Consider historical data showing that the average annual rate of return on theS&P $500$ portfolio over the past $85$ years has averaged roughly $8\%$ more than theTreasury bill return and that the S&P $500$ standard deviation has been about$30\%$ per year. Assume these values are representative of investors expectationsfor future performance and that the current T$-$bill rate is $5\%.$ Calculate theexpected return and variance of portfolios invested in T$-$bills and the S&P $500$index with weights as follows:Weight on T$-$bill Weight on index$0,20,80,40,60,80,2$