Question

An investment has an expected return of 9.25 percent and standard deviation of 3.38 percent. Another investment has an expected return of 14 percent and a standard deviation of 4.93 percent. What is the expected return of the portfolio and its standard deviation if both are combined into a portfolio with 70 percent invested in the first investment and 30 percent in the second? Assume the correlation coefficient (ij) is -.40

Answer 1

Given that,

An investment has an expected return of 9.25 percent and standard deviation of 3.38 percent.

=> Ra = 9.25%

SDa = 3.38%

Another investment has an expected return of 14 percent and a standard deviation of 4.93 percent.

Rb = 14%

SDb = 4.93%

A portfolio is made of  70 percent invested in the first investment and 30 percent in the second

=> Wa = 0.7 and Wb = 0.3

So, expected return on portfolio is weighted average return on its assets

E(p) = Wa*Ra + Wb*Rb = 0.7*9.25 + 0.3*14 = 10.675%

correlation coefficient Corr(a,b) = -0.40

So, standard deviation of portfolio is

SD(p) = SQRT((Wa*SDa)^2 + (Wb*SDb)^2 + 2*Wa*Wb*SDa*SDb*Corr(a,b))

=> SD(p) = SQRT((0.7*3.38)^2 + (0.3*4.93)^2 + 2*0.7*0.3*3.38*4.93*(-0.40)) = 2.23%