CURRENCY MANAGEMENT: AN INTRODUCTION
by William A. Barker, PhD, CFA
William A. Barker, PhD, CFA (Canada).
LEARNING OUTCOMES
The candidate should be able to:
analyze the effects of currency movements on portfolio risk and return
discuss strategic choices in currency management
formulate an appropriate currency management program given financial market conditions and portfolio objectives and constraints
compare active currency trading strategies based on economic fundamentals, technical analysis, carry-trade, and volatility trading
describe how changes in factors underlying active trading strategies affect tactical trading decisions
describe how forward contracts and FX (foreign exchange) swaps are used to adjust hedge ratios
describe trading strategies used to reduce hedging costs and modify the risk–return characteristics of a foreign-currency portfolio
describe the use of cross-hedges, macro-hedges, and minimum-variance-hedge ratios in portfolios exposed to multiple foreign currencies
discuss challenges for managing emerging market currency exposures
INTRODUCTION
Globalization has been one of the most persistent themes in recent history, and this theme applies equally to the world of finance.
New investment products, deregulation, worldwide financial system integration, and better communication and information networks have opened new global investment opportunities.
At the same time, investors have increasingly shed their “home bias” and sought investment alternatives beyond their own borders.
The benefits of this trend for portfolio managers have been clear, both in terms of the broader availability of higher-expected-return investments as well as portfolio diversification opportunities.
Nonetheless, investments denominated in foreign currencies also bring a unique set of challenges: measuring and managing foreign exchange risk.
Buying foreign-currency denominated assets means bringing currency risk into the portfolio.
Exchange rates are volatile and, at least in the short to medium term, can have a marked impact on investment returns and risks—currency matters.
The key to the superior performance of global portfolios is the effective management of this currency risk.
This reading explores basic concepts and tools of currency management.
Section 2 reviews some of the basic concepts of foreign exchange (FX) markets.
The material in subsequent sections presumes an understanding of these concepts.
Section 3 examines some of the basic mathematics involved in measuring the effects of foreign-currency investments on portfolio return and risk.
Sections 4–6 discuss the strategic decisions portfolio managers face in setting the target currency exposures of the portfolio.
The currency exposures that the portfolio can accept range from a fully hedged position to active management of currency risk.
Sections 7–8 discuss some of the tactical considerations involving active currency management if the investment policy statement (IPS) extends some latitude for active currency management.
A requisite to any active currency management is having a market view; so these sections includes various methodologies by which a manager can form directional views on future exchange rate movements and volatility.
Sections 9–12 cover a variety of trading tools available to implement both hedging and active currency management strategies.
Although the generic types of FX derivatives tools are relatively limited—spot, forward, option, and swap contracts—the number of variations within each and the number of combinations in which they can be used is vast.
Section 13 examines some of the issues involved in managing the currency exposures of emerging market currencies—that is, those that are less liquid than the major currencies.
FOREIGN EXCHANGE CONCEPTS
We begin with a review of the basic trading tools of the foreign exchange market: spot, forward, FX swap, and currency option transactions. The concepts introduced in this section will be used extensively in our discussion of currency management techniques in subsequent sections.
Most people think only of spot transactions when they think of the foreign exchange market, but in fact the spot market accounts for less than 40% of the average daily turnover in currencies.
Although cross-border business may be transacted in the spot market (making and receiving foreign currency payments), the risk management of these flows takes place in FX derivatives markets (i.e., using forwards, FX swaps, and currency options). So does the hedging of foreign currency assets and liabilities.
It is unusual for market participants to engage in any foreign currency transactions without also managing the currency risk they create.
Spot transactions typically generate derivative transactions.
As a result, understanding these FX derivatives markets, and their relation to the spot market, is critical for understanding the currency risk management issues examined in this reading.
Spot Markets
Exhibit 1:
Currency Codes
EUR
Euro
GBP
British pound
JPY
Japanese yen
MXN
Mexican peso
CHF
Swiss franc
CAD
Canadian dollar
SEK
Swedish krona
AUD
Australian dollar
KRW
Korean won
NZD
New Zealand dollar
BRL
Brazilian real
RUB
Russian ruble
CNY
Chinese yuan
INR
Indian rupee
ZAR
South African rand
An exchange rate is the number of units of one currency (called the price currency) that one unit of another currency (called the base currency) will buy.
For example, in the notation we will use a USD/EUR rate of 1.1650 which means that one euro buys $1.1650; equivalently, the price of one euro is 1.1650 US dollars.
Thus, the euro here is the base currency and the US dollar is the price currency.
The exact notation used to represent exchange rates can vary widely between sources, and occasionally the same exchange rate notation will be used by different sources to mean completely different things.
The reader should be aware that the notation used here may not be the same as that encountered elsewhere.
To avoid confusion, this reading will identify exchange rates using the convention of “P/B,” which refers to the price of one unit of the base currency “B” expressed in terms of the price currency “P.”
How the professional FX market quotes exchange rates—which is the base currency, and which is the price currency, in any currency pair—is not arbitrary but follows conventions that are broadly agreed on throughout the market.
Generally, there is a hierarchy as to which currency will be quoted as the base currency in any given P/B currency pair:
Currency pairs involving the EUR will use the EUR as the base currency (for example, GBP/EUR).
Currency pairs involving the GBP, other than those involving the EUR, will use the GBP as the base currency (for example, CHF/GBP).
Currency pairs involving either the AUD or NZD, other than those involving either the EUR or GBP, will use these currencies as the base currency (for example, USD/AUD and NZD/AUD). The market convention between these two currencies is for a NZD/AUD quote.
All other currency quotes involving the USD will use USD as the base currency (for example, MXN/USD).
Exhibit 2:
Select Market-Standard Currency Pair Quotes
Quote convention
Market name
USD/EUR
Euro-dollar
GBP/EUR
Euro-sterling
USD/GBP
Sterling-dollar
JPY/USD
Dollar-yen
USD/AUD
Aussie-dollar
CHF/USD
Dollar-Swiss
CAD/USD
Dollar-Canada
JPY/EUR
Euro-yen
CHF/EUR
Euro-Swiss
JPY/GBP
Sterling-yen
Another convention used in professional FX markets is that most spot currency quotes are priced out to four decimal places: for example, a typical USD/EUR quote would be 1.1500 and not 1.15.
The price point at the fourth decimal place is commonly referred to as a “pip.”
Professional FX traders also refer to what is called the “big figure” or the “handle,” which is the integer to the left side of the decimal place as well as the first two decimal places of the quote.
For example, for a USD/EUR quote of 1.1568, 1.15 is the handle and there are 68 pips.
There are exceptions to this four decimal place rule.
First, forward quotes—discussed later—will often be quoted out to five and sometimes six decimal places.
Second, because of the relative magnitude of some currency values, some currency quotes will only be quoted out to two decimal places. For example, because it takes many Japanese yen to buy one US dollar, the typical spot quote for JPY/USD is priced out to only two decimal places (for example, 111.35 and not 111.3500).2
The spot exchange rate is usually for settlement on the second business day after the trade date, referred to as T + 2 settlement.
In foreign exchange markets—as in other financial markets—market participants confront a two-sided price in the form of a bid price and an offer price (also called an ask price) being quoted by potential counterparties.
The bid price is the price, defined in terms of the price currency, at which the counterparty providing a two-sided price quote is willing to buy one unit of the base currency.
Similarly, offer price is the price, in terms of the price currency, at which that counterparty is willing to sell one unit of the base currency.
For example, given a price request from a client, a dealer might quote a two-sided price on the spot USD/EUR exchange rate of 1.1648/1.1652.
This quote means that the dealer is willing to pay USD1.1648 to buy one euro (bid) and that the dealer will sell one euro (offer) for USD1.1652.
The market width, usually referred to as dealer’s spread or the bid–offer spread, is the difference between the bid and the offer.
When transacting on a dealer’s bid-offer two-sided price quote, a client is said to either “hit the bid” (selling the base currency) or “pay the offer” (buying the base currency).
An easy check to see whether the bid or offer should be used for a specific transaction is that the party asking the dealer for a price should be on the more expensive side of the market.
For example, if one wants to buy 1 EUR, 1.1652 is more USD per EUR than 1.1648.
Hence, paying the offer involves paying more USD.
Similarly, when selling 1 EUR, hitting the bid at 1.1648 means less USD received than 1.1652.
Forward Markets
Forward contracts are agreements to exchange one currency for another on a future date at an exchange rate agreed on today.
In contrast to spot rates, forward contracts are any exchange rate transactions that occur with settlement longer than the usual T + 2 settlement for spot delivery.
In professional FX markets, forward exchange rates are typically quoted in terms of “points.”
The points on a forward rate quote are simply the difference between the forward exchange rate quote and the spot exchange rate quote; that is, the forward premium or discount, with the points scaled so that they can be related to the last decimal place in the spot quote.
Forward points are adjustments to the spot price of the base currency, using our standard price/base (P/B) currency notation.
This means that forward rate quotes in professional FX markets are typically shown as the bid–offer on the spot rate and the number of forward points at each maturity.
Exhibit 3:
Sample Spot and Forward Quotes (Bid–Offer)
Maturity
Spot Rate or Forward Points
Spot (USD/EUR)
1.1649/1.651
One month
5.1/5.6
Three months
25.3/25.9
Six months
46.0/46.7
Twelve months
92.3/93.8
To convert any of these quoted forward points into a forward rate, one would divide the number of points by 10,000 (to scale down to the fourth decimal place, the last decimal place in the USD/EUR spot quote) and then add the result to the spot exchange rate quote.
But one must be careful about which side of the market (bid or offer) is being quoted.
For example, suppose a market participant was selling the EUR forward against the USD.
Given the USD/EUR quoting convention, the EUR is the base currency.
This means the market participant must use the bid rates (i.e., the market participant will “hit the bid”) given the USD/EUR quoting convention.
This result means that the market participant would be selling EUR three months forward at a price of USD1.1674 per EUR.
Note that the quoted points are already scaled to each maturity—they are not annualized—so there is no need to adjust them.
Although there is no cash flow on a forward contract until settlement date, it is often useful to do a mark-to-market valuation on a forward position before then to
(1) judge the effectiveness of a hedge based on forward contracts (i.e., by comparing the change in the mark-to-market of the underlying asset with the change in the mark-to-market of the forward), and
(2) to measure the profitability of speculative currency positions at points before contract maturity.
As with other financial instruments, the mark-to-market value of forward contracts reflects the profit (or loss) that would be realized from closing out the position at current market prices. To close out a forward position, it must be offset with an equal and opposite forward position using the spot exchange rate and forward points available in the market when the offsetting position is created. When a forward contract is initiated, the forward rate is such that no cash changes hands (i.e., the mark-to-market value of the contract at initiation is zero). From that moment onward, however, the mark-to-market value of the forward contract will change as the spot exchange rate changes as well as when interest rates change in either of the two currencies.
Consider an example. Suppose that a market participant bought GBP10,000,000 for delivery against the AUD in six months at an “all-in” forward rate of 1.8600 AUD/GBP. (The all-in forward rate is simply the sum of the spot rate and the forward points, appropriately scaled to size.) Three months later, the market participant wants to close out this forward contract. To do that would require selling GBP10,000,000 three months forward using the AUD/GBP spot exchange rate and forward points in effect at that time. Assume the bid–offer for spot and forward points three months prior to the settlement date are as follows:
Three-month points
−4/−2
To sell GBP (the base currency in the AUD/GBP quote) means calculating the bid side of the market. Hence, the appropriate all-in three-month forward rate to use is1.8810 + −4/10,000 = 1.8806Thus, the market participant originally bought GBP10,000,000 at an AUD/GBP rate of 1.8600 and subsequently sold them at a rate of 1.8806. These GBP amounts will net to zero at settlement date (GBP10 million both bought and sold), but the AUD amounts will not net to zero because the forward rate has changed. The AUD cash flow at settlement date will be equal to(1.8806 − 1.8600) × 10,000,000 = AUD206,000This amount is a cash inflow because the market participant was long the GBP with the original forward position and the GBP subsequently appreciated (the AUD/GBP rate increased).
This is the mark-to-market value of the original long GBP10 million six-month forward contract when it is closed out three months prior to settlement.
To summarize, the process for marking-to-market a forward position is relatively straightforward:
Create an equal and offsetting forward position to the original forward position. (In the example earlier, the market participant is long GBP10 million forward, so the offsetting forward contract would be to sell GBP10 million.)
Determine the appropriate all-in forward rate for this new, offsetting forward position. If the base currency of the exchange rate quote is being sold (bought), then use the bid (offer) side of the market.
Calculate the cash flow at settlement day. This calculation will be based on the original contract size times the difference between the original forward rate and the rate calculated in Step 2. If the currency the market participant was originally long (short) subsequently appreciated (depreciated), then there will be a cash inflow. Otherwise, there will be a cash outflow. (In the earlier example, the market participant was long the GBP and it subsequently appreciated; this appreciation led to a cash inflow at the settlement day.)
Calculate the present value of this cash flow at the future settlement date. The currency of the cash flow and the discount rate must match. (In the example earlier, the cash flow at the settlement date is in AUD, so the market reference rate (MRR) is used to calculate the present value.)
Finally, we note that in the example, the mark-to-market value is given in AUD. It would be possible to translate this AUD amount into any other currency value using the current spot rate for the relevant currency pair. In the example above, this would be done by redenominating the mark-to-market in USD, by selling 240,000 AUD 90-days forward against the USD at the prevailing USD/AUD 90-day forward bid rate. This will produce a USD cash flow in 90 days. This USD amount can then be present-valued at the 90-day US rate to get the USD mark-to-market value of the AUD/GBP forward position. The day-count convention used here is an “actual/360” basis.
FX Swap Markets
An FX swap transaction consists of offsetting and simultaneous spot and forward transactions, in which the base currency is being bought (sold) spot and sold (bought) forward. These two transactions are often referred to as the “legs” of the swap.
The two legs of the swap can either be of equal size (a “matched” swap) or one can be larger than the other (a “mismatched” swap). FX swaps are distinct from currency swaps.
Similar to currency swaps, FX swaps involve an exchange of principal amounts in different currencies at swap initiation that is reversed at swap maturity.
Unlike currency swaps, FX swaps have no interim interest payments and are nearly always of much shorter term than currency swaps.
FX swaps are important for managing currency risk because they are used to “roll” forward contracts forward as they mature.
For example, consider the case of a trader who bought GBP1,000,000 one month forward against the CHF in order to set up a currency hedge. One month later, the forward contract will expire.
To maintain this long position in the GBP against the CHF, two days prior to contract maturity, given T + 2 settlement, the trader must
(1) sell GBP1,000,000 against the CHF spot, to settle the maturing forward contract; and
(2) buy GBP1,000,000 against the CHF forward.
That is, the trader is engaging in an FX swap (a matched swap in this case because the GBP currency amounts are equal).
If a trader wanted to adjust the size of the currency hedge (i.e., the size of the outstanding forward position), the forward leg of the FX swap can be of a different size than the spot transaction when the hedge is rolled.
Continuing the previous example, if the trader wanted to increase the size of the long-GBP position by GBP500,000 as the outstanding forward contract expires, the transactions required would be to
(1) sell GBP1,000,000 against the CHF spot, to settle the maturing forward contract; and
(2) buy GBP1,500,000 against the CHF forward. This would be a mismatched swap.
The pricing of swaps will differ slightly depending on whether they are matched or mismatched swaps. If the amount of the base currency involved for the spot and forward legs of the swap are equal (a matched swap), then these are exactly offsetting transactions; one is a buy, the other a sell, and both are for the same amount. Because of this equality, a common spot exchange rate is typically applied to both legs of the swap transaction; it is standard practice to use the mid-market spot exchange rate for a matched swap transaction. However, the forward points will still be based on either the bid or offer, depending on whether the market participant is buying or selling the base currency forward. In the earlier example, the trader is buying the GBP (the base currency) forward and would hence pay the offer side of the market for forward points.
If the FX swap is mismatched, then pricing will need to reflect the difference in trade sizes between the two legs of the transaction. Continuing the example in which the trader increased the size of the long-GBP position by GBP500,000, this mismatched swap is equivalent to (1) a matched swap for a size of GBP1,000,000, and (2) an outright forward contract buying GBP500,000. Pricing for the mismatched swap must reflect this net GBP purchase amount. Because the matched swap would already price the forward points on the offer side of the market, typically this mismatched size adjustment would be reflected in the spot rate quoted as the base for the FX swap. Because a net amount of GBP is being bought, the spot quote would now be on the offer side of the CHF/GBP spot rate quote. (In addition, the trader would still pay the offer side of the market for the forward points.)
We will return to these topics later in the reading when discussing in more depth the use of forward contracts and FX swaps to adjust hedge ratios. (A hedge ratio is the ratio of the nominal value of the derivatives contract used as a hedge to the market value of the hedged asset.)
