# Portfolio Management Q

Now DON’T check your formula sheet, whoever knows this one is my hero for the day. Consider an equally-weighted portfolio comprised of five assets in which the average asset standard deviation equals 0.57 and the average correlation between all asset pairs is -0.21. Calculate the variance of the portfolio.

std^2 = 0.57^2(1+.21)/5-.21=0.0103968 i think.

var = (1/n)*(avg asset variance) + ((n-1)/(n))*(covariance of assets) am I way off?

Var = 0.57^2*(1/5+4/5*(-.21))=0.010397

portfolio variance = 0.3249*((1-(-0.21))/5 -0.21) variance = 0.0104

I get the same as maratikus. The trick is to remember to get COV and square the std for the first part of the equation.

Wait, you get the same answer multiplying the correlation for the (4/5) just as the COV?

schweser has the formula I used…I did it with just the variance and correlation

Awesome gets the title with his calc which is identical (just mix it up a little) to the one from Dinesh. Great work team!

deep2002 Wrote: ------------------------------------------------------- > schweser has the formula I used…I did it with > just the variance and correlation I didn’t use COV, I used correlation and variance only: Port variance = Sample Variance*((1-correlation)/n + correlation)

mcpass Wrote: ------------------------------------------------------- > Awesome gets the title with his calc which is > identical (just mix it up a little) to the one > from Dinesh. > > Great work team! im a girl

Hi Awesome, how are you ?

dinesh.sundrani Wrote: ------------------------------------------------------- > Hi Awesome, how are you ? Im good, how are you?

So dinesh, is this like the new place to pick up girls? Now get back to studying…

haha wandering … you seem to have recovered well after the Break’up. You should try this out too…

deep2002 Wrote: ------------------------------------------------------- > portfolio variance = 0.3249*((1-(-0.21))/5 -0.21) > variance = 0.0104 at the end of this formula, is it +r? so ((1-(-0.21))/5 ) + (-.21)? thx

• correlation.

yes. portfolio_var = ave_var * { (1 - ave_rho)/n + ave_rho }

(1/n)(avg var) + (n-1/n)(avg cov)