Question

An investor has $100 to invest and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X while if she invests the entire amount in the second investment her return will by Y. Both X and Y have mean $9 and standard deviation $3.7. The correlation between x and y is 0.3. find the mean return and risk if she invests $31 in the first investment and $69 in the second.

Answer 1

The mean return is $9 and the risk is $3.1.

Explanation:

It is provided that on investing an amount of $100 in the two investments the return will be X and Y.

Given:

`E(X)=E(Y)=\$9\\SD(X)=SD(Y)=\$3.7\\r(X, Y)=0.3`

It is also provided that the investor invested $31 and $69 in the first and second investment respectively.

The return equation will be:

`R=0.31X+0.69Y`

Compute the expected value of return as follows:

`E(R)=E(0.31X+0.69Y)\\=0.31E(X)+0.69E(Y)\\=(0.31* 9)+(0.69*9)\\=\$9`

Thus, the mean return is $9.

Compute the risk as follows:

Risk = SD (0.31X + 0.69Y)

`=√(V(0.31X)+V(0.69Y)+2Cov(0.31X,0.69Y))\\=\sqrt{0.31^(2)V(X)+0.69^(2)V(Y)+(2*031*0.69* r(X,Y)* SD(X)* SD(Y))}\\=\sqrt{(0.31^(2)*3.7^(2))+(0.69^(2)*3.7^(2))+(2*031*0.69* r(X,Y)* SD(X)* SD(Y))}\\=√(9.5903926)\\=3.09\\\approx3.1`Thus, the risk is $3.1.