In: Finance
) Consider the following situation:
State of Economy |
Probability of State of Economy |
Returns if State Occurs |
||
Stock A |
Stock B |
Stock C |
||
Boom |
20% |
25% |
10% |
5% |
Recession |
80% |
-30% |
5% |
10% |
The expected return on the market portfolio is 7% and the US Treasury bill yields 3%. The capital market is currently in equilibrium.
a) Systematic Risk = Beta | |||||||
Returns if State Occurs | Expected Return | ||||||
State of Economy | Probability of State of Economy | Stock A | Stock B | Stock C | Prob. x Stock A 's Return | Prob. x Stock A 's Return | Prob. x Stock A 's Return |
Boom | 20.00% | 25.00% | 10.00% | 5.00% | 5.00% | 2.00% | 1.00% |
Recession | 80.00% | -30.00% | 5.00% | 10.00% | -24.00% | 4.00% | 8.00% |
Total | -19.00% | 6.00% | 9.00% | ||||
According CAPM Expected Return E(R)= Risk free Rate + Beta x (Market Return - Risk free Rate) | |||||||
Risk Free Rate RF = | 3.00% | ||||||
Return on market RM | 7.00% | ||||||
Stock A 's Beta = -19% - 3% = Beta x (7% -3%) | -5.5 | ||||||
Stock B 's Beta = 6% - 3% = Beta x (7% -3%) | 0.75 | ||||||
Stock C 's Beta = 9% - 3% = Beta x (7% -3%) | 1.5 | ||||||
Stock C has the most systematic risk because it has the highest beta. | |||||||
b) | |||||||
Stock A has the most unsystematic risk because it has the negative Beta. |