OF INTERESTFinally, it is worth mentioning that currency overlay management, even passive management,is a process which requires the management skill of an overlay ﬁrm or the currency team of aninvestment manager. They will need to be paid for this service, and therefore fees will need tobe added to the above costs. Annual passive hedging fees range from around 1 bp up to 10 bp,depending on the complexity and scale of the overlay programme. Small, complex overlayscost proportionately more.However, it is not uncommon for ‘overlay’ to be offered to institutional investors either verycheaply (i.e. at very low fees) or free. Two reasons can exist for this:(a) The currency manager has an existing investment management relationship with the client,and the ‘free’ currency overlay service is cross-subsidised from the fees from the other relationship. This is not ‘free currency overlay’, it is more expensive investment managementsubsidising the currency overlay. From a transparency perspective, it is probably betterfor the client to negotiate a lower investment management fee and a currency overlay feeto add up to the same overall. Investment managers who charge for hedging or overlayservices are more likely to tackle the process in a professional way. The level of detailin this chapter illustrates that there are design decisions, and execution processes, all ofwhich can have far more effect on the overall cost of overlay than a few notionally ‘saved’basis points in fees.(b) Far more important from a cost point of view is the execution of passive hedging forwardcontracts with counterparties associated with the overlay/investment manager. This conﬂictof interest can arise in three ways:1. Bank dealing rooms offering (more or less) informal arrangements whereby they willtake responsibility for executing deals on behalf of the customer in line with the customer’s orders. This kind of activity has had a long history, and is part and parcel ofthe bank FX sales team’s effort to generate customer volume for their dealers. It canbe evidenced in ‘limit’ orders (where the bank agrees to ‘watch’ a particular exchangerate, and execute a deal on behalf of the client when the market rate reaches a speciﬁed limit), in ‘rate matching’ orders, where for example a bank agrees to execute adeal at WM/Reuters London Close prices, or simply in having control over the ordersgiven to the interbank dealers, and the decision-making process once the price comesback.2. It can also arise when investment managers (or custodians) are part of an organisationwhich maintains an FX business, and an FX dealing room. If an investment manager orcustodian undertakes an FX deal with their own organisation, it creates a very fundamental conﬂict of interest:
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r It is the job of the investment or overlay manager to act on behalf of the client and inthe client’s interests.
r It is the job of the dealer in a bank dealing room to get the best possible price for thebank, which means the worst price for the customer (there is nowhere for deals thatare good for the bank to go – they have to go to the customer!).r If the manager is able (under the terms of the contract and regulatory arrangements)to deal with another part of the same organisation (as well as external bank dealingrooms), then he will naturally come under pressure to do so.r There may be arrangements under which the investment manager is obliged to dealwith the in-house bank. This will yield the most damaging conﬂict and be the mostexpensive solution.3. Finally, it can arise that an investor has negotiated arrangements with the custodian forthe custodian’s FX dealing room to have a monopoly on the FX transactions arising in thefund. This obliges investment managers and overlay managers to utilise the custodian’sFX rates (whether they are competitive or not). This is not so much a conﬂict of interest asa waste of money. The investment or overlay manager may be fully aware of the problem,and complain at poor rates, but be powerless to change them. In these circumstances, thecost-conscious investor should re-negotiate the arrangements to unwind the custodian’smonopoly.In all these situations, the investor client can experience costs way above those cited here.It is almost universal in these situations (except 3 above) that the ‘manager’ will not seekto charge the client fees: this often acts as a magnet to the client, since fees are a visibleoverhead.The scale of the cost implications arising from conﬂict situations can be startling. Theauthor’s ﬁrm has audited the foreign exchange transactions for a number of pension funds.In a particularly bad example, a large public sector pension fund was found to have beensuffering executions on spot trades (with the custodian as the captive FX provider) at singlesided transaction costs of 58 bp, compared to 3 bp indicated by WM/Reuters spreads (halfof the values in Table 3.3), and 1.4 bp by the author’s ﬁrm (Table 3.4). Over the 6-monthperiod in 2001 that this report covered, there were 1378 FX deals reviewed, so this wasnot an accidental ‘one-off’.Costly pricing on this scale can have a dramatic impact on investors’ returns, and thecosts are almost completely invisible. They arise out of pricing, not out of commissions,fees or brokerage, and it requires expert analysis to establish that mispricing is taking place.This makes it all the more imperative that investor’s Investment Management Agreements(IMAs) with managers for overlay or hedging include the provision that the manager is prohibited from dealing with any afﬁliated or associated bank FX dealing room, and that themanager has the freedom to choose a range of banks (subject to client veto on credit grounds)which will be assessed principally on deal execution pricing.
