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# Cross Rates and Arbitrage

1. On June 23, 2004, the Philippine Peso/US\$ rate was 56.20-28/\$. The Zloty/Peso rate was 0.0669-71 Zloty/Peso. The Zloty/Dollar rate is 3.7660-7710 Zloty/\$. (Source: Yahoo) Can you make money through arbitrage? Show exactly how you would accomplish it. If it's not possible to make money, show that, as well.

2. The following exchange rates are available: ¥64.00/SF; SF1.60000/\$; ¥105/\$.  You have \$100,000 available.  Can you make money by triangular arbitrage?  How?  How much money will you make?

3. Here are some quotes from http://www.ozforex.com.au/cgi-bin/spotrates.asp, as of 4:15 p.m. on June 27, 2005.

 Bid Ask USD/CAD 1.2306 1.2311 CAD/GBP 0.4439 0.4444 USD/JPY 109.29 109.34
1. Compute the implied bid and ask for the British Pound in American terms.
2. If the CAD/JPY rate were 89.78 bid/89.83 ask, would there be arbitrage opportunities?

4. (Summer 2005, Midterm) According to data from Catranis.com (http://sites.barchart.com/pl/cta/quote.htx?sym=BPU5&mode=i), the following were the last transactions prices for the GB pound (as of around 3:10 p.m. on June 27, 2005).

 Contract Month Last Price Sep 2005 1.8228 Dec 2005 1.8179 Mar 2006 1.8130 Jun 2006 1.8081 1.8032 1.7983
1. According to the Unbiased Expectations Hypothesis, what is the market's forecast for the value of the US dollar in terms of British pounds, on December 2005.
2. Assuming the Unbiased Expectations Hypothesis holds, what is the 3-month risk-free interest rate in the UK, today, if the 3-mth T-bill rate is 2.98% (Source: http://online.wsj.com/page/mdc/0,,2_0500-bondkir-10,00.html)?
3. Using the data in the table above, what would be your hypothesis regarding the relative growth rates in GNP in the UK versus the US, if you know that relative money growth rates are expected to be similar in the near future and money velocities are also similar? (You may assume that the unbiased expectations hypothesis holds.)

5. (Summer 2005, Midterm) According to http://www.ozforex.com.au/, the GB pound was trading at \$1.8264 on June 28, 2004. If the rate on June 27, 2005 was 1.8231, what is the change in the real value of the GB pound in terms of dollars over the last year? According to the BBC, inflation in the UK over the last year has been steady at 2.7%, while in the US, (estimated from www.economagic.com data), inflation has been about 2.82%.

# Parity Relationships

1. (Fall 2002 Midterm) Pittsburgh Steel has received an order from a Mexican manufacturing company for stainless steel worth Ps. 15,000,000.  The export sale would be denominated in Mexican pesos on a one-year open account basis.  The current spot rate is Ps.10.00/\$, and the forward peso sells at a discount of 8% per annum.  However, the finance staff of Pittsburgh Steel forecasts that the peso will drop only 6% in value over the next year.  Pittsburgh Steel can borrow pesos in Mexico City at 8% per annum.

1. If Pittsburgh Steel hedges in the forward market, what will its dollar proceeds from the sale of the steel, received one year hence?
2. If Pittsburgh Steel hedges in the money market, what will its dollar proceeds be, received today?

2. (Fall 2005, Exam 1) (You have the following information on spot rates as of the close of Oct. 21, 2005 (all information from Moneyline):

 Spot Rates (USD) Ask EUR 1.2039 JPY 115.24 GBP 1.7771 AUD 0.7525 CAD 1.1779

One-month, three-month and six-month US treasuries yield 3.476, 3.879 and 4.165% respectively. (Note these are bond-equivalent yields, based on a 365-day year.) The corresponding rates for the euro-currency area are 2.11, 2.19 and 2.28%, respectively. (These are actually brokered deposits in euros, but you may use them as the equivalent of rates on government securities.)

1. What would the 1-month, 3-month and 6-month forward rates on the euro have to be to prevent arbitrage?
2. The 6-month rate in Japan is 0%. What is the 6-month yen-dollar forward rate?

3. (Summer 2004, Practice Midterm) Suppose today's exchange rate is \$0.90/€. The six-month interest rates on dollars and euros are 6% and 3% respectively. The six-month forward rate is \$0.8978. A foreign exchange advisory service has predicted that the euro will appreciate to \$0.9290 within six months.

1. How would you use forward contracts to profit in this situation?
2. How would you use money-market instruments (borrowing and lending) to profit?
3. Which alternatives (forward contracts or money market instruments) would you prefer? Why?

4. (Summer 2004, Practice Midterm) You are given the following exchange rate and interest rate quotes:

 Currency 90-Day Interest Rates (annualized) Spot Rates 90-day Forward Rates Dollar 4.99%-5.03% Swiss France 3.14%-3.19% \$0.711-22 \$0.727-32
1. Can you find an arbitrage opportunity?
2. What steps must you take to capitalize on it?
3. What is the profit per \$1m. arbitraged?

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