Currency Options
The final product type within FX markets is currency options. The market for currency options is, in many ways, similar to option markets for other asset classes, such as bonds and equities. As in other markets, the most common options in FX markets are call and put options, which are widely used for both risk management and speculative purposes. However, in addition to these vanilla options, the FX market is also characterized by active trading in exotic options. (“Exotic” options have a variety of features that make them exceptionally flexible risk management tools, compared with vanilla options.)
The risk management uses of both vanilla and exotic currency options will be examined in subsequent sections. Although daily turnover in FX options market is small in relative terms compared with the overall daily flow in global spot currency markets, because the overall currency market is so large, the absolute size of the FX options market is still very considerable.
CURRENCY RISK AND PORTFOLIO RISK AND RETURN
Learning Outcome
analyze the effects of currency movements on portfolio risk and return
In this section, we examine the effect of currency movements on asset returns and portfolio risk. We then turn to how these effects help determine construction of a foreign asset portfolio.
Return Decomposition
In this section, we examine how international exposure affects a portfolio’s return.
A domestic asset is an asset that trades in the investor’s domestic currency (or home currency).
From a portfolio manager’s perspective, the domestic currency is the one in which portfolio valuation and returns are reported.
Domestic refers to a relation between the currency denomination of the asset and the investor; it is not an inherent property of either the asset or the currency.
An example of a domestic asset is a USD-denominated bond portfolio from the perspective of a US-domiciled investor.
The return on a domestic asset is not affected by exchange rate movements of the domestic currency.
Foreign assets are assets denominated in currencies other than the investor’s home currency.
An example of a foreign asset is a USD-denominated bond portfolio from the perspective of a eurozone-domiciled investor (and for whom the euro is the home currency).
The return on a foreign asset will be affected by exchange rate movements in the home currency against the foreign currency.
Continuing with our example, the return to the eurozone-domiciled investor will be affected by the USD return on the USD-denominated bond as well as movements in the exchange rate between the home currency and the foreign currency, the EUR and USD respectively.
The return of the foreign asset measured in foreign-currency terms is known as the foreign-currency return.
Extending the example, if the value of the USD-denominated bond increased by 10%, measured in USD, that increase is the foreign-currency return to the eurozone-domiciled investor.
The domestic-currency return on a foreign asset will reflect both the foreign-currency return on that asset as well as percentage movements in the spot exchange rate between the home and foreign currencies.
The domestic-currency return is multiplicative with respect to these two factors:RDC = (1 + RFC)(1 + RFX) − 1 1where RDC is the domestic-currency return (in percent), RFC is the foreign-currency return, and RFX is the percentage change of the foreign currency against the domestic currency.
Returning to the example, the domestic-currency return for the eurozone-domiciled investor on the USD-denominated bond will reflect both the bond’s USD-denominated return as well as movements in the exchange rate between the USD and the EUR. Suppose that the foreign-currency return on the USD-denominated bond is 10% and the USD appreciates by 5% against the EUR. In this case, the domestic-currency return to the eurozone investor will be:
(1 + 10%)(1 + 5%) − 1 = (1.10)(1.05) − 1 = 0.155 = 15.5%
In other words, RFX is calculated as the change in the directly quoted exchange rate, where the domestic currency is defined as the investor’s home currency. Because market quotes are not always in direct terms, analysts will need to convert to direct quotes before calculating percentage changes.
Assume the following information for a portfolio held by an investor in India. Performance is measured in terms of the Indian rupee (INR) and the weights of the two assets in the portfolio, at the beginning of the period, are 80% for the GBP-denominated asset and 20% for the EUR-denominated asset, respectively. (Note that the portfolio weights are measured in terms of a common currency, the INR, which is the investor’s domestic currency in this case.)
One Year Ago
Today*
INR/GBP spot rate
95.80
101.60
INR/EUR spot rate
86.95
86.45
GBP-denominated asset value, in GBP millions
43.80
50.70
EUR-denominated asset value, in EUR millions
14.08
12.17
GBP-denominated asset value, in INR millions
4,196.04
5,151.12
EUR-denominated asset value, in INR millions
1,224.26
1,052.10
GBP-denominated assets, portfolio weight (INR)
80%
EUR-denominated assets, portfolio weight (INR)
20%
* Today’s asset values are prior to rebalancing.
Volatility Decomposition
RDC ≈ RFC + RFX 3
Thus, rather than attempt to give the complete mathematical formula for the variance of domestic-currency returns for a multi-currency portfolio, we will instead focus on the key intuition behind this expression.
Namely, that the domestic-currency risk exposure of the overall portfolio—that is, σ(RDC)—will depend not only on the variances of each of the foreign-currency returns (RFC) and exchange rate movements (RFX) but also on how each of these interacts with the others.
Generally speaking, negative correlations among these variables will help reduce the overall portfolio’s risk through diversification effects.
Note as well that the overall portfolio’s risk exposure will depend on the portfolio weights (ωi) used. If short-selling is allowed in the portfolio, some of these ωi can be negative as long as the total portfolio weights sum to one.
So, for two foreign assets with a strong positive return correlation, short selling one can create considerable diversification benefits for the portfolio. (This approach is equivalent to trading movements in the price spread between these two assets.)
As before with the difference between realized and expected domestic-currency portfolio returns (RDC), there is a difference between realized and expected domestic-currency portfolio risk, σ(RDC).
This can be challenging, not only because it potentially involves a large number of variables but also because historical price patterns are not always a good guide to future price behavior.
Variance and correlation measures are sensitive to the time period used to estimate them and can also vary over time.
These variance and correlation measures can either drift randomly with time, or they can be subject to abrupt movements in times of market stress.
It should also be clear that these observed, historical volatility and correlation measures need not be the same as the forward-looking implied volatility (and correlation) derived from option prices.
Although sometimes various survey or consensus forecasts can be used, these too can be sensitive to sample size and composition and are not always available on a timely basis or with a consistent starting point.
As with any forecast, they are also not necessarily an accurate guide to future developments; judgment must be used.
Hence, to calculate the expected future risk of the foreign asset portfolio, the portfolio manager would need a market opinion—however derived—on the variance of each of the foreign-currency asset returns (RFC) over the investment horizon as well the variance of future exchange rate movements (RFX) for each currency pair.
The portfolio manager would also need a market opinion of how each of these future variables would interact with each other (i.e., their expected correlations).
Historical price patterns can serve as a guide, and with computers and large databases, this modeling problem is daunting but not intractable. But the portfolio manager must always be mindful that historical risk patterns may not repeat going forward.
EXAMPLE 1
Portfolio Risk and Return Calculations
The following table shows current and future expected asset prices, measured in their domestic currencies, for both eurozone and Canadian assets (these can be considered “total return” indexes). The table also has the corresponding data for the CAD/EUR spot rate.
Eurozone
Canada
Today
Expected
Today
Expected
Asset price
100.69
101.50
101.00
99.80
CAD/EUR
1.4500
1.4700
What is the expected domestic-currency return for a eurozone investor holding the Canadian asset?
Solution to 1:
For the eurozone investor, the RFC = (99.80/101.00) − 1 = −1.19%. Note that, given we are considering the eurozone to be “domestic” for this investor and given the way the RFX expression is defined, we will need to convert the CAD/EUR exchange rate quote so that the EUR is the price currency. This leads to RFX = [(1/1.4700)/(1/1.4500)] − 1 = −1.364%. Hence, for the eurozone investor, RDC = (1 − 1.19%)(1 ‒ 1.364%) − 1 = −2.53%.
What is the expected domestic-currency return for a Canadian investor holding the eurozone asset?
Solution to 2:
For the Canadian investor, the RFC = (101.50/100.69) − 1 = +0.80%. Given that in the CAD/EUR quote the CAD is the price currency, for this investor the RFX = (1.4700/1.4500) − 1 = +1.38%. Hence, for the Canadian investor the RDC = (1 + 0.80%)(1 + 1.38%) − 1 = 2.19%.
From the perspective of the Canadian investor, assume that σ(RFC) = 3% (the expected risk for the foreign-currency asset is 3%) and the σ(RFX) = 2% (the expected risk of exchange rate movements is 2%). Furthermore, the expected correlation between movements in foreign-currency asset returns and movements in the CAD/EUR rate is +0.5. What is the expected risk of the domestic-currency return [σ(RDC)]?
Solution to 3:
σ2(RDC) ≈ σ2(RFC) + σ2(RFX) + 2σ(RFC)σ(RFX)ρ(RFC,RFX)
Inserting the relevant data leads to
σ2(RDC) ≈ (3%)2 + (2%)2 + 2(3%)(2%)(0.50) = 0.0019
Taking the square root of this leads to σ(RDC) ≈ 4.36%. (Note that the units in these expressions are all in percent, so in this case 3% is equivalent to 0.03 for calculation purposes.)
STRATEGIC DECISIONS IN CURRENCY MANAGEMENT
Learning Outcome
discuss strategic choices in currency management
There are a variety of approaches to currency management, ranging from trying to avoid all currency risk in a portfolio to actively seeking foreign exchange risk in order to manage it and enhance portfolio returns.
There is no firm consensus—either among academics or practitioners—about the most effective way to manage currency risk. Some investment managers try to hedge all currency risk, some leave their portfolios unhedged, and others see currency risk as a potential source of incremental return to the portfolio and will actively trade foreign exchange. These widely varying management practices reflect a variety of factors including investment objectives, investment constraints, and beliefs about currency markets.
Concerning beliefs, one camp of thought holds that in the long run currency effects cancel out to zero as exchange rates revert to historical means or their fundamental values. Moreover, an efficient currency market is a zero-sum game (currency “A” cannot appreciate against currency “B” without currency “B” depreciating against currency “A”), so there should not be any long-run gains overall to speculating in currencies, especially after netting out management and transaction costs. Therefore, both currency hedging and actively trading currencies represent a cost to a portfolio with little prospect of consistently positive active returns.
At the other extreme, another camp of thought notes that currency movements can have a dramatic impact on short-run returns and return volatility and holds that there are pricing inefficiencies in currency markets. They note that much of the flow in currency markets is related to international trade or capital flows in which FX trading is being done on a need-to-do basis and these currency trades are just a spinoff of the other transactions. Moreover, some market participants are either not in the market on a purely profit-oriented basis (e.g., central banks, government agencies) or are believed to be “uninformed traders” (primarily retail accounts). Conversely, speculative capital seeking to arbitrage inefficiencies is finite. In short, marketplace diversity is believed to present the potential for “harvesting alpha” through active currency trading.
This ongoing debate does not make foreign-currency risk in portfolios go away; it still needs to managed, or at least, recognized. Ultimately, each portfolio manager or investment oversight committee will have to reach their own decisions about how to manage risk and whether to seek return enhancement through actively trading currency exposures.
Fortunately, there are a well-developed set of financial products and portfolio management techniques that help investors manage currency risk no matter what their individual objectives, views, and constraints. Indeed, the potential combinations of trading tools and strategies are almost infinite, and can shape currency exposures to custom-fit individual circumstance and market opinion. In this section, we explore various points on a spectrum reflecting currency exposure choices (a risk spectrum) and the guidance that portfolio managers use in making strategic decisions about where to locate their portfolios on this continuum. First, however, the implication of investment objectives and constraints as set forth in the investment policy statement must be recognized.
The Investment Policy Statement
The Investment Policy Statement (IPS) mandates the degree of discretionary currency management that will be allowed in the portfolio, how it will be benchmarked, and the limits on the type of trading polices and tools (e.g., such as leverage) than can be used.
The starting point for organizing the investment plan for any portfolio is the IPS, which is a statement that outlines the broad objectives and constraints of the beneficial owners of the assets. Most IPS specify many of the following points:
the general objectives of the investment portfolio;
the risk tolerance of the portfolio and its capacity for bearing risk;
the time horizon over which the portfolio is to be invested;
the ongoing income/liquidity needs (if any) of the portfolio; and
the benchmark against which the portfolio will measure overall investment returns.
The IPS sets the guiding parameters within which more specific portfolio management policies are set, including the target asset mix; whether and to what extent leverage, short positions, and derivatives can be used; and how actively the portfolio will be allowed to trade its various risk exposures.For most portfolios, currency management can be considered a sub-set of these more specific portfolio management policies within the IPS. The currency risk management policy will usually address such issues as the
target proportion of currency exposure to be passively hedged;
latitude for active currency management around this target;
frequency of hedge rebalancing;
currency hedge performance benchmark to be used; and
hedging tools permitted (types of forward and option contracts, etc.).
Currency management should be conducted within these IPS-mandated parameters.
The Portfolio Optimization Problem
Having described the IPS as the guiding framework for currency management, we now examine the strategic choices that have to be made in deciding the benchmark currency exposures for the portfolio, and the degree of discretion that will be allowed around this benchmark. This process starts with a decision on the optimal foreign-currency asset and FX exposures.
Optimization of a multi-currency portfolio of foreign assets involves selecting portfolio weights that locate the portfolio on the efficient frontier of the trade-off between risk and expected return defined in terms of the investor’s domestic currency. As a simplification of this process, consider the portfolio manager examining the expected return and risk of the multi-currency portfolio of foreign assets by using different combinations of portfolio weights (ωi) that were shown in Equations 2 and 6, respectively, which are repeated here:
When deciding on an optimal investment position, these equations would be based on the expected returns and risks for each of the foreign-currency assets; and hence, including the expected returns and risks for each of the foreign-currency exposures. As we have seen earlier, the number of market parameters for which the portfolio manager would need to have a market opinion grows geometrically with the complexity (number of foreign-currency exposures) in the portfolio. That is, to calculate the expected efficient frontier, the portfolio manager must have a market opinion for each of the RFC,i, RFX,i,, σ(RFC,i), σ(RFX,i), and ρ(RFC,i RFX,i), as well as for each of the ρ(RFC,i RFC,j) and ρ(RFX,i RFX,j). This would be a daunting task for even the most well-informed portfolio manager.
In a perfect world with complete (and costless) information, it would likely be optimal to jointly optimize all of the portfolio’s exposures—over all currencies and all foreign-currency assets—simultaneously. In the real world, however, this can be a much more difficult task. Confronted with these difficulties, many portfolio managers handle asset allocation with currency risk as a two-step process: (1) portfolio optimization over fully hedged returns; and (2) selection of active currency exposure, if any. Derivative strategies can allow the various risk exposures in a portfolio to be “unbundled” from each other and managed separately. The same applies for currency risks. Because the use of derivatives allows the price risk (RFC,i) and exchange rate risk (RFX,j) of foreign-currency assets to be unbundled and managed separately, a starting point for the selection process of portfolio weights would be to assume a complete currency hedge. That is, the portfolio manager will choose the exposures to the foreign-currency assets first, and then decide on the appropriate currency exposures afterward (i.e., decide whether to relax the full currency hedge). These decisions are made to simplify the portfolio construction process.
Removing the currency effects leads to a simpler, two-step process for portfolio optimization. First the portfolio manager could pick the set of portfolio weights (ωi) for the foreign-currency assets that optimize the expected foreign-currency asset risk–return trade-off (assuming there is no currency risk). Then the portfolio manager could choose the desired currency exposures for the portfolio and decide whether and by how far to relax the constraint to a full currency hedge for each currency pair.
Choice of Currency Exposures
A natural starting point for the strategic decisions is the “currency-neutral” portfolio resulting from the two-step process described earlier. The question then becomes, How far along the risk spectrum between being fully hedged and actively trading currencies should the portfolio be positioned?
Diversification Considerations
The time horizon of the IPS is important. Many investment practitioners believe that in the long run, adding unhedged foreign-currency exposure to a portfolio does not affect expected long-run portfolio returns; hence in the long run, it would not matter if the portfolio was hedged. (Indeed, portfolio management costs would be reduced without a hedging process.) This belief is based on the view that in the long run, currencies “mean revert” to either some fair value equilibrium level or a historical average; that is, that the expected %ΔS = 0 for a sufficiently long time period. This view typically draws on the expectation that purchasing power parity (PPP) and the other international parity conditions that link movements in exchange rates, interest rates, and inflation rates will eventually hold over the long run.
Supporting this view, some studies argue that in the long-run currencies will in fact mean revert, and hence that currency risk is lower in the long run than in the short run (an early example is Froot 1993). Although much depends on how long run is defined, an investor (IPS) with a very long investment horizon and few immediate liquidity needs—which could potentially require the liquidation of foreign-currency assets at disadvantageous exchange rates—might choose to forgo currency hedging and its associated costs. Logically, this would require a portfolio benchmark index that is also unhedged against currency risk.
Although the international parity conditions may hold in the long run, it can be a very long time—possibly decades. Indeed, currencies can continue to drift away from the fair value mean reversion level for much longer than the time period used to judge portfolio performance. Such time periods are also typically longer than the patience of the portfolio manager’s oversight committee when portfolio performance is lagging the benchmark. If this very long-run view perspective is not the case, then the IPS will likely impose some form of currency hedging.
It is often asserted that the correlation between foreign-currency returns and foreign-currency asset returns tends to be greater for fixed-income portfolios than for equity portfolios. This assertion makes intuitive sense: both bonds and currencies react strongly to movements in interest rates, whereas equities respond more to expected earnings. As a result, the implication is that currency exposures provide little diversification benefit to fixed-income portfolios and that the currency risk should be hedged. In contrast, a better argument can be made for carrying currency exposures in global equity portfolios.
