Question

You invest 58% of your money in Stock A and the rest in Stock B. The standard deviation of annual returns is 43% for Stock A and 43% for Stock B. The correlation between the two stocks is -0.1. By how many percentage points does diversifying between these two stocks reduce your risk? Go out three decimals - for example, write 5.6% as .056.

Answer 1

Given about a portfolio,

weight of stock A wa = 58%

weight of stock B wb = 42%

standard deviation of stock A SDa = 43%

standard deviation of stock B SDb = 43%

correlation between the two stocks Corr(a,B) = -0.1

So standard deviation of the portfolio is

SD(p) = SQRT(((wa*SD(a))^2) + ((wb*SD(b))^2) + 2*wa*wb*SD(a)*SD(b)*Corr(a,b))

=> SD(p) = SQRT((0.58*43)^2 + (0.42*43)^2 + 2*0.58*0.42*43*43*(-0.1)) = 29.29%

So, diversification benefit = 43% - 29.29% = 13.7% or 0.137