# P1.T3. Financial Markets & Products Anthony Saunders and Marcia Millon Cornett, Financial Institutions Management: A Risk Management Approach ...

```P1.T3. Financial Markets & Products

Anthony Saunders and Marcia Millon Cornett, Financial
Institutions Management: A Risk Management Approach

Foreign Exchange Risk

Bionic Turtle FRM Video Tutorials
By David Harper, CFA FRM```
```Foreign Exchange Risk
• 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.

- continued on next page -

Page 2```
```Foreign Exchange Risk (continued)
• 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; 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.

Page 3```
```Calculate a financial institution’s overall foreign exchange
exposure.
An FI’s overall FX exposure in any given currency can be measured by the net
position exposure, which is measured in local currency as

=(               −                    )+(                 −             )
=                             +
where = th currency

• Positive net exposure ⇒ net long a currency.
• Negative net exposure ⇒ net short a currency.
• A positive net exposure position implies a U.S. FI is overall net long in
a currency (i.e., the FI has bought more foreign currency than it has
sold) and faces the risk that the foreign currency will fall in value against
the U.S. dollar, the domestic currency.
• A negative net exposure position implies that a U.S. FI is net short in a
foreign currency (i.e., the FI has sold more foreign currency than it has
purchased) and faces the risk that the foreign currency could rise in
value against the dollar.

Page 4```
```Calculate a financial institution’s overall foreign exchange
exposure.
The table below replicates Saunders’ Table 13-3. The net position of each currency
is the sum of (assets minus liabilities) and (FX Bought minus FX Sold). For example,
in the case of Japanese yen (59,620 - 54,591) + (471,248 - 481,227) = -4,950.

Page 5```
```Explain how a financial institution could alter its net position
exposure to reduce foreign exchange risk.
To reduce its foreign currency exposure:
• An FI could match its foreign currency assets to its liabilities
in a given currency and match buys and sells in its trading
book in that foreign currency to reduce its foreign exchange
net exposure to zero and thus avoid FX risk.

• FIs could also offset an imbalance in its foreign asset–liability
portfolio by an opposing imbalance in its trading book so that
its net exposure position in that currency would be zero.

• Financial holding companies can aggregate their
foreign exchange exposure even more. Financial
holding companies might have a commercial bank,
an insurance company, and a pension fund all
under one umbrella that allows them to reduce their
net foreign exchange exposure across all units.

Page 6```
```Calculate a financial institution’s potential dollar gain or loss
exposure to a particular currency.
We can measure the potential size of an FI’s FX exposure by analyzing the
asset, liability, and currency trading mismatches on its balance sheet and the
underlying volatility of exchange rate movements.
Specifically, the potential size of a bank’s FX exposure given by:

=

[                                                                       \$]

×                                   \$/

The larger the FI’s net exposure in a foreign currency and the larger the
foreign currency’s exchange rate volatility, the larger is the potential dollar
loss or gain to an FI’s earnings. The underlying causes of FX volatility
reflect fluctuations in the demand for and supply of a country’s currency.
That is, an FX rate is like the price of any good and will appreciate in
value relative to other currencies when demand is high or supply is low
and will depreciate in value when demand is low or supply is high.

Page 7```
```Identify and describe the different types of foreign exchange
A bank’s position in the FX markets generally reflects four trading
activities. It involves the purchase and sale of foreign currencies:
1. To allow customers to complete international commercial trade transactions.
2. To allow customers (or the FI itself) to take positions in foreign real and
financial investments.
3. For hedging purposes to offset customer (or FI) exposure in any given
currency.
4. For speculative purposes, to forecast or anticipate future movements in FX
rates.

Page 8```
```Identify the sources of foreign exchange trading gains and
losses.
• In the first two activities shown on the previous slide (to allow
customers to participate in international commercial trade
transactions; and to allow customers to take positions in foreign
investments, real or financial assets), the FI normally acts as an
agent of its customers for a fee but does not assume the FX
risk itself.

• In the third activity, the FI acts defensively as a hedger to reduce FX
exposure. For example, an FI may take a short (sell) position in the foreign
exchange of a country to offset a long (buy) position in the foreign exchange
of that same country.

• Consequently, the FX risk exposure essentially relates to open positions
taken as a principal by the FI for speculative purposes, the fourth activity. An
FI usually creates an open position by taking an unhedged position in a
foreign currency in its FX trading with other FIs.

Page 9```
```Identify the sources of foreign exchange trading gains and
losses (continued)
FIs can make speculative trades directly with other FIs or arrange them
through specialist FX brokers.
• The Federal Reserve Bank of New York estimates that approximately 45 % of
speculative or open position trades are accomplished through specialized
• Speculative trades can be instituted through a variety of FX instruments. Spot
currency trades are the most common, with FIs seeking to make a profit on
the difference between buy and sell prices. However, FIs can also take
speculative positions in foreign exchange forward contracts, futures, and
options.

Most profits or losses on foreign trading come from
taking an open position or speculating in currencies.
from acting as agents for retail or wholesale customers
generally provide only a secondary or supplementary
revenue source.

