Portfolio Math

Lets not make this too difficult.  In a nutshell, E(r) is a weighted average of probabilities and weights.  The same is NOT true for standard deviations of portfolios.



Single asset


Expected Return on a asset

                    Bust Normal  Boom   

Problibility    .1        .6             .2

E(r)                -.2     .10        .20

E(r)= .1(-.2) +.6(.1) +.2(.20)=.08

  

Variance= Summation [(prob)(r-e(r))2

            =.1(-.2-.08)2+ .6(.1-.08)2+.2(.2-.08)2

            = .03688

std deviation= sqr root of variance

                    = 19.2%


Portfolio

E(Rp) = weighted average of expected returns
           = Summation of weight of A * E(Ra) + weight of B * E(Rb) etc


This is NOT true for calculating the standard deviation for a portfolio!!

The variance of a portfolio is

 

where p = the correlation coefficient and N is the number of assets. Wi is the weight (market value weight) invested in asset i.


The standard deviation is then just the square root of the variance.