1) You go out to the market and see that MMM stock is trading for $182.03 today and the 2 year forward price is $187.26. Assume MMM doesn’t pay dividends. You also see that the interest rate is 2.1% per year, continuously compounded. Create an arbitrage portfolio that pays exactly $15 in 2 years and costs nothing today.
2) We assumed that MMM doesn’t pay dividends. Now what if MMM pays dividends at a constant rate of 3.5% per year. Create an arbitrage portfolio that pays exactly $100 today and has no obligations in the future.
3) Now suppose you don’t know what the actual interest rate is, based on the current MMM price, dividend rate, and the forward price what is the effective annual interest rate? Create a 2 year, zero coupon bond with a face value of $100 from a portfolio of stock and forward. That is, create a portfolio that costs a little less than $100 today, and at time T pays $100. Your answer should tell me exactly how many shares of stock and forward to go long/short.