1. Lecture 7: The Forward Exchange Market
Determining the Appropriate Forward Exchange Rate Quote: The Interest Rate Parity Model

2. Where is this Financial Center?

3. How do Market Makers Determine the Forward Exchange Rate?
The quoted forward rate is not a reflection of where market makers think the spot exchange rate will be on that forward date .
Lloyds Bank, UK (Corporate Banking and Treasury Training Publication) : “Forward rates .. are not the dealer's [i.e., market maker bank’s] opinion of where the spot rate will be at the end of the period quoted.”
So what determines the forward rate?
Quick answer: Interest rate differentials between currencies being quoted, or the Interest Rate Parity Model.
To develop this concept, and the Interest Rate Parity Model, we will work through the following example.

4. Thinking About Cross Border Investing
Assume a U.S. investor has $1 million to invest for 1 year and can select from either of the following 1 year investments:
(1) Invest in a U.S. government bond and earn 2.0% p.a.
(2) Invest in an Australian government bond and earn 5.5% p.a.
If the U.S. investor invests in Australian government bonds, he/she will receive a known amount of Australian dollars in 1 year when the bond matures.
Principal repayment and interest payment both in AUD.

5. Risk of Investing Cross Border
Question: Using the previous example, what is the risk for the U.S. investor if he/she buys the 1 year Australian government bond?
Answer: The risk associated with foreign exchange exposure in AUD.
The U.S. investor will be paid a specified amount of Australian dollars 1 year from now:
The risk is the uncertainty about the Australian dollar spot rate 1year from now.
If the Australian dollar (spot) weakens, the U.S. investor will receive fewer U.S. dollars at maturity:
Example: If the Australian dollar weakened by 2% by the end of the year, this reduces the return on the Australian investment (from 5.5 % to 3.5%).

6. Solution to The Currency Risk for the U.S. Investor
Question: Using the previous example, how could the U.S. investor manage the risk associated with this Australian dollar exposure?
Solution: The US investor can cover the Australian dollar investment by selling Australian dollars 1 year forward.
Australian dollar amount which the investor will sell forward would be equal to the principal repayment plus earned interest (Note: this was the known amount of AUD to be received in 1 year).

7. Calculating the U.S. Dollar Equivalent of the Maturing AUD Government Bond when Covered
Assume:
A 1 year Australian Government Bond with a par value of 1,000AUD (assume you purchased 100 of these at par)
Assume an annual coupon of 5.5% (payable at the end of the year)
Assume the following market maker bank quoted exchange rates:
AUD/USD spot /1.0009
AUD/USD 1 year forward /0.9657
Calculate the USD covered amount when the bond matures:
______________________

8. Concept of Covered Return
The covered return (i.e., hedged return) on a cross border investment, is the return after the investment’s foreign exchange risk has been covered with the appropriate forward contract.
The forward exchange rate will determine the “covered” investment return for the U.S. investor.
In the previous example, how would you determine the covered return to the U.S. investor?

9. Calculating the Covered Return
Answer: Calculate the yield to maturity on the investment when covered.
Note: Yield to Maturity is the internal rate of return (IRR), which is the discount rate that sets the present value of the future cash inflow to the price of the investment.
USD Purchase Price = AUD100,000 x = USD100,090
USD Hedged Equivalent Cash Inflow in 1 year = USD101,807.50
Solve for the IRR (k): -100,090 = 101,807.50/(1+k)
k = 1.72% (Why is this different from the 5.5%)
Answer: Because AUD is selling at a 1 year forward discount.

10. Another Example of a Covered Return
Assume the following:
A 1 year Japanese Government Bond with a coupon of 1%.
Par value of 100,000 yen and selling at par.
Exchange Rates:
USD/JPY spot: 76.61/76.65
1 year forward: 73.50/73.55
Calculate the covered return for a U.S. investor on the above JGB. Use the web site on the previous page to do this.

11. Covered Interest Arbitrage
Covered interest “arbitrage” is a situation that occurs when a covered return offers a higher return than that in the investor’s home market.
As an example assume:
1 year interest rate in U.S. is 4%
1 year interest rate in Australia is 7%
AUD 1 year forward rate is quoted at a discount of 2%.
In this case, a U.S. investor could invest in Australia and
Cover (sell Australian dollars forward) and earn a covered return of 5% (7% - 2%) which is 100 basis points greater than the U.S. return
This is covered interest arbitrage: earning more (when covering) than the rate at home.

12. Explanation for Covered Interest Arbitrage Opportunities
Covered interest arbitrage will exist whenever the quoted forward exchange rate is not priced correctly.
If the forward rate were priced correctly, the covered return should equal the
If the forward rate is priced correctly, covered interest arbitrage should not exist.
Going back to our original example:
(1) Invest in a U.S. government bond and earn 2.0%.
(2) Invest in an Australian government bond and earn 5.5%
If the AUD 1 year forward were quoted at a discount of 3.5%, then the covered return (2%) and the home return (2%) would be equal.

13. The Appropriate Forward Exchange Rate and the Interest Rate Parity Model
The Interest Rate Parity Model (IRP) offers an explanation of the market’s correctly priced (i.e., “equilibrium”) forward exchange rate.
This equilibrium rate is the forward rate that precludes covered interest arbitrage
The Interest Rate Parity Model states:
“That in equilibrium the forward rate on a currency will be equal to, but opposite in sign to, the difference in the interest rates associated with the two currencies in the forward transaction.”
Thus, the equilibrium forward rate is whatever forward exchange rate will insure that the two cross border investments will yield similar returns when covered.

