### Should the fund manager receive performance bonus

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##### Reference no: EM132049408

Recall the Alpha fund from the previous problem which had a beta of 1.5 and earned a return of 25% over a period in which the market portfolio earned 15% and the risk-free rate was 5%.

a) Suppose that, due to a lack of diversification, the Alpha fund has the same total risk as a perfectly diversified portfolio with a beta of 2.0 (its adjusted beta is 2). Decompose the portfolio's return due to selectivity into its return due to net selectivity and its return due to lack of diversification (graphs are not necessary here).

b) Suppose that portfolio A has a target beta of 2.0. Decompose the portfolio's return due to risk into its return due to target risk and its return due to the manager's choice of risk (graphs are not necessary here).

c) Should the fund manager receive a performance bonus? Explain.

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