The Following Notes Are from Professor David Hsieh's BA450 Course

Lecture 4. The Foreign Exchange Market and the Eurocurrency Market

To understand the global bond market, we need to understand the intimate link between foreign exchange and short term interest rates.

We will do this in greater detail in International Corporate Finance (BA452).

Importance of Foreign Exchange (FX) Firms operating in more than one country must use different currencies. They use the FX market to convert cash flows from one currency to another currency.

Importance of the Eurocurrency Market The Eurocurrency market is a short term money market in which banks and firms can borrow and lend to each other in any currency of denomination. The maturity ranges from overnight to 1 year.

Linkage of the FX Market and the Eurocurrency Market The two markets are linked together, through short term money flows between currencies.

4-1 4.1. FX Spot Market

The Interbank FX Market is a network of telephones, telexes, computer terminals. The participants are mainly large companies and banks. Spot and Forward FX Contracts are traded. Quotation. American style: US Dollars per unit of currency. European style: Units of currency per US Dollar. Major centers: NY, London, Tokyo. Three major currency blocks: US Dollar (USD), Deutsche mark (DEM), Japanese Yen (JPY). Most trades are against the USD. Size of FX market: $1 trillion a day!

4-2 FX Quotes: July 31, 1996 NEW YORK (Dow Jones)--The New York foreign exchange selling rates below apply to trading among banks in amounts of $1 million and more, as quoted at 3 p.m. Eastern time by Dow Jones Telerate, Inc. and other sources. Retail transactions provide fewer units of foreign currency per dollar. U.S. $ Equiv. Currency Per U.S. $ 7/31 7/30 7/31 7/30 Argentina (Peso) 1.0012 1.0012 .9988 .9988 Australia (Dollar) .7736 .7796 1.2927 1.2827 Austria (Schilling) .09681 .09583 10.330 10.435 Bahrain (Dinar) 2.6525 2.6525 .3770 .3770 Belgium (Franc) .03301 .03287 30.290 30.425 Brazil (Real) .9766 .9775 1.0240 1.0230 Britain (Pound) 1.5561 1.5578 .6426 .6419 30-Day Forward 1.5556 1.5574 .6428 .6421 90-Day Forward 1.5556 1.5574 .6429 .6421 180-Day Forward 1.5565 1.5587 .6425 .6416 Canada (Dollar) .7274 .7275 1.3747 1.3745 30-Day Forward .7280 .7281 1.3737 1.3735 90-Day Forward .7292 .7293 1.3714 1.3711 180-Day Forward .7308 .7310 1.3684 1.3680 Chile (Peso) .002433 .002427 410.95 411.95 China (Renminbi) .1199 .1199 8.3407 8.3409 Colombia (Peso) .0009533 .0009547 1049.00 1047.50 Czech. Rep. (Koruna) .03793 .03763 26.367 26.576 Denmark (Krone) .1757 .1750 5.6930 5.7153 Ecuador (Sucre) Float .0003132 .0003133 3193.00 3192.00 Finland (Markka) .2227 .2214 4.4906 4.5168 France (Franc) .2002 .1996 4.9960 5.0090 30-Day Forward .2005 .2000 4.9883 5.0011 90-Day Forward .2011 .2006 4.9727 4.9855 180-Day Forward .2021 .2016 4.9482 4.9610 Germany (Mark) .6791 .6770 1.4725 1.4772 30-Day Forward .6804 .6782 1.4698 1.4744 90-Day Forward .6831 .6809 1.4639 1.4687 180-Day Forward .6876 .6853 1.4544 1.4592 Greece (Drachma) .004261 .004243 234.66 235.67 Hong Kong (Dollar) .1293 .1293 7.7337 7.7332 Hungary (Forint) .006580 .006552 151.97 152.62 India (Rupee) .02795 .02796 35.778 35.770 Indonesia (Rupiah) .0004255 .0004254 2350.25 2350.50 Ireland (Punt) 1.6176 1.6189 .6182 .6177 Israel (Shekel) .3172 .3164 3.1530 3.1605 Italy (Lira) .0006581 .0006557 1519.50 1525.00

4-3 July 31, 1996 (cont)

