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Homework answers / question archive / A single mispriced asset has a reward to risk ratio of 0
A single mispriced asset has a reward to risk ratio of 0.5, while the market has a reward to risk ratio of 2.5. Given the asset has a beta β = 2.0, in constructing an optimal allocation between the mispriced asset and the market, what proportion of your investment would you place in the mispriced asset?
Answer:
Given:
Weighted RR and Beta model |
Stock | Allocation | Beta | Weighted Beta | Weighted Risk Reward |
Mispriced Asset | 0.25 | 2 | =(0.25 * 2) = 0.5 | = (0.25 * 0.5) = 0.125 |
Market | 0.75 | 1 | =(0.75 * 1) = 0.75 | = (0.75 * 2.5) = 1.875 |
Total | 1 | 3 | 1.25 | 2 |
Stock | Allocation | Beta | Weighted Beta | Weighted Risk Reward |
Mispriced Asset | 0.50 | 2 | =(0.50*2) = 1 | = (0.50 * 0.5) = 0.25 |
Market | 0.50 | 1 | =(0.50*1) = 0.50 | = (0.50 * 2.5) = 1.2 |
Total | 1 | 3 | 1.50 | 1.45 |
Stock | Allocation | Beta | Weighted Beta | Weighted Risk Reward |
Mispriced Asset | 0.75 | 2 | =(0.75*2) = 1.5 | = (0.75 * 0.5) = 0.375 |
Market | 0.25 | 1 | =(0.25*1) = 0.25 | = (0.25 * 2.5) = 0.625 |
Total | 1 | 3 | 1.75 | 1 |
Conclusion : We need to get the maximum RIsk Reward and Beta above 1 but not too high, our best bet would the Safer model with 75% in the broader market and 25% in the asset as we get the highest risk reward of 2 and beta just above 1 for a higher and moderately risky investment.