Question

# You've estimated the following expected returns for a stock, depending on the strength of the economy:...

You've estimated the following expected returns for a stock, depending on the strength of the economy:

 State (s) Probability Expected return Recession 0.3 -0.02 Normal 0.5 0.09 Expansion 0.2 0.14

1. What is the expected return for the stock?

2. What is the standard deviation of returns for the stock?

1. Expected return = Respective probabilities of states * expected return of states

= (0.3*-0.02)+(0.5*0.09)+(0.2*0.14)

= 6.70%

2. Variance = Product of Deviation Squared and Probability

 State of Economy Probability Probable Return Deviation ( Probable Return- Expected Return) Deviation Squared Product ( Deviation Squared* Probability) Recession 0.30 -2.00 -8.700 75.690000 22.7070 Normal 0.50 9.00 2.300 5.290000 2.6450 Expansion 0.20 14.00 7.300 53.290000 10.6580 Variance ( Sum of Product) 36.01

Standard Deviation = Square root of Variance

= 36.01^(1/2)

= 6.00%

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