14. Test of the Interest Rate Parity Model: 1974-1992

15. Interest Rate Parity Model, 2004

16. IRP Today: September 28, 2011 Currency Pair FX Rate:
Spot and 3 Month Forward
Is the Foreign Currency Forward at a Discount or Premium ?
What is the IRP Interest Rate Explanation for the Forward Rate?
AUD/USD
FX Rate
Spot
0.9781
3 months
0.9744
GBP/USD
1.5576
1.5563
USD/JPY
76.61
76.52
USD/CHF
0.9001
0.8985

17. How is the Forward Rate Calculated?
Market maker banks calculate their quoted forward rate is calculated from three observable elements:
The (current) spot rate.
A foreign currency interest rate.
A home currency interest rate (assume to be a the U.S.).
Note: The maturities of the interest rates used should be approximately equal to the calculated forward rate period (i.e., maturity of the forward contract).
What interest rates are used?
Interbank market (wholesale) interest rates for currencies (euro-deposit rates). Large global banks continuously quote each other and clients market interest rates in a range of currencies.

18. Forward Rate Formula for European Terms Quote Currencies
The formula for the calculation of the equilibrium European terms forward foreign exchange rate is as follows:
FTet = Set x [(1 + INTf) / (1 + INTus)]
Where:
FTet = forward foreign exchange rate at time period T, expressed as units of foreign currency per 1 U.S. dollar; thus European terms, i.e., “et”
Set = today's European terms spot foreign exchange rate,
INTf = foreign interest rate for a maturity of time period T (expressed as a percent, e.g., 1% = 0.01)
INTus = U.S. interest rate for a maturity of time period T

19. Example: Solving for the Forward European Terms Exchange Rate
Assume the following data:
USD/JPY spot = ¥120.00
Japanese yen 1 year interest rate = 1%
US dollar 1 year interest rate = 4%
Calculate the 1 year yen forward exchange rate.
Set up the formula and insert data:

20. Forward Rate Formula for American Terms Quote Currencies
The formula for the calculation of the equilibrium American terms forward foreign exchange rate is as follows:
FTat = Sat x [(1 + INTus) / (1 + INTf)]
Where:
FTat = forward foreign exchange rate at time period T, expressed as the amount of 1 U.S. dollars per 1 unit of the foreign currency; thus American terms, or at)
Sat = today's American terms spot foreign exchange rate.
INTus = U.S. interest rate for a maturity of time period T (expressed as a percent, e.g., 4% = 0.04)
INTf = Foreign interest rate for a maturity of time period T

21. Example: Solving for the American Terms Forward Exchange Rate
Assume the following data:
GPB/USD spot = $1.9800
UK 1 year interest rate = 6%
US dollar 1 year interest rate = 4%
Calculate the 1 year pound forward exchange rate.
Set up the formula and insert data.

22. Appendix A
Calculating the forward rate for periods less than and greater than one year

23. Formulas and Interest Rates
The formulas used in the previous slides show you how to calculate the forward exchange rate 1 year forward.
The following slides illustrate how to adjust the forward rate formula for periods other than 1 year.
Important:
All interest rates quoted in financial markets are on an annual basis, thus and adjustment must be made to allow for other than annual interest periods.

24. Forwards Less Than 1 Year: European Terms
FTet = Set x [(1 + ((INTf) x n/360)) / (1 + ((INTus) x n/360))]
Where:
FT = forward foreign exchange rate at time period T, expressed as units of foreign currency per 1 U.S. dollar;
Set = today's European terms spot foreign exchange rate.
INTf = foreign interest rate for a maturity of time period T
INTus = U.S. interest rate for a maturity of time period T
n = number of days in the forward contract (note: we use a 360 day year in this formula).
Note: What we have added to the original formula is an adjustment for the time period (n/360)

25. European Terms Example: Less than 1 year
Assume:
USD/JPY spot = 82.00
6 month Japanese interest rate = 0.12%*
6 month U.S. interest interest rate= 0.17%*
*These are interest rates expressed on an annual basis.
Calculate the 6 month forward yen
FTet = Set x [(1 + ((INTf) x n/360))/ (1 + ((INTus) x n/360))]
Ftet = x [(1 + (( x 180/360))/((1 + (( x 180/360))]
FTet = x (1.0006/ )
FTet = x .9997
FTet =

26. Forwards More Than 1 Year: American Terms
FTat = Sat x [(1 + (INTus)n / (1 + (INTf)n]
Where:
FT = forward foreign exchange rate at time period T, expressed as the amount of 1 U.S. dollars per 1 unit of the foreign currency.
Sat = today's American terms spot foreign exchange rate.
INTus = U.S. interest rate for a maturity of time period T
INTf = Foreign interest rate for a maturity of time period T
n = number of years in the forward contract.

27. American Terms Example: More than 1 Year
Assume:
GBP/USD spot =
5 year United Kingdom interest rate = 1.05%*
5 year United States interest rate = 1.07%*
*These are interest rates expressed on an annual basis.
Calculate the 5 year forward pound:
FTat = Sat x ((1 + INTus)n/(1 + INTf)n)
FTat = x (( )5/( )5)
FTat = x ( / )
FTat = x 1.001
FTat = (Note: This is the forward 5 year rate)