Question

There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return 11%, standard deviation 12%. You are not sure about the correlation between 2 assets. You hold 30% of your portfolio in asset 1 and 70% in asset 2.

What is the highest possible variance of your portfolio?

Hint 1: Think how the portfolio variance depends on the correlation between 2 assets.

Hint 2: Think which values the correlation between Asset 1 and Asset 2 can get.

Answer 1

Let the correlation between the two assets be denoted by p. Further, asset correlation can take values only between -1 and +1.

The variance of a portfolio of two assets is given by the following relationship:

V(p) = [{w(1) x sd(1)}(2) + {w(2) x sd(2)}^(2) + 2 x w(1) x w(2) x sd(1) x sd(2) x p]

As is clearly observable the correlation is directly related to the portfolio's variance and consequently the portfolio will possess the highest variance only when its correlation is +1.

V(p) =  [{0.3 x 9}(2) + {0.7 x 12}^(2) + 2 x 0.3 x 0.7 x 9 x 12 x (+1)] = 123.21