Consider the following scenario analysis for a stock (Stock 1) and the S&P 500 Index.(assume...
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Consider the following scenario analysis for a stock (Stock 1) and the S&P 500 Index.(assume that risk free rate is zero)
| Scenario | Probability | Stock 1 | S&P 500 Index |
| Depression | 0.1 | -1% | -5% |
| Recession | 0.2 | 0 | 3% |
| Normal | 0.5 | 4% | 9% |
| Boom | 0.2 | 14% | 16% |
A. Calculate (1) the expected return on Stock 1, (2) the expected return on the S&P 500Index, and (3) the variance of the S&P 500 Index.
B. Calculate the covariance between Stock 1 and the S&P 500 Index. What is the beta ofStock 1?
C. You want to construct a 3-asset portfolio which will have a beta of 1.2. You will invest 40% of your money in Stock 1, 10% in the risk-free asset, and the remaining 50% in another stock (Stock 2). What should be the beta of Stock 2?
(Hint: The beta of a portfolio is equal to the weighted average of the beta of each asset in the portfolio)
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