This document discusses hedging foreign exchange risk. It begins by defining exchange risk as the exposure individuals and firms face when investing or doing business abroad due to fluctuations in exchange rates, interest rates, and inflation between countries. It then examines various methods of calculating exposure, such as using value-at-risk models. The document also explores hedging techniques like using currency derivatives and forwards to minimize risk. Finally, it notes that while hedging can reduce volatility, it may also limit gains, so firms must decide if hedging aligns with their objectives.

1. Hedging Risk in a Volatile Market
A Study of Foreign Exchange Risk
Presented to:
Dr. Mark Wu
By:
Carsten Fredrickson

2. I. Introduction
Diversify by investing abroad – a slogan ingrained in the mind of most modern day
players in financial markets. The concept is mirrored in the asset allocation of one’s profile
when handed over to an investment manager. At face value it’s a peculiar trend. European
markets have lagged compared to the meteoric rise seen in American markets in the wake of
the sub-prime mortgage crisis or even the dot-com bubble. “The past 25 years, large-cap U.S.
funds have gained an average 691%, vs. 338% for international funds.”1 The European market is
not the only one to approach stagnation. The perennially volatile Asian market has seen a
drastic downturn over the last few weeks. However the FOREX market is the largest in the
world and foreign exchange transactions are made every second between individuals, firms,
and governments. Foreign exchange risk is implicit when investing in the global market. This
brings about an interesting query; to hedge or not to hedge? Due to the complexities of
accurately measuring exposure and balancing that with the exposure that should be hedged,
the lines tend to blur when answering this question.
II. What is Exchange Risk?
Exchange risk is derived from the exposure an individual or firm faces when investing, or
doing business, in a foreign country. When identifying exposure it helps to acknowledge that
exchange rate, interest rate and inflation are all linked. The relationships between the three are
identified by the Purchasing Power Parity theory, the International Fisher Effect, and the
Unbiased forward rate theory. The Purchasing Power Parity theory states that exchange rate
can be identified as the difference in interest rates. “The relationship is derived from the basic
idea that, in the absence of trade restrictions changes in the exchange rate mirror changes in
the relative price levels in the two countries. At the same time, under conditions of free trade,
prices of similar commodities cannot differ between two countries, because arbitragers will
take advantage of such situations until price differences are eliminated. This "Law of One Price"
leads logically to the idea that what is true of one commodity should be true of the economy as
a whole--the price level in two countries should be linked through the exchange rate--and
hence to the notion that exchange rate changes are tied to inflation rate differences.”2 The
International Fisher Effect takes into consideration the expected rate of change of the exchange
rate which is equivalent to the interest rate differential. Essentially an investor can convert his
funds from a low interest country to a high interest country but his gain (which is the interest
rate differential) will be offset by his expected loss due to exchange rate change. The Unbiased
Forward Rate Theory is the idea that the expected exchange rate is equal to the forward
exchange rate. Firms must draw conclusions and forward contracts from the expected rate.
Given that all three of these theories hold up, exchange risk would not cause any gains of losses.
However that only holds true at equilibrium. Firms and individuals tend to have the propensity
1 J. Waggnoner, “Why invest in international funds? It’s a mystery” USA Today, 2015
2 I. Giddy, G. Dufey “The Management of Foreign Exchange Risk” New York University and University of Michigan,
2014

