| Consider the following information: |
| Rate of Return If State Occurs | |||||||||
| State of | Probability of | ||||||||
| Economy | State of Economy | Stock A | Stock B | ||||||
| Recession | .15 | .04 | − | .15 | |||||
| Normal | .61 | .07 | .14 | ||||||
| Boom | .24 | .12 | .31 | ||||||
| Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
| Expected return | |
| Stock A | % |
| Stock B | % |
| Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
| Standard deviation | |
| Stock A | % |
| Stock B | % |
Answer:
E(RA)
= .15(.04) + .61(.07) + .24(.12)
= 0.0775, or 7.75%
E(RB)
= .15(–.15) + .61(.14) + .24(.31)
= 0.1823, or 18.23%
To calculate the standard deviation ,One should calculate the variance. To Calculate the variance, You must find the squared deviations from the expected return. After multiply each possible squared deviation by its probability, then add all of these up. What comes is the variance. So, the variance and standard deviation ofeach stock is
:A2=.15(.04 – .0775)2+ .61(.07 – .0775)2+ .24(.12 – .0775)2
= .00067872
sA= (.00067872)1/2
= .02605, or 2.61%
sB2=.15(–.15 – .1823)2+ .61(.14 – .1823)2+ .24(.31 – .1823)2
= .005162
sB
= (.005162)1/2
= .0.0718
, or 7.18%
