Question 1
In early 2020, the spot exchange rate between the US dollar and the Euro was 1.855700 $/Euro. The 6-month interest rate in the US is 3.5700% and the Euro rate is 2.3400%. Based on the table below, what should the 6-month $/Euro forward rate be to prevent arbitrage opportunities? Show all calculation to 6 decimal places.
A) What should the 6-month $/Euro forward rate be to prevent arbitrage opportunities?
B) Suppose the the 6-month $/Euro forward rate is 1.871795. What arbitrage opportunities are there? Construct an arbitrage/payoff table to outline your strategy. What is the aggregate arbitrage profit that can be made (if any)?
C) Suppose the the 6-month $/Euro forward rate is 1.865367. What arbitrage opportunities are there? Construct an arbitrage/payoff table to outline your strategy. What is the aggregate arbitrage profit that can be made (if any)?
Question 2
Based on the risk-free yield curve given below and assuming semi-annual compounding using a 30/360 day count convention (as used in class) calculate:
1) the discount factors (6 decimal places)
2) the zero-coupon yield curve (spot rate curve) (6 decimal places)
3) All implied forward rates contained within the yield curve (6 decimal places)
4) Suppose you are quoted a 6-month forward rate starting 6 months from today (0.5 F*1.0) that is 10 basis points (0.10%) higher than the theoretical 6-month forward rate starting 6 months from today (0.5 F1.0) that you calculated in part 3. Create an investment strategy using an arbitrage table, to exploit this arbitrage opportunity.
5) Suppose you are quoted a 6-month forward rate starting 6 months from today (0.5 F*1.0) that is 15 basis points (0.15%) lower than the theoretical 6-month forward rate starting 6 months from today (0.5 F1.0) that you calculated in part 3. Create an investment strategy using an arbitrage/payoff table, to exploit this arbitrage opportunity.
