Please show all steps! Thanks! The expected returns and variances (of returns) f

Question

Please show all steps! Thanks!

The expected returns and variances (of returns) for three assets are: The correlation between the returns is rho 12 = 0.20. Calculate the portfolio expected return and variance for the weights (0.2,0.8); that is, invest 0.2 in asset 1, and invest 0.8 in asset 2. Calculate the portfolio expected return and variance for the weights (0.5,0.5). Give the portfolio (consisting of the above two assets) which has an average return of 0.12. What is the variance of that portfolio? Give a portfolio (consisting of the above two assets) which has a variance of 0.16.

Explanation / Answer

12=0.04 --> 1=0.2    22=0.09 ---> 2=0.3

(a) Expected return = w1r1+w2r2=0.2*0.1+0.8*0.15 = 0.14 = 14%
Variance = w1212+w2222+2w1w21212 = 0.22(0.04)+0.82(0.09)+2(0.2)(0.8)(0.2)(0.2)(0.3)

Variance= 0.06304

(b) Expected return = w1r1+w2r2=0.5*0.1+0.5*0.15 = 0.125 = 12.5%
Variance = w1212+w2222+2w1w21212 = 0.52(0.04)+0.52(0.09)+2(0.5)(0.5)(0.2)(0.2)(0.3)

Variance= 0.0385

(c) Expected return = w1r1+w2r2=w1*0.1+(1-w1)*0.15 = 0.12 = 12%

w1= 0.4   w2=0.6
Variance = w1212+w2222+2w1w21212 = 0.42(0.04)+0.62(0.09)+2(0.4)(0.6)(0.2)(0.2)(0.3)

Variance= 0.04456

(d)

Variance = w1212+w2222+2w1w21212 = 0.16

This is impossible since portfolio variance >> each stock variance

Cannot create this portfolio

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