Consider the following information: |
Probability of State | Rate of Return if State Occurs | ||
Economy | of Economy | Stock A | Stock B |
Recession | .24 | .055 | –.34 |
Normal | .64 | .135 | .24 |
Boom | .12 | .230 | .47 |
a. | Calculate the expected return for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
b. | Calculate the standard deviation for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
Consider the following information:
Rate of Return if State Occurs | |||
State of | Probability of State | ||
Economy | of Economy | Stock A | Stock B |
Recession | .24 | .055 | –.34 |
Normal | .64 | .135 | .24 |
Boom | .12 | .230 | .47 |
Requirement 1= Expected Return of=
Stock A= (0.24*0.055) + (0.64*0.135) + (0.12*0.230) = 12.72%
Stock B=(0.24*-0.34) + (0.64*0.24) + (0.12*0.47) = 12.84%
Requirement 2=The Standard Deviation for the two Stocks:
Stock A=
Probability | Rate of Return | XP | X2P |
P | X | ||
0.24 | 0.055 | 0.0132 | 0.000726 |
0.64 | 0.135 | 0.0864 | 0.011664 |
0.12 | 0.230 | 0.0276 | 0.006348 |
0.1272 | 0.018738 |
Standard Deviation = Square Root (0.018738- (0.1272)2 )
= Square Root (0.018738-0.01617984) = Square Root (0.00255816)
= 0.0505 = 5.05 %
Stock B=
Probability | Rate of Return | XP | X2P |
P | X | ||
0.24 | -0.34 | -0.0816 | 0.027744 |
0.64 | 0.24 | 0.1536 | 0.036864 |
0.12 | 0.47 | 0.0564 | 0.026508 |
0.1284 | 0.091116 |
Standard Deviation = Square Root (0.091116- (0.1284)2 )
= Square Root (0.091116-0.01648656) = Square Root (0.07462944)
= 0.27318 = 27.32 %
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