Consider historical data showing that the average annual rate of return on the S&P $500$ portfolio over the past $90$ years has averaged roughly $8\%$ more than the Treasury bill return, and that the S&P $500$ standard deviation has been about $20\%$ per year. Assume these values are representative of investors$$ expectations for future performance and that the current T$-$bill rate is $5\%.$ a$.$ Calculate the expected return and variance of portfolios invested in T$-$bills and the S&P $500$ index with weights as follows: a$.$ Calculate the expected return and variance of portfolios invested in T$-$bills and the S&P $500$ index with weights as follows: