For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: passive fund before fees stock index = r = 6% + Ut ractive active fund before fees + Et = 1.80% + 1.1 * r* stock index where the error terms u and are independent over time and of each other, have zero means E(ut) = E(&) = 0, and volatilities of var(u+) = 15% and (var(&) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: hedge fund before fees rt' = 4 * (ractive fund before fees. stock index) r Question 1 What is the active mutual fund's beta (with respect to the stock index)? a. 1 b. 1.018 C. 1.1 d. 0 e. 0.909 ? For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: rpassive fund before fees = rt stock index = 6% + Ut + Et active fund before fees = 1.80% + 1.1 * rstock index where the error terms u and are independent over time and of each other, have zero means E(ut) = E(&) = 0, and volatilities of var(u+) = 15% and (var(&) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: hedge fund before fees rt = 4 * (ractive fund before fees - stock index) rt Question 2 What is the hedge fund's beta? a. 4.4 b. 0.4 C. 0 d. 1.1 e. 0.1 f. 0.04 ? For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: active fund before fees rpassive fund before fees =rt rtactive stock index = 6% + Ut + Et = 1.80% + 1.1 * r. stock index where the error terms ut and are independent over time and of each other, have zero means E(u) = E() = 0, and volatilities of var(u) = 15% and (var(&) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: rt _hedge fund before fees = 4 * (rt active fund before fees - Question 3 stock index) r What is the hedge fund's volatility? a. 17.09% b. 16.00% c. 6.00% d. 16.07% e. 22.00% ? For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: rpassive fund before fees stock index = rt = 6% + Ut r+active fund before fees = 1.80% 1.1 * r stock index + Et where the error terms u and are independent over time and of each other, have zero means E(u) = E(&) = 0, and volatilities of var(u+) = 15% and (var(+) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: Question 4 rt' - hedge fund before fees = 4 * (ractive fund before fees _ r stock index) What is the hedge fund's alpha before fees? a. 9.6% O b. 4% C. 0% d. 7.2% e. 1.8% f. 2.4% ? For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: passive fund before fees =r+stock index = 6% + Ut stock index + Et _active fund before fees = 1.80% + 1.1 * r+ where the error terms u and are independent over time and of each other, have zero means E(ut) = E(t) = 0, and volatilities of var(ut) = 15% and (var(&) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: rhedge fund before fees = 4 * (ractive fund before fees - stock index) r Question 5 What is the hedge fund's expected return before fees? a. 1.8% b. 0% C. 9.6% d. 4% e. 7.2% f. 2.4% For Q1-Q6, consider a passive mutual fund, an active mutual fund, and a hedge fund. The risk-free interest rate is zero and the mutual funds claim to deliver the following gross returns: rpassive fund before fees =r+stock index = 6% + Ut active fund before fees = 1.80% + 1.1 * r stock index. r + Et where the error terms u and are independent over time and of each other, have zero means E(ut) = E(t) = 0, and volatilities of var(ut) = 15% and (var(+) = 4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 4 times leverage, generating the following return before fees: Question 6 rt' hedge fund before fees = 4 * (ractive fund before fees _ r stock index) - Suppose that the passive fund has a fee of 0.30% and the active fund has a fee of 1.40%. An investor has $40 invested in the active fund and $60 in cash. He changes his investment to an equivalent investment in the hedge fund, the passive mutual fund, and cash (i.e., with the same alpha and the same exposures to restock index and t). Which management fee for the hedge fund makes the two investments identical in terms of net returns (assume that the hedge fund charges a zero performance fee)? a. 5.30% b. 4.44% c. 5.60% d. 4.00% e. 4.52% f. 4.40%