Question 6: Zadie has invested 20% of her funds in Treasury bills and 80% in an index fund that represents all U.S. common stocks. The rate of return of an investment over a time period is the percent change in the price during the time period, plus any income received. If x is the annual return on T-bills and Y is the annual return on stocks, the portfolio rate of return is R=0.2X+0.89 The returns X and Y are random variables because they vary from year to year. Based on annual returns between 1950 and 2003, we have X=annual return on T-bills 4x=5.0% 0x =2.9% Y=annual return on stocks Hy = 13.2% 0, -17.6% Correlation between X and Y p=-0.11 Stocks had higher returns than T-bills on the average, but the standard deviations show that retums on stocks varied much more from year to year: That is, the risk of investing in stocks is greater than the risk for T-bills because their returns are less predictable. a) Compute the expected return R on Zadie's portfolio of 20% T-bills and 80% stocks. (2.5 marks) b) The portfolio has a smaller mean return than an all-stock portfolio, but it is also less risky. Find the variance of the portfolio returns. (2.5 marks)