To some degree, various studies have corroborated this relative advantage to currency hedging for fixed income portfolios. But the evidence seems somewhat mixed and depends on which markets are involved. One study found that the hedging advantage for fixed-income portfolios is not always large or consistent (Darnell 2004). Other studies (Campbell 2010; Martini 2010) found that the optimal hedge ratio for foreign-currency equity portfolios depended critically on the investor’s domestic currency. (Recall that the hedge ratio is defined as the ratio of the nominal value of the hedge to the market value of the underlying.) For some currencies, there was no risk-reduction advantage to hedging foreign equities (the optimal hedge ratio was close to 0%), whereas for other currencies, the optimal hedge ratio for foreign equities was close to 100%.
Other studies indicate that the optimal hedge ratio also seems to depend on market conditions and longer-term trends in currency pairs. For example, Campbell, Serfaty-de Medeiros, and Viceira (2007) found that there were no diversification benefits from currency exposures in foreign-currency bond portfolios, and hence to minimize the risk to domestic-currency returns these positions should be fully hedged. The authors also found, however, that during the time of their study (their data spanned 1975 to 2005), the US dollar seemed to be an exception in terms of its correlations with foreign-currency asset returns. Their study found that the US dollar tended to appreciate against foreign currencies when global bond prices fell (for example, in times of global financial stress there is a tendency for investors to shift investments into the perceived safety of reserve currencies). This finding would suggest that keeping some exposure to the US dollar in a global bond portfolio would be beneficial. For non-US investors, this would mean under-hedging the currency exposure to the USD (i.e., a hedge ratio less than 100%), whereas for US investors it would mean over-hedging their foreign-currency exposures back into the USD. Note that some currencies—the USD, JPY, and CHF in particular—seem to act as a safe haven and appreciate in times of market stress. Keeping some of these currency exposures in the portfolio—having hedge ratios that are not set at 100%--can help hedge losses on riskier assets, especially for foreign currency equity portfolios (which are more risk exposed than bond portfolios).
Given this diversity of opinions and empirical findings, it is not surprising to see actual hedge ratios vary widely in practice among different investors. Nonetheless, it is still more likely to see currency hedging for fixed-income portfolios rather than equity portfolios, although actual hedge ratios will often vary between individual managers.
Cost Considerations
The costs of currency hedging also guide the strategic positioning of the portfolio. Currency hedges are not a “free good” and they come with a variety of expenses that must be borne by the overall portfolio. Optimal hedging decisions will need to balance the benefits of hedging against these costs.
Hedging costs come mainly in two forms: trading costs and opportunity costs. The most immediate costs of hedging involve trading expenses, and these come in several forms:
Trading involves dealing on the bid–offer spread offered by banks. Their profit margin is based on these spreads, and the more the client trades and “pays away the spread,” the more profit is generated by the dealer. Maintaining a 100% hedge and rebalancing frequently with every minor change in market conditions would be expensive. Although the bid–offer spreads on many FX-related products (especially the spot exchange rate) are quite narrow, “churning” the hedge portfolio would progressively add to hedging costs and detract from the hedge’s benefits.
Some hedges involve currency options; a long position in currency options requires the payment of up-front premiums. If the options expire out of the money (OTM), this cost is unrecoverable.
Although forward contracts do not require the payment of up-front premiums, they do eventually mature and have to be “rolled” forward with an FX swap transaction to maintain the hedge. Rolling hedges will typically generate cash inflows or outflows. These cash flows will have to be monitored, and as necessary, cash will have to be raised to settle hedging transactions. In other words, even though the currency hedge may reduce the volatility of the domestic mark-to-market value of the foreign-currency asset portfolio, it will typically increase the volatility in the organization’s cash accounts. Managing these cash flow costs can accumulate to become a significant portion of the portfolio’s value, and they become more expensive (for cash outflows) the higher interest rates go.
One of the most important trading costs is the need to maintain an administrative infrastructure for trading. Front-, middle-, and back-office operations will have to be set up, staffed with trained personnel, and provided with specialized technology systems. Settlement of foreign exchange transactions in a variety of currencies means having to maintain cash accounts in these currencies to make and receive these foreign-currency payments. Together all of these various overhead costs can form a significant portion of the overall costs of currency trading.
A second form of costs associated with hedging are the opportunity cost of the hedge. To be 100% hedged is to forgo any possibility of favorable currency rate moves. If skillfully handled, accepting and managing currency risk—or any financial risk—can potentially add value to the portfolio, even net of management fees. (We discuss the methods by which this might be done in Sections 7–8.)
These opportunity costs lead to another motivation for having a strategic hedge ratio of less than 100%: regret minimization. Although it is not possible to accurately predict foreign exchange movements in advance, it is certainly possible to judge after the fact the results of the decision to hedge or not. Missing out on an advantageous currency movement because of a currency hedge can cause ex post regret in the portfolio manager or client; so too can having a foreign-currency loss if the foreign-currency asset position was unhedged. Confronted with this ex ante dilemma of whether to hedge, many portfolio managers decide simply to “split the difference” and have a 50% hedge ratio (or some other rule-of-thumb number). Both survey evidence and anecdotal evidence show that there is a wide variety of hedge ratios actually used in practice by managers, and that these variations cannot be explained by more “fundamental” factors alone. Instead, many managers appear to incorporate some degree of regret minimization into hedging decisions (for example, see Michenaud and Solnik 2008).
All of these various hedging expenses—both trading and opportunity costs—will need to be managed. Hedging is a form of insurance against risk, and in purchasing any form of insurance the buyer matches their needs and budgets with the policy selected. For example, although it may be possible to buy an insurance policy with full, unlimited coverage, a zero deductible, and no co-pay arrangements, such a policy would likely be prohibitively expensive. Most insurance buyers decide that it is not necessary to insure against every outcome, no matter how minor. Some minor risks can be accepted and “self-insured” through the deductible; some major risks may be considered so unlikely that they are not seen as worth paying the extra premium. (For example, most ordinary people would likely not consider buying insurance against being kidnapped.)
These same principles apply to currency hedging. The portfolio manager (and IPS) would likely not try to hedge every minor, daily change in exchange rates or asset values, but only the larger adverse movements that can materially affect the overall domestic-currency returns (RDC) of the foreign-currency asset portfolio. The portfolio manager will need to balance the benefits and costs of hedging in determining both strategic positioning of the portfolio as well as any latitude for active currency management. However, around whatever strategic positioning decision taken by the IPS in terms of the benchmark level of currency exposure, hedging cost considerations alone will often dictate a range of permissible exposures instead of a single point. (This discretionary range is similar to the deductible in an insurance policy.)
SPECTRUM OF CURRENCY RISK MANAGEMENT STRATEGIES
Learning Outcome
discuss strategic choices in currency management
The strategic decisions encoded in the IPS with regard to the trade-off between the benefits and costs of hedging, as well as the potential for incremental return to the portfolio from active currency management, are the foundation for determining specific currency management strategies. These strategies are arrayed along a spectrum from very risk-averse passive hedging, to actively seeking out currency risk in order to manage it for profit. We examine each in turn.
Passive Hedging
In this approach, the goal is to keep the portfolio’s currency exposures close, if not equal to, those of a benchmark portfolio used to evaluate performance. Note that the benchmark portfolio often has no foreign exchange exposure, particularly for fixed-income assets; the benchmark index is a “local currency” index based only on the foreign-currency asset return (RFC). However, benchmark indexes that have some foreign exchange risk are also possible.
Passive hedging is a rules-based approach that removes almost all discretion from the portfolio manager, regardless of the manager’s market opinion on future movements in exchange rates or other financial prices. In this case, the manager’s job is to keep portfolio exposures as close to “neutral” as possible and to minimize tracking errors against the benchmark portfolio’s performance. This approach reflects the belief that currency exposures that differ from the benchmark portfolio inject risk (return volatility) into the portfolio without any sufficiently compensatory return. Active currency management—taking positional views on future exchange rate movements—is viewed as being incapable of consistently adding incremental return to the portfolio.
But the hedge ratio has a tendency to “drift” with changes in market conditions, and even passive hedges need periodic rebalancing to realign them with investment objectives. Often the management guidance given to the portfolio manager will specify the rebalancing period—for example, monthly. There may also be allowance for intra-period rebalancing if there have been large exchange rate movements.
Discretionary Hedging
This approach is similar to passive hedging in that there is a “neutral” benchmark portfolio against which actual portfolio performance will be measured. However, in contrast to a strictly rules-based approach, the portfolio manager now has some limited discretion on how far to allow actual portfolio risk exposures to vary from the neutral position. Usually this discretion is defined in terms of percentage of foreign-currency market value (the portfolio’s currency exposures are allowed to vary plus or minus x% from the benchmark). For example, a eurozone-domiciled investor may have a US Treasury bond portfolio with a mandate to keep the hedge ratio within 95% to 105%. Assuming no change in the foreign-currency return (RFC), but allowing exchange rates (RFX) to vary, this means the portfolio can tolerate exchange rate movements between the EUR and USD of up to 5% before the exchange rate exposures in the portfolio are considered excessive. The manager is allowed to manage currency exposures within these limits without being considered in violation of the IPS.
This discretion allows the portfolio manager at least some limited ability to express directional opinions about future currency movements—to accept risk in an attempt to earn reward—in order to add value to the portfolio performance. Of course, the portfolio manager’s actual performance will be compared with that of the benchmark portfolio.
Active Currency Management
Further along the spectrum between extreme risk aversion and purely speculative trading is active currency management. In principle, this approach is really just an extension of discretionary hedging: the portfolio manager is allowed to express directional opinions on exchange rates, but is nonetheless kept within mandated risk limits. The performance of the manager—the choices of risk exposures assumed—is benchmarked against a “neutral” portfolio. But for all forms of active management (i.e., having the discretion to express directional market views), there is no allowance for unlimited speculation; there are risk management systems in place for even the most speculative investment vehicles, such as hedge funds. These controls are designed to prevent traders from taking unusually large currency exposures and risking the solvency of the firm or fund.
In many cases, the difference between discretionary hedging and active currency management is one of emphasis more than degree. The primary duty of the discretionary hedger is to protect the portfolio from currency risk. As a secondary goal, within limited bounds, there is some scope for directional opinion in an attempt to enhance overall portfolio returns. If the manager lacks any firm market conviction, the natural neutral position for the discretionary hedger is to be flat—that is, to have no meaningful currency exposures. In contrast, the active currency manager is supposed to take currency risks and manage them for profit. The primary goal is to add alpha to the portfolio through successful trading. Leaving actual portfolio exposures near zero for extended periods is typically not a viable option.
Currency Overlay
Active management of currency exposures can extend beyond limited managerial discretion within hedging boundaries. Sometimes accepting and managing currency risk for profit can be considered a portfolio objective. Active currency management is often associated with what are called currency overlay programs, although this term is used differently by different sources.
In the most limited sense of the term, currency overlay simply means that the portfolio manager has outsourced managing currency exposures to a firm specializing in FX management. This could imply something as limited as merely having the external party implement a fully passive approach to currency hedges. If dealing with FX markets and managing currency hedges is beyond the professional competence of the investment manager, whose focus is on managing foreign equities or some other asset class, then hiring such external professional help is an option. Note that typically currency overlay programs involve external managers. However, some large, sophisticated institutional investors may have in-house currency overlay programs managed by a separate group of specialists within the firm.
A broader view of currency overlay allows the externally hired currency overlay manager to take directional views on future currency movements (again, with the caveat that these be kept within predefined bounds). Sometimes a distinction is made between currency overlay and “foreign exchange as an asset class.” In this classification, currency overlay is limited to the currency exposures already in the foreign asset portfolio. For example, if a eurozone-domiciled investor has GBP- and CHF-denominated assets, currency overlay risks are allowed only for these currencies.
In contrast, the concept of foreign exchange as an asset class does not restrict the currency overlay manager, who is free to take FX exposures in any currency pair where there is value-added to be harvested, regardless of the underlying portfolio. In this sense, the currency overlay manager is very similar to an FX-based hedge fund. To implement this form of active currency management, the currency overlay manager would have a joint opinion on a range of currencies, and have market views not only on the expected movements in the spot rates but also the likelihood of these movements (the variance of the expected future spot rate distribution) as well as the expected correlation between future spot rate movements. Basically, the entire portfolio of currencies is actively managed and optimized over all of the expected returns, risks, and correlations among all of the currencies in the portfolio.
We will focus on this latter form of currency overlay in this reading: active currency management conducted by external, FX-specialized sub-advisors to the portfolio.
It is quite possible to have the foreign-currency asset portfolio fully hedged (or allow some discretionary hedging internally) but then also to add an external currency overlay manager to the portfolio. This approach separates the hedging and alpha function mandates of the portfolio. Different organizations have different areas of expertise; it often makes sense to allocate managing the hedge (currency “beta”) and managing the active FX exposures (currency “alpha”) to those individuals with a comparative advantage in that function.
Adding this form of currency overlay to the portfolio (FX as an asset class) is similar in principle to adding any type of alternative asset class, such as private equity funds or farmland. In each case, the goal is the search for alpha. But to be most effective in adding value to the portfolio, the currency overlay program should add incremental returns (alpha) and/or greater diversification opportunities to improve the portfolio’s risk–return profile. To do this, the currency alpha mandate should have minimum correlation with both the major asset classes and the other alpha sources in the portfolio.
Once this FX as an asset class approach is taken, it is not necessary to restrict the portfolio to a single overlay manager any more than it is necessary to restrict the portfolio to a single private equity fund. Different overlay managers follow different strategies (these are described in more detail in Sections 7–8). Within the overall portfolio allocation to “currency as an alternative asset class”, it may be beneficial to diversify across a range of active management styles, either by engaging several currency overlay managers with different styles or by applying a fund-of-funds approach, in which the hiring and management of individual currency overlay managers is delegated to a specialized external investment vehicle.
Whether managed internally or externally (via a fund of funds) it will be necessary to monitor, or benchmark, the performance of the currency overlay manager: Do they generate the returns expected from their stated trading strategy? Many major investment banks as well as specialized market-information firms provide a wide range of proprietary indexes that track the performance of the investible universe of currency overlay managers; sometimes they also offer sub-indexes that focus on specific trading strategies (for example, currency positioning based on macroeconomic fundamentals). However, the methodologies used to calculate these various indexes vary between suppliers. In addition, different indexes show different aspects of active currency management. Given these differences between indexes, there is no simple answer for which index is most suitable as a benchmark; much depends on the specifics of the active currency strategy.
EXAMPLE 2
Currency Overlay
Windhoek Capital Management is a South Africa-based investment manager that runs the Conservative Value Fund, which has a mandate to avoid all currency risk in the portfolio. The firm is considering engaging a currency overlay manager to help with managing the foreign exchange exposures of this investment vehicle. Windhoek does not consider itself to have the in-house expertise to manage FX risk.
Brixworth & St. Ives Asset Management is a UK-based investment manager, and runs the Aggressive Growth Fund. This fund is heavily weighted toward emerging market equities, but also has a mandate to seek out inefficiencies in the global foreign exchange market and exploit these for profit. Although Brixworth & St. Ives manages the currency hedges for all of its investment funds in-house, it is also considering engaging a currency overlay manager.
Using a currency overlay manager for the Conservative Value Fund is most likely to involve:
joining the alpha and hedging mandates.
a more active approach to managing currency risks.
using this manager to passively hedge their foreign exchange exposures.
Solution to 1:
C is correct. The Conservative Value Fund wants to avoid all currency exposures in the portfolio and Windhoek believes that it lacks the currency management expertise to do this.
Using a currency overlay manager for the Aggressive Growth Fund is most likely to involve:
separating the alpha and hedging mandates.
a less discretionary approach to managing currency hedges.
an IPS that limits active management to emerging market currencies.
Solution to 2:
A is correct. Brixworth & St. Ives already does the FX hedging in house, so a currency overlay is more likely to be a pure alpha mandate. This should not change the way that Brixworth & St. Ives manages its hedges, and the fund’s mandate to seek out inefficiencies in the global FX market is unlikely to lead to a restriction to actively manage only emerging market currencies.
Brixworth & St. Ives is more likely to engage multiple currency overlay managers if:
their returns are correlated with asset returns in the fund.
the currency managers’ returns are correlated with each other.
the currency managers’ use different active management strategies.
Solution to 3:
C is correct. Different active management strategies may lead to a more diversified source of alpha generation, and hence reduced portfolio risk. Choices A and B are incorrect because a higher correlation with foreign-currency assets in the portfolio or among overlay manager returns is likely to lead to less diversification.
