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You own a portfolio with the following expected returns given the various states of the economy
You own a portfolio with the following expected returns given the various states of the economy. State of Economy Probability of State of Economy Rate of Return if State Occurs Boom 30% 20% Normal 50% 5% Recession 20% -10% The market rate of return is 10 percent, and the risk-free rate is 3 percent. What is the beta of the portfolio? 0 0.73 0 0.84 0 0.50 0 0.35 0 1.03
Expert Solution
| Computation of Expected Return: | |||
| State of Economy | Probability | Rate of Return | Probability*Rate of Return |
| Boom | 30% | 20% | 6.00% |
| Normal | 50% | 5% | 2.50% |
| Recession | 20% | -10% | -2.00% |
| Expected Return = | 6.50% | ||
Computation of Beta:
Expected Return = Risk-free Rate + Beta*(Market Return - Risk-free Rate)
6.50% = 3% + Beta * (10% - 3%)
6.50% - 3% = Beta*7%
3.50%/7% = Beta
Beta = 0.50
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