State of Economy Probability of state of economy Rate of return if state occurs
Boom 30% 15%
Normal 65% 12%
Recession 5% 6%
4.01 percent
2.89 percent
1.57 percent
3.42 percent
2.03 percent
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Question
What is the standard deviation of the returns on a stock given the following information?
State of Economy Probability of state of economy Rate of return if state occurs
Boom 30% 15%
Normal 65% 12%
Recession 5% 6%
4.01 percent
2.89 percent
1.57 percent
3.42 percent
2.03 percent
Solution
Calculation of dtandard deviation
Variance = = 0.01629  0.126 * 0.126 = 0.0000414 and standard deviation = root of variance = root of 0.000414 = 2.03 %.
Answer is 2.03 percent
State of economy 
Probability 
Rete of return 
P*R 
R2P 
Boom 
0.30 
0.15 
0.045 
0.00675 
Normal 
0.65 
0.12 
0.078 
0.00936 
Recession 
0.05 
0.06 
0.003 
0.00018 



0.126 
0.01629 
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