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Answer:
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a) Expected return = Probability of recession*Return during recession + Probability of normal*Return during normal + Probability of boom*Return during boom
Expected return for stock A = 0.21*0.04 +0.61*0.12 + 0.18*0.30
Expected return for stock A = 0.1356
Expected return for stock A = 13.56%
Expected return for stock B = 0.21*-0.41 + 0.61*0.31 + 0.18*0.54
Expected return for stock B = 0.2002
Expected return for stock B = 20.02%
b) Standard deviation of stock = √{Probability(Recession)*(Rate during recession - expected rate )^2 + Probability(Normal)(Rate during normal - expected return)^2 + Probability(Boom)*(Rate in boom - Expected return)^2}
Standard deviation of stock A = √[(0.21*(0.04-0.1356)^2 + 0.61*(0.12 - 0.1356)^2 + 0.18*(0.30-0.1356)^2)^0.5]
Standard deviation of stock A = 0.0832
Standard deviation of stock A = 8.32
Standard deviation of stock B = √(0.21*(-0.41-0.2002)^2 + 0.61*(0.31 - 0.2002)^2 + 0.18*(0.54-0.2002)^2)^0.5]
Standard deviation of stock B = 0.3260
Standard deviation of stock B = 32.60%
