Chapter 12
Foreign Exchange Exposure and Risk
The Nature of Exchange-Rate Risk and Exposure
Definition of Foreign Exchange Exposure
Exposure as a Regression Slope
Estimating Exposure
Units of Measurement of Exposure
Exposure When Local-Currency Values Vary with Unanticipated Changes in Exchange Rates
Exposure against Numerous Exchange Rates
Exposure on “Domestic” Assets, Liabilities, and Operating Incomes
Estimation Difficulties
Definition of Foreign Exchange Risk
Exposure, Risk, and the Parity Relationships
Exposure, Risk, and Interest Parity
Exposure, Risk, and Purchasing-Power Parity
The Nature of Exchange-Rate Risk and Exposure - Definition of Foreign Exchange Exposure
1. To clarifying the nature and measurement of risk and exposure
To explaining the factors contributing to them
To managing the risk and exposure
2. Definition: Foreign exchange exposure is the sensitivity of changes in the real domestic-currency value of assets, liabilities, or operating incomes to unanticipated changes in exchange rates.
（1）sensitivity：the extent or degree to which the home-currency value of something is changed by exchange rate changes
（2）real domestic-currency value：inflation-adjusted
（3）assets, liabilities, and operating incomes：exposure exists on stocks and flows
◎Stocks—so much in a particular moment in time：the values of assets and liabilities
◎Flows—so much per period of time：the values of incomes
（4）unanticipated changes in exchange rates can affect both domestic and foreign exposed items
（5）unanticipated changes
Exposure as a Regression Slope
1. Figure 12.1. Exposure as the Slope of a Regression Line
（1）Two axes.
◎Horizontal axis：unexpected changes in exchange rates, SU(＄/￡)
◎Vertical axis：the changes in the real values of assets, liabilities, and operating incomes in terms of a reference currency, V（＄）
（2）A systematic relationship
The dollar value of a foreign-currency item is influenced by exchange rates among other factors. There is a tendency for values to change in more or less predictable ways. When there is such a tendency we say that there is a systematic relationship between the dollar value of the item and the exchange rate.
（3）An example：When the pound unexpectedly jumps from ＄1.50/￡to ＄1.70/￡, the U.S. dollar value of a ￡1 million bank deposit changes from ＄1.5 million to ＄1.7 million, and this change in dollar value can be accurately known.
◎Point A in Figure 12.1.（a）：SU(＄/￡) = ＄0.2/￡and V = ＄200,000
（4）With the pound value of the bank deposit unchanged by changes in exchange rates, all points sit exactly on the exposure line, which for the bank deposit is upward-sloping.
2. Extensions
（1）the pound value of British items might change, but not always in the same way, as the same time as the exchange rate changes
（2）domestic assets, liabilities, and operating incomes may also change with changes in exchange rates
3. Regression equation
（1）The form
（12.1）V = SU(＄/￡) +
◎Systematic relationship：SU and V are on average related to each other
◎Regression coefficient： describes the tendency for SU and V to be related
◎Regression error： is the random error in the relationship
（2） is the sensitivity measure we have called foreign exchange exposure.
（3）Redefine exposure：Foreign exchange exposure is the slope of the regression equation which relates changes in the real domestic currency value of asset, liabilities, and operating incomes to unanticipated changes in exchange rates.
Estimating Exposure
1. Observations of SU and V
（1）SU：forward exchange rates, which are predictions of future spot exchange rates, and subtracting the forward rates from the actual exchange rates
（2）V：dollar values of assets and liabilities may be apparent in stock and bond prices
2. The exact exposure line versus the scatters
When there is noise in the relationship between the unanticipated changes in exchange rates and changes in the dollar values, we must use statistical procedures to fit the line and find the systematic relationship through the scatter of points.
3. The estimate of exposure is the estimated value of .
Units of Measurement of Exposure
1. If V is measured in U.S. dollars, as it will be if we are measuring exposure from a U.S. perspective, and if SU is measured in dollars per pound, then exposure, that is, , must be measured in pounds.
2. An example
（1）In equation（12.1）, assuming = 0
＄200,000 = × ＄0.2/￡
Thus, = ￡1,000,000.
（2）We find that exposure is ￡1 million. This is the amount that is at risk to unanticipated changes in exchange rates.
（3）Long exposure：when the slope is positive; short exposure：when the slope is negative
Exposure When Local-Currency Values Vary with Unanticipated Changes in Exchange Rates
1. An example
（1）Before British inflation：the British value of a piece of British real estate is ￡1 million and the exchange rate is ＄1.8/￡
The dollar value of the real estate is
＄1.80/￡× ￡1 million = ＄1.8 million
（2）After British inflation：the British value of the real estate is ￡1.125 million and the exchange rate is ＄1.6/￡
The dollar value of the real estate is
＄1.60/￡× ￡1.125 million = ＄1.8 million
（3）In equation（12.1）, assuming all change in exchange rate is unanticipated, then
SU = -＄0.2/￡and V = 0, so that
（12.2）0=（-＄0.2/￡）+
If is zero, then the only way equation （12.2）can hold is if = 0. That is, if the pound value of the British real estate and the exchange rate of the pound change systematically as in the example, the real estate is not exposed.
