Question

The expected returns and standard deviation of returns for two securities are as follows:Security Z Security YExpected 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:1i. all in Zii. .75 in Z and .25 in Yiii. .5 in Z and .5 in Yiv. .25 in Z and .75 in Yv. all in Y

Answer 1

Answer:

Given that,

Expected return on Z and Y,

Rz = 0.15 and Ry =0.35

Standard deviations:

Sz = 0.2, Sy = 0.4

correlation coefficient: rxy = 0.25

Expected return on portfolio = Rz × wz + Ry × wy

where, wz and wy are weights of Z and Y respectively in portfolio.

Standard deviation of portfolio:

$\sqrt{(wz\times Sz)^{2}+(wy\times Sy)^{2}+2\times rxy\times wz\times wy\times Sz\times Sy }$

Table attached with this answer shows mean return and standard deviation at different combinations of weights: