 # Foreign Exchange Risk

After completing this reading, you should be able to:

• Calculate a financial institution’s overall foreign exchange exposure.
• Explain how a financial institution could alter its net position exposure to reduce foreign exchange risk.
• Calculate a financial institution’s potential dollar gain or loss exposure to a particular currency.
• Identify and describe the different types of foreign exchange trading activities.
• Identify the sources of foreign exchange trading gains and losses.
• Calculate the potential gain or loss from a foreign currency denominated investment.
• Explain balance-sheet hedging with forwards.
• Describe how a non-arbitrage assumption in the foreign exchange markets leads to the interest rate parity theorem, and use this theorem to calculate forward foreign exchange rates.
• Explain why diversification in multicurrency asset-liability positions could reduce portfolio risk.
• Describe the relationship between nominal and real interest rates.

## Types of Foreign Exchange Quotes

A currency quote always appears as $${ A }/{ B }$$, where $$A$$ and $$B$$ are different currencies. The currency to the left of the slash is the base currency, while the currency to the right of the slash is the quote currency.

The base currency (in this case, $$A$$) is always equal to one unit, and the quoted currency (in this case, $$B$$) is what that one base unit is equivalent to in the other currency.

A foreign exchange quote can be direct or indirect.

In a direct quote, the domestic currency is the quoted currency. In an indirect quote, the domestic currency is the base currency. So if we take the example of the USD as the domestic currency and the CAD as the foreign currency,

A direct quote would be CAD/USD. For example, we might have 0.79CAD/USD, implying that 1

CAD is equivalent to (would purchase) USD 0.79.

An indirect quote would be USD/CAD. For example, we might have 1.27 USD/CAD, implying that 1 USD is equivalent to (would purchase) CAD 1.27.

An indirect quote is the inverse of a direct quote.

## Overall Foreign Exchange Exposure

For a bank that regularly participates in foreign exchange trading, its aggregate position in a particular currency may look extremely large. However, buys and sells offset one another, and hence the net exposure may actually be quite small.

The net position exposure to currency $$i$$ is given by:

$${ Net\quad exposure }_{ i }=\left( FX\quad { assets }_{ i }-FX\quad { laibilities }_{ i } \right) +\left( FX\quad { bought }_{ i }-FX\quad { sold }_{ i }\quad \right)$$

$$=Net\quad FX\quad { assets }_{ i }+Net\quad FX\quad { bought }_{ i }$$

where $$i$$ is the $$i$$th currency

A positive net exposure implies that a bank is net long in a currency,i.e., the bank holds more assets than liabilities in that currency. In such a scenario, the bank’s overall position would worsen if the foreign currency falls in value against the domestic currency.

A negative net exposure implies that a bank is net short in a currency,i.e., the bank holds more liabilities than assets in that currency. In such a scenario, the bank’s overall position would worsen if the foreign currency rises in value against the domestic currency.

To reduce its foreign exchange risk, a bank can:

• Match its foreign currency assets to its liabilities

## Potential Dollar Gain Or Loss Exposure to A Particular Currency

The dollar loss or gain in currency $$i$$ can be given by:

$$dollar\quad gain\quad or\quad loss=\left[ Net\quad exposure\quad in\quad foreign\quad currency\quad { i }_{ measured\quad in\quad USD } \right] \times { volatility\quad of\quad USD }/{ i\quad exchange\quad rate }.$$

## The Effect of An Appreciation/Depreciation of a Currency Relative to a Foreign Currency

Other factors constant, the appreciation of country A’s currency (or a rise in its value relative to other currencies) has two implications:

• The country’s goods are more expensive for foreign buyers
• Foreign goods are cheaper for foreign sellers (from country A)

When a country’s currency appreciates, foreign manufacturers find it easier (and more profitable) to sell their merchandise to domestic purchasers. However, domestic sellers find it harder to sell their goods abroad.

Example

On Feb 7, 2019, the exchange rate of the U.S. dollar for the British pound was 1.29. It is now March 7, 2019, and the one pound is now worth 1.33 U.S dollars. A U.S.-made Tesla model 3 car costs \$35,000 over the entire period.

Questions

• Has the U.S. dollar appreciated or depreciated in value relative to the pound?
• The USD has depreciated against the pound. In other words, the pound has risen in value relative to the dollar. On March 7, it would be cheaper for a British citizen to buy the car (by converting pounds into dollars).
• What is the British citizen’s £ gain or loss on the purchase of the car if he waits to buy on March 7?
• Purchase price on Feb 7: The Briton needs 35,000/1.29 = £27,132 to purchase the car.
• Purchase price on March 7: The Briton needs £35,000/1.33 = £26,316 to purchase the car.
• The gain from waiting (from the depreciation of the USD relative to the pound) is £27,132 – £26,316 = £816

## Types of Foreign Exchange Trading Activities

A bank can participate in FX trading for several purposes:

• To give customers the opportunity to participate in international commercial trade transactions
• To allow customers to take positions in foreign investments, both real and financial.
• For hedging purposes, i.e., to offset foreign exchange exposure
• For speculative reasons

The primary FX exposure essentially arises from open positions taken as a principal by the bank for speculative purposes.

## Balance Sheet Hedges

A bank’s on-balance sheet hedge is a position which offsets a foreign denominated asset or liability on its financial statements. For example, if a U.S. based bank knows that it will need to make a future liability payment denominated in a foreign currency, it could take U.S. dollars, convert them into the foreign currency at the spot exchange rate, and then invest in financial assets denominated in the foreign currency.

#### Example of Balance Sheet Hedges

Suppose that a U.S. bank must make a liability payment of $${ EUR\quad 10,000,000 }$$ in six months. The bank is exposed to FX risk because of the uncertainty associated with the relative value of Euros and U.S. dollars six months from now. For example, if the Euro strengthens against the dollar, the bank will end up spending more U.S. dollars to pay up the liability than it would spend now.

In this case, the bank could take U.S. dollars, convert them into Euros at the spot exchange rate, and then invest in financial assets denominated in the Euro.The bank would need (in dollar-denominated cash) the six-month present value of $${ EUR\quad 10,000,000 }$$ on a spot basis, i.e.,

$$\frac { EUR\quad 10,000,000 }{ { \left( 1+{ r }_{ Eur } \right) }^{ 0.5 } }$$

where $${ r }_{ Eur }$$ is the Euro risk-free rate.

For example, if we take the Euro risk-free rate to be $$5\%$$ pa and the spot exchange rate to be $$1.16{ EUR }/{ USD }$$,

$$\frac { EUR\quad 10,000,000 }{ { \left( 1+0.05 \right) }^{ 0.5 } } EUR\quad 9,759,001$$

Thus, the bank would need to convert $$USD\quad 11,320,441\left( =9,759,001\times 1.16 \right)$$ into Euros and invest that amount $$\left( EUR\quad 9,759,001 \right)$$ at $$5\%$$ so that, in six months, the $$EUR \quad 10,000,000$$ liability payment would be covered.

If the bank already has assets denominated in Euros, it could “earmark” some of them for the upcoming liability payment.

## Off-Balance Sheet Hedging Using Forward Contracts

With respect to the $$EUR \quad 10,000,000$$ liability payment example, the bank could hedge the FX risk inherent in the future payment transaction by entering, now, into a six-month forward contract. This would essentially be an agreement with a counterparty to purchase six months from now, at a pre-specified price, $$EUR \quad 10,000,000$$. That pre-specified price would be the six-month EUR/USD forward rate.

By entering into a forward, the bank effectively locks the EUR/USD exchange rate six months from now, thus eliminating the potential FX volatility over the next six months. However, the profitability of such a transaction relies on the actual spot exchange rate six months from now. If the Euro strengthens against the USD, the hedge will have worked in the bank’s favor. However, if the Euro weakens against the dollar, the bank would have been better off without the hedge. (Recall that a forward contract is legally binding, meaning that once initiated, the parties must deliver on their promises).

### How does diversification in multicurrency asset-liability positions reduce portfolio risk?

In reality, most financial institutions hold positions in multiple currencies in their asset-liability portfolios. Currencies are usually not perfectly correlated. As such, diversification across several asset and liability markets can potentially reduce portfolio risk, including the cost of funds. Domestic and foreign interest rates generally do not move together perfectly over time. Thus, the potential risks from mismatching one-currency positions may very well be offset by gains from asset-liability portfolio diversification.

