10) An investment firm is considering a portfolio with equal weighting in a cycl

Question

10) An investment firm is considering a portfolio with equal weighting in a cyclical stock and a countercyclical stock. It is expected that there will be three economic states Good, Average and Bad, each with equal probabilities of occurrence. The cyclical stock is expected to have returns of 12%, 5% and 1% in Good, Average and Bad economies respectively. The countercyclical stock is expected to have returns of-8%, 2% and 14% in Good, Average and Bad economies respectively, Given this information, calculate portfolio variance. )00094 B)0084 C).00054D)00074 E ) 00064

Explanation / Answer

In Good Scenario the expected return for portfolio is as follows

Portfolio has equal weightage to cyclical stock and counter cyclical stock

Expected Returns (ER) in good time = 0.12*0.5+(-0.08)*0.5 = 0.06-0.04 = 0.02

ER in Average time = 0.05*0.5+ 0.02*0.5= 0.035

ER in Bad time = (0.01×0.14)*0.5= 0.075

All the outcomes with equal probability

ER in Total = (0.02+0.035+0.075)*(1/3)=0.13/3=0.0433

ER^2 in Total =(0.02^2+0.035^2+0.075^2)/3=(0.0004+0.001225+0.005625)/3=0.007250/3=0.002417

(ER in total)^2 = (0.0433)^2=0.001875

Variance of ER = ER^2 in Total - (ER in Total)^2=0.002417-0.001875=0.00054

Hence option C

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