Question

The following information is available for two stocks: Stock Shares Price per share Expected Return Standard Deviation A 500 $40 14% 18% B 400 $25 21% 22% You are fully invested in the two stocks. The correlation coefficient between the two stock returns is .80

a. Compute the weights of the two stocks in your portfolio.

b. Compute the portfolio expected return.

c. Compute the portfolio standard deviation.

d. You consider selling 250 shares of stock A, and buy with the proceeds shares of stock C. Share C expected return is 14%, 20% standard deviation and 0.10 correlation with A and with B. Will you do that transaction? (For this you will need the three stock portfolio variance formula).

Answer #1

1.

Weight of Stock A=500*14/(500*14+400*25)=0.411764706

Weight of Stock B=400*25/(500*14+400*25)=0.588235294

2.

=0.411764706*14%+(1-0.411764706)*21%=18.1176%

3.

=sqrt((0.411764706*18%)^2+((1-0.411764706)*22%)^2+2*0.411764706*(1-0.411764706)*18%*22%*0.80)=19.3875%

4.

=sqrt()

4.

Weight of Stock A=250*14/(250*14+400*25+250*14)=0.205882353

Weight of Stock B=400*25/(250*14+400*25+250*14)=0.588235294

Weight of Stock C=250*14/(250*14+400*25+250*14)=0.205882353

Standard Deviation=sqrt((0.205882353*18%)^2+(0.588235294*22%)^2+(0.205882353*20%)^2+2*0.205882353*0.588235294*18%*22%*0.80+2*0.205882353*0.205882353*18%*20%*0.1+2*0.205882353*0.588235294*22%*20%*0.1)=16.9884%

Expected return=0.205882353*14%+0.588235294*21%+0.205882353*14%=18.1176%

Yes we will consider the transaction as for the same return we are getting lower standard deviation

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