Page 10```
```Calculate the potential gain or loss from a foreign currency
denominated investment.
Baseline Scenario: Un-hedged Balance Sheet is exposed to FX Risk.

In this scenario (Saunders Example 13-1), the U.S. FI raises all of its \$200
million liabilities in dollars (one-year CDs) but invests 50% in U.S. dollar assets
(one-year maturity loans) and 50% in U.K. pound assets (one-year maturity
loans).
We assume the FI has matched the duration of its assets and liabilities ( =
= 1 year) but has mismatched the currency composition of its asset and
liability portfolios. Suppose the promised one-year U.S. CD rate is 8.0%, to be
paid in dollars at the end of the year, and that one-year, default risk–free loans
in the United States are yielding 9.0%. The FI would have a positive spread of
1.0% from investing domestically. Suppose, however, that default risk–free, one-
year loans are yielding 15.0% in the United Kingdom.

Page 11```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
To invest in the United Kingdom, the FI decides to take 50.0% of its \$200 million in
funds and make one-year maturity U.K. pound loans while keeping 50.0% of its funds
to make U.S. dollar loans. To invest \$100 million (of the \$200 million in CDs issued) in
one-year loans in the United Kingdom, the U.S. FI engages in the following
transaction:

• At the beginning of the year, sells \$100 million for pounds on the spot currency
markets. If the exchange rate is \$1.60 to £1, this translates into \$100 million/1.6 =
£62.5 million.

• Takes the £62.5 million and makes one-year U.K. loans at a 15.0% interest rate.

• At the end of the year, pound revenue from these loans will be £62.5 × 1.15 =
£71.875 million.

• Repatriates these funds back to the United States at the end of the year. That is,
the U.S. FI sells the £71.875 million in the foreign exchange market at the spot
exchange rate that exists at that time, the end of the year spot rate.

Page 12```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
First unhedged scenario: suppose the spot foreign exchange rate does not
change over the year: it remains fixed at \$1.60/£1.
Then the dollar proceeds from the U.K. investment will be:
£71.875 million × \$1.60 / £1 = \$115 million.

• This can be shown as a return of
(115 million -100 million) / 100
million = 15.0%
• Given this, the weighted return on
the bank’s portfolio of investments
would be:
• (0.5) (0.09) + (0.5) (0.15) = 0.12 or
12%.
• This exceeds the cost of the FI’s
CDs by 4% (12% - 8%). See
exhibit here.

Page 13```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)

Page 14```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
Second unhedged scenario (foreign currency depreciation erodes unhedged
returns): Suppose, however, that at the end of the year the British pound falls in value
relative to the dollar, or the U.S. dollar appreciates in value relative to the pound. The
return on the U.K. loans could be far less than 15.0% even in the absence of interest rate
or credit risk. For example, suppose the exchange rate falls from \$1.60/£1 at the beginning
of the year to \$1.45/£1 at the end of the year when the FI needs to repatriate the principal
and interest on the loan.
• At an exchange rate of \$1.45/£1, the
pound loan revenues at the end of the
year translate into:
• £71.875 million × \$1.45/£1 = \$104.22
million
• This expressed as a return on the
original dollar investment is: (\$ 104.22 -
\$ 100) / \$ 100 = 0.0422 = 4.22%
• The weighted return on the FI’s asset
portfolio would be: (0.5) (0.09) + (0.5)
(0.0422) = 0.0661 = 6.61%
• In this case, the FI actually has a loss
or has a negative interest margin on its
balance sheet investments: (6.61% -
8% = -1.39%)
Page 15```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)

Page 16```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
On balance-sheet hedging

In principle, an FI manager can better control the scale of its FX exposure in two
major ways: on-balance-sheet hedging and off-balance-sheet hedging.

• On balance-sheet hedging involves making changes in
the on-balance-sheet assets and liabilities to protect FI
profits from FX risk.

• Off-balance-sheet hedging involves no on-balance-sheet
changes, but rather involves taking a position in forward or
other derivative securities to hedge FX risk.

Page 17```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
The following example illustrates how an FI manager can control FX exposure by
making changes on the balance sheet.
Suppose, as seen in the earlier example that instead of funding the \$100 million
investment in 15.0% British loans with U.S. CDs, the FI manager funds the British
loans with \$100 million equivalent one-year pound CDs at a rate of 11.0% as
illustrated below.

In this situation, the FI has both a matched maturity and currency foreign asset–liability
book. We might now consider the FI’s profitability or spread between the return on assets
and the cost of funds under two scenarios: first, when the pound depreciates in value
against the dollar over the year from \$1.60/£1 to \$1.45/£1 and second, when the pound
appreciates in value over the year from \$1.60/£1 to \$1.70/£1.

Page 18```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
The Depreciating Pound (under on balance-sheet hedging): When the pound falls
in value to \$1.45/£1, the return on the British loan portfolio is 4.22%. Consider now
what happens to the cost of \$100 million in pound liabilities in dollar terms:

1. At the beginning of the year, the FI borrows \$100
million equivalent in pound CDs for one year at a
promised interest rate of 11.0%. At an exchange
rate of \$1.60£, this is a pound equivalent amount
of borrowing of \$100 million/1.6 = £62.5 million.
2. At the end of the year, the bank has to pay back
the pound CD holders their principal and interest,
£62.5 million (1.11) = £69.375 million.
3. If the pound depreciates to \$1.45/£1 over the
year, the repayment in dollar terms would be
£69.375 million × \$1.45/£1 = \$100.59 million, or
a dollar cost of funds of 0.59%.

Page 19```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
Thus, at the end of the year the following occurs:

Average return on assets:

(0.5) (0.09)         + (0.5) (0.0422)     = 0.0661 = 6.61%
U.S. asset return    U.K. asset return    Overall return

Average cost of funds:

(0.5) (0.08)         + (0.5) (0.0059)     = 0.04295 = 4.295%
U.S. cost of funds   U.K. cost of funds   Overall cost

Net return:

Average return on assets       - Average cost of funds
6.61%                          - 4.295%              = 2.315%

Page 20```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)

Page 21```
```Calculate the potential gain or loss from a foreign currency
denominated investment (continued)
The Appreciating Pound (under on balance-sheet hedging): When the
pound appreciates over the year from \$1.60/£1 to \$1.70/£1, the return on British
loans is equal to 22.188%.

Now consider the dollar cost of British one-year
CDs at the end of the year when the U.S. FI
has to pay the principal and interest to the CD
holder:
£69.375million × \$1.70/£1 = \$117.9375 million
or a dollar cost of funds of 17.9375 %.
• Thus, at the end of the year, average return
on assets is: (0.5) (0.09) + (0.5) (0.22188) =
0.15594 or 15.594%
• Average cost of funds: (0.5) (0.08) + (0.5)
(0.179375) = 0.12969 or 12.969%
• Net return: 15.594 -12.969 = 2.625%