## The Purchasing Power Parity Theorem (PPP)

The PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the two countries.

$${ i }_{ domestic }-{ i }_{ foreign }=\frac { { \Delta }_{ \frac { domestic }{ foreign } } }{ { S }_{ \frac { domestic }{ foreign } } }$$

Where:

$${ \Delta }_{ \frac { domestic }{ foreign } }$$ = Change in the one-period foreign exchange rate

$${ S }_{ \frac { domestic }{ foreign } }$$ = Spot exchange rate of the domestic currency for the foreign currency (e.g., U.S. dollars for British pounds)

PPP propagates the idea that in open economies, differences in prices (which are caused by inflation) drive trade flows and thus demand for and supplies of currencies.

#### Example of the Purchasing Power Parity Theorem (PPP)

Suppose that the current spot exchange rate of U.S. dollars for British pounds, SUS/BP , is 1.30 (i.e., 1.30 dollars can be received for 1 pound). The price of British-produced goods increases by 8 percent (i.e., inflation in Great Britain, iB, is 8 percent), and the U.S. price index increases by 2 percent (i.e., inflation in the United States, iUS, is 2 percent). According to PPP, the 8 percent rise in the price of British goods relative to the 2 percent rise in the price of U.S. goods results in a depreciation of the British pound (by 6%). Specifically, the exchange rate of British pound to U.S. dollars should fall, so that:

US Inflation – British inflation = (Change in spot exchange rate of U.S. dollars for British pounds / Initial spot exchange rate of U.S. dollars for British pounds

$${ i }_{ US }-{ i }_{ British }=\frac { { \Delta }_{ \frac { USD }{ BP } } }{ { S }_{ \frac { USD }{ BP } } }$$

$$0.02-0.08=\frac { { \Delta }_{ \frac { USD }{ BP } } }{ 1.30 }$$

$${ \Delta }_{ \frac { USD }{ BP } }=-0.06\times 1.30=-0.078$$

Thus, it costs 0.078 USD less to receive a pound (i.e., 1 pound costs 1.30 – 0.078 = 1.22 U.S. dollars), or 1.22 dollars can be received for 1 pound. The British pound depreciates in value by 6% against the U.S. dollar as a result of its higher inflation rate.

## Interest Rate Parity Theorem

IRP propagates the idea that the hedged dollar return on foreign investments should be equal to the return on domestic investments. In other words, a firm should not be able to make excess profits from foreign investments. In our earlier example, the bank should not make a risk-free profit by lending in a foreign currency (EUR) and locking in the forward rate of exchange).

The IRP equation is represented as:

$$forward=spot{ \left[ \frac { 1+{ r }_{ DC } }{ 1+{ r }_{ FC } } \right] }^{ T }$$

where:

$${ r }_{ DC }$$=domestic currency rate

$${ r }_{ FC }$$=foreign currency rate

$$T$$=time in years

In the presence of continuous compounding,

$$forward=spot\times { e }^{ \left( { r }_{ DC }-{ r }_{ Fc } \right) T }$$

### Nominal vs. Real Interest Rates

$$Nominal\quad interest\quad rate=real\quad interest\quad rate+expected\quad inflation\quad rate$$

$${ r }_{ n }=r{ r }_{ i }+{ i }_{ e }$$

where:

$${ r }_{ n }$$=nominal interest rate

$$r{ r }_{ i }$$=real rate of interest

$${ i }_{ e }$$=expected one period inflation rate

## Question

The current spot exchange rate of Canadian dollars for Euro, SCAD/EUR, is 0.68. The price of the European price index increase by 7% and the Canadian price index increases by 2%. According to the purchasing power theorem, one euro should buy:

Specifically, the exchange rate of Euro to Canadian dollars should fall so that:

$${ i }_{ CAD }-{ i }_{ EUR }=\frac { { \Delta }_{ \frac { CAD }{ EUR } } }{ { S }_{ \frac { CAD }{ EUR } } }$$

$$0.02-0.07=\frac { { \Delta }_{ \frac { CAD }{ EUR } } }{ 0.68 }$$

$${ \Delta }_{ \frac { CAD }{ EUR } } = 0.0735$$

Thus, it costs 0.0735 CAD less to receive a Euro (i.e., 1 Euro costs 0.68 – 0.0735 = 0.6065 Canadian dollars), or 1/0.6065 =  1.65 Canadian dollars can be received for 1 Euro.

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