U.S. $ Equiv. Currency Per U.S. $ 7/31 7/30 7/31 7/30

Japan (Yen) .009361 .009263 106.83 107.96 30-Day Forward .009403 .009305 106.35 107.47 90-Day Forward .009486 .009382 105.42 106.59 180-Day Forward .009608 .009507 104.08 105.19 Jordan (Dinar) 1.4104 1.4104 .7090 .7090 Kuwait (Dinar) 3.3445 3.3422 .2990 .2992 Lebanon (Pound) .0006384 .0006384 1566.50 1566.50 Malaysia (Ringgit) .4008 .4009 2.4953 2.4943 Malta (Lira) 2.8249 2.8090 .3540 .3560 Mexico (Peso) Float .1320 .1322 7.5770 7.5660 Netherland (Guilder) .6047 .6030 1.6536 1.6585 New Zealand (Dollar) .6888 .6933 1.4518 1.4424 Norway (Krone) .1570 .1566 6.3685 6.3850 Pakistan (Rupee) .02863 .02872 34.930 34.820 Peru (new Sol) .4112 .4112 2.4318 2.4318 Philippines (Peso) .03812 .03812 26.230 26.230 Poland (Zloty) .3705 .3701 2.6990 2.7018 Portugal (Escudo) .006591 .006578 151.72 152.03 Russia (Ruble) (a) .0001919 .0001921 5212.00 5206.00 Saudi Arabia (Riyal) .2666 .2666 3.7505 3.7505 Singapore (Dollar) .7072 .7072 1.4140 1.4140 Slovak Rep. (Koruna) .03304 .03304 30.265 30.265 South Africa (Rand) .2219 .2239 4.5065 4.4660 South Korea (Won) .001231 .001230 812.65 813.25 Spain (Peseta) .007938 .007933 125.97 126.05 Sweden (Krona) .1515 .1513 6.6020 6.6090 Switzerland (Franc) .8350 .8315 1.1976 1.2026 30-Day Forward .8372 .8336 1.1945 1.1996 90-Day Forward .8415 .8381 1.1883 1.1932 180-Day Forward .8486 .8449 1.1784 1.1836 Taiwan (Dollar) .03634 .03634 27.516 27.516 Thailand (Baht) .03958 .03954 25.267 25.293 Turkey (Lira) .00001205 .00001202 83003.00 83209.50 United Arab (Dirham) .2724 .2724 3.6715 3.6715 Uruguay (New Peso) Fin .1232 .1232 8.1200 8.1200 Venezuela (Bolivar) b .002119 .002120 472.00 471.75 Brady Rate .002111 .002111 473.75 473.75 SDR 1.4655 1.4612 .6823 .6843 ECU 1.2784 1.2718

4-4 Notes:

Special Drawing Rights (SDR) are based on exchange rates for the U.S., German, British, French , and Japanese currencies. Source: International Monetary Fund. European Currency Unit (ECU) is based on a basket of community currencies. a-fixing, Moscow Interbank Currency Exchange. b-Changed to market rate effective Apr. 22. Special Drawing Rights (SDR) are based on exchange rates for the U.S., German, British, French , and Japanese currencies. Source: International Monetary Fund. European Currency Unit (ECU) is based on a basket of community currencies.

4-5 4.2. FX Forward Market

An FX forward contract is an customized agreement between a buyer and a seller to exchange currency at some time in the future.

There is a mutually agreed transaction date and amounts. (No money changes hands immediately.)

Forwards are traded over-the-counter.

4-6 Forward Exchange Rates: July 31, 1996

DEM JPY

Spot 1.4720 106.75 1 Month 1.4693 106.395 3 Month 1.4634 105.345 6 Month 1.4539 104.025 12 Month 1.4353 101.47

4-7 4.3. Uses of Forward Exchange Market

Lock in exchange rate. Value future cash flows in foreign currencies. Hedging foreign currency denominated investments (stocks, bonds).

4-8 Example 4.1

Today is July 31, 1996. In 6 months, I am paying DM 1,450,000. What is the PV today? How do I hedge the FX risk?

4-9 Example 4.2

Today is July 31, 1996. Suppose I am receiving ¥ 105,000,000 and paying DM 1,450,000 in 6 months. Will I have enough money to do this transaction?

Spot Valuation: ¥ 105,000,000 = $ 105,000,000 / 106.75 = $ 983,607. DM 1,450,000 = $ 1,450,000 / 1.4720 = $ 985,054.

Forward Valuation: ¥ 105,000,000 = $ 105,000,000 / 104.25 = $ 1,000,194. DM 1,450,000 = $ 1,450,000 / 1.4539 = $ 997,318.

