Assuming Gordon's formula for valuation, we can estimate the loss in value of the S\&P 500 since January 1,2022 . See above for the time series of prices. Suppose that at January 1,2022 , the estimated earnings for the next year are equal to $215, and the 10 -year government bond rate on January 1=1.63%. Let's assume that the long-term growth of earnings remains at 6%. a. Given a risk premium =9%, what is the fair value of SP500 on January 1, 2022? b. Given that the price on January 1 was $4713, what is the implied risk premium. c. What is the fair value on October 5 , given that the 10 -year bond rate is 3.89% and earnings equals $235 ? d. How much drop in the fair price would have been expected over the Jan 1 to Oct 5 period If we had known the interest rate and earnings changes? e. How does this compare with the actual drop =23.62%. What might cause any difference? f. Suppose that we would like to estimate the futures prices or S\&P500 in 3 years, given the current price of SP500=$3628. Assume that dividends =2%, and the interest rate on 3 year notes =4.33%, what is the arbitrage price of SP500 for 3 years ahead? Be sure to careful draw the network depicting this problem. Assuming Gordon's formula for valuation, we can estimate the loss in value of the S\&P 500 since January 1,2022 . See above for the time series of prices. Suppose that at January 1,2022 , the estimated earnings for the next year are equal to $215, and the 10 -year government bond rate on January 1=1.63%. Let's assume that the long-term growth of earnings remains at 6%. a. Given a risk premium =9%, what is the fair value of SP500 on January 1, 2022? b. Given that the price on January 1 was $4713, what is the implied risk premium. c. What is the fair value on October 5 , given that the 10 -year bond rate is 3.89% and earnings equals $235 ? d. How much drop in the fair price would have been expected over the Jan 1 to Oct 5 period If we had known the interest rate and earnings changes? e. How does this compare with the actual drop =23.62%. What might cause any difference? f. Suppose that we would like to estimate the futures prices or S\&P500 in 3 years, given the current price of SP500=$3628. Assume that dividends =2%, and the interest rate on 3 year notes =4.33%, what is the arbitrage price of SP500 for 3 years ahead? Be sure to careful draw the network depicting this