Question
In: Finance
Use the following information on states of the economy and stock returns to calculate the standard...
Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
| State of Economy | Probability of State of Economy |
Security
Return if State Occurs |
||||||||||
| Recession | .35 | −10.00 | % | |||||||||
| Normal | .50 | 7.00 | ||||||||||
| Boom | .15 | 17.00 | ||||||||||
Solutions
Expert Solution
Expected return=Respective return*Respective probability
=(0.35*-10)+(0.5*7)+(0.15*17)
=2.55%
| probability | Return | probability*(Return-Expected Return)^2 |
| 0.35 | -10 | 0.35*(-10-2.55)^2=55.125875 |
| 0.5 | 7 | 0.5*(7-2.55)^2=9.90125 |
| 0.15 | 17 | 0.15*(17-2.55)^2=31.320375 |
| Total=96.3475% |
Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=(96.3475)^(1/2)
=9.82%(Approx)
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