Assume you invest all your wealth ($ 500, 000) in the S&P 500 index fund. You expect the annual return of the fund to be 8% and the standard deviation in returns to be 20%. Now you are considering to add treasury bill to your portfolio.a) Estimate the expected return and standard deviation of your portfolio, if you decide to shift $ 200, 000 from the S&P 500 index fund to T-bill. The T-bill rate is 3%.b) Estimate the expected return and standard deviation of your portfolio, if you want to minimize your portfolio’s risk.c) Calculate the proportion of the wealth you would invest in the S&P 500 index and T-bill, if you prefer a portfolio with a standard deviation of 10%.