Question

Suppose we are uncertain what the actual correlation between the assets are. Show that the volatility of an equally weighted portfolio is always greater than or equal to 5% regardless of what the correlation is.

Answer 1

Suppose the two assets

Asset A has a standard deviation of 38%

and Asset B has a standard deviation of 18%

both are equally weighted, let the correlation between the assets be 0.8

Now, the standard deviation of the equally weighted portfolio will be :

root over of [ (0.5)^2*(0.38)^2 + (0.5)^2*(0.18)^2 + 2 *(0.5*0.5 *0.8*0.38*0.18) ]

=root over (0.0361 +0.0081 + 0.0274)

= 26.75%

Now, taking the correlation as -0.6 we get,

root over of [ 0.0361 + 0.0081 + 2* 0.5*0.5*-0.6*0.38*0.18]

=root over of [ 0.0361 + 0.0081 - 0.0205]

= 15.39%

So, whatever the covariance the volatility of an equally weighted portfolio is always greater than 5%.