FORMULATING A CURRENCY MANAGEMENT PROGRAM
Learning Outcome
formulate an appropriate currency management program given financial market conditions and portfolio objectives and constraints
We now try to bring all of these previous considerations together in describing how to formulate an appropriate currency management program given client objectives and constraints, as well as overall financial market conditions. Generally speaking, the strategic currency positioning of the portfolio, as encoded in the IPS, should be biased toward a more-fully hedged currency management program the more
short term the investment objectives of the portfolio;
risk averse the beneficial owners of the portfolio are (and impervious to ex post regret over missed opportunities);
immediate the income and/or liquidity needs of the portfolio;
fixed-income assets are held in a foreign-currency portfolio;
cheaply a hedging program can be implemented;
volatile (i.e., risky) financial markets are;8 and
skeptical the beneficial owners and/or management oversight committee are of the expected benefits of active currency management.
The relaxation of any of these conditions creates latitude to allow a more proactive currency risk posture in the portfolio, either through wider tolerance bands for discretionary hedging, or by introducing foreign currencies as a separate asset class (using currency overlay programs as an alternative asset class in the overall portfolio). In the latter case, the more currency overlay is expected to generate alpha that is uncorrelated with other asset or alpha-generation programs in the portfolio, the more it is likely to be allowed in terms of strategic portfolio positioning.
Investment Policy Statement
Kailua Kona Advisors runs a Hawaii-based hedge fund that focuses on developed market equities located outside of North America. Its investor base consists of local high-net-worth individuals who are all considered to have a long investment horizon, a high tolerance for risk, and no immediate income needs. In its prospectus to investors, Kailua Kona indicates that it actively manages both the fund’s equity and foreign-currency exposures, and that the fund uses leverage through the use of loans as well as short-selling.
Exhibit 4:
Hedge Fund Currency Management Policy: An Example
Overall Portfolio Benchmark:
MSCI EAFE Index (local currency)
Currency Exposure Ranges:
Foreign-currency exposures, based on the USD market value of the equities actually held by the fund at the beginning of each month, will be hedged back into USD within the following tolerance ranges of plus or minus:
EUR: 20%
GBP: 15%
JPY: 10%
CHF: 10%
AUD: 10%
SEK: 10%
Other currency exposures shall be left unhedged.
Rebalancing:
The currency hedges will be rebalanced at least monthly, to reflect changes in the USD-denominated market value of portfolio equity holdings.
Hedging Instruments:
Forward contracts up to 12 months maturity;
European put and call options can be bought or written, for maturities up to 12 months; and
Exotic options of up to 12 months maturity can be bought or sold.
Reporting:
Management will present quarterly reports to the board detailing net foreign-currency exposures and speculative trading results. Speculative trading results will be benchmarked against a 100% hedged currency exposure.
With this policy, Kailua Kona Advisors is indicating that it is willing to accept foreign-currency exposures within the portfolio but that these exposures must be kept within pre-defined limits. For example, suppose that at the beginning of the month the portfolio held EUR10 million of EUR-denominated assets. Also suppose that this EUR10 million exposure, combined with all the other foreign-currency exposures in the portfolio, matches Kailua Kona Advisors’ desired portfolio weights by currency (as a US-based fund, these desired percentage portfolio allocations across all currencies will be based in USD).
The currency-hedging guidelines indicate that the hedge (for example, using a short position in a USD/EUR forward contract) should be between EUR8 million and EUR12 million, giving some discretion to the portfolio manager on the size of the net exposure to the EUR. At the beginning of the next month, the USD values of the foreign assets in the portfolio are measured again, and the process repeats. If there has been either a large move in the foreign-currency value of the EUR-denominated assets and/or a large move in the USD/EUR exchange rate, it is possible that Kailua Kona Advisors’ portfolio exposure to EUR-denominated assets will be too far away from the desired percentage allocation.9 Kailua Kona Advisors will then need to either buy or sell EUR-denominated assets. If movements in the EUR-denominated value of the assets or in the USD/EUR exchange rate are large enough, this asset rebalancing may have to be done before month’s end. Either way, once the asset rebalancing is done, it establishes the new EUR-denominated asset value on which the currency hedge will be based (i.e., plus or minus 20% of this new EUR amount).
If the portfolio is not 100% hedged—for example, continuing the Kailua Kona illustration, if the portfolio manager only hedges EUR9 million of the exposure and has a residual exposure of being long EUR1 million—the success or failure of the manager’s tactical decision will be compared with a “neutral” benchmark. In this case, the comparison would be against the performance of a 100% fully hedged portfolio—that is, with a EUR10 million hedge.
ECONOMIC FUNDAMENTALS, TECHNICAL ANALYSIS AND THE CARRY TRADE
Learning Outcomes
compare active currency trading strategies based on economic fundamentals, technical analysis, carry-trade, and volatility trading
describe how changes in factors underlying active trading strategies affect tactical trading decisions
The previous section discussed the strategic decisions made by the IPS on locating the currency management practices of the portfolio along a risk spectrum ranging from a very conservative approach to currency risk to very active currency management.
In this section, we consider the case in which the IPS has given the portfolio manager (or currency overlay manager) at least some limited discretion for actively managing currency risk within these mandated strategic bounds.
This then leads to tactical decisions: which FX exposures to accept and manage within these discretionary limits.
In other words, tactical decisions involve active currency management.
A market view is a prerequisite to any form of active management. At the heart of the trading decision in FX (and other) markets, lies a view on future market prices and conditions.
This market opinion guides all decisions with respect to currency risk exposures, including whether currency hedges should be implemented and, if so, how they should be managed.
In what follows, we will explore some of the methods used to form directional views about the FX market.
However, a word of caution that cannot be emphasized enough: There is no simple formula, model, or approach that will allow market participants to precisely forecast exchange rates (or any other financial prices) or to be able to be confident that any trading decision will be profitable.
Active Currency Management Based on Economic Fundamentals
This section sets out a broad framework for developing a view about future exchange rate movements based on underlying fundamentals.
In contrast to other methods for developing a market view (which are discussed in subsequent sections), at the heart of this approach is the assumption that, in a flexible exchange rate system, exchange rates are determined by logical economic relationships and that these relationships can be modeled.
The simple economic framework is based on the assumption that in the long run, the real exchange rate will converge to its “fair value,” but short- to medium-term factors will shape the convergence path to this equilibrium.10
Recall that the real exchange rate reflects the ratio of the real purchasing power between two countries; that is, the once nominal purchasing power in each country is adjusted by its respective price level as well as the spot exchange rate between the two countries.
The long-run equilibrium level for the real exchange rate is determined by purchasing power parity or some other model of an exchange rate’s fair value, and serves as the anchor for longer-term movements in exchange rates.
Over shorter time frames, movements in real exchange rates will also reflect movements in the real interest rate differential between countries.
Recall that the real interest rate (r) is the nominal interest rate adjusted by the expected inflation rate, or r = i − πε, where i is the nominal interest rate and πε is the expected inflation rate over the same term as the nominal and real interest rates.
Movements in risk premiums will also affect exchange rate movements over shorter-term horizons.
The riskier a country’s assets are perceived to be by investors, the more likely they are to move their investments out of that country, thereby depressing the exchange rate.
Finally, the framework recognizes that there are two currencies involved in an exchange rate quote (the price and base currencies) and hence movements in exchange rates will reflect movements in the differentials between these various factors.
As a result, all else equal, the base currency’s real exchange rate should appreciate if there is an upward movement in
its long-run equilibrium real exchange rate;
either its real or nominal interest rates, which should attract foreign capital;
expected foreign inflation, which should cause the foreign currency to depreciate; and
the foreign risk premium, which should make foreign assets less attractive compared with the base currency nation’s domestic assets.
The real exchange rate should also increase if it is currently below its long-term equilibrium value. All of this makes intuitive sense.
In summary, the exchange rate forecast is a mix of long-term, medium-term, and short-term factors.
The long-run equilibrium real exchange rate is the anchor for exchange rates and the point of long-run convergence for exchange rate movements.
Movements in the short- to medium-term factors (nominal interest rates, expected inflation) affect the timing and path of convergence to this long-run equilibrium.
Exhibit 5:
Interaction of Long-term and Short-term Factors in Exchange Rates
Source: Based on Rosenberg (2002), page 32.
It needs to be stressed that it can be very demanding to model how each of these separate effects—nominal interest rate, expected inflation, and risk premium differentials—change over time and affect exchange rates.
It can also be challenging to model movements in the long-term equilibrium real exchange rate. A broad variety of factors, such as fiscal and monetary policy, will affect all of these variables in our simple economic model.11
Active Currency Management Based on Technical Analysis
Another approach to forming a market view is based on technical analysis. This approach is based on quite different assumptions compared with modeling based on economic fundamentals.
Whereas classical exchange rate economics tends to view market participants as rational, markets as efficient, and exchange rates as driven by underlying economic factors, technical analysis ignores economic analysis. Instead, technical analysis is based on three broad themes.
First, market technicians believe that in a liquid, freely traded market the historical price data can be helpful in projecting future price movements.
The reason is because many traders have already used any useful data external to the market to generate their trading positions, so this information is already reflected in current prices.
Therefore, it is not necessary to look outside of the market to form an opinion on future price movements.
This means it is not necessary to examine interest rates, inflation rates, or risk premium differentials (the factors in our fundamentally based model) because exchange rates already incorporate these factors.
Second, market technicians believe that historical patterns in the price data have a tendency to repeat, and that this repetition provides profitable trade opportunities.
These price patterns repeat because market prices reflect human behavior and human beings have a tendency to react in similar ways to similar situations, even if this repetitive behavior is not always fully rational.
For example, when confronted with an upward price trend, many market participants eventually come to believe that it will extrapolate (an attitude of “irrational exuberance” or “this time it is different”).
When the trend eventually breaks, a panicked position exit can cause a sharp overshoot of fair value to the downside.
Broadly speaking, technical analysis can be seen as the study of market psychology and how market participant emotions—primarily greed and fear—can be read from the price data and used to predict future price moves.
Third, technical analysis does not attempt to determine where market prices should trade (fair value, as in fundamental analysis) but where they will trade.
Because these price patterns reflect trader emotions, they need not reflect—at least immediately—any cool, rational assessment of the underlying economic or fundamental situation.
Although market prices may eventually converge to fair value in the long run, the long run can be a very long time indeed.
In the meanwhile, there are shorter-term trading opportunities available in trading the technical patterns in the price data.
Combined, these three principles of technical analysis define a discipline dedicated to identifying patterns in the historical price data, especially as it relates to identifying market trends and market turning points. (Technical analysis is less useful in a trendless market.)
Technical analysis tries to identify when markets have become overbought or oversold, meaning that they have trended too far in one direction and are vulnerable to a trend reversal, or correction.
Technical analysis also tries to identify what are called support levels and resistance levels, either within ongoing price trends or at their extremities (i.e., turning points).
These support and resistance levels are price points on dealers’ order boards where one would except to see clustering of bids and offers, respectively.
At these exchange rate levels, the price action is expected to get “sticky” because it will take more order flow to pierce the wall of either bids or offers. But once these price points are breached, the price action can be expected to accelerate as stops are triggered.
(Stops, in this sense, refer to stop-loss orders, in which traders leave resting bids or offers away from the current market price to be filled if the market reaches those levels. A stop-loss order is triggered when the price action has gone against a trader’s position, and it gets the trader out of that position to limit further losses.)
Technical analysis uses visual cues for market patterns as well as more quantitative technical indicators.
There is a wide variety of technical indexes based on market prices that are used in this context.
Some technical indicators are as simple as using moving averages of past price points.
The 200-day moving average of daily exchange rates is often seen as an important indicator of likely support and resistance.
Sometimes two moving averages are used to establish when a price trend is building momentum. For example, when the 50-day moving average crosses the 200-day moving average, this is sometimes seen as a price “break out” point.
Other technical indicators are based on more complex mathematical formulae. There is an extremely wide variety of these more mathematical indicators, some of them very esoteric and hard to connect intuitively with the behavior of real world financial market participants.
In summary, many FX active managers routinely use technical analysis—either alone or in conjunction with other approaches—to form a market opinion or to time position entry and exit points.
Even though many technical indicators lack the intellectual underpinnings provided by formal economic modeling, they nonetheless remain a prominent feature of FX markets.
Active Currency Management Based on the Carry Trade
The carry trade is a trading strategy of borrowing in low-yield currencies and investing in high-yield currencies.
The term “carry” is related to what is known as the cost of carry—that is, of carrying or holding an investment.
This investment has either an implicit or explicit cost (borrowing cost) but may also produce income. The net cost of carry is the difference between these two return rates.
If technical analysis is based on ignoring economic fundamentals, then the carry trade is based on exploiting a well-recognized violation of one of the international parity conditions often used to describe these economic fundamentals: uncovered interest rate parity.
Recall that uncovered interest rate parity asserts that, on a longer-term average, the return on an unhedged foreign-currency asset investment will be the same as a domestic-currency investment.
Assuming that the base currency in the P/B quote is the low-yield currency, stated algebraically uncovered interest rate parity asserts that%ΔSH/L ≈ iH − iL
where %ΔSH/L is the percentage change in the SH/L spot exchange rate (the low-yield currency is the base currency), iH is the interest rate on the high-yield currency and iL is the interest rate on the low-yield currency.
If uncovered interest rate parity holds, the yield spread advantage for the high-yielding currency (the right side of the equation) will, on average, be matched by the depreciation of the high-yield currency (the left side of the equation; the low-yield currency is the base currency and hence a positive value for %ΔSH/L means a depreciation of the high-yield currency).
According to the uncovered interest rate parity theorem, it is this offset between (1) the yield advantage and (2) the currency depreciation that equates, on average, the unhedged currency returns.
But in reality, the historical data show that there are persistent deviations from uncovered interest rate parity in FX markets, at least in the short to medium term.
Indeed, high-yield countries often see their currencies appreciate, not depreciate, for extended periods of time.
The positive returns from a combination of a favorable yield differential plus an appreciating currency can remain in place long enough to present attractive investment opportunities.
This persistent violation of uncovered interest rate parity described by the carry trade is often referred to as the forward rate bias.
An implication of uncovered interest rate parity is that the forward rate should be an unbiased predictor of future spot rates.
The historical data, however, show that the forward rate is not the center of the distribution for future spot rates; in fact, it is a biased predictor (for example, see Kritzman 1999). Hence the name “forward rate bias.”
With the forward rate premium or discount defined as FP/B − SP/B the “bias” in the forward rate bias is that the premium typically overstates the amount of appreciation of the base currency, and the discount overstates the amount of depreciation.
Indeed, the forward discount or premium often gets even the direction of future spot rate movements wrong.
The carry trade strategy (borrowing in low-yield currencies, investing in high-yield currencies) is equivalent to a strategy based on trading the forward rate bias.
Trading the forward rate bias involves buying currencies trading at a forward discount, and selling currencies trading at a forward premium. This makes intuitive sense: It is desirable to buy low and sell high.
To show the equivalence of the carry trade and trading the forward rate bias, recall that covered interest rate parity (which is enforced by arbitrage) is stated as
This equation shows that when the base currency has a lower interest rate than the price currency (i.e., the right side of the equality is positive) the base currency will trade at a forward premium (the left side of the equality is positive).
That is, being low-yield currency and trading at a forward premium is synonymous.
Similarly, being a high-yield currency means trading at a forward discount.
Borrowing in the low-yield currency and investing in the high-yield currency (the carry trade) is hence equivalent to selling currencies that have a forward premium and buying currencies that have a forward discount (trading the forward rate bias).
Exhibit 6:
The Carry Trade: A Summary
Buy/Invest
Sell/Borrow
Implementing the carry trade
High-yield currency
Low-yield currency
Trading the forward rate bias
Forward discount currency
Forward premium currency
The gains that one can earn through the carry trade (or equivalently, through trading the forward rate bias) can be seen as the risk premiums earned for carrying an unhedged position—that is, for absorbing currency risk. (In efficient markets, there is no extra reward without extra risk.)
Long periods of market stability can make these extra returns enticing to many investors, and the longer the yield differential persists between high-yield and low-yield currencies, the more carry trade positions will have a tendency to build up.
But these high-yield currency advantages can be erased quickly, particularly if global financial markets are subject to sudden bouts of stress.
This is especially true because the carry trade is a leveraged position: borrowing in the low-yielding currency and investing in the high-yielding currency.
These occasional large losses mean that the return distribution for the carry trade has a pronounced negative skew.
This negative skew derives from the fact that the funding currencies of the carry trade (the low-yield currencies in which borrowing occurs) are typically the safe haven currencies, such as the EUR, CHF, and JPY.
In contrast, the investment currencies (the high-yielding currencies) are typically currencies perceived to be higher risk, such as several emerging market currencies.
Any time global financial markets are under stress there is a flight to safety that causes rapid movements in exchange rates, and usually a panicked unwinding of carry trades.
As a result, traders running carry trades often get caught in losing positions, with the leverage involved magnifying their losses.
Because of the tendency for long periods of relatively small gains in the carry trade to be followed by brief periods of large losses, the carry trade is sometimes characterized as “picking up nickels in front of a steamroller.”
One guide to the riskiness of the carry trade is the volatility of spot rate movements for the currency pair; all else equal, lower volatility is better for a carry trade position.
We close this section by noting that although the carry trade can be based on borrowing in a single funding currency and investing in a single high-yield currency, it is more common for carry trades to use multiple funding and investment currencies.
