Consider historical data showing that the average annual rate of return on the S&P $500$ portfolio over the past $85$ years has

averaged roughly $8\%$ more than the Treasury bill return and that the S&P $500$ standard deviation has been about $31\%$ per year.

Assume these values are representative of investors' expectations for future performance and that the current T$-$bill rate is $3\%.$

Calculate the expected return and variance of portfolios invested in T$-$bills and the S&P $500$ index with weights as shown

below. $($Enter your answers as decimals rounded to $4$ places. Leave no cells blank $-$ be certain to enter $"0"$ wherever

required.$)$