Today is Thursday, April 9, 2020.

The SPY (S&P 500 ETF) has a current price of $278. Below is the U.S. Treasury yield curve from Treasury.gov; people often use the U.S. Treasury curve as the risk-free interest rate.

1. Today is 04/9/20, and the one-year treasury rate is 0.25% per year (Wow! That is low!)

What should be the one-year forward price for SPY if the spot price is $278?

2. You buy the year forward contract on the SPY. What will be your profit or loss if the SPY declines by ten percentage points next year? Assume no dividends.
3. Assume the SPY will have one of two values in a year. The price will be 25% higher than today, or it will be 20% lower than today. What are the two spot prices, and what are the two corresponding payoffs from a long forward position?
4. What is the risk neutral probability of an increase in SPY spot price based on this scenario?
5. What is the price of buying insurance for a long forward position against a loss?