1. You observe that one U.S. dollar is currently equal to 24 Mexican pesos in th
ID: 2616533 • Letter: 1
Question
1. You observe that one U.S. dollar is currently equal to 24 Mexican pesos in the spot market. The one year US interest rate is 4% and the one year Mexican interest rate is 8%. One year later, you observe that one U.S. dollar is now equal to 26 Mexican pesos in the spot market. You would have made a profit if you had borrowed Mexican pesos and invested in U.S. dollars. How do you calculate the profit.
2. As of today, the spot exchange rate is €1.00 = $1.60 and the rates of inflation expected to prevail for the next year in the U.S. is 2% and 3% in the euro zone. What is the one-year forward rate that should prevail?
3. Suppose you observe a spot exchange rate of $1.50/€. If interest rates are 5% APR in the U.S. and 3% APR in the euro zone, what is the no-arbitrage 1-year forward rate?
4. You observe that the expected rate of inflation over the next year is 3.53% and current one year Treasury bills are yielding 5.82%. Based on the domestic Fisher effect, what is the approximate one year real rate of interest?
5. Suppose that the annual interest rate is 2.0 percent in the United States and 4 percent in Germany, and that the spot exchange rate is $1.60/€ and the forward exchange rate, with one-year maturity, is $1.58/€. Assume that an arbitrager can borrow up to $1,000,000 or €625,000. If an astute trader finds an arbitrage, what is the net cash flow in one year?
Please show your work. I am having trouble with my formulas and I need some help. Thank you.
Explanation / Answer
1. 1 USD = 24 Mexican Peso (MXP); interest rate US (rUS) = 4% and Mexico (rMX) = 8%; as per the interest rate parity
Expected Future Spot Rate = Spot Rate * (1+rMX)/(1+rUS) which will given us = 24 * (1+8%)/(1+4%) = 24.92308
Since the spot rate after 1 year is 1 USD = 26 MXP, there is a possible arbitrage as below:
2. Spot exchange rate 1 Euro = USD 1.60; Inflation US (IUS) = 2% and Inflation Euro (IEU) = 3%. Now as per the relative purchasing power parity, the exchange rates are determined by the purchasing power across two countries and as the purchasing power changes due to inflation the exchange rates will also move accordingly (high inflation country will see currency depreciation).
Forward Rate = Spot Rate * (1+ IUS) / (1+IEU) = 1.60 * (1+2%)/(1+3%) = 1.5845
3. Spot Exchange rate 1 Euro = USD 1.50; Interest rate US (rUS) = 5% and Euro (rEU) = 3%
As per interest rate parity: Forward Rate = Spot Rate * (1+rUS)/(1+rEU) = 1.50 * (1+5%)/(1+3%) = 1.5291
4. As per the fisher effect, the approximate real rate = nominal rate - expected inflation
Hence real rate = 5.82% - 3.53% = 2.29%
5. Spot rate 1Euro = 1.60 USD; rUS = 2% and rGR = 4%; Forward rate is 1 Euro = 1.58 USD
As per the interest rate parity the Forward rate should be Spot Rate * (1+rUS)/(1+rGR) = 1.60 * (1+2%)/(1+4%) = 1.5692
Since the current Forward rate at 1 Euro = 1.58USD is different, it suggests that we can arbitrage as below:
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.