Question

Stock ABC has an expected return of 10% and a standard deviation of returns of 5%. Stock XYZ has an expected return of 12% and a standard deviation of returns of 7%. You would like to invest $3000 in stock ABC and $2000 in stock XYZ. The correlation between the two stocks is .5. The expected market return is 11% and the risk free rate is 4%. Which of the following is false?

1,The expected return of the portfolio is 10.8%

2, The standard deviation of portfolio returns is 5.02%.

3, The beta of the portfolio is 1.3.

4, Based on the mean-standard deviation rule, we cannot choose between stock XYZ to stock ABC.

Answer 1

Stock ABC:

Return = r(abc) = 10%, Standard Deviation = sd(abc) = 5% and Investment Proportion = w(abc) = (3000/5000) = 0.6

Stock XYZ:

Return = r(xyz) = 12 %, Standard Deviation = sd(xyz) = 7% and Investment Proportion =w(xyz) = (2000/5000) = 0.4

Correlation between ABC and XYZ = C = 0.5

Portfolio Return = r(p) = w(abc) x r(abc) + w(xyz) x r(xyz) = 10 x 0.6 + 12 x 0.4 = 10.8 %

Portfolio Standard Deviation = sd(p) = [{w(abc) x sd(abc)}^(2) + {w(xyz) x sd(xyz)}^(2) + 2 x w(abc) x w(xyz) x C x sd(abc) x sd(xyz)]^(1/2) = 5.024% or 5.02 % approximately.

Assuming that the CAPM is valid, then the expected return of the portfolio ER(p) would be given by:

ER(p) = Risk Free Rate + Portfolio Beta x (Expected Market Return - Risk Free Rate) = 4 + 1.3 x (11-4) = 13.1 %

This, however, does not match with the calculated expected portfolio return of 10.8% and hence the beta is less than 1.3.

We cannot choose between the two stocks on the basis of mean-standard deviation rule as the one which gives the higher return is also the one which has the higher risk in the form of a higher standard deviation and vice-versa. Hence, both stocks adhere to the risk-return principle.

Therefore, the only false statement is statement (3).