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Total return generated on both bull and bear predictions

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Chuck, an imperfect forecaster correctly predicts 57% of all bull markets and 68% of all bear markets. Roy is a perfect forecaster. If Chuck is able to charge a fee of $125000, what is the fee that Roy should charge? (assume both of them manage similar size funds)

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Solution Summary

Total return generated on both bull and bear predictions by Chuck is illustrated in this tutorial.

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Before answering this we need to make few assumptions:
1. Market have equally likely tendency to move up and down.
2. The percentage change on upside and downside are same and we assume that this is X.

For correct bull prediction ...

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