2. Other examples
（1）On selecting different numbers we would have found the real estate to be exposed to unanticipated changes in exchange rates
（2）Examples on page 299
Exposure against Numerous Exchange Rates
1. When many different exchange rates can affect V, as when V is the value of a firm that holds assets and liabilities in many countries and currencies or earns incomes in many countries and currencies, we can use an extension of equation （12.1）to estimate exposure.
（1）The multiple regression equation
（12.3）V = 1SU(＄/￡) + 2SU(＄/DM) + 3SU(＄/￥) + 4SU(＄/SFr) +
If V could be influenced by the exchange rates of the dollar versus the British pound, German mark, Japanese yen, French franc, and so on.
（2）Each slope coefficient gives exposure to the associated foreign currency.
◎For example：2 gives the sensitivity of V to unanticipated changes in the U.S. dollar value of the German mark.
（3）The coefficients are all measured in units of the foreign currency.
2. Summary：Exposure to an individual currency is the sensitivity of the real home-currency value of an asset, liability, or operating income to unanticipated changes in the foreign exchange value of that currency, assuming unanticipated changes in all other exchange rates are zero.
Exposure on “Domestic” Assets, Liabilities, and Operating Incomes
1. A U.S. perspective
The U.S. dollar values of U.S. assets may be systematically affected by exchange rates, that is, these items may well be exposed to exchange rates.
（1）For example：the case of U.S. bonds
The U.S. dollar falls against other currencies
The Fed adopts a policy called leaning against the wind
The Fed tries to reduce the dollar’s depreciation by increasing interest rates
The market values of U.S. bonds decline
◎If the relationship between exchange rates and interest rates is systematic, the U.S. holders of U.S. bonds are exposed to exchange rates.
◎There is a negative association between SU(＄/￡) and V.
（2）For example：the case of U.S. stocks
If U.S. stock prices systematically decline as U.S. interest rates increase, then the Federal Reserve’s policy of leaning against the wind will expose U.S. stocks.
◎While stock prices in general might decline when the U.S. dollar unexpectedly depreciates, some stocks may benefit from the dollar depreciation.
◎U.S. export-oriental and import-competing firms
Estimation Difficulties
The calculation of exposure is not easy, because exposure changes over time. We might need an analysis of possible scenarios. This involves the generation of values of V which might occur for different SU’s.
Definition of Foreign Exchange Risk
1. Adler and Dumas’s definition：They define foreign exchange risk in terms of the variance of unanticipated changes in exchange rates, that is, var(SU).
2. The author’s definition：Foreign exchange risk is measured by the variance of the domestic-currency value of an asset, liability, or operating income that is attributable to unanticipated changes in exchange rates.
（1）Exchange–rate risk depends on exposure as well as on var(SU).
（2）（12.5）V +
◎We have partitioned the total change in value, V, into that due to changes in exchange rates, , and that due to other influences, .
◎We define the variable = SU(＄/￡), that is, the change in value of an asset, liability, or operating income that is due to unanticipated changes in the exchange rate.
◎The author’s definition of exchange rate risk is var().
（12.6）var() = 2var(SU)
Exchange–rate risk depends on exposure as well as on var(SU).
Exposure, Risk, and the Parity Relationships - Exposure, Risk, and Interest Parity
1. Covered Interest Parity
(1) Equation (11.10)
The RHS of equation (11.10) gives the hedged dollar receipts to an investor on a covered n-year British pound interest-bearing security.
◎If the pound security is hedged (by a forward contract) and held to maturity, unanticipated changes in exchange rates can have no effect on the dollar value of the security. That is, the hedged pound security is not exposed and faces no foreign exchange risk.
◎When a foreign-currency-denominated security is not hedged with a forward contract or may be sold before maturity, the security is exposed and subject to exchange-rate risk.
(2) Implication of interest parity
While interest parity dose suggest that anticipated changes in exchange rates are compensated for in interest differentials, there is no compensation for unanticipated changes in exchange rates. With NO implication of interest parity for a systematic effect of SU(＄/￡) on the value of pound-denominated interest-bearing securities, there is NO implication for exposureandexchange-rate risk.
Exposure, Risk, and Purchasing-Power Parity– PPP and Real-Asset Exposure
1. Table 12.1. PPP and Real-Asset Values
(1) These numbers imply that the dollar value of the real estate is unchanged and equal to ＄1.8 million despite the change in exchange rate. If this situation systematically occurred the real-estate investment would not be exposed (causing an exposure of zero).
(2) Why?
◎If British real-estate prices followed the overall British rate of inflation
◎If the relative form of PPP holds, S-dot could be calculated
◎From S at time 0 and S-dot, the S at time 1 cold be calculated
(3) Summary
If PPP held precisely in an expost sense, and if the pound value of the British real estate precisely followed the British rate of inflation. In such a situation there is zero exposure and also no foreign exchange risk.
TM12-1