30 May evening study
Last updated
Last updated
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:
𝑅𝐷𝐶=∑𝑖=1𝑛𝜔𝑖(1+𝑅𝐹𝐶,𝑖)(1+𝑅𝐹𝑋,𝑖)−1𝜎2(𝜔1𝑅1+𝜔2𝑅2)≈𝜔12𝜎2(𝑅1)+𝜔22𝜎2(𝑅2)+2𝜔1𝜎(𝑅1)𝜔2𝜎(𝑅2)𝜌(𝑅1,𝑅2)Recall that the Ri in the equation for variance are the RDC for each of the foreign-currency assets. Likewise, recall that the RFX term is defined such that the investor’s “domestic” currency is the price currency in the P/B exchange rate quote. In other words, this calculation may require using the algebraic reciprocal of the standard market quote convention. These two equations together show the domestic-currency return and risk for a multi-currency portfolio of foreign assets.
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.)
Learning Outcomes
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
This section has covered only some of the most common currency management tools and strategies used in FX markets—there are a great many other derivatives products and strategies that have not been covered.
The key points are that there are many different hedging and active trading strategies, there are many possible variations within each of these strategies, and these strategies can be used in combination with each other.
There is no need to cover all of what would be a very large number of possible permutations and combinations.
Instead, we will close this section with a key thought: Each of these many approaches to either hedging or expressing a directional view on currency movements has its advantages and disadvantages, its risks, and its costs.
As a result, there is no single “correct” approach to initiating and managing currency exposures.
Instead, at the strategic level, the IPS of the portfolio sets guidelines for risk exposures, permissible hedging tools, and strategies, which will vary among investors.
At the tactical level, at which the portfolio manager has discretion on risk exposures, currency strategy will depend on the manager’s management style, market view, and risk tolerance. It will also depend on the manager’s perceptions of the relative costs and benefit of any given strategy.
Market conditions will affect the cost/benefit calculations behind the hedging decision, as movements in forward points (expected roll yield) or exchange rate volatility (option premiums) affect the expected cost of the hedge; the same hedge structure can be “rich” or “cheap” depending on current market conditions.
Reflecting all of these considerations, different managers will likely make different decisions when confronted with the same opportunity set; and each manager will likely have a good reason for their individual decision.
The most important point is that the portfolio manager be aware of all the benefits, costs, and risks of the chosen strategy and be comfortable that any remaining residual currency risks in the hedge are acceptable.
To summarize the key insights of Sections 9–12—and continuing our example of a portfolio manager who is long the base currency in the P/B quote and wants to hedge that price risk—the manager needs to understand the following:
Because the portfolio has a long exposure to base currency, to neutralize this risk the hedge will attempt to build a short exposure out of that currency’s derivatives using some combination of forward and/or option contracts.
A currency hedge is not a free good, particularly a complete hedge. The hedge cost, real or implied, will consist of some combination of lost upside potential, potentially negative roll yield (forward points at a discount or time decay on long option positions), and upfront payments of option premiums.
The cost of any given hedge structure will vary depending on market conditions (i.e., forward points and implied volatility).
The cost of the hedge is focused on its “core.” For a manager with a long exposure to a currency, the cost of this “core” hedge will be the implicit costs of a short position in a forward contract (no upside potential, possible negative roll yield) or the upfront premium on a long position in a put option. Either of these two forms of insurance can be expensive. However, there are various cost mitigation methods that can be used alone or in combination to reduce these core hedging costs:
Writing options to gain upfront premiums.
Varying the strike prices of the options written or bought.
Varying the notional amounts of the derivative contracts.
Using various “exotic” features, such as knock-ins or knock-outs.
There is nothing inherently wrong with any of these cost mitigation approaches—but the manager must understand that these invariably involve some combination of reduced upside potential and/or reduced downside protection. A reduced cost (or even a zero-cost) hedge structure is perfectly acceptable, but only as long as the portfolio manager fully understands all of the residual risks in the hedge structure and is prepared to accept and manage them.
There are often “natural” hedges within the portfolio, in which some residual risk exposures are uncorrelated with each other and offer portfolio diversification effects. Cross hedges and macro hedges bring basis risk into the portfolio, which will have to be monitored and managed.
