The risk-free interest rate r_f is zero and the mutual funds (passive and active, respectively) claim to deliver the following total returns (before fees):

Rt^PF=R_t^M=6%+u_t

R_t^AF=1.5%+1.2R_t^M+_t

where R_t^M is the return of market index, the error terms u_t and _t are independent over time and of each other, have zero means [u_t]=[_t]=0, and volatilities of (u_t)=15% and (_t)=4%. The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long-short hedge fund, applying 3 times leverage, generating the following return before fees:

R_t^HF=3(R_t^AFR_t^M)

a) What is the hedge funds volatility? b)What is the hedge fund's R-squared relative to the market index? c)Suppose that the passive fund has a fee of 0.30% and the active fund has a fee of 1.40%. An investor has $30 invested in the active fund and $70 in cash. She/he changes her/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

R_t^M stock 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)?