 # quickest method to portfolio variance

equal weight of two stocks in a portfolio Scenario 1: probability is 0.5, stock A return 25%, Stock B return 1% Scenario 2: … 0.3, … 10%, … -5% Scenario 3…0.2, …-25%, …35 What’s the portfolio expected return and variance? I want to know the most time-saving way to solve this question? Thanks

there’s no quick way. return is straight forward. use total probability rule or draw a tree .5 [.25*.5 + .01*.5] + .3* [.10*.5 + -.05*5] + .3* [-.25*.5 + .35*5] = 0.0875 variance is difficult especially since covariance is not given.

Pepp, little error in your calulation, expected return should be 8.25%. As to portfolio variance, Schweser provide a easy solution which I don’t agree First, it get mean return of two stocks in each senario: 13%, 2.5%, and 5% Then it applies thes numbers and portfolio expected return to get portfolio variance = 0.5 (13-8.25)^2+0.3(2.5-8.25)^2+0.2(5-8.25)^2 = 23.31. So portfolio variance is 23.31%. Do you agree?

Yes, that is the equation for probablistic variance.

So you are saying we can get portfolio variance without knowing variance of each stock and covariance between each stock ?

According to Schweser’s quick sheet, yes. I don’t know the difference in definition b/t probabilistic variance and variance of a 2 stock portfolio, but I would like to know this!