The number of funding currencies and investment currencies need not be equal: for example, there could be five of one and three of the other.
Sometimes the portfolio weighting of exposures between the various funding and investment currencies are simply set equal to each other.
But the weights can also be optimized to reflect the trader’s market view of the expected movements in each of the exchange rates, as well as their individual risks (σ[%ΔS]) and the expected correlations between movements in the currency pairs.
These trades can be dynamically rebalanced, with the relative weights among both funding and investment currencies shifting with market conditions.
VOLATILITY TRADING
Learning Outcomes
compare active currency trading strategies based on economic fundamentals, technical analysis, carry-trade, and volatility trading
describe how changes in factors underlying active trading strategies affect tactical trading decisions
Another type of active trading style is unique to option markets and is known as volatility trading (or simply “vol trading”).To explain this trading style, we will start with a quick review of some option basics.
The derivatives of the option pricing model show the sensitivity of the option’s premium to changes in the factors that determine option value.
These derivatives are often referred to as the “Greeks” of option pricing.
There is a very large number of first, second, third, and cross-derivatives that can be taken of an option pricing formula, but the two most important Greeks that we will consider here are the following:
Delta: The sensitivity of the option premium to a small change in the price of the underlying15 of the option, typically a financial asset. This sensitivity is an indication of price risk.
Vega: The sensitivity of the option premium to a small change in implied volatility. This sensitivity is an indication of volatility risk.
The most important concept to grasp in terms of volatility trading is that the use of options allows the trader, through a variety of trading strategies, to unbundle and isolate all of the various risk factors (the Greeks) and trade them separately.
Once an initial option position is taken (either long or short), the trader has exposure to all of the various Greeks/risk factors. The unwanted risk exposures, however, can then be hedged away, leaving only the desired risk exposure to express that specific directional view.
Delta hedging is the act of hedging away the option position’s exposure to delta, the price risk of the underlying (the FX spot rate, in this case).
Because delta shows the sensitivity of the option price to changes in the spot exchange rate, it thus defines the option’s hedge ratio: The size of the offsetting hedge position that will set the net delta of the combined position (option plus delta hedge) to zero.
Typically implementing this delta hedge is done using either forward contracts or a spot transaction (spot, by definition, has a delta of one, and no exposure to any other of the Greeks; forward contracts are highly correlated with the spot rate).
For example, if a trader was long a call option on USD/EUR with a nominal value of EUR1 million and a delta of +0.5, the delta hedge would involve a short forward position in USD/EUR of EUR0.5 million.
That is, the size of the delta hedge is equal to the option’s delta times the nominal size of the contract.
This hedge size would set the net delta of the overall position (option and forward) to zero.
Once the delta hedge has set the net delta of the position to zero, the trader then has exposure only to the other Greeks, and can use various trading strategies to position in these (long or short) depending on directional views.
Although one could theoretically trade any of the other Greeks, the most important one traded is vega; that is, the trader is expressing a view on the future movements in implied volatility, or in other words, is engaged in volatility trading.
Implied volatility is not the same as realized, or observed, historical volatility, although it is heavily influenced by it.
By engaging in volatility trading, the trader is expressing a view about the future volatility of exchange rates but not their direction (the delta hedge set the net delta of the position to zero).
One simple option strategy that implements a volatility trade is a straddle, which is a combination of both an at-the-money (ATM) put and an ATM call. A long straddle buys both of these options.
Because their deltas are −0.5 and +0.5, respectively, the net delta of the position is zero; that is, the long straddle is delta neutral.
This position is profitable in more volatile markets, when either the put or the call go sufficiently in the money to cover the upfront cost of the two option premiums paid.
Similarly, a short straddle is a bet that the spot rate will stay relatively stable. In this case, the payout on any option exercise will be less than the twin premiums the seller has collected; the rest is net profit for the option seller.
A similar option structure is a strangle position for which a long position is buying out-of-the-money (OTM) puts and calls with the same expiry date and the same degree of being out of the money (we elaborate more on this subject later).
Because OTM options are being bought, the cost of the position is cheaper—but conversely, it also does not pay off until the spot rate passes the OTM strike levels. As a result, the risk–reward for a strangle is more moderate than that for a straddle.
The interesting thing to note is that by using delta-neutral trading strategies, volatility is turned into a product that can be actively traded like any other financial product or asset class, such as equities, commodities, fixed-income products, and so on.
Volatility is not constant nor are its movements completely random. Instead volatility is determined by a wide variety of underlying factors—both fundamental and technical—that the trader can express an opinion on.
Movements in volatility are cyclical, and typically subject to long periods of relative stability punctuated by sharp upward spikes in volatility as markets come under periodic bouts of stress (usually the result of some dramatic event, financial or otherwise).
Speculative vol traders—for example, among currency overlay managers—often want to be net-short volatility. The reason is because most options expire out of the money, and the option writer then gets to keep the option premium without delivery of the underlying currency pair.
The amount of the option premium can be considered the risk premium, or payment, earned by the option writer for absorbing volatility risk.
It is a steady source of income under “normal” market conditions.
Ideally, these traders would want to “flip” their position and be long volatility ahead of volatility spikes, but these episodes can be notoriously difficult to time.
Most hedgers typically run options positions that are net-long volatility because they are buying protection from unanticipated price volatility. (Being long the option means being exposed to the time decay of the option’s time value; that is similar to paying insurance premiums for the protection against exchange rate volatility.)
We can also note that just as there are currency overlay programs for actively trading the portfolio’s currency exposures (as discussed in Section 5) there can also be volatility overlay programs for actively trading the portfolio’s exposures to movements in currencies’ implied volatility.
Just as currency overlay programs manage the portfolio’s exposure to currency delta (movements in spot exchange rates), volatility overlay programs manage the portfolio’s exposure to currency vega.
These volatility overlay programs can be focused on earning speculative profits, but can also be used to hedge the portfolio against risk (we will return to this concept in the discussion of macro hedges in Section 11.).
Enumerating all the potential strategies for trading foreign exchange volatility is beyond the scope of this reading.
Instead, the reader should be aware that this dimension of trading FX volatility (not price) exists and sees a large amount of active trading.
Moreover, the best traders are able to think and trade in both dimensions simultaneously. Movements in volatility are often correlated with directional movements in the price of the underlying.
For example, when there is a flight to safety as carry trades unwind, there is typically a spike in volatility (and options prices) at the same time.
Although pure vol trading is based on a zero-delta position, this need not always be the case; a trader can express a market opinion on volatility (vega exposure) and still have a directional exposure to the underlying spot exchange rate as well (delta exposure). That is, the overall trading position has net vega and delta exposures that reflect the joint market view.
We end this section by explaining how currency options are quoted in professional FX markets. (This information will be used in Sections 9–12 when we discuss other option trading strategies.)
Unlike exchanged-traded options, such as those used in equity markets, OTC options for currencies are not described in terms of specific strike levels (i.e., exchange rate levels).
Instead, in the interdealer market, options are described in terms of their “delta.”
Deltas for puts can range from a minimum of −1 to a maximum of 0, with a delta of −0.5 being the point at which the put option is ATM; OTM puts have deltas between 0 and −0.5.
For call options, delta ranges from 0 to +1, with 0.5 being the ATM point.
In FX markets, these delta values are quoted both in absolute terms (i.e., in positive rather than negative values) and as percentages,
with standard FX option quotes usually in terms of 25-delta and 10-delta options (i.e., a delta of 0.25 and 0.10, respectively; the 10-delta option is deeper OTM and hence cheaper than the 25-delta option).
The FX options market is the most liquid around these standard delta quoting points (ATM, 25-delta, 10-delta), but of course, as a flexible OTC market, options of any delta/strike price can be traded.
The 25-delta put option (for example) will still go in the money if the spot price dips below a specific exchange rate level; this implied strike price is backed out of an option pricing model once all the other pricing factors, including the current spot rate and the 25-delta of the option, are put into the option pricing model. (The specific option pricing model used is agreed on by both parties to the trade.)
These standard delta price points are often used to define option trading strategies. For example, a 25-delta strangle would be based on 25-delta put and call options. Similarly, a 10-delta strangle would be based on 10-delta options (and would cost less and have a more moderate payoff structure than a 25-delta strangle). Labeling option structures by their delta is common in FX markets.
EXAMPLE 3
Active Strategies
Annie McYelland works as an analyst at Scotland-based Kilmarnock Advisors, an investment firm that offers several investment vehicles for its clients. McYelland has been put in charge of formulating the firm’s market views for some of the foreign currencies that these vehicles have exposures to. Her market views will be used to guide the hedging and discretionary positioning for some of the actively managed portfolios.
McYelland begins by examining yield spreads between various countries and the implied volatility extracted from the option pricing for several currency pairs. She collects the following data:
One-Year Yield Levels
Switzerland
‒0.80%
United States
0.30%
Poland
1.26%
Mexico
5.98%
One-Year Implied Volatility
PLN/CHF
7.58%
MXN/CHF
12.7%
MXN/PLN
11.8%
MXN/USD
9.81%
Note: PLN = Polish zloty; the Swiss yields are negative because of Swiss policy actions.
McYelland is also examining various economic indicators to shape her market views. After studying the economic prospects for both Japan and New Zealand, she expects that the inflation rate for New Zealand is about to accelerate over the next few years, whereas the inflation rate for Japan should remain relatively stable. Turning her attention to the economic situation in India, McYelland believes that the Indian authorities are about to tighten monetary policy, and that this change has not been fully priced into the market. She reconsiders her short-term view for the Indian rupee (i.e., the INR/USD spot rate) after conducting this analysis.
McYelland also examines the exchange rate volatility for several currency pairs to which the investment trusts are exposed. Based on her analysis of the situation, she believes that the exchange rate between Chilean peso and the US dollar (CLP/USD) is about to become much more volatile than usual, although she has no strong views about whether the CLP will appreciate or depreciate.
One of McYelland’s colleagues, Catalina Ortega, is a market technician and offers to help McYelland time her various market position entry and exit points based on chart patterns. While examining the JPY/NZD price chart, Ortega notices that the 200-day moving average is at 77.5035 and the current spot rate is 77.1905.
Based on the data she collected, all else equal, McYelland’s best option for implementing a carry trade position would be to fund in: 🟠
USD and invest in MXN.
CHF and invest in MXN.
CHF and invest in PLN.
Solution to 1:
A is correct. The tradeoff between the yield spread between the funding and investment currencies and the implied volatility (risk) is the most attractive. The other choices have a narrower yield spread and higher risk (implied volatility).
Based on McYelland’s inflation forecasts, all else equal, she would be more likely to expect a(n): 🟠
depreciation in the JPY/NZD.
increase in capital flows from Japan to New Zealand.
more accommodative monetary policy by the Reserve Bank of New Zealand.
Solution to 2:
A is correct. All else equal, an increase in New Zealand’s inflation rate will decrease its real interest rate and lead to the real interest rate differential favoring Japan over New Zealand. This would likely result in a depreciation of the JPY/NZD rate over time. The shift in the relative real returns should lead to reduced capital flows from Japan to New Zealand (so Choice B is incorrect) and the RBNZ—New Zealand’s central bank—is more likely to tighten monetary policy than loosen it as inflation picks up (so Choice C is incorrect).
Given her analysis for India, McYelland’s short-term market view for the INR/USD spot rate is now most likely to be: 🟠
biased toward appreciation.
biased toward depreciation.
unchanged because it is only a short-run view.
Solution to 3:
B is correct. Tighter monetary policy in India should lead to higher real interest rates (at least in the short run). This increase will cause the INR to appreciate against the USD, but because the USD is the base currency, this will be represented as depreciation in the INR/USD rate. Choice C is incorrect because a tightening of monetary policy that is not fully priced-in to market pricing is likely to move bond yields and hence the exchange rate in the short run (given the simple economic model in Section 7).
Using CLP/USD options, what would be the cheapest way for McYelland to implement her market view for the CLP? ✅
Buy a straddle
Buy a 25-delta strangle
Sell a 40-delta strangle
Solution to 4:
B is correct. Either a long straddle or a long strangle will profit from a marked increase in volatility in the spot rate, but a 25-delta strangle would be cheaper (because it is based on OTM options). Writing a strangle—particularly one that is close to being ATM, which is what a 40-delta structure is—is likely to be exercised in favor of the counterparty if McYelland’s market view is correct.
Based on Ortega’s analysis, she would most likely expect: ✅
support near 77.5035.
resistance near 77.1095.
resistance near 77.5035.
Solution to 5:
C is correct. The 200-day moving average has not been crossed yet, and it is higher than the current spot rate. Hence this technical indicator suggests that resistance lies above the current spot rate level, likely in the 77.5035 area. Choice A is incorrect because the currency has not yet appreciated to 77.5035, so it cannot be considered a “support” level. Given that the currency pair has already traded through 77.1905 and is still at least 90 pips away from the 200-day moving average, it is more likely to suspect that resistance still lies above the current spot rate.
FORWARD CONTRACTS, FX SWAPS, AND CURRENCY OPTIONS
Learning Outcome
describe how forward contracts and FX (foreign exchange) swaps are used to adjust hedge ratios
In this section, we focus on how the portfolio manager uses financial derivatives to implement both the strategic positioning of the portfolio along the risk spectrum (i.e., the performance benchmark) as well as the tactical decisions made in regard to variations around this “neutral” position.
The manager’s market view—whether based on carry, fundamental, currency volatility, or technical considerations—leads to this active management of risk positioning around the strategic benchmark point.
Implementing both strategic and tactical viewpoints requires the use of trading tools, which we discuss in this section.
The balance of this reading will assume that the portfolio’s strategic foreign-currency asset exposures and the maximum amount of currency risk desired have already been determined by the portfolio’s IPS.
We begin at the conservative end of the risk spectrum by describing a passive hedge for a single currency (with a 100% hedge ratio).
After discussing the costs and limitations of this approach, we move out further along the risk spectrum by describing strategies in which the basic “building blocks” of financial derivatives can be combined to implement the manager’s tactical positioning and construct much more customized risk–return profiles.
Not surprisingly, the basic trading tools themselves—forwards, options, FX swaps—are used for both strategic and tactical risk management and by both hedgers and speculators alike (although for different ends).
Note that the instruments covered as tools of currency management are not nearly an exhaustive list. For example, exchange-traded funds for currencies are a vehicle that can be useful in managing currency risk.
Forward Contracts
In this section, we consider the most basic form of hedging: a 100% hedge ratio for a single foreign-currency exposure. Futures or forward contracts on currencies can be used to obtain full currency hedges, although most institutional investors prefer to use forward contracts for the following reasons:
Futures contracts are standardized in terms of settlement dates and contract sizes. These may not correspond to the portfolio’s investment parameters.
Futures contracts may not always be available in the currency pair that the portfolio manager wants to hedge. For example, the most liquid currency futures contracts trade on the Chicago Mercantile Exchange (CME). Although there are CME futures contracts for all major exchange rates (e.g., USD/EUR, USD/GBP) and many cross rates (e.g., CAD/EUR, JPY/CHF), there are not contracts available for all possible currency pairs. Trading these cross rates would need multiple futures contracts, adding to portfolio management costs. In addition, many of the “second tier” emerging market currencies may not have liquid futures contracts available against any currency, let alone the currency pair in which the portfolio manager is interested.
Futures contracts require up-front margin (initial margin). They also have intra-period cash flow implications, in that the exchange will require the investor to post additional variation margin when the spot exchange rate moves against the investor’s position. These initial and ongoing margin requirements tie up the investor’s capital and require careful monitoring through time, adding to the portfolio management expense. Likewise, margin flows can go in the investor’s favor, requiring monitoring and reinvestment.
In contrast, forward contracts do not suffer from any of these drawbacks. Major global investment dealers (such as Deutsche Bank, Royal Bank of Scotland, UBS, etc.) will quote prices on forward contracts for practically every possible currency pair, settlement date, and transaction amount. They typically do not require margin to be posted or maintained.
Moreover, the daily trade volume globally for OTC currency forward and swap contracts dwarfs that for exchange-traded currency futures contracts; that is, forward contracts are more liquid than futures for trading in large sizes.
Reflecting this liquidity, forward contracts are the predominant hedging instrument in use globally.
For the balance of this section, we will focus only on currency forward contracts.
However, separate side boxes discuss exchange-traded currency futures contracts and currency-based exchange-traded funds (ETFs).
Hedge Ratios with Forward Contracts
In principle, setting up a full currency hedge is relatively straight forward: match the current market value of the foreign-currency exposure in the portfolio with an equal and offsetting position in a forward contract.
In practice, of course, it is not that simple because the market value of the foreign-currency assets will change with market conditions.
This means that the actual hedge ratio will typically drift away from the desired hedge ratio as market conditions change.
A static hedge (i.e., unchanging hedge) will avoid transaction costs, but will also tend to accumulate unwanted currency exposures as the value of the foreign-currency assets change.
This characteristic will cause a mismatch between the market value of the foreign-currency asset portfolio and the nominal size of the forward contract used for the currency hedge; this is pure currency risk.
