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A single mispriced asset has a reward to risk ratio of 0

Finance

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?

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Answer:

Given:

  • Risk Reward ratio for an asset = 0.5 : which essentially means that your risk is 2 times the reward , which in numbers would be risking 200 USD for a reward of a mere 100 USD .
  • While the risk reward for the market lets say the S&P 500 is 2.5, which means your reward is 2.5 times the risk. which in numbers would be a gain of 250 USD by risking a 100 USD.
  • Also considering the beta of 2.0 for the mispriced asset, which is twice the volatility of the market, which means that if the market moved by 10 base points upwards, the asset would move 20 base points in the same direction, which is a postive thing because you're earning twice than you would if you would have invested entirely in the broader market. But there is a negative side to it, if the overall market came down by 10 base points, your asset would also come down by 20 base points and loose more than you would if you would've fully invested in the broader market.
  • To neutralize this much of volatility and risk, we try to do a trial and error with 3 models and find whats best suitable
Weighted RR and Beta model
  • Moderately safer approach with the 75 - 25 model, where The market has the larger allocation of funds and the mispriced asset 25% of the allocation.
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
  • Balanced apporach with 50:50 allocation
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
  • Aggresive approach with 75% in the mispriced asset and 25% in broader market
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.