Zadie has invested 25% of her funds in Treasury bills and 75% 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.

(a) If X is the annual return on T-bills and Y is the annual return on stocks, find the rate of return of the portfolio.

(b) The returns X and Y are random variables because they vary from year to year. Find the average return and standard deviation of the returns of the portfolio based on annual returns between 1980 and 2021:

X= annual return on T-bills: X=6.5%X=2.5% Y= annual return on stocks: X=11%X=12.5% Correlation between X and Y:=15.2