Kevin doubts that Stock 1 is a good choice. However, he asks you to provide a benchmark to compare Stock 1 with. You propose to use a price-weighted index as a benchmark. The index is composed of 3 stocks. The table below displays the price of each stock on September 22, 2022. Firms A, B, and C have a 60% chance to be in a good state on October 22,2022 , which would imply that the prices of the three stocks would increase by 12%. However, the three firms also have 40% chance to be in a bad state on October 22,2022 , which would imply that their prices would decrease by 5%. a) Compute the price of the index on September 22, 2022 as well as the expected price of the index on October 22, 2022. b) Compute the expected simple return of the index between September 22, 2022 and October 22, 2022. c) Compute the variance of the index returns on October 22, 2022. d) Compute the Sharpe ratio of the index on October 22, 2022. (Suppose a risk-free rate of 0.5\%) e) Compare the Sharpe ratio of the index with the Sharpe ratio that you computed in question 3(e). Based on the Sharpe ratios, is the portfolio that you proposed a better/worse investment than the index? f) Suppose that on September 22 the economy is in a good state. If you want to replace Stock C by Stock 1, what would the divisor of your price index need to become such that the price of the index would not change? Kevin doubts that Stock 1 is a good choice. However, he asks you to provide a benchmark to compare Stock 1 with. You propose to use a price-weighted index as a benchmark. The index is composed of 3 stocks. The table below displays the price of each stock on September 22, 2022. Firms A, B, and C have a 60% chance to be in a good state on October 22,2022 , which would imply that the prices of the three stocks would increase by 12%. However, the three firms also have 40% chance to be in a bad state on October 22,2022 , which would imply that their prices would decrease by 5%. a) Compute the price of the index on September 22, 2022 as well as the expected price of the index on October 22, 2022. b) Compute the expected simple return of the index between September 22, 2022 and October 22, 2022. c) Compute the variance of the index returns on October 22, 2022. d) Compute the Sharpe ratio of the index on October 22, 2022. (Suppose a risk-free rate of 0.5\%) e) Compare the Sharpe ratio of the index with the Sharpe ratio that you computed in question 3(e). Based on the Sharpe ratios, is the portfolio that you proposed a better/worse investment than the index? f) Suppose that on September 22 the economy is in a good state. If you want to replace Stock C by Stock 1, what would the divisor of your price index need to become such that the price of the index would not change
