Lecture 7: The Forward Exchange Market

Determining the Appropriate Forward Exchange Quote: The

Interest Rate Parity Model

Where is this Financial Center?

Pudong, Shanghai: The Bund and the Oriental Pearl Tower

Shanghai Foreign Exchange Trade Center (1901)

China’s Foreign Exchange Trade System China’s Foreign Exchange Trade System (CFETS)

was founded in April 1994 as part of China’s FX reforms. Today CFETS plays a significant role in managing the Yuan exchange rate.

CFETS is a sub-institution of the People's Bank of China (PBC). Its main foreign exchange functions include: providing a system for foreign exchange trading; organizing interbank FX trading, providing information on the FX, market; and engaging in other businesses authorized by the PBC.

CFETS is headquartered in Shanghai.

Inside China’s Foreign Exchange Trade System (2003)

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.

Consider 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.

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 (open position). 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%).

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 (a short position). 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).

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 1.0005/1.0009 AUD/USD 1 year forward 0.9650/0.9657

Calculate the USD covered amount when the bond matures:

______________________

Answer: U.S. Dollar Equivalent of the Maturing AUD Government Bond Amount of AUD to be received in 1 year from

maturing bonds: Par value = AUD1,000 x 100 = AUD100,000 Interest (5.5% coupon) = 100,000 x 0.055 = AUD5,500 Total received = AUD105,500 (to be sold forward)

Exchange rates: AUD/USD spot 1.0005/1.0009 AUD/USD 1 year forward 0.9650/0.9657

USD covered amount (to be received in 1 year) = AUD105,500 x 0.9650 = USD101,807.50

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 (as a %) to the U.S. investor?

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), or the

discount rate that sets the present value of the future cash inflow to the price of the investment, So given: AUD/USD spot 1.0005/1.0009 AUD/USD 1 year forward 0.9650/0.9657

USD Purchase Price = AUD100,000 x 1.0009 = USD100,090 USD Hedged Equivalent Cash Inflow in 1 year = AUD105,500 x

0.9650 = USD101,807.50 Solve for the IRR (k): -100,090 = 101,807.50/(1+k)

http://www.datadynamica.com/IRR.asp k = 1.72% (Why is this different from the 5.5%)

Answer: Because AUD is selling at a 1 year forward discount.

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

Answer to JGB Covered Return Step 1: Calculate the USD purchasing price of

the JGB: 100,000/76.61 (note this is spot bid) = 1305.31

Step 2: Calculate the yen inflow expected in 1 year: 100,000 x 1.01 = 101,000 (note: coupon rate is 1%)

Step 3: Calculate the USD equivalent of the 1 year yen inflow using a forward contract. 101,000/73.55 = 1373.22 (note this is 1 year ask)

Ask is the price at which the bank will sell you dollars. Step 4: Calculate the IRR (using the web site)

-1305.31= 1373.22/(1+k); k = 5.21% (Why is this different from the 1%)

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.

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 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.

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.

Test of the Interest Rate Parity Model: 1974-1992

Interest Rate Parity Model, 2004

IRP: October 16, 2012Currency 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 1.0275

3 months 1.0200

GBP/USD

Spot 1.6111

3 months 1.6109

USD/JPY

Spot 78.89

3 months 78.82

USD/CHF

Spot 0.9260

3 months 0.9247

IRP: October 16, 2012

Currency FX Rate What is the IRP Interest Rate Explanation for the Forward Rate?

Actual 3 Month Interest Rates (%): Source: The Economist

AUD/USD FX Rate

Spot 1.0275 AUD selling at a forward discount

3 months 1.0200 Australian interest rates must be higher than U.S interest rates

Australia = 3.63%U.S. = 0.34%

GBP/USD

Spot 1.6111 GBP selling at a forward discount

3 months 1.6109 U.K. interest rates must be higher than U.S. interest rates

U.K. = 0.54%U.S. = 0.34%

IRP: October 16, 2012Currency FX Rate What is the IRP Interest

Rate Explanation for the Forward Rate?

Actual 3 Month Interest Rates (%): Source: The Economist and Bloomberg

USD/JPY FX Rate

Spot 78.89 JPY selling at a forward premium

3 months 78.82 Japanese interest rates must be lower than U.S. interest rates

Japan = 0.19%U.S. = 0.34%

USD/CHF

Spot 0.9260 CHF selling at a forward premium

3 months 0.9247 Swiss interest rates must be lower than U.S. interest rates

Switzerland = 0.04%U.S. = 0.34%

How is the Forward Rate Calculated? Market maker banks calculate their quoted forward rate

is calculated from three observable numbers: The (current) spot rate. A foreign currency interest rate. A home currency interest rate (assume to be 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

(sometimes called euro-deposit rates). Large global banks quote each other and clients market interest rates in a range of currencies.

Example: October 11, 2012 http://www.forexpros.com/rates-bonds/forwar

d-rates

Forward Rate Pips off of SpotEUR Selling at a Forward Premium

CAD Selling at a Forward Discount

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

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. FTet = Set x [(1 + INTf) / (1 + INTus)]

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: FTet = Set x [(1 + INTf) / (1 + INTus)] FTet = ¥120 x [(1 + .01) / (1 + .04)] FTet = ¥120 x .971153846 FTet = ¥116.5384615

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

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: FTat = Sat x [(1 + INTus) / (1 + INTf)]

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: FTat = Sat x [(1 + INTus) / (1 + INTf)] FTat = $1.9800 x [(1 + .04) / (1 + .06)] FTat= $1.9800 x .9811 FTat = $1.9426

Appendix A

Calculating the forward rate for periods less than and greater than one year

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.

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)

European Terms Example: Less than 1 year Assume:

USD/JPY spot = 82.006 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 = 82.00 x [(1 + ((0.0012 x 180/360))/((1 + ((0.0017 x 180/360))] FTet = 82.00 x (1.0006/1.00085)FTet = 82.00 x .9997FTet = 81.9795

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.

American Terms Example: More than 1 Year Assume:

GBP/USD spot = 1.58005 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 = 1.5800 x ((1 + 0.0107)5/(1 + 0.0105)5) FTat = 1.5800 x (1.05466/1.05361) FTat = 1.5800 x 1.001FTat = 1.5816 (Note: This is the forward 5 year rate)