Which is correct?

How do I use the FX forward market to guarantee that I can make the DM payment?

4-10 4.4. Value At Risk (VAR)

Value At Risk (VAR) is an accepted method to measure the risk of future losses.

For large banks: VAR is mandated by bank supervisors. (Basle Commission, Federal Reserve, Comptroller of the Currency, FDIC)

Web sites: The Basle Commission on Banking Supervision: http://www.bis.org/publ/index.htm Especially publications no. 4, 12a, 12b, 13, 18, 21, 22, 23, 24, 25. Comptroller of the Currency: http://www.occ.treas.gov/ See the bulletin at: http://www.occ/treas.gov/ftp/bulletin/96%2D49.txt Board of Governors, Federal Reserve System: See the SR Letters, especially: http://www.bog.frg.fed.us/boarddocs/SRLETTERS/1997/SR9718.HTM http://www.bog.frg.fed.us/boarddocs/SRLETTERS/1996/SR9629.HTM

For large firms: VAR is approved by the SEC for reporting derivative exposure.

Securities & Exchange Commission's Web site is at http://www.sec.gov/ See document in: http://www.sec.gov/rules/final/33-7386.txt

VAR: What is the maximum loss, over the next n-days, that my current position would sustain with an probability of p? [For banks, n=10, p=1%.]

The answer depends on a statistical model of the prices that affects that position.

4-11 VAR Calculations for Example 4.1

Suppose I am paying DM 1,450,000 in 6 months. What is the risk (i.e. maximum cost) of this position?

Let St be the $ price of 1 DM at date t. Today, t=0. In 6 month, t=0.5.

Let x = ln[S0.5/S0] be the continuously compounded rate of change between today and 6 months from today. The $ cost in 6 months

= 1,450,000 S0.5 x = 1,450,000 S0 e .

x The distribution of 1,450,000 S0 e depends on the distribution of x.

4-12 VAR Method 1: Using a Normality Model

Assume that x is iid N(,). Estimate  and  from observed data. [ =1.38%, =8.99%. ] Then z = (x-)/ is iid N(0,1). We obtain the following probabilities:

Prob z x Maximum $ Cost in 6 months 1% 2.326 0.2229 $ 1,230,977 5% 1.645 0.1617 $ 1,157,894 10% 1.282 0.1290 $ 1,120,728 25% 0.675 0.0745 $ 1,061,225 50% 0 0.0138 $ 998,759

4-13 VAR Method 2: Using The Historical Distribution

Take the distribution of x from historical data.

Prob x Maximum $ Cost in 6 months 1% 0.2056 $ 1,209,914 5% 0.1504 $ 1,145,018 10% 0.1238 $ 1,114,899 25% 0.0794 $ 1,066,414 50% 0.0165 $ 1,001,444

4-14 VAR Method 3: Simulating from A Statistical Model

We can built a statistical model on x. The statistical model implies a distribution for x, and hence a distribution for x $1,450,000 S0 e .

For an analysis of the statistical models on exchange rates, see David Hsieh, Journal of Business, 1989.

A popular model is the ARCH/GARCH volatility forecasting model. See: Robert Engle, Econometrica, 1982. Tim Bollerslev, Journal of Econometrics, 1986. ARCH/GARCH models are covered by Steve Gray in the Advanced Futures & Option Course.

For an application of volatility forecasting models to currency futures, see: David Hsieh, Journal of Financial and Quantitative Analysis, 1993.

4-15 Which Method to Use?

It is clear that there is no "right" or "wrong" answer to VAR. A lot depends on the assumptions you make about the world. There is no single statistical model that can capture all aspects of reality. Changing the assumptions can change the results.

But VAR forces you to think in a more systematic way about potential losses than just mere "educated", or even "uneducated" guesses.

In a multi-variate setting, VAR also forces you to think about the relationships (e.g. correlations) between different variables that affect your position.

VAR References For Advanced/Highly Quantitative Readers: D. Hsieh, Journal of Quantitative and Financial Analysis, 1993. P. Jorion, Value at Risk.

4-16 Value At Risk Calculation for Example 4.2

Suppose I am receiving ¥ 105,000,000 and paying DM 1,450,000 in 6 months. How do I use VAR to analyze the risk of this exposure?

For historical FX data going back to the 1970s, see the Federal Reserve's Web Site: http://www.bog.frb.fed.us/relseases/h10/hist/