Reference no: EM132796992
You estimate that a passive portfolio, for example, one invested in a risky portfolio that mimics the SP500 index, yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with an expected return of 18% and a standard deviation of 28%. The risk-free rate is 8%.
1. The Capital Market Line (CML) is defined as the Capital Allocation Line (CAL) provided by a portfolio that consists of the risk-free bond and a broad index of common stocks (the passive portfolio in this problem).
(a) Draw the CML and your funds' CAL (provided by a portfolio that consists of the active portfolio and the risk-free bond) on an expected return-standard deviation diagram.
(b) What is the slope of the CML?
(c) Briefly characterize the advantage of your fund over the passive fund.
2. Your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio.
(a) Explain to your client the disadvantage of the switch.
(b) Show him the maximum fee you could charge (as a percentage of the investment in your fund, deducted at the end of the year) that would leave him at least as well of investing in your fund as in the passive one. (Hint: The fee will lower the slope of his CAL by reducing the expected return net of the fee.)
3. Suppose that your client's risk aversion coefficient is A = 3.5.
(a) If he chose to invest in the passive portfolio, what proportion y would he select?
(b) Is the fee (percentage of the investment in your fund, deducted at the end of the year) that you can charge to make the client indifferent between your fund and the passive strategy affected by his capital allocation decision (i.e., his choice of y)?
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