Consider the following information: |
Rate of Return if State Occurs | |||
State of | Probability of State | ||
Economy | of Economy | Stock A | Stock B |
Recession | .23 | .025 | –.28 |
Normal | .58 | .105 | .18 |
Boom | .19 | .170 | .41 |
Requirement 1: |
Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) |
Expected return | |
E(R_{A}) | % |
E(R_{B}) | % |
Requirement 2: |
Calculate the standard deviation for the two stocks |
Expected return=Respective return*Respective probability
A:
Expected return=(0.23*2.5)+(0.58*10.5)+(0.19*17)=9.90%(Approx)
Probability | Return | Probability*(Return-Mean)^2 |
0.23 | 2.5 | 0.23*(2.5-9.895)^2=12.57778575 |
0.58 | 10.5 | 0.58*(10.5-9.895)^2=0.2122945 |
0.19 | 17 | 0.19*(17-9.895)^2=9.59139475 |
Total=22.381475% |
Standard deviation=[Total Probability*(Return-Mean)^2/Total Probability]^(1/2)
=4.73%(Approx).
B:
Expected return=(0.23*-28)+(0.58*18)+(0.19*41)=11.79%
Probability | Return | Probability*(Return-Mean)^2 |
0.23 | -28 | 0.23*(-28-11.79)^2=364.146143 |
0.58 | 18 | 0.58*(18-11.79)^2=22.367178 |
0.19 | 41 | 0.19*(41-11.79)^2=162.112579 |
Total=548.6259% |
Standard deviation=[Total Probability*(Return-Mean)^2/Total Probability]^(1/2)
=23.42%(Approx).
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