Homework SourseConsider the following information Calculate the expected re
Consider the following information:
Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the \"%\" sign in your response.)
Calculate the standard deviation for the two stocks. (Do not round your intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the \"%\" sign in your response.)
| Rate of Return If State Occurs | |||
| State of | Probability of | ||
| Economy | State of Economy | Stock A | Stock B |
| Recession | .25 | .04 | –.17 |
| Normal | .30 | .10 | .17 |
| Boom | .45 | .15 | .37 |
Solution
(A) EXPECTED RETURN
Expected Returns - Stock A
= [0.04 x 0.25] + [0.10 x 0.30] + [0.15 x 0.45]
= 0.01 + 0.03 + 0.0675
= 0.1075
= 10.75%
Expected Returns - Stock B
= [-0.17 x 0.25] + [0.17 x 0.30] + [0.37 x 0.45]
= -0.0425 + 0.051 + 0.1665
= 0.175
= 17.50%
(B) STANDARD DEVIATION
Stock A
Variance
= [(4 – 10.75)2 x 0.25] + [(10 – 10.75)2 x 0.30] + [(15 – 10.75)2 x 0.45]
= 11.3906 + 0.1688 + 8.1281
= 19.6875
Therefore, Standard Deviation = Square Root of (19.6875) = 4.44%
Stock B
Variance
= [(-17 – 17.50)2 x 0.25] + [(17 – 17.50)2 x 0.30] + [(37 – 17.50)2 x 0.45]
= 297.56 + 0.08 + 171.11
= 468.75
Therefore, Standard Deviation = Square Root of (468.75) = 21.65%