3. to make strategic commitments causing temporary deviations from equilibrium which, in turn,
causes exposure to exchange risk.
III. Calculating Exposure
Calculating exposure is a tricky but necessary step when deciding what position to take.
In order to do this, a value-at-risk calculation must be done. When performing a value-at-risk
calculation, there are three parameters one must identify; the holding period, the confidence
level, and the unit of currency. The VaR will measure what the maximum loss due to exchange
risk will be given a confidence level. A standard holding period is one day. So given a confidence
level of 99%, a one day $10 million VaR, one shouldn’t expect, with a probability of 99%, to see
their position decrease by more than $10 million. To clarify, on 99 out of 100 trading days, one
should not expect their position to decrease by more than $10 million.
There are a multitude methods available for calculating VaR. The three most widely
exercised are: the historical simulation, the variance-covariance model, and the Monte Carlo
simulation. The historical simulation is, by far, the most simple. One must run the firms current
exchange position across a set of historical exchange rate changes to identify the distribution of
losses given the value of the position. Thus, with 99% confidence and a one day holding period,
the VaR could be computed by sorting, in ascending order, the 1,000 daily losses. The top 10
losses, or 1%, will exceed the VaR. Thus with a 99% probability the 11th largest loss will be your
VaR. Historical simulation is a good method because it does not assume a normal distribution of
currency returns because currency returns are, more often, leptokurtic. The downside is that it
takes time and a large database. The variance-covariance model acts on two assumptions. The
first being that the total foreign exchange position is a linear combination of all the changes in
the values of individual foreign exchange positions. So the total currency return is linearly
dependent on all individual currency returns. The second assumption is that the currency
returns are jointly normally distributed. At 99% confidence it can be calculated as VaR=-
Vp(Mp+2.33 Sp). Vp is the initial value of the foreign exchange position, Mp is the mean of the
currency return on the total position which is a weighted average of individual foreign exchange
positions. Sp is the standard deviation of the currency return on the total position. Variance-
covariance is easy to calculate but is heavily limited by its assumptions. The Monte Carlo
simulation is similar to the variance-covariance model. Its benefit is that it facilitates any
underlying distribution as well as assessing the VaR when non-linear currency factors are
present. The downside of Monte Carlo is the computational intensity.
IV. What is Hedging?
To hedge is to take a position that minimizes risk of price movements. The result of
which may lead to lower returns. An extremely logical concept considering higher risk should
always garner a higher reward. By hedging, an investor has a few options available. First
hedging allows the investor to take a position on a country (such as betting against Abenomics
in Japan). Taking a position allows the investor to focus on the underlying asset instead of the

4. overarching currency risk. Perhaps more importantly, hedging can limit the swings in an
investor’s portfolio. "When you hedge out currency exposure you actually reduce volatility by
20% to 25%. It can be a way to execute a low-volatility strategy without having to optimize the
equity position."3 Hedging can hurt a portfolio if the currency in question sees favorable
volatility, by the same token, and to the point, it minimizes unfavorable exchange rate volatility.
V. Tools for Hedging Exchange Risk
There are a number of ways to hedge exchange risk. Derivatives are the favored tool of
many investors. Forwards, futures, debt, swaps, and options all have the potential to minimize
exchange risk. The exchange market is divided into two parts; the spot market and the forward
market. The spot market is where payment delivery is made immediately, or within two
business days. The forward market is a price, value date, and payment procedure are set upon
at the time of the transaction where the transaction will take place at a future time. Forward
contracts are the most common way to hedge risk. The downfall of a forward contract is default
risk. As with all promises of future performance, it takes two to tango. If one party defaults, the
hedge disappears.
Second to the forward contract market is the currency future market. The concept of a
future is similar to that of a forward. A future contracts delivery at a future date of a set upon
amount, at a set upon price. Futures are often looked at by investors as standardized forward
contracts. The amount is often smaller and the currency future delivery date is rarely changed
(the normal dates are: March, June, September and December). This concept differs from
forward which are executed at any time explicitly enumerated in the contract. Perhaps the
most important distinction is that pattern of cash flows in a futures contract. Forward contracts
require full payment upon maturity. In future contracts, cash changes hands daily. Due to daily
cash flows, default risk is primarily eliminated. Is credit risk is involved it would be wise to use a
future instead of a forward.
Borrowing the transaction currency to which the investor is exposed, or debt, is also an
applicable way to hedge exchange risk. Debt involves using the borrowing market to achieve
the same goal as the forwards or futures. Consider this example, “A German Company has
shipped equipment to a company in Calgary, Canada. The exporter's treasurer has sold
Canadian dollars forward to protect against a fall in the Canadian currency. Alternatively she
could have used the borrowing market to achieve the same objective. She would borrow
Canadian dollars, which she would then change into Euros in the spot market, and hold them in
a Euro deposit for two months. When payment in Canadian dollars was received from the
customer, she would use the proceeds to pay down the Canadian dollar debt.”4 This transaction
is called a money market hedge. A commonly raised question is where is the substitute for the
3 M, Brown. "To Hedge Or Not To Hedge?." Canadian Business 87.3 (2014): 35-36. Academic Search Complete. Web.
16 July 2015
4 I, Giddy. “Corporate Hedging: Tools and Techniques” New York University Stern School of Business,2014

5. forward exchange premium? The cost of a money market hedge is the difference between the
transaction currency interest rate paid and the domestic currency interest rate earned. This is
referred to as the interest rate parity theorem. Money market hedges work if the investors
(often large firms) already have to borrow anyway; they just change the debt to the exposed
currency. However this method is not practical if it is being done solely for the sake of the
hedge. “The firm ends up borrowing from one bank and lending to another, thus losing on the
spread. This is costly, so the forward hedge would probably be more advantageous except
where the firm had to borrow for ongoing purposes anyway.”3
So is it possible to hedge exchange risk without losing the benefit of favorable volatility?
The answer is yes. When practical, a foreign exchange option is used. A foreign exchange option
is a contract for a future transaction where the holder of the option has the right to buy the
currency at the previously agreed upon price but is not obligated to do so. Options are not
without cost, an option premium must be paid in order for the option to hold value. The seller
receives the premium and is then obligated to buy or sell at the agreed upon price. It is
important to note that American options allow the holder to exercise the option at any time
before expiration, whereas European options only allow it to be exercised on the expiration
date.
Are there also times that hedging does not make sense? Yes, hedging is rarely value
adding. By reducing risk, one might also reduce cash flow, so unless the cash flow is big enough
to compensate for the cost of hedging, it is inadvisable. Also, as previously enumerated, if all
three of the variables in an efficient market are at equilibrium, hedging wouldn’t do anything.
Trading derivatives can also be a source of income and, thus, does not focus on the underlying
asset. For example, in 1999 the gold mining firms were involved in hedging. All of a sudden gold
prices skyrocketed and they lost out on huge sums due to forward contracts and other
derivatives.
VI. Hedging by U.S. Firms
There is a large degree of separation between individuals and firms when it comes to
hedging exchange risk. Individuals, at times, may not hedge due to circumstances such as
insignificant cash flows, or investments that if hedged, would not see a return. U.S. firms
however, are far more amicable to hedging techniques. Non-financial firms are far more likely
to hedge due to their emphasis on the underlying asset. Three fourths of firms report taking
positions, using derivatives, when conducting international transactions. The choice derivative
instrument for U.S. firms are OTC (over the counter) currency forwards. OTC currency forwards
make up over 50% of foreign exchange derivative instruments. The second most preferred
hedging instrument is OTC currency options at around 20%. Futures are primarily suggested
when exposure arises from a U.S. firm’ contractual commitments (e.g. accounts receivable and
accounts payable). Options are used to hedge uncertainty in foreign currency denominated
future cash flows, or cash flows related to anticipated transactions beyond one year.

6. VII. OTC vs. Exchange-Traded
It is important for an investor or firm to be able to differentiate OTC from exchange-
traded derivatives. Over the counter derivatives are contracts that are negotiated and traded
privately between two parties. The OTC market is the largest market for derivatives, as well as
being the least regulated. Exchange-traded derivatives are true to their name. That is to say,
they are derivatives that are traded on an exchange.
VIII. Concluding Remarks
Risk has long been a point of contention. Higher risk ushers in higher returns but at what
cost? It is up the firm or individual to decide what they’re comfortable with. There is no surefire
way to guarantee windfall. If there was one, risk would be a thing of the past. Deciding when to
hedge exchange risk depends on: value at risk, investment climate within a foreign country, and
volatility of the exchange rate. Given the options presented it becomes the prerogative of the
investor to decide whether or not hedging tailors to their financial actions.

7. Works Cited
M, Brown."To Hedge Or NotTo Hedge?." CanadianBusiness 87.3 (2014): 35-36. AcademicSearch
Complete.Web.16 July2015
Giddy, I., and Dufey. "Managing Foreign Exchange Risk." Stern School of Business. N.p., n.d.
Web. 03 Aug. 2015.
Giddy, I. "Corporate Hedging: Tools and Techniques." Giddy: Hedging Tools and Techniques.
N.p., n.d. Web. 03 Aug. 2015.
Hoffstein, Corey. "The Ups and Downs of Currency Hedged ETFs." Forbes. Forbes Magazine, n.d.
Web. 03 Aug. 2015.
Papaioannou, Michael G. "Exchange Rate Risk Measurement and Management: Issues and
Approaches for Firms." IMF Working Papers 06.255 (2006): 1. Web.
Sjo, Bo. "For and Against Hedging." The Complete Guide to Hedge Funds and Hedge Fund
Strategies (2013): n. pag. Web.
Waggoner, John. "Why Invest in International Funds? It's a Mystery." USA Today. Gannett, 16
Jan. 2015. Web. 03 Aug. 2015.