Page 22```
```Explain balance‐sheet hedging with forwards.
Off-balance sheet hedging

As a lower-cost alternative, the FI could hedge by taking
a position in the forward market for foreign currencies.
Any forward position would be as a contingent off-
balance-sheet claim (an item below the bottom line)
and would not appear on the balance sheet.

The role of the forward FX contract is to offset the uncertainty regarding the
future spot rate on pounds at the end of the one-year investment horizon.
Instead of waiting until the end of the year to transfer pounds back into dollars at
an unknown spot rate, the FI can enter into a contract to sell forward its
expected principal and interest earnings on the loan, at today’s known forward
exchange rate for dollars/pounds, with delivery of pound funds to the buyer of
the forward contract taking place at the end of the year. Essentially, by selling
the expected proceeds on the pound loan forward, at a known (forward FX)
exchange rate today, the FI removes the future spot exchange rate uncertainty
and thus the uncertainty relating to investment returns on the British loan.

Page 23```
```Explain balance‐sheet hedging with forwards (continued)
Consider the following transactions when the FI hedges its FX risk immediately
by selling its expected one-year pound loan proceeds in the forward FX market
which is illustrated below.

Page 24```
```Explain balance‐sheet hedging with forwards (continued)
1. The U.S. FI sells \$100 million for pounds at the spot exchange rate today and
receives \$100 million/1.6 = £62.5 million.

2. FI immediately lends the £62.5 million to a British customer at 15.0% for one year.

3. The FI also sells the expected principal and interest proceeds from the pound
loan forward for dollars at today’s forward rate for one-year delivery. Let the
current forward one-year exchange rate between dollars and pounds stand at
\$1.55/£1, or at a 5 cent discount to the spot pound; as a percentage discount:
(\$1.55 - \$1.60)/\$1.6 = - 3.125%
This means that the forward buyer of pounds promises to pay: £62.5 million
(1.15) × \$1.55 / £1 = £71.875million × \$1.55 / £1 = \$111.406million to the FI (the
forward seller) in one year when the FI delivers the £71.875 million proceeds of
the loan to the forward buyer.

4. In one year, the British borrower repays the loan to the FI plus interest in pounds
(£71.875 million).

5. The FI delivers the £71.875 million to the buyer of the one-year forward contract
and receives the promised \$111.406 million.

Page 25```
```Explain balance‐sheet hedging with forwards (continued)
• Barring the pound borrower’s default on the loan
or the forward buyer’s reneging on the forward
contract, the FI knows from the very beginning of
the investment period that it has locked in a
guaranteed return on the British loan of:
(\$111.406 - \$100)/ \$100 = 0.11406 = 11.406%
• Specifically, this return is fully hedged against any
dollar/pound exchange rate changes over the
one-year holding period of the loan investment.
Given this return on British loans, the overall
expected return on the FI’s asset portfolio is:
(0.5) (0.09) + (0.5) (0.11406) = 0.10203 or
10.203%
• Since the cost of funds for the FI’s \$200 million
U.S. CDs is an assumed 8%, it has been able to
lock in a risk-free return spread over the year of
2.203% regardless of spot exchange rate
fluctuations between the initial foreign (loan)
investment and repatriation of the foreign loan
proceeds one year later.

Page 26```
```Describe how a non‐arbitrage assumption in the foreign exchange markets
leads to the interest rate parity theorem; use this theorem to calculate
forward foreign exchange rates.

In general, spot rates and forward rates for a given currency
differ. The forward exchange rate is determined by the spot
exchange rate and the interest rate differential between the two
countries. The specific relationship that links spot exchange
rates, interest rates, and forward exchange rates is described as
the interest rate parity theorem (IRPT).

Intuitively, the IRPT implies that by hedging in the forward exchange rate market, an
investor realizes the same returns whether investing domestically or in a foreign
country. This is a so-called no-arbitrage relationship in the sense that the investor
cannot make a risk-free return by taking offsetting positions in the domestic and
foreign markets. That is, the hedged dollar return on foreign investments just equals
the return on domestic investments. The eventual equality between the cost of
domestic funds and the hedged return on foreign assets, or the IRPT, can be
expressed as:
1
1+                     =     × 1+        ×

Page 27```
```Describe how a non‐arbitrage assumption in the foreign exchange markets
leads to the interest rate parity theorem; use this theorem to calculate
forward foreign exchange rates (continued).

