Suppose you are a fund-of-funds manager with investments in n different hedge funds for some n > 2. Let ri denote the annualized return of the 2-th fund. Suppose that ri = Brm +in var(ei) = 0; where rm denotes the return of the market portfolio (approximated by the S&P 500 in the US) with variance om. Suppose that b and ej are independent random variables if i + j, and that ; is independent from rm for all i = 1, ..., n. Suppose that your fund-of-funds has invested hi > 0 dollars in the i-th hedge fund, so their profit/loss is = 7 = h'r = hiri. = Throughout the following, assume h= (1, 1, ...,1) ER for simplicity, ie. the fund-of-funds has one unit of capital evenly distributed across its constituents. (a) Calculate E[h'r] and V[h'r]. Note that V[h'r] can be expressed as V(h'r) = f(8,0) +go,...,02) and find functions f() and g() explicitly. Suppose you are a fund-of-funds manager with investments in n different hedge funds for some n > 2. Let ri denote the annualized return of the 2-th fund. Suppose that ri = Brm +in var(ei) = 0; where rm denotes the return of the market portfolio (approximated by the S&P 500 in the US) with variance om. Suppose that b and ej are independent random variables if i + j, and that ; is independent from rm for all i = 1, ..., n. Suppose that your fund-of-funds has invested hi > 0 dollars in the i-th hedge fund, so their profit/loss is = 7 = h'r = hiri. = Throughout the following, assume h= (1, 1, ...,1) ER for simplicity, ie. the fund-of-funds has one unit of capital evenly distributed across its constituents. (a) Calculate E[h'r] and V[h'r]. Note that V[h'r] can be expressed as V(h'r) = f(8,0) +go,...,02) and find functions f() and g() explicitly