Expected returns
Stocks X and Y have the following probability distributions of expected future returns:
| Probability | X | Y |
| 0.1 | -9% | -33% |
| 0.2 | 6 | 0 |
| 0.3 | 14 | 20 |
| 0.2 | 21 | 28 |
| 0.2 | 31 | 49 |
Calculate the expected rate of return, rY, for Stock Y (rX = 14.90%.) Round your answer to two decimal places.
___ %
Calculate the standard deviation of expected returns, σX, for Stock X (σY = 23.20%.) Round your answer to two decimal places.
___%
Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places.
___ answer
Is it possible that most investors might regard Stock Y as being less risky than Stock X? (CHOOSE ONE)
A.)If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
B.)If Stock Y is less highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be more risky in a portfolio sense.
C.)If Stock Y is more highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be less risky in a portfolio sense.
D.)If Stock Y is more highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
E.)If Stock Y is more highly correlated with the market than X, then it might have the same beta as Stock X, and hence be just as risky in a portfolio sense.
| Probability | X | Y |
| 0.1 | -9% | -33% |
| 0.2 | 6 | 0 |
| 0.3 | 14 | 20 |
| 0.2 | 21 | 28 |
| 0.2 | 31 | 49 |
expected rate of return, rY, =21.367 %
Calculation is as follow
| Probability | Y | Return |
| 0.1 | -33% | -0.033 |
| 0.2 | 0 | 0 |
| 0.3 | 20 | 6 |
| 0.2 | 28 | 5.6 |
| 0.2 | 49 | 9.8 |
| Total | 21.367 |
Calculate the standard deviation of expected returns, σX, for Stock X (σY = 23.20%.) Round your answer to two decimal places.
Answer : 11.51
Calculation is as follow
| X | RX | Diffrance | Squeare | Probabelity | standard deviation |
|
| -9 | 14.9 | – 9 -14.9 | 23.9 | 571.21 | 0.1 | 57.121 |
| 6 | 14.9 | 14.9- 6 | 8.9 | 79.21 | 0.2 | 15.842 |
| 14 | 14.9 | 14.9 – 14 | 0.9 | 0.81 | 0.3 | 0.243 |
| 21 | 14.9 | 21 – 14.9 | 6.1 | 37.21 | 0.2 | 7.442 |
| 31 | 14.9 | 31 -14.9 | 16.1 | 259.21 | 0.2 | 51.842 |
| 132.49 |
Squeare root of 132.49 = 11.51
Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places.
___ answer
CVX = sX/ rX
= 11.51%/14.90% = 0.77, while
CVY = 23.20%/21.36%
= 1.086
Is it possible that most investors might regard Stock Y as being less risky than Stock X? (CHOOSE ONE)
D.)If Stock Y is more highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