There is no single or “best” way to hedge currency risk. The portfolio manager will have to perform a due diligence examination of potential hedge structures and make a rational decision on a cost/benefit basis.
EXAMPLE 8
Hedging Strategies
Ireland-based Old Galway Capital runs several investment trusts for its clients. Fiona Doyle has just finished rebalancing the dynamic currency hedge for Overseas Investment Trust III, which has an IPS mandate to be fully hedged using forward contracts. Shortly after the rebalancing, Old Galway receives notice that one of its largest investors in the Overseas Investment Trust III has served notice of a large withdrawal from the fund.
Padma Bhattathiri works at Malabar Coast Capital, an India-based investment company. Her mandate is to seek out any alpha opportunities in global FX markets and aggressively manage these for speculative profit.
The Reserve Bank of New Zealand (RBNZ) is New Zealand’s central bank, and is scheduled to announce its policy rate decision within the week. The consensus forecast among economists is that the RBNZ will leave rates unchanged, but Bhattathiri believes that the RBNZ will surprise the markets with a rate hike.
Jasmine Khan, analyst at UK-based Brixworth & St. Ives Asset Management, has been instructed by the management team to reduce hedging costs for the firm’s Aggressive Growth Fund, and that more currency exposure—both downside risk and upside potential—will have to be accepted and managed. Currently, the fund’s ZAR-denominated foreign-currency asset exposures are being hedged with a 25-delta risk reversal (on the ZAR/GBP cross rate). The current ZAR/GBP spot rate is 20.1350.
Bao Zhang is a market analyst at South Korea–based Kwangju Capital, an investment firm that offers several actively managed investment trusts for its clients. She notices that the exchange rate for the Philippines Peso (PHP/USD) is increasing (PHP is depreciating) toward its 200-day moving average located in the 50.2500 area (the current spot rate is 50.2475).
She mentions this to Akiko Takahashi, a portfolio manager for one of the firm’s investment vehicles. Takahashi’s view, based on studying economic fundamentals, is that the PHP/USD rate should continue to increase, but after speaking with Zhang she is less sure. After further conversation, Zhang and Takahashi come to the view that the PHP/USD spot rate will either break through the 50.2500 level and gain upward momentum through the 50.2600 level, or stall at the 50.2500 level and then drop down through the 50.2400 level as frustrated long positions exit the market. They decide that either scenario has equal probability over the next month.
Annie McYelland is an analyst at Scotland-based Kilmarnock Capital. The firm is considering a USD10,000,000 investment in an S&P 500 Index fund. McYelland is asked to calculate the minimum-variance hedge ratio. She collects the following statistics based on 10 years of monthly data:
s(%ΔSGBP/USD)
σ(RDC)
ρ(RDC;%ΔSGBP/USD)
2.7%
4.4%
0.2
Source: Data are from Bloomberg.
Given the sudden liquidity need announced, Doyle’s best course of action with regard to the currency hedge is to:
do nothing.
reduce the hedge ratio.
over-hedge by using currency options.
Solution to 1:
A is correct. After rebalancing, the Overseas Investment Trust III is fully hedged; currency risk is at a minimum, which is desirable if liquidity needs have increased. Choices B and C are incorrect because they increase the currency risk exposures.
Given her market view, Bhattathiri would most likely choose which of the following long positions?
5-delta put option on NZD/AUD
10-delta put option on USD/NZD
Put spread on JPY/NZD using 10-delta and 25-delta options
Solution to 2:
A is correct. The surprise rate hike should cause the NZD to appreciate against most currencies. This appreciation would mean a depreciation of the NZD/AUD rate, which a put option can profit from. A 5-delta option is deep-OTM, but the price reaction on the option premiums will be more extreme than a higher-delta option. That is to say, the percentage change in the premiums for a 5-delta option for a given percentage change in the spot exchange rate will be higher than the percentage change in premiums for a 25-delta option. In a sense, a very low delta option is like a highly leveraged lottery ticket on the event occurring. With a surprise rate hike, the odds would swing in Bhattathiri’s favor. Choice B is incorrect because the price reaction in the USD/NZD spot rate after the surprise rate hike would likely cause the NZD to appreciate; so Bhattathiri would want a call option on the USD/NZD currency pair. Choice C is incorrect because an appreciation of the NZD after the surprise rate hike would best be captured by a call spread on the JPY/NZD rate, which will likely increase (the NZD is the base currency).
