Question

The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 35% Standard Deviation 20% 40% The correlation between the returns is .25. (a) Calculate the expected return and standard deviation for the following portfolios: i. all in Z ii. .75 in Z and .25 in Y iii. .5 in Z and .5 in Y iv. .25 in Z and .75 in Y

Answer 1

Answer:

The expected return and standard deviation for the portfolios are shown in the table.

Step-by-step explanation:

The two securities are Z and Y.

The expected values and the standard deviation of the two securities are:

E (Z) = 0.15          E (Y) = 0.35

SD (X) = 0.20      SD (Y) = 0.40

The correlation between the two returns is, Corr (Z, Y) = r = 0.25.

The expected return is computed using the formula:

$E (return) = [W(Z)\times E(Z)]+[W(Y)\times E(Y)]$

The standard deviation is computed using the formula:

$SD(return)=\sqrt{(W(Z)\times SD(Z))^{2}+(W(Y)\times SD(Y))^{2}+2r\times W(Z)W(Y)SD(Z)SD(Y)}$

Consider the table below for the expected return and standard deviation of return.