Suppose that the borrowing rate that your client faces is 11%. Assume that the S&P 500 index has an expected return of 16% and standard deviation of 23%. Also assume that the risk-free rate is rf = 5%. Your fund manages a risky portfolio, with the following details: E(rp) = 13%, σp = 18%.
What is the largest percentage fee that a client who currently is lending (y < 1) will be willing to pay to invest in your fund? What about a client who is borrowing (y > 1)? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)
Y<1= (0.61%) (or -0.61%)
Y>1=???
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Let us conside 'x' be the fee willing be invested in the fund.
=> For y < 1, we solve for x from (E(r) - Rf -x) / std.dev(portfolio) = (E(i) -Rf)/ std dev.(index)
=> (8–x) / 18 = (11) / 23
=> x = 8 - 8.61 = -0.61 %
for Y>1 we can infer that from no fees, the active fund is inferior to the passive fund.,
=> (16 – 11) / 23 = 0.217 < (13 – 11) /18 = 0.111 (Since, 11% from the clieant expectation return)
As More risk bearing investors have inclination for borrowing, not prefer to be client of the said fund even without a fee.They won;t be interested in borrowing in this case
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