Among the following, replacing the current risk reversal hedge with a long position in which of the following would best meet Khan’s instructions? (All use the ZAR/GBP.)
10-delta risk reversal
Put option with a 20.1300 strike
Call option with a 20.1350 strike
Solution to 3:
A is correct. Moving to a 10-delta risk reversal will be cheaper (these options are deeper-OTM than 25-delta options) and widen the bands in the corridor being created for the ZAR/GBP rate. Choice B is incorrect because a long put provides no protection against an upside movement in the ZAR/GBP rate, which Brixworth & St. Ives is trying to hedge (recall that the fund is long ZAR in its foreign-currency asset exposure and hence needs to sell ZAR/buy GBP to hedge). Also, if Brixworth & St. Ives exercises the option, they would “put” GBP to the counterparty at the strike price and receive ZAR in return. Although this option position may be considered profitable in its own right, it nonetheless causes the firm to double-up its ZAR exposure. Choice C is incorrect because although an ATM call option on ZAR/GBP will provide complete hedge protection, it will be expensive and clearly more expensive than the current 25-delta risk reversal.
Which of the following positions would best implement Zhang’s and Takahashi’s market view?
Long a 50.2450 put and long a 50.2550 call
Long a 50.2450 put and short a 50.2400 put
Long a 50.2450 put and short a 50.2550 call
Solution to 4:
A is correct. Zhang’s and Takahashi’s market view is that, over the next month, a move in PHP/USD to either 50.2400 or 50.2600 is equally likely. A strangle would express this view of heightened volatility but without a directional bias, and would require a long put and a long call positions. Choice B is incorrect because it is a put spread; it will profit by a move in PHP/USD between 50.2450 and 50.2400. If it moves below 50.2400 the short put gets exercised by the counterparty and neutralizes the long put. Although less costly than an outright long put position, this structure is not positioned to profit from a move higher in PHP/USD. Choice C is incorrect because it is a short risk reversal position. It provides relatively cheap protection for a down-move in PHP/USD but is not positioned to profit from an up-move in PHP/USD.
Which of the following positions would best implement Kilmarnock Capital’s minimum-variance hedge?
Long a USD/GBP forward contract with a notional size of USD1.2 million
Long a USD/GBP forward contract with a notional size of USD3.3 million
Short a USD/GBP forward contract with a notional size of USD2.0 million
Solution to 5:
B is correct. The formula for the minimum-variance hedge ratio (h) is:ℎ=𝜌(𝑅𝐷𝐶;𝑅𝐹𝑋)×[𝜎(𝑅𝐷𝐶)𝜎(𝑅𝐹𝑋)]After inputting the data from the table, this equation solves to 0.33. This means that for a USD10 million investment in the S&P 500 (long position), Kilmarnock Capital would want to be short approximately USD3.3 million in a forward contract. Because the standard market quote for this currency pair is USD/GBP, to be short the USD means one would have to buy the GBP; that is, a long position in a USD/GBP forward contract. Choice A is incorrect because it inverts the ratio in the formula. Choice C is incorrect because it shows a short position in the USD/GBP forward, and because it only uses the correlation to set the contract size.
If the currency exposures of foreign assets could be perfectly and costlessly hedged, the hedge would completely neutralize the effect of currency movements on the portfolio’s domestic-currency return (RDC).7 In , this would set RFX = 0, meaning that the domestic-currency return is then equal to the foreign-currency return (RDC = RFC). In , this would set σ2(RDC) = σ2(RFC), meaning that the domestic-currency return risk is equal to the foreign-currency return risk.
Diversification considerations will also depend on the asset composition of the foreign-currency asset portfolio. The reason is because the foreign-currency asset returns (RFC) of different asset classes have different correlation patterns with foreign-currency returns (RFX). If there is a negative correlation between these two sets of returns, having at least some currency exposure may help portfolio diversification and moderate the domestic-currency return risk, σ(RDC). (Refer to in Section 3.)
