in time. Assume that the investor estimates variance using a rolling five-year window of monthly data. a. Compute the optimal portfolio of the stock market and T-bills for the investor each month, assuming that the investor has mean-variance preferences with risk aversion y = 3.2. Impose realistic portfolio constraints, preventing the investor from shorting stocks or taking more than 50% leverage: that is, conning the portfolio weight on the market portfolio mm to lie between 0% and 150%. Plot the time series of the weight on the market portfolio [wmI]; 1. (Note: Be careful with the timing here. The weight for a given month is computed using forecasts of the market return and variance for that month using the information available in the previous month.) b. Compute the time series of the return from this optimal portfolio, T {Hill}: 1 ' c. Decompose the portfolio return into a benchmark return (also referred to as \"factor return" or \"passive return\") and an active return: _ hm]: hm]: 1"th ' Tp't _ rt + T: . . 1.._..,._..r Active Retum Benchmark Return. You can set the benchmark as the portfolio for this investor when he does not try to time the market (is. the portfolio from (1)). The average active return is referred to as \"alpha.\" What is the alpha of the optimal portfolio? d. What is the Sharpe Ratio of the optimal portfolio? e. What is the Tracking Error of the optimal portfolio? {The tracking error is defined as the standard deviation of the active return. It measures how disperse the active returns are relative to the benchmark.)