For this reason, the portfolio manager will typically need to implement a dynamic hedge by rebalancing the portfolio periodically. This hedge rebalancing will mean adjusting some combination of the size, number, and maturities of the forward currency contracts.
A simple example will illustrate this rebalancing process. Suppose that an investor domiciled in Switzerland has a EUR-denominated portfolio that, at the start of the period, is worth EUR1,000,000. Assume a monthly hedge-rebalancing cycle.
To hedge this portfolio, the investor would sell EUR1,000,000 one month forward against the CHF.
Assume that one month later, the EUR-denominated investment portfolio is then actually worth only EUR950,000. To roll the hedge forward for the next month, the investor will engage in a mismatched FX swap. (Recall that a “matched” swap means that both the spot and forward transactions—the near and far “legs” of the swap, respectively—are of equal size).
For the near leg of the swap, EUR1 million will be bought at spot to settle the expiring forward contract. (The euro amounts will then net to zero, but a Swiss franc cash flow will be generated, either a loss or a gain for the investor, depending on how the CHF/EUR rate has changed over the month). For the far leg of the swap, the investor will sell EUR950,000 forward for one month.
Another way to view this rebalancing process is to consider the case in which the original short forward contract has a three-month maturity.
In this case, rebalancing after one month would mean that the manager would have to buy 50,000 CHF/EUR two months forward.
There is no cash flow at the time this second forward contract is entered, but the net amount of euro for delivery at contract settlement two months into the future is now the euro hedge amount desired (i.e., EUR950,000).
There will be a net cash flow (denominated in CHF) calculated over these two forward contracts on the settlement date two months hence.
Although rebalancing a dynamic hedge will keep the actual hedge ratio close to the target hedge ratio, it will also lead to increased transaction costs compared with a static hedge.
The manager will have to assess the cost–benefit trade-offs of how frequently to dynamically rebalance the hedge.
These will depend on a variety of idiosyncratic factors (manager risk aversion, market view, IPS guidelines, etc.), and so there is no single “correct” answer—different managers will likely make different decisions.
However, we can observe that the higher the degree of risk aversion, the more frequently the hedge is likely to be rebalanced back to the “neutral” hedge ratio.
Similarly, the greater the tolerance for active trading, and the stronger the commitment to a particular market view, the more likely it is that the actual hedge ratio will be allowed to vary from a “neutral” setting, possibly through entering into new forward contracts. (For example, if the P/B spot rate was seen to be oversold and likely to rebound higher, an actively traded portfolio might buy the base currency through forward contracts to lock in this perceived low price—and thus change the actual hedge ratio accordingly.)
The sidebar on executing a hedge illustrates the concepts of rolling hedges, FX swaps and their pricing (bid–offer), and adjusting hedges for market views and changes in market values.
Executing a Hedge
Jiao Yang works at Hong Kong SAR-based Kwun Tong Investment Advisors; its reporting currency is the Hong Kong Dollar (HKD). She has been put in charge of managing the firm’s foreign-currency hedges. Forward contracts for two of these hedges are coming due for settlement, and Yang will need to use FX swaps to roll these hedges forward three months.
Hedge #1: Kwun Tong has a short position of JPY800,000,000 coming due on a JPY/HKD forward contract. The market value of the underlying foreign-currency assets has not changed over the life of the contract, and Yang does not have a firm opinion on the expected future movement in the JPY/HKD spot rate.
Hedge #2: Kwun Tong has a short position of EUR8,000,000 coming due on a HKD/EUR forward contract. The market value of the EUR-denominated assets has increased (measured in EUR). Yang expects the HKD/EUR spot rate to decrease.
The following spot exchange rates and three-month forward points are in effect when Yang transacts the FX swaps necessary to roll the hedges forward:
Spot Rate
Three-Month Forward Points
JPY/HKD
14.4/14.4
−1.2/−1.1
HKD/EUR
9.0200/9.0210
173/176
Note: The JPY/HKD forward points will be scaled by 100; the HKD/EUR forward points will be scaled by 10,000
As a result, Yang undertakes the following transactions:
For Hedge #1, the foreign-currency value of the underlying assets has not changed, and she does not have a market view that would lead her to want to either over- or under-hedge the foreign-currency exposure. Therefore, to roll these hedges forward, she uses a matched swap. For matched swaps (see Section 2), the convention is to base pricing on the mid-market spot exchange rate. Thus, the spot leg of the swap would be to buy JPY800,000,000 at the mid-market rate of 10.81 JPY/HKD. The forward leg of the swap would require selling JPY800,000,000 forward three months. Selling JPY (the price currency in the JPY/HKD quote) is equivalent to buying HKD (the base currency). Therefore, she uses the offer-side forward points, and the all-in forward rate for the forward leg of the swap is as follows:
For Hedge #2, the foreign-currency value of the underlying assets has increased; Yang recognizes that this implies that she should increase the size of the hedge greater than EUR8,000,000. She also believes that the HKD/EUR spot rate will decrease, and recognizes that this implies a hedge ratio of more than 100% (Kwun Tong Advisors has given her discretion to over- or under-hedge based on her market views). This too means that the size of the hedge should be increased more than EUR8,000,000, because Yang will want a larger short position in the EUR to take advantage of its expected depreciation. Hence, Yang uses a mismatched swap, buying EUR8,000,000 at spot rate against the HKD, to settle the maturing forward contract and then selling an amount more than EUR8,000,000 forward to increase the hedge size. Because the EUR is the base currency in the HKD/EUR quote, this means using the bid side for both the spot rate and the forward points when calculating the all-in forward rate:
The spot leg of the swap—buying back EUR8,000,000 to settle the outstanding forward transaction—is also based on the bid rate of 9.0200. This is because Yang is selling an amount larger than EUR8,000,000 forward, and the all-in forward rate of the swap is already using the bid side of the market (as it would for a matched swap). Hence, to pick up the net increase in forward EUR sales, the dealer Yang is transacting with would price the swap so that Yang also has to use bid side of the spot quote for the spot transaction used to settle the maturing forward contract.
Roll Yield
Exhibit 7:
The Forward Curve and Roll Yield
Exhibit 8:
The Carry Trade and Roll Yield
Buy/Invest
Sell/Borrow
Implementing the carry trade
High-yield currency
Low-yield currency
Earning a positive roll yield
Trading the forward rate bias
Forward discount currency
Forward premium currency
Because the level of and movements in forward points can either enhance or reduce currency-hedged returns, it explains an observed tendency in foreign exchange markets for the amount of currency hedging to generally vary with movements in forward points. As forward points move against the hedger, the amount of hedging activity typically declines as the cost/benefit ratio of the currency hedge deteriorates. The opposite occurs when movements in forward points reduce hedging costs. Essentially the tendency to hedge will vary depending on whether implementing the hedge happens to be trading in the same direction of the forward rate bias strategy or against it. It is easier to sell a currency forward if there is a “cushion” when it is selling at a forward premium. Likewise, it is more attractive to buy a currency when it is trading at a forward discount. This swings the forward rate bias (and carry trade advantage) in favor of the hedge.
Combined with the manager’s market view of future spot rate movements, what this concept implies is that, when setting the hedge ratio, the portfolio manager must balance the effect of expected future exchange rate movements on portfolio returns against the expected effect of the roll yield (i.e., the expected cost of the hedge).
A simple example can illustrate this effect. Consider a portfolio manager that needs to sell forward the base currency of a currency pair (P/B) to implement a currency hedge. Clearly, the manager would prefer to sell this currency at as high a price as possible. Assume that given the forward points for this currency pair and the time horizon for the hedge, the expected roll yield (cost of the hedge) is −3%. Suppose the portfolio manager had a market view that the base currency would depreciate by 4%. In this case, the hedge makes sense: It is better to pay 3% for the hedge to avoid an expected 4% loss.
Now, suppose that with a movement in forward points the new forward discount on the base currency is 6% away from the current spot rate. If the manager’s market view is unchanged (an expected depreciation of the base currency of 4%), then now the use of the hedge is less clear: Does it make sense to pay 6% for the hedge to avoid an expected 4% loss? A risk-neutral manager would not hedge under these circumstances because the net expected value of the hedge is negative. But a risk-averse manager might still implement the hedge regardless of the negative net expected value. The reason is because it is possible that the market forecast is wrong and that the actual depreciation of the base currency (and realized loss to the portfolio) may be higher than the 6% cost of the hedge. The risk-averse manager must then weigh the certainty of a hedge that costs 6% against the risk that actual unhedged currency losses might be much higher than that.
Clearly, the cost/benefit analysis has shifted against hedging in this case, but many risk-averse investors would still undertake the hedge anyway. The risk-averse manager would likely only take an unhedged currency position if the difference between the expected cost of the hedge and the expected return on an unhedged position was so great as to make the risk acceptable. Balancing these two considerations would depend on the type of market view the manager held and the degree of conviction in it, as well as the manager's degree of risk aversion. The decision taken will vary among investors, so no definitive answer can be given as to what would be the appropriate hedging choice (different portfolio managers will make different choices given the same opportunity set). But hedging costs will vary with market conditions and the higher the expected cost of the hedge (negative roll yield) the more the cost/benefit calculation moves against using a fully hedged position. Or put another way, if setting up the hedge involves selling the low-yield currency and buying the high-yield currency in the P/B pair (i.e., an implicit carry position), then the more likely the portfolio will be fully hedged or even over-hedged. The opposite is also true: Trading against the forward rate bias is likely to lead to lower hedge ratios, all else equal.
EXAMPLE 4
The Hedging Decision
The reporting currency of Hong Kong SAR-based Kwun Tong Investment Advisors is the Hong Kong dollar (HKD). The investment committee is examining whether it should implement a currency hedge for the firm’s exposures to the GBP and the ZAR (the firm has long exposures to both of these foreign currencies). The hedge would use forward contracts. The following data relevant to assessing the expected cost of the hedge and the expected move in the spot exchange rate has been developed by the firm’s market strategist.
Current Spot Rate
Six-Month Forward Rate
Six-Month Forecast Spot Rate
HKD/GBP
10.6000
10.5895
10.2000
HKD/ZAR
0.5210
0.5082
0.5100
Recommend whether to hedge the firm’s long GBP exposure. Justify your recommendation.
Solution to 1:
Kwun Tong is long the GBP against the HKD, and HKD/GBP is selling at a small forward discount of −0.106% compared with the current spot rate. All else equal, this is the expected roll yield—which is not in the firm’s favor, in this case, because to implement the hedge Kwun Tong would be selling GBP, the base currency in the quote, at a price lower than the current spot rate. However, the firm’s market strategist expects the GBP to depreciate by 3.92% against the HKD. Thus, the negative carry of hedging is small in comparison to the potential loss. Both of these considerations argue for hedging this exposure.
Discuss the trade-offs in hedging the firm’s long ZAR exposure.
Solution to 2:
Kwun Tong is long the ZAR against the HKD, and HKD/ZAR is selling at a forward discount of −2.5% compared with the current spot rate. Implementing the hedge would require the firm to sell the base currency in the quote, the ZAR, at a price lower than the current spot rate. This would imply that, all else equal, the roll yield would go against the firm; that is, the expected cost of the hedge would be 2.5%. But the firm’s strategist also forecasts that the ZAR will depreciate against the HKD by 2.2%. This makes the decision to hedge less certain. A risk-neutral investor would not hedge because the expected cost of the hedge is more than the expected depreciation of the ZAR. But this is only a point forecast and comes with a degree of uncertainty—there is a risk that the HKD/ZAR spot rate might depreciate by more than the 2.5% cost of the hedge. In this case, the decision to hedge the currency risk would depend on the trade-offs between (1) the level of risk aversion of the firm; and (2) the conviction the firm held in the currency forecast—that is, the level of certainty that the ZAR would not depreciate by more than 2.5%.
Currency Options
One of the costs of forward contracts is the opportunity cost. Once fully hedged, the portfolio manager forgoes any upside potential for future currency moves in the portfolio’s favor. Currency options remove this opportunity cost because they provide the manager the right, but not the obligation, to buy or sell foreign exchange at a future date at a rate agreed on today. The manager will only exercise the option at the expiry date if it is favorable to do so.17
Consider the case of a portfolio manager who is long the base currency in the P/B quote and needs to sell this currency to implement the hedge. One approach is to simply buy an at-the-money put option on the P/B currency pair. Matching a long position in the underlying with a put option is known as a protective put strategy. Suppose the current spot rate is 1.3650 and the strike price on the put option bought is 1.3650. If the P/B rate subsequently goes down (P appreciates and B depreciates) by the expiry date, the manager can exercise the option, implement the hedge, and guarantee a selling price of 1.3650. But if the P/B rate increases (P depreciates and B appreciates), the manager can simply let the option expire and collect the currency gains.
Unfortunately, like forward contracts, currency options are not “free goods” and, like any form of insurance, there is always a price to be paid for it. Buying an option means paying an upfront premium. This premium is determined, first, by its intrinsic value, which is the difference between the spot exchange rate and the strike price of the option (i.e., whether the option is in the money, at the money, or out of the money, respectively). ATM options are more expensive than OTM options, and frequently these relatively expensive options expire without being exercised.
The second determinant of an option’s premium is its time value, which in turn is heavily influenced by the volatility in exchange rates. Regardless of exchange rate volatility, however, options are always moving toward expiry. In general, the time value of the option is always declining. This is the time decay of the option’s value (theta, one of the “Greeks” of option prices, describes this effect) and is similar in concept to that of negative roll yield on forward contracts described earlier. Time decay always works against the owner of an option.
As with forward contracts, a portfolio manager will have to make judgments about the cost/benefit trade-offs of options-based strategies. Although options do allow the portfolio upside potential from favorable currency movements, options can also be a very expensive form of insurance. The manager will have to balance any market view of potential currency gains against hedging costs and the degree of risk aversion. There is no “right” answer; different managers will make different decisions about the cost/benefit trade-offs when given the same opportunity set.
EXAMPLE 5
Hedging Problems
Brixworth & St. Ives Asset Management is a UK-based firm managing a dynamic hedging program for the currency exposures in its Aggressive Growth Fund. One of the fund’s foreign-currency asset holdings is denominated in the Mexican peso (MXN), and one month ago Brixworth & St. Ives fully hedged this exposure using a two-month MXN/GBP forward contract. The following table provides the relevant information.
One Month Ago
Today
Value of assets (in MXN)
10,000,000
9,500,000
MXN/GBP spot rate (bid–offer)
29.0500/29.0580
27.5985/28.0065
One-month forward points (bid–offer)
1,475/1,510
1,500/1,536
Two-month forward points (bid–offer)
2,590/2,650
2,640/2,700
The Aggressive Growth Fund also has an unhedged foreign-currency asset exposure denominated in the South African rand (ZAR). The current mid-market spot rate in the ZAR/GBP currency pair is 20.1050.
One month ago, Brixworth & St. Ives most likely sold:
MXN9,500,000 forward at an all-in forward rate of MXN/GBP 19.6635.
MXN10,000,000 forward at an all-in forward rate of MXN/GBP 29.3090.
MXN10,000,000 forward at an all-in forward rate of MXN/GBP 29.3230.
Solution to 1:
C is correct. Brixworth & St. Ives is long the MXN and hence must sell the MXN forward against the GBP. Selling MXN against the GBP means buying GBP, the base currency in the MXN/GBP quote. Therefore, the offer side of the market must be used. This means the all-in rate used one month ago would have been 29.058 + 2,650/10,000, which equals 29.3230. Choice A is incorrect because it uses today’s asset value and the incorrect forward quotes and Choice B is incorrect because it uses the wrong side of the market (the bid side).
To rebalance the hedge today, the firm would most likely need to:
buy MXN500,000 spot.
buy MXN500,000 forward.
sell MXN500,000 forward.
Solution to 2:
B is correct. The foreign investment went down in value in MXN terms. Therefore Brixworth & St. Ives must reduce the size of the hedge. Previously it had sold MXN10,000,000 forward against the GBP, and this amount must be reduced to MXN9,500,000 by buying MXN500,000 forward. Choice A is incorrect because hedging is done with forward contracts not spot deals. Choice C is incorrect because selling MXN forward would increase the size of the hedge, not decrease it.
Given the data in the table, the roll yield on this hedge at the forward contracts’ maturity date is most likely to be:
zero.
negative.
positive.
Solution to 3:
B is correct. To implement the hedge, Brixworth & St. Ives must sell MXN against the GBP, or equivalently, buy GBP (the base currency in the P/B quote) against the MXN. The base currency is selling forward at a premium, and—all else equal—its price would “roll down the curve” as contract maturity approached. Having to settle the forward contract means then selling the GBP spot at a lower price. Buying high and selling low will define a negative roll yield. Moreover, the GBP has depreciated against the MXN, because the MXN/GBP spot rate declined between one month ago and now, which will also add to the negative roll yield.
Assuming that all ZAR/GBP options considered have the same notional amount and maturity, the most expensive hedge that Brixworth & St. Ives could use to hedge its ZAR exposure is a long position in a(n):
ATM GBP call.
25-delta GBP call.
GBP put with a strike of 20.1050.
Solution to 4:
A is correct. The Aggressive Growth Fund is long the ZAR through its foreign-currency assets, and to hedge this exposure it must sell the ZAR against the GBP, or equivalently, buy GBP—the base currency in the P/B quote—against the ZAR. Hedging a required purchase means a long position in a call option (not a put, which is used to hedge a required sale of the base currency in the P/B quote). An ATM call option is more expensive than a 25-delta call option.
CURRENCY MANAGEMENT STRATEGIES
Learning Outcome
describe trading strategies used to reduce hedging costs and modify the risk–return characteristics of a foreign-currency portfolio
In the previous sections, we showed that completely hedging currency risk is possible—but can also be expensive. It can be even more expensive when trying to avoid all downside risk while keeping the full upside potential for favorable currency movements (i.e., a protective put strategy with ATM options). Hedging can be seen as a form of insurance, but it is possible to overpay for insurance. Judgments have to be made to determine at what point the costs outweigh the benefits.
As with any form of insurance, there are always steps that can be taken to reduce hedging costs. For most typical insurance products, these cost-reduction measures include such things as higher deductibles, co-pay arrangements, and lower maximum payouts. The same sorts of measures exist in the FX derivatives market; we will explore these various alterative measures in this section. The key point to keep in mind is that all of these various cost-reduction measures invariably involve some combination of less downside protection and/or less upside potential for the hedge. In efficient markets, lower insurance premiums mean lower insurance.
These cost-reduction measures also start moving the portfolio away from a passively managed 100% hedge ratio toward discretionary hedging in which the manager is allowed to take directional positions. Once the possibility of accepting some downside risk, and some upside potential, is introduced into the portfolio, the manager is moving away from a rules-based approach to hedging toward a more active style of trading. The portfolio manager can then use the trading tools and strategies described in the following sections to express a market view and/or cut hedging costs.
Exhibit 9:
Select Currency Management Strategies
Forward Contracts
Over-/under-hedging
Profit from market view
Option Contracts
OTM options
Cheaper than ATM
Risk reversals
Write options to earn premiums
Put/call spreads
Write options to earn premiums
Seagull spreads
Write options to earn premiums
Exotic Options
Knock-in/out features
Reduced downside/upside exposure
Digital options
Extreme payoff strategies
We will make one simplifying assumption for the following sections. Currency management strategies will differ fundamentally depending on whether the base currency of the P/B price quote must be bought or sold to decrease the foreign-currency exposure. To simplify the material and impose consistency on the discussions that follow, we will assume that the portfolio manager must sell the base currency in the P/B quote to reduce currency risk. In addition, unless otherwise noted, the notional amounts and expiration dates on all forward and options contracts are the same.18
Over-/Under-Hedging Using Forward Contracts
When the IPS gives the manager discretion either to over- or under-hedge the portfolio, relative to the “neutral” benchmark, there is the possibility to add incremental value based on the manager’s market view. Profits from successful tactical positioning help reduce net hedging costs. For example, if the neutral benchmark hedge ratio is 100% for the base currency being hedged, and the portfolio manager has a market opinion that the base currency is likely to depreciate, then over-hedging through a short position in P/B forward contracts might be implemented—that is, the manager might use a hedge ratio higher than 100%. Similarly, if the manager’s market opinion is that the base currency is likely to appreciate, the currency exposure might be under-hedged.
A variant of this approach would be to adjust the hedge ratio based on exchange rate movements: to increase the hedge ratio if the base currency depreciated, but decrease the hedge ratio if the base currency appreciated. Essentially, this approach is a form of “delta hedging” that tries to mimic the payoff function of a put option on the base currency. That is, this form of dynamic hedging with forward contracts tries to increasingly participate in any upside moves of the base currency, but increasingly hedge any downside moves. Doing so adds “convexity” to the portfolio, meaning that the hedge’s payoff function will be a convex curve when this function is graphed with profit on the vertical axis and the spot rate on the horizontal axis. (Note that this concept of convexity is identical in intent to the concept of convexity describing bonds; as convexity increases the price of a bond rises more quickly in a declining yield environment and drops more slowly in a rising yield environment. Convexity is a desirable characteristic in both the fixed-income and currency-hedging contexts.)
Protective Put Using OTM Options
In the previous section, we examined a dynamic hedging strategy using forward contracts that tries to mimic the payoff function of an option and put convexity into the hedge’s payoff function. The payoff functions for options are naturally convex to begin with. However, this can be a costly form of convexity (relatively high option premiums), and fully hedging a currency position with a protective put strategy using an ATM option is the most expensive means of all to buy convexity.
One way to reduce the cost of using options is to accept some downside risk by using an OTM option, such as a 25- or 10-delta option. These options will be less costly, but also do not fully protect the portfolio from adverse currency movements. Conversely, it makes sense to insure against larger risks but accept some smaller day-to-day price movements in currencies. As an analogy, it may be possible to buy a home or car insurance policy with a zero deductible—but the premiums would be exorbitant. It may be more rational to have a cheaper insurance policy and accept responsibility for minor events, but insure against extreme damage.
Risk Reversal (or Collar)
Another set of option strategies involves selling options (also known as writing options) to earn income that can be used to offset the cost of buying a put option, which forms the “core” of the hedge. Recall that in this section, we are using the simplifying convention that the manager is long the base currency in the P/B quote; hence puts and not calls would be used for hedging in this case.
One strategy to obtain downside protection at a lower cost than a straight protective put position is to buy an OTM put option and write an OTM call option. Essentially, the portfolio manager is selling some of the upside potential for movements in the base currency (writing a call) and using the option’s premiums to help pay the cost of the long put option being purchased. This approach is similar to creating a collar in fixed-income markets. The portfolio is protected against downside movements, but its upside is limited to the strike price on the OTM call option; the exchange rate risk is confined to a corridor or “collar.”
In professional FX markets, having a long position in a call option and a short position in a put option is called a risk reversal. For example, buying a 25-delta call and writing a 25-delta put is referred to as a long position in a 25-delta risk reversal. The position used to create the collar position we just described (buying a put, writing a call) would be a short position in a risk reversal.
The majority of currency hedging for foreign-currency asset portfolios and corporate accounts is based on the use of forward contracts and simple option strategies (protective puts/covered calls and risk reversals/collars). We now begin to transition to more active trading strategies that are designed to express market views for speculative profit.
Put Spread
A variation of the short risk reversal position is a put spread, which is also used to reduce the upfront cost of buying a protective put. The short risk reversal is structured by buying a put option and writing a call option: the premiums received by writing the call help cover the cost of the put. Similarly, the put spread position involves buying a put option and writing another put option to help cover the cost of the long put’s premiums. This position is typically structured by buying an OTM put, and writing a deeper-OTM put to gain income from premiums; both options involved have the same maturity.
To continue our previous example, with the current spot rate at 1.3550, the portfolio manager might set up the following put spread: buy a put with a strike of 1.3500 and write a put with a strike of 1.3450. The payoff on the put spread position will then be as follows: there is no hedge protection between 1.3550 and 1.3500; the portfolio is hedged from 1.3500 down to 1.3450; at spot rates below 1.3450, the portfolio becomes unhedged again. The put spread reduces the cost of the hedge, but at the cost of more limited downside protection. The portfolio manager would then use this spread only for cases in which a modest decline in the spot exchange rate was expected, and this position would have to be closely monitored against adverse exchange rate movements.
Note that the put spread structure will not be zero-cost because the deeper-OTM put (1.3450) being written will be cheaper than the less-OTM put (1.3500) being bought. However, there are approaches that will make the put spread (or almost any other option spread position) cheaper or possibly zero-cost: the manager could alter: (a) the strike prices of the options; (b) the notional amounts of the options; or (c) some combination of these two measures.
Altering the strike prices of the put options would mean moving them closer together (and hence more equal in cost). However, this would reduce the downside protection on the hedge. Instead, the portfolio manager could write a larger notional amount for the deeper-OTM option; for example, the ratio for the notionals for the options written versus bought might be 1:2. (In standard FX market notation, this would be a 1 × 2 put spread—the option with exercise price closest to being ATM is given first. However, to avoid confusion it is good practice to specify explicitly in the price quote which is the long and short positions, and what their deltas/strike prices are.) Although this structure may now be (approximately) zero-cost it is not without risks: for spot rates below 1.3450 the portfolio has now seen its exposure to the base currency double-up (because of the 1:2 proportion of notionals) and at a worse spot exchange rate for the portfolio on top of it. Creating a zero-cost structure with a 1 × 2 put spread is equivalent to adding leverage to the options position, because you are selling more options than you are buying. This means that this put spread position will have to be carefully managed. For example, the portfolio manager might choose to close out the short position in the deep-OTM put (by going long/buying an equivalent put option) before the base currency depreciates to the 1.3450 strike level. This may be a costly position exit, however, as the market moves against the manager’s original positioning. Because of this, this sort of 1 × 2 structure may be more appropriate for expressing directional opinions rather than as a pure hedging strategy.
Seagull Spread
An alternative, and somewhat safer approach, would be to combine the original put spread position (1:1 proportion of notionals) with a covered call position. This is simply an extension of the concept behind risk reversals and put spreads. The “core” of the hedge (for a manager long the base currency) is the long position in a put option. This is expensive. To reduce the cost, a short risk reversal position writes a call option while a put spread writes a deep-OTM put option. Of course, the manager can always do both: that is, be long a protective put and then write both a call and a deep-OTM put. This option structure is sometimes referred to as a seagull spread.
As with the names for other option strategies based on winged creatures, the “seagull” indicates an option structure with at least three individual options, and in which the options at the most distant strikes—the wings—are on the opposite side of the market from the middle strike(s)—the body. For example, if the current spot price is 1.3550, a seagull could be constructed by going long an ATM put at 1.3550 (the middle strike is the “body”), short an OTM put at 1.3500, and short an OTM call at 1.3600 (the latter two options are the “wings”). Because the options in the “wings” are being written (sold) this is called a short seagull position. The risk/return profile of this structure gives full downside protection from 1.3550 to 1.3500 (at which point the short put position neutralizes the hedge) and participation in the upside potential in spot rate movements to 1.3600 (the strike level for the short call option).
Note that because two options are now being written to gain premiums instead of one, this approach allows the strike price of the long put position to be ATM, increasing the downside protection. The various strikes and/or notional sizes of these options (and hence their premiums) can always be adjusted up or down until a zero-cost structure is obtained. However, note that this particular seagull structure gives away some upside potential (the short call position) as well as takes on some downside risk (if the short put position is triggered, it will disable the hedge coverage coming from the long put position). As always, lower structure costs come with some combination of lower downside protection and/or less upside potential.
There are many variants of these seagull strategies, each of which provides a different risk–reward profile (and net cost). For example, for the portfolio manager wishing to hedge a long position in the base currency in the P/B quote when the current spot rate is 1.3550, another seagull structure would be to write an ATM call at 1.3550 and use the proceeds to buy an OTM put option at 1.3500 and an OTM call option at 1.3600. Note that in this seagull structure, the “body” is now a short option position, not a long position as in the previous example, and the “wings” are the long position. Hence, it is a long seagull spread. This option structure provides cheap downside protection (the hedge kicks in at the put’s 1.3500 strike) while providing the portfolio manager with unlimited participation in any rally in the base currency beyond the 1.3600 strike of the OTM call option. As before, the various option strikes and/or notional sizes on the options bought and written can be adjusted so that a zero-cost structure is obtained.
Exotic Options
In this section, we move even further away from derivatives and trading strategies used mainly for hedging, and toward the more speculative end of the risk spectrum dominated by active currency management. Exotic options are often used by more sophisticated players in the professional trading market—for example, currency overlay managers—and are less frequently used by institutional investors, investment funds, or corporations for hedging purposes. There are several reasons for this relatively light usage of “exotics” for hedging purposes, some related to the fact that many smaller entities lack familiarity with these products. Another reason involves the difficulty of getting hedge accounting treatment in many jurisdictions, which is more advantageous for financial reporting reasons. Finally, the specialized terms of such instruments make them difficult to value for regulatory and accounting purposes.
In general, the term “exotic” refers to all options that are not “vanilla.” In FX, vanilla refers essentially to European-style put and call options. The full range of exotic options is both very broad and constantly evolving; many are extraordinarily complex both to price and even to understand. However, all exotics, no matter how complex, typically share one defining feature in common: They are designed to customize the risk exposures desired by the client and provide them at the lowest possible price.19 Much like the trading strategies described previously, they usually involve some combination of lower downside protection and/or lower upside potential while providing the client with the specific risk exposures they are prepared to manage, and to do so at what is generally a lower cost than vanilla options.
The two most common type of exotic options encountered in foreign exchange markets are those with knock-in/knock-out features and digital options.
An option with a knock-in feature is essentially a vanilla option that is created only when the spot exchange rate touches a pre-specified level (this trigger level, called the “barrier,” is not the same as the strike price). Similarly a knock-out option is a vanilla option that ceases to exist when the spot exchange rate touches some pre-specified barrier level. Because these options only exist (i.e., get knocked-in or knocked-out) under certain circumstances, they are more restrictive than vanilla options and hence are cheaper. But again, the knock-in/out features provide less upside potential and/or downside protection.
Digital options are also called binary options, or all-or-nothing options. The expiry value of an in-the-money vanilla option varies based on the amount of difference between the expiry level and strike price. In contrast, digital options pay out a fixed amount if they are determined to be in-the-money. For example, American digital options pay a fixed amount if they “touch” their exercise level at any time before expiry (even if by a single pip). This characteristic of “extreme payoff” options makes them almost akin to a lottery ticket. Because of these large payoffs, digital options usually cost more than vanilla options with the same strike price. But digitals also provide highly leveraged exposure to movements in the spot rate. This makes these exotic products more appropriate as trading tools for active currency management, rather than as hedging tools. In practice, digital options are typically used by more sophisticated speculative accounts in the FX market to express directional views on exchange rates.
A full exposition of exotic options is beyond the scope of this reading, but the reader should be aware of their existence and why they exist.
Section Summary
Clearly, loosening the constraint of a fully hedged portfolio begins to introduce complicated active currency management decisions. The following steps can be helpful to sort things out:
First, identify the base currency in the P/B quote (currency pair) you are dealing with. Derivatives are typically quoted in terms of either buying or selling the base currency when the option is exercised. A move upward in the P/B quote is an appreciation of the base currency.
Then, identify whether the base currency must be bought or sold to establish the hedge. These are the price movements you will be protecting against.
If buying the base currency is required to implement the hedge, then the core hedge structure will be based on some combination of a long call option and/or a long forward contract. The cost of this core hedge can be reduced by buying an OTM call option or writing options to earn premiums. (But keep in mind, lower hedging costs equate to less downside protection and/or upside potential.)
If selling the base currency is required to implement the hedge, then the core hedge structure will be based on some combination of a long put option and/or a short forward contract. The cost of this core hedge can be reduced by buying an OTM put option or writing options to earn premiums.
The higher the allowed discretion for active management, the lower the risk aversion; and the firmer a particular market view is held, the more the hedge is likely to be structured to allow risk exposures in the portfolio. This approach involves positioning in derivatives that “lean the same way” as the market view. (For example, a market view that the base currency will depreciate would use some combination of short forward contracts, writing call options, buying put options, and using “bearish” exotic strategies.) This directional bias to the trading position would be superimposed on the core hedge position described in steps “c” and “d,” creating an active-trading “tilt” in the portfolio.
For these active strategies, varying the strike prices and notional amounts of the options involved can move the trading position toward a zero-cost structure. But as with hedges, keep in mind that lower cost implies less downside protection and/or upside potential for the portfolio.
A lot of different hedging tools and strategies have been named and covered in this section. Rather than attempting to absorb all of them by rote memorization (a put spread is “X” and a seagull is “Y”), the reader is encouraged instead to focus on the intuition behind a hedge, and how and why it is constructed. It matters less what name (if any) is given to any specific approach; what is important is understanding how all the moving parts fit together. The reader should focus on a “building blocks” approach in understanding how and why the parts of the currency hedge are assembled in a given manner.
EXAMPLE 6
Alternative Hedging Strategies
Brixworth & St. Ives Asset Management, the UK-based investment firm, has hedged the exposure of its Aggressive Growth Fund to the MXN with a long position in a MXN/GBP forward contract. The fund’s foreign-currency asset exposure to the ZAR is hedged by buying an ATM call option on the ZAR/GBP currency pair. The portfolio managers at Brixworth & St. Ives are looking at ways to modify the risk–reward trade-offs and net costs of their currency hedges.
Jasmine Khan, one of the analysts at Brixworth & St. Ives, proposes an option-based hedge structure for the long-ZAR exposure that would replace the hedge based on the ATM call option with either long or short positions in the following three options on ZAR/GBP:
ATM put option
25-delta put option
25-delta call option
Khan argues that these three options can be combined into a hedge structure that will have some limited downside risk, but provide complete hedge protection starting at the relevant 25-delta strike level. The structure will also have unlimited upside potential, although this will not start until the ZAR/GBP exchange rate moves to the relevant 25-delta strike level. Finally, this structure can be created at a relatively low cost because it involves option writing.