Rate on U.S. investment = Hedged return on foreign (U.K.) investment
1+         = 1 plus interest rate on US CDs for the FI at time t
= \$/£ spot exchange rate at time t
1+         = 1 plus interest rate on UK CDs at time t
= \$/£ forward exchange at time t

Thus, the IRPT is motivated by arbitrage arguments: if interest rates are higher in, say the UK,
than in the US, it is attractive for investors to invest in UK assets, earning a higher rate of return. If
US investors borrow USD to buy Pound Sterling denominated CDs, the cost of Pound Sterling in
terms of USD appreciates (becomes more expensive). As the spot price increases, the forward
exchange rate simultaneously decreases. Thus, it becomes less attractive to but Pound Sterling
denominated CDs as you get fewer Pounds per USD, and you know that the exchange rate one
year from now will be lower (you will receive less for your Pound Sterling). These forces will
ensure that Covered Interest Rate Parity holds, with any deviation quickly being seized upon by
arbitrageurs.

Page 28```
```Describe how a non‐arbitrage assumption in the foreign exchange markets
leads to the interest rate parity theorem; use this theorem to calculate
forward foreign exchange rates (continued).

Saunders Example 13-5: An application of Interest Rate Parity Theorem

Suppose         = 8% and        = 11%, as in our preceding example. As the FI
moves into more British CDs, suppose the spot exchange rate for buying
pounds rises from \$1.60/£1 to \$1.63/£1. In equilibrium, the forward exchange
rate would have to fall to \$1.5859/£1 to eliminate completely the attractiveness
of British investments to the U.S. FI manager.

That is:
(1.08) = (1/ 1.63) [1.11] (1.5859)

Page 29```
```Describe how a non‐arbitrage assumption in the foreign exchange markets
leads to the interest rate parity theorem; use this theorem to calculate
forward foreign exchange rates (continued).

This is a no-arbitrage relationship in the sense that the hedged dollar return on
foreign investments just equals the FI’s dollar cost of domestic CDs.
Rearranging, the IRPT can be expressed as:

−           −
=
1+

0.08 − 0.11 1.5859 − 1.63
≈
1.11         1.63

−0.0270 ≈ −0.0270

That is, the discounted spread between domestic and foreign interest rates is
approximately equal to the percentage spread between forward and spot
exchange rates.

Page 30```
```Explain why diversification in multicurrency asset‐liability
positions could reduce portfolio risk.
So far, we have used a one-currency example of a matched or mismatched
foreign asset–liability portfolio. Many FIs, including banks, mutual funds, and
pension funds, hold multicurrency asset–liability positions.
As for multicurrency trading portfolios, diversification across many asset and
liability markets can potentially reduce the risk of portfolio returns and the cost of
funds. To the extent that domestic and foreign interest rates or stock returns for
equities do not move closely together over time, potential gains from asset–
liability portfolio diversification can offset the risk of mismatching individual
currency asset–liability positions.

Page 31```
```Describe the relationship between nominal and real interest
rates.
Theoretically speaking, the one-period nominal interest rate ( ) on fixed
income securities in any particular country has two major components.

• First, the real interest rate reflects underlying real sector demand
and supply for funds in that currency.

• Second, the expected inflation rate reflects an extra amount of
interest lenders demand from borrowers to compensate the lenders
for the erosion in the principal (or real) value of the funds they lend
due to inflation in goods prices expected over the period of the loan.

=     +
= Nominal interest rate in country i
= real interest rate in country i
= expected one-period inflation rate in country i
Nominal interest rate ≅ real interest rate + [expected] inflation rate.
This can also be defined slightly more mathematically precise as so,
Nominal interest rate = [(1 + real interest rate) x (1 + expected inflation)] -1.

Page 32```
```The End

P1.T3. Financial Markets & Products

Anthony Saunders and Marcia Millon Cornett, Financial Institutions
Management: A Risk Management Approach

Foreign Exchange Risk``` 