8. Spot Price vs Futures Price (12 points) Today, the 125-trading-day futures contract on stock Jigglypuff has just expired. Let's call today day 0 . The stock does not pay any dividend. 125 trading days ago, the stock price was 100 . Download "Spot Price vs Futures Price.xlsx" from eClass. The following are provided in the spreadsheet: - trading day - number of trading days to maturity - years to maturity - the spot price of the stock at each trading day. - risk-free rate per annum: r=2% Assume there are 250 trading days per annum. (a) (5 points) Assuming the futures price follows no-arbitrage principle, calculate the futures price for each trading day. In 1 chart, plot the two time series (spot price for each trading day, futures price for each trading day). X-axis: trading day, y-axis: price. Make proper legends. (b) (2 points) What are the values of the spot price and futures price today at maturity of the futures contract (trading day 0 )? What explains your observation? (c) (5 points) Using the historical volatility method to calculate S : the annualized standard deviation of returns of the spot. Apply the same method to calculate F : the annualized standard 5 deviation of returns of the futures. What is value for S and F. What do you find about the relationship between S and F ? - note 1: gross return for day t is defined as St1St for spot price and Ft1Ft for futures price. - note 2: you may store your intermediate calculations in columns F-M and do not have to report them