50%^2*6%^2)+(2*50%*50%*0.75*5%*6%)= 5.15%
25% in Stock X:
rp= (25%*10%)+(75%*12%)= 11.5%
sp= ((25%^2*5%^2)+(75%^2*6%^2)+(2*25%*75%*0.75*5%*6%)= 5.5%
0% in Stock X:
rp= (0%*10%)+(100%*12%)= 12%
sp= ((0%^2*5%^2)+(100%^2*6%^2)+(2*0%*100%*0.75*5%*6%)= 6%
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