Question

Assume that you have invested in two stock A and B. Stock A has a standard deviation of return of 10 percent. Stock B has a standard deviation of return of 20 percent. The correlation coefficient between the two stocks is 0.25. If you invest 70 percent of your funds in stock A and 30 percent in stock B, what is the standard deviation of your portfolio?

Answer 1

Given a portfolio,

It is made of two stocks A and B,

Standard deviation of stock A SDa = 10%

Standard deviation of stock B SDb = 20%

Weight of stock A, Wa = 70%

Weight of stock B, Wb = 30%

correlation coefficient between two stock Corr(a,b) = 0.25

Standard deviation of portfolio is

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

=> SDp = SQRT((0.7*0.1)^2 + (0.3*0.2)^2 + 2*0.7*0.3*0.1*0.2*0.25) = 0.103 or 10.30%

So standard deviation of portfolio is 10.30%