4. Suppose that an investor has $40 invested in the active fund and $60 in cash (measured in thousands, say). What investments in the passive fund, the hedge fund, and cash (i.e., the riskfree asset) would yield the same market exposure, same alpha, same volatility, and same exposure to t ? As a result, what is the fair management fee for the hedge fund in the sense that it would make the investor indifferent between the two allocations (assume that the hedge fund charges a zero performance fee)?

Question 5 (Hedge funds vs. mutual funds 4pt ) Consider a passive mutual fund, an active mutual fund, and a hedge fund. The mutual funds claim to deliver the following gross returns: rtpassivefundbeforefees=rtstockindex rtactivefundbeforefees=2.20%+rtstockindex+t The stock index has a volatility of var(rtstockindex)=15%. The active mutual fund has a tracking error with a mean of E(t)=0, a volatility of var(t)=3.5%, and Cov(t,rtstockindex)=0 such that it's beta to the stock index is 1 . The passive fund charges an annual fee of 0.10% and the active mutual fund charges a fee of 1.20%. The hedge fund uses the same strategy as the active mutual fund to identify "good" and "bad" stocks, but implements the strategy as a long-short hedge fund, applying 4 times leverage. The risk-free interest rate is rf=1% and the financing spread is zero (meaning that borrowing and lending rates are equal). Therefore, the hedge fund's return before fees is rthedgefundbeforefees= 1%+4(rtactivefundbeforefeesrtstockindex) Question 5 (Hedge funds vs. mutual funds 4pt ) Consider a passive mutual fund, an active mutual fund, and a hedge fund. The mutual funds claim to deliver the following gross returns: rtpassivefundbeforefees=rtstockindex rtactivefundbeforefees=2.20%+rtstockindex+t The stock index has a volatility of var(rtstockindex)=15%. The active mutual fund has a tracking error with a mean of E(t)=0, a volatility of var(t)=3.5%, and Cov(t,rtstockindex)=0 such that it's beta to the stock index is 1 . The passive fund charges an annual fee of 0.10% and the active mutual fund charges a fee of 1.20%. The hedge fund uses the same strategy as the active mutual fund to identify "good" and "bad" stocks, but implements the strategy as a long-short hedge fund, applying 4 times leverage. The risk-free interest rate is rf=1% and the financing spread is zero (meaning that borrowing and lending rates are equal). Therefore, the hedge fund's return before fees is rthedgefundbeforefees= 1%+4(rtactivefundbeforefeesrtstockindex)