7Currency Overlay BenchmarksThe theory and practice of investment benchmarks, and particularly currency benchmarks, hasundergone a huge revolution in the last few years. I do not propose to reinvent the wheel in thischapter’s discussion, but rather I will adopt the basic principles and methodology recommendedby AIMR in the AIMR Benchmarks and Performance Attribution Subcommittee Report ofAugust 1998 (the ‘AIMR Report’) – reproduced here as Appendix 3.
7.1 WHAT IS A CURRENCY BENCHMARK?Currencies and currency returns and currency benchmarks are not as intuitively easy to understand or conceptualise as other asset classes. I will start by describing currency benchmarksusing equities as an analogy.Box 7.1
Benchmarks
Benchmarks perform two purposes in modern portfolio management. Firstly they set outthe strategic exposure which the investor wishes to embrace, and secondly they act as areference point against which the investor can judge the performance of his investments(or investment manager). Occasionally there are benchmarks which fulﬁl only the latterpurpose – the most obvious example being peer group benchmarks popular in the UK inthe 1980s and 1990s.An investor wishing to hold a high proportion of equities in his portfolio might adopt astrategic portfolio benchmark which includes, say, 70% equities. This choice establishesa basis for allocating specialist mandates, and it is taken as the ‘neutral’ position. Theperformance of the investor’s equity managers will be judged against the performance ofan equity index acting as an equity benchmark. Similarly with currency benchmarks.An investor wishing to hold no currency exposure in his strategic benchmark will seta fully hedged benchmark – i.e. a strategic position that eliminates all currency risk. Aninvestor who wishes to hold all the currency exposure that comes with his internationalexposure will choose an unhedged benchmark. Choosing to strategically hold half thecurrency exposure would imply a 50% hedged benchmark. The decision of which currencybenchmark to adopt is commonly made by default. The default benchmark (when theissue is not thought about or analysed) is always unhedged – i.e. to accept full currencyexposure.When either an active or a passive currency manager is engaged, he will be judged byreference to a benchmark portfolio. That portfolio will include passive hedging at the samehedge ratio (proportion hedged) as the benchmark.Suppose an investor wishes to invest in equities. The investor may wish to provide a guideto the equity manager as to the returns, and asset mix, he expects. Let us suppose the investor
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wants the manager to invest in US equities, weighted by market cap. He may well specifythe S&P500 index as a benchmark. The manager then knows that if he holds the stocksin the S&P500 in the index weights he will have established a riskless (as well as a novalue-added) portfolio. A well-constructed benchmark will be such that if the manager adoptsthe riskless portfolio, the manager’s relative performance (i.e. versus the benchmark) willbe close to zero. There will almost inevitably always remain a small tracking error; it maybe marginally negative through transactions costs, it may be marginally positive if the taxtreatment of dividends is more favourable in the live portfolio than the benchmark assumptions.The investor will use the relative performance of the manager as his guide to the manager’sperformance.Now let us translate this into a currency context. An investor wishes to know what contribution (and risk) currency exposure is making to his international returns. He may wish to alterhis currency exposure in some way, and he needs objective information on which to base hisjudgements, and to measure his currency overlay manager.7.1.1 Misleading currency attributionA popular but misleading way for this to be done in the past was for the investor to break downinternational returns between the ‘local’ equity return and the spot currency return. The ‘local’return is the return of the asset expressed in local currency. The spot return is the change in thespot exchange rate. Geometrically link the two returns and you have the return in the investor’scurrency – the unhedged return.We have already seen how this method was misleading because neither the local returns, northe spot returns, are independently investable by the investor. Dividing a return series betweentwo component returns is not a useful exercise if neither of the components is independentlyinvestable. By naming the two components ‘equity return’ and ‘currency return’, the investoris encouraged to believe that the returns are truly individually available from these assets. Formany US investors, this meant that they saw that ‘currency returns’ were positive, and thereforejumped to the conclusion that hedging would be loss-making. These two statements do notfollow on from each other, as we shall see.7.1.2 Benchmark as portfolioA currency benchmark is a portfolio. In calculating benchmark returns, the constituents of this‘benchmark portfolio’ must be enumerated, and the constituents’ behaviour, their characteristics and their pricing must be deﬁned. Unlike, say, an equity portfolio, the constituents of acurrency benchmark portfolio are not straightforward assets. They are concepts like ‘currencysurprise’ (see Box 2.2 and fuller description in Chapter 3) and ‘contribution from hedging’. