Hello AFers, I could not post this on the Analystforum.com site ...it kept giving me an error: 'An error occured while trying to post this message'
As I am winding up on the quant session- just wanted to point out the various variance formulas that were thrown out. At first, it was quite confusing to apply them in the right context, but after doing some problems they are finally making sense.
Can you guys please confirm whether these formulas cover all that is to know about variance.
By definition, variance is simply a measure of dispersion...
1) Calculating a variance from a population
Var = (( x - mean(x) )^2) / n
2) Calculating a variance from a sample
S^2 = ((x - mean(x) ) ^2) / (n-1)
Consider 3 risky assets in a portfolio: A, B, C
3) Calculating variance for individual asset portfolio returns
Var (RA) = P( RA, RB, RC ) * ( RA-(E(RA)) ) ^2
Var (RB) = P( RA, RB, RC ) * ( RB-(E(RB)) ) ^2
Var (RC) = P( RA, RB, RC ) * ( RC-(E(RC)) ) ^2
4) Calculating variance for 2 asset portfolio returns
Var (RP) = wAwA Cov(RA, RA) + wAwB Cov(RA, RB) + wBwA Cov(RB, RA) + wBwB Cov(RB, RB)
which can be converted to...
Var (RP) = wA^2 Cov(RA) + wB^2 Cov(RB) + 2wAwB Corr(RA,RB) SD(RA) SD(RB)
5) Calculating variance for 3 asset portfolio returns
Var (RP) = wA^2 Cov(RA) + wB^2 Cov(RB) + wC^2 Cov (RC) + 2wAwB Cov(RA, RB) + 2wAwC Cov(RA, RC) + 2wBwC Cov(RB, RC)
Also, given that Cov and Corr are used often in the above calculation, the formula for calculation are:
6) Cov(RA, RB) = P(RA, RB) * (RA-E(RA)) * (RB-E(RB))
7) Corr(RA, RB) = Cov (RA, RB) / ( SD(RA) * SD(RB) )
Thanks!
