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Aussteak is a company which enjoys good sales during boom times but struggles when people cut back on their luxuries in a recession. Returns in boom times are 40% but  during  recessions  these  fall  to  12%.  Ausspam  by  contrast  is  more  resilient showing returns of 15% in the boom and 14% in the recession. An investor holds a portfolio  comprising  200  shares  in  Aussteak  and  320  shares  in  Ausspam.  The correlation between returns of the two firms is just 0.1. If the probability of recession is 0.6 calculate the expected return, and variance of the portfolio.

Solution:

The probability of recession is 0.6, and the probability of boom is 1-0.6=0.4.       First we apply a simple scenario analysis table for each company to construct the variance:

Aussteak

Ausspam

We now need the weights for each share. The total number of shares is 520 so the      weight of Aussteak is   = 0.3846, and the weight of Ausspam is 1-0.3846=0.6154.

Portfolio return: rp  = wDrD  + wErE

    wD = Bond weight

    rD = Bond return

    wE = Equity weight

    rE = Equity return

E(rp) = wD E(rD) + wEE(rE)= 0.3846*23.2+0.6154*14.4=17.78448

Portfolio variance:

p(2)  wD(2)D(2)   wE(2)E(2)   2wD wE Cov  rD , rE 

               D(2)     = Bond variance

               E(2)     = Equity variance

      Cov rD , rE    = Covariance of returns for bond and equity

=0.3846^2*188. 16+0.6154^2*0.24+2*0.3846*0.6154*0. 1*13.72*0.49=28.241219