(a) Expected Return of Stock ER = ΣPiRi, where Pi is the probability and Ri is the return for economy state i
=> ERA = 0.2*0.4 + 0.8*0.2 = 0.24
ERB = 0.2*0.12 + 0.8*0.05 = 0.064
(b) Variance of stock = σ2 = Σ Pi(Ri - ER)2
=> σA2 = 0.2(0.4 - 0.24)2 + 0.8(0.2 - 0.24)2 = 0.0064
σB2 = 0.2(0.12 - 0.064)2 + 0.8(0.05 - 0.064)2 = 0.000784
Standard Deviation = σ = sqrt (σ2 )
=> σA = sqrt(0.0064) = 0.08
σB = sqrt(0.000784) = 0.028
(c) Covariance = Cov(A, B) = Σ Pi(RiA - ERA)(RiB - ERB) = 0.2(0.4 - 0.24)(0.12 - 0.064) + 0.8(0.2 - 0.24)(0.05 - 0.064) = 0.00224
Correlation = Cov(A, B) / σA σB = 0.00224/(0.08*0.028) = 1
(d) Expected Return of Portfolio = wAERA + wBERB = 0.40*0.24 + 0.60*0.064 = 0.1344
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