The best method for Brixworth & St. Ives to gain some upside potential for the hedge on the Aggressive Growth Fund’s MXN exposure using MXN/GBP options is to replace the forward contract with a:
long position in an OTM put.
short position in an ATM call.
long position in a 25-delta risk reversal.
Solution to 1:
C is correct. The Aggressive Growth Fund has a long foreign-currency exposure to the MXN in its asset portfolio, which is hedged by selling the MXN against the GBP, or equivalently, buying the GBP—the base currency in the P/B quote—against the MXN. This need to protect against an appreciation in the GBP is why the hedge is using a long position in the forward contract. To set a collar around the MXN/GBP rate, Brixworth & St. Ives would want a long call option position with a strike greater than the current spot rate (this gives upside potential to the hedge) and a short put position with a strike less than the current spot rate (this reduces net cost of the hedge). A long call and a short put defines a long position in a risk reversal.
Choice A is incorrect because, if exercised, buying a put option would increase the fund’s exposure to the MXN (sell GBP, buy MXN). Similarly, Choice B is incorrect because, if exercised, the ATM call option would increase the MXN exposure (the GBP is “called” away from the fund at the strike price with MXN delivered). Moreover, although writing the ATM call option would gain some income from premiums, writing options (on their own) is never considered the “best” hedge because the premium income earned is fixed but the potential losses on adverse currency moves are potentially unlimited.
While keeping the ATM call option in the ZAR/GBP, the method that would lead to greatest cost reduction on the hedge would be to:
buy a 25-delta put.
write a 10-delta call.
write a 25-delta call.
Solution to 2:
C is correct. As before, the hedge is implemented in protecting against an appreciation of the base currency of the P/B quote, the GBP. The hedge is established with an ATM call option (a long position in the GBP). Writing an OTM call option (i.e., with a strike that is more than the current spot rate of 20.1050) establishes a call spread (although hedge protection is lost if ZAR/GBP expires at or above the strike level). Writing a 25-delta call earns more income from premiums than a deeper-OTM 10-delta call (although the 25-delta call has less hedge protection). Buying an option would increase the cost of the hedge, and a put option on the ZAR/GBP would increase the fund’s ZAR exposure if exercised (the GBP is “put” to the counterparty at the strike price and ZAR received).
Setting up Khan’s proposed hedge structure would most likely involve being:
long the 25-delta options and short the ATM option.
long the 25-delta call, and short both the ATM and 25-delta put options.
short the 25-delta call, and long both the ATM and 25-delta put options.
Solution to 3:
A is correct. Once again, the hedge is based on hedging the need to sell ZAR/buy GBP, and GBP is the base currency in the ZAR/GBP quote. This means the hedge needs to protect against an appreciation of the GBP (an appreciation of the ZAR/GBP rate). Based on Khan’s description, the hedge provides protection after a certain loss point, which would be a long 25-delta call. Unlimited upside potential after favorable (i.e., down) moves in the ZAR/GBP past a certain level means a long 25-delta put. Getting the low net cost that Khan refers to means that the cost of these two long positions is financed by selling the ATM option. (Together these three positions define a long seagull spread). Choice B is incorrect because although the first two legs of the position are right, a short position in the put does not provide any unlimited upside potential (from a down-move in ZAR/GBP). Choice C is incorrect because any option-based hedge, given the need to hedge against an up-move in the ZAR/GBP rate, is going to be based on a long call position. C does not contain any of these.
HEDGING MULTIPLE FOREIGN CURRENCIES
Learning Outcome
describe the use of cross-hedges, macro-hedges, and minimum-variance-hedge ratios in portfolios exposed to multiple foreign currencies
We now expand our discussion to hedging a portfolio with multiple foreign-currency assets. The hedging tools and strategies are very similar to those discussed for hedging a single foreign-currency asset, except now the currency hedge must consider the correlation between the various foreign-currency risk exposures.
For example, consider the case of a US-domiciled investor who has exposures to foreign-currency assets in Australia and New Zealand.
These two economies are roughly similar in that they are resource-based and closely tied to the regional economy of the Western Pacific, especially the large emerging markets in Asia.
As a result, the movements in their currencies are often closely correlated; the USD/AUD and USD/NZD currency pairs will tend to move together.
If the portfolio manager has the discretion to take short positions, the portfolio may (for example) possibly have a net long position in the Australian foreign-currency asset and a net short position in the New Zealand foreign-currency asset.
In this case, there may be less need to hedge away the AUD and NZD currency exposures separately because the portfolio’s long exposure to the AUD is diversified by the short position on the NZD.
Cross Hedges and Macro Hedges
A cross hedge occurs when a position in one asset (or a derivative based on the asset) is used to hedge the risk exposures of a different asset (or a derivative based on it).
Normally, cross hedges are not needed because, as we mentioned earlier, forward contracts and other derivatives are widely available in almost every conceivable currency pair. However, if the portfolio already has “natural” cross hedges in the form of negatively correlated residual currency exposures—as in the long-AUD/short-NZD example in Section 11—this helps moderate portfolio risk (σ[RDC]) without having to use a direct hedge on the currency exposure.
Sometimes a distinction is made between a “proxy” hedge and a “cross” hedge. When this distinction is made, a proxy hedge removes the foreign currency risk by hedging it back to the investor’s domestic currency—such as in the example with USD/AUD and USD/NZD discussed in the text. In contrast, a cross hedge moves the currency risk from one foreign currency to another foreign currency. For example, a US-domiciled investor may have an exposure to both the Indonesian rupiah (IDR) and the Thai baht (THB), but based on a certain market view, may only want exposure to the THB. In this context, the manager might use currency derivatives as a cross hedge to convert the IDR/USD exposure to a THB/USD exposure. But not all market participants make this sharp of a distinction between proxy hedges and cross hedges, and these terms are often used interchangeably. The most common term found among practitioners in most asset classes is simply a cross hedge, as we are using the term here: hedging an exposure with a closely correlated product (i.e., a proxy hedge when this distinction is made). The cross hedge of moving currency exposures between various foreign currencies is more of a special-case application of this concept. In our example, a US investor wanting to shift currency exposures between the IDR and THB would only need to shift the relative size of the IDR/USD and THB/USD forward contracts already being used. As mentioned earlier, forwards are available on almost every currency pair, so a cross hedge from foreign currency “A” to foreign currency “B” would be a special case when derivatives on one of the currencies are not available.
EXAMPLE 7
Cross Hedges
Mai Nguyen works at Cape Henlopen Advisors, which runs a US-domiciled fund that invests in foreign-currency assets of Australia and New Zealand. The fund currently has equally weighted exposure to one-year Australian and New Zealand treasury bills (i.e., both of the portfolio weights, ωi = 0.5). Because the foreign-currency return on these treasury bill assets is risk-free and known in advance, their expected σ(RFC) is equal to zero.
Nguyen wants to calculate the USD-denominated returns on this portfolio as well as the cross hedging effects of these investments. She collects the following information:
Expected Values
Australia
New Zealand
Foreign-currency asset return RFC
4.0%
6.0%
Foreign-currency return RFX
5.0%
5.0%
Asset risk σ(RFC)
0%
0%
Currency risk σ(RFX)
8.0%
10.0%
Correlation (USD/AUD; USD/NZD)
+0.85
Together, the result is that the expected domestic-currency return (RDC) on the equally weighted foreign-currency asset portfolio is the weighted average of these two individual country returns, or
RDC = 0.5(9.2%) + 0.5(11.3%) = 10.3%
Nguyen now turns her attention to calculating the portfolio’s investment risk [σ(RDC)].
To calculate the expected risk for the domestic-currency return, the currency risk of RFX needs to be multiplied by the known return on the treasury bills.
The portfolio’s investment risk, σ(RDC), is found by calculating the standard deviation of the right-hand-side of:RDC = (1 + RFC)(1 + RFX) − 1
Although RFX is a random variable—it is not known in advance—the RFC term is in fact known in advance because the asset return is risk-free.
Because of this Nguyen can make use of the statistical rules that, first, σ(kX) = kσ(X), where X is a random variable and k is a constant;
and second, that the correlation between a random variable and a constant is zero.
These results greatly simplify the calculations because, in this case, she does not need to consider the correlation between exchange rate movements and foreign-currency asset returns.
Instead, Nguyen needs to calculate the risk only on the currency side. Applying these statistical rules to the above formula leads to the following results:
The expected risk (i.e., standard deviation) of the domestic-currency return for the Australian asset is equal to (1.04) × 8% = 8.3%.
The expected risk (i.e., standard deviation) of the domestic-currency return for the New Zealand asset is equal to (1.06) × 10% = 10.6%.
σ2(RDC) = (0.5)2(8.3%)2 + (0.5)2(10.6%)2 + [(2)0.5(8.3%)0.5(10.6%)0.85]
= 0.8%
The standard deviation of this amount—that is, σ(RDC)—is 9.1%. Note that in the expression, all of the units are in percent, so for example, 8.3% is equivalent to 0.083 for calculation purposes. The careful reader may also note that Nguyen is able to use an exact expression for calculating the variance of the portfolio returns, rather than the approximate expressions shown in Equations 3 and 5. This is because, with risk-free foreign-currency assets, the variance of these foreign-currency returns σ2(RFC) is equal to zero.
Nguyen now considers an alternative scenario in which, instead of an equally weighted portfolio (where the ωi = 0.5), the fund has a long exposure to the New Zealand asset and a short exposure to the Australian asset (i.e., the ωi are +1 and −1, respectively; this is similar to a highly leveraged carry trade position). Putting these weights into Equations 2 and 4 leads to
RDC = −1.0(9.2%) + 1.0(11.3%) = 2.1%
σ2(RDC) = (1.0)2(8.3%)2 + (1.0)2(10.6%)2 + [−2.0(8.3%)(10.6%)0.85]
= 0.3%
The standard deviation—that is, σ(RDC)—is now 5.6%, less than either of the expected risks for foreign-currency asset returns (results A and B). Nguyen concludes that having long and short positions in positively correlated currencies can lead to much lower portfolio risk, through the benefits of cross hedging. (Nguyen goes on to calculate that if the expected correlation between USD/AUD and USD/NZD increases to 0.95, with all else equal, the expected domestic-currency return risk on the long–short portfolio drops to 3.8%.)
Some types of cross hedges are often referred to as macro hedges. The reason is because the hedge is more focused on the entire portfolio, particularly when individual asset price movements are highly correlated, rather than on individual assets or currency pairs. Another way of viewing a macro hedge is to see the portfolio not just as a collection of financial assets, but as a collection of risk exposures. These various risk exposures are typically defined in categories, such as term risk, credit risk, and liquidity risk. These risks can also be defined in terms of the potential financial scenarios the portfolio is exposed to, such as recession, financial sector stress, or inflation. Often macro hedges are defined in terms of the financial scenario they are designed to protect the portfolio from.
Putting gold in the portfolio sometimes serves this purpose by helping to provide broad portfolio protection against extreme market events. Using a volatility overlay program can also hedge the portfolio against such risks because financial stress is typically associated with a spike in exchange rates’ implied volatility. Using a derivative product based on an index, rather than specific assets or currencies, can also define a macro hedge. One macro hedge specific to foreign exchange markets uses derivatives based on fixed-weight baskets of currencies (such derivatives are available in both exchange-traded and OTC form). In a multi-currency portfolio, it may not always be cost efficient to hedge each single currency separately, and in these situations a macro hedge using currency basket derivatives is an alternative approach.
Minimum-Variance Hedge Ratio
But the minimum-variance hedge ratio can be quite different from 100% when the hedge is jointly optimized over both exchange rate movements RFX and changes in the foreign-currency value of the asset RFC. A sidebar discusses this case.
There can also be cases when the optimal hedge ratio may not be 100% because of the market characteristics of a specific currency pair. For example, a currency pair may not have a (liquid) forward contract available and hence an alternative cross hedging instrument or a macro hedge must be used instead. We examine when such situations might come up in Section 13.
Basis Risk
For an example of basis risk, return to the illustration earlier of the foreign-currency asset portfolio that cross hedged a long USD/AUD exposure with a short USD/NZD exposure. It is not only possible, but highly likely, that the correlation between movements in the USD/AUD and the USD/NZD spot rates will vary with time. This varying correlation would reflect movements in the NZD/AUD spot rate. Another example of basis risk would be that the correlation between a multi-currency portfolio’s domestic-currency market value and the value of currency basket derivatives being used as a macro hedge will neither be perfect nor constant.
At a minimum, this means that all cross hedges and macro hedges will have to be carefully monitored and, as needed, rebalanced to account for the drift in correlations. It also means that minimum-variance hedge ratios will have to be re-estimated as more data become available. The portfolio manager should beware that sudden, unexpected spikes in basis risk can sometimes turn what was once a minimum-variance hedge or an effective cross hedge into a position that is highly correlated with the underlying assets being hedged—the opposite of a hedge.
Basis risk is also used in the context of forward and futures contracts because the price movements of these derivatives products do not always correspond exactly with those of the underlying currency. This is because the price of the forward contract also reflects the interest rate differential between the two countries in the currency pair as well as the term to contract maturity. But with futures and forwards, the derivatives price converges to the price of the underlying as maturity approaches, which is enforced by arbitrage. This convergence is not the case with cross hedges, which potentially can go disastrously wrong with sudden movements in market risk (price correlations), credit risk, or liquidity risk.
Optimal Minimum-Variance Hedges
For simple foreign-currency asset portfolios, it may be possible to use the single-variable OLS regression technique to do a joint optimization of the hedge over both the foreign-currency value of the asset RFC and the foreign-currency risk exposure RFX. This approach will reduce the variance of the all-in domestic-currency return RDC, which is the risk that matters most to the investor, not just reducing the variance of the foreign exchange risk RFX.
Calculating the minimum-variance hedge for the foreign exchange risk RFX proceeds by regressing changes in the spot rate against changes in the value of the hedging instrument (i.e., the forward contract). But as indicated in the text, performing this regression is typically unnecessary; for all intents and purposes, the minimum-variance hedge for a spot exchange rate using a forward contract will be close to 100%.
But when there is only a single foreign-currency asset involved, one can perform a joint optimization over both of the foreign-currency risks (i.e., both RFC and RFX) by regressing changes in the domestic-currency return (RDC) against percentage changes in the value of the hedging instrument. Basing the optimal hedge ratio on the OLS estimate for β in this regression will minimize the variance of the domestic-currency return σ2(RDC). The result will be a better hedge ratio than just basing the regression on RFX alone because this joint approach will also pick up any correlations between RFX and RFC. (Recall from Section 4 that the asset mix in the portfolio, and hence the correlations between RFX and RFC, can affect the optimal hedge ratio.) This single-variable OLS approach, however, will only work if there is a single foreign-currency asset in the portfolio.
Work by Campbell (2010) has shown that the optimal hedge ratio based jointly on movements in RFC and RFX for international bond portfolios is almost always close to 100%. However, the optimal hedge ratio for single-country foreign equity portfolios varies widely between currencies, and will depend on both the investor’s domestic currency and the currency of the foreign investment. For example, the optimal hedge ratio for a US equity portfolio will be different for UK and eurozone-based investors; and for eurozone investors, the optimal hedge ratio for a US equity portfolio can be different from that of a Canadian equity portfolio. The study found that the optimal hedge ratio for foreign equity exposures can vary widely from 100% between countries. But as the author cautions, these optimal hedge ratios are calculated on historical data that may not be representative of future price dynamics.
Minimum-Variance Hedge Ratio Example
Annie McYelland is an analyst at Scotland- based Kilmarnock Capital. Her firm is considering an investment in an equity index fund based on the Swiss Stock Market Index (SMI). The SMI is a market-cap weighted average of the twenty largest and most liquid Swiss companies, and captures about 85% of the overall market capitalization of the Swiss equity market.
McYelland is asked to formulate a currency-hedging strategy. Because this investment involves only one currency pair and one investment (the SMI), she decides to calculate the minimum-variance hedge ratio for the entire risk exposure, not just the currency exposure. McYelland collects 10 years of monthly data on the CHF/GBP spot exchange rate and movements in the Swiss Market Index.
On the basis of these calculations, she recommends that the minimum-variance hedge ratio for Kilmarnock Capital’s exposure to the SMI be set at approximately 135%. This recommendation means that a long CHF1,000,000 exposure to the SMI should be hedged with a short position in CHF against the GBP of approximately CHF1,350,000. Because forward contracts in professional FX markets are quoted in terms of CHF/GBP for this currency pair, this would mean a long position in the forward contract (FCHF/GBP)—that is, selling the CHF means buying the base currency GBP.
McYelland cautions the Investment Committee at Kilmarnock Capital that this minimum-variance hedge ratio is only approximate and must be closely monitored because it is estimated over historical data that may not be representative of future price dynamics. For example, the +0.6 correlation estimated between %ΔSMI and %ΔSGBP/CHF is the 10-year average correlation; future market conditions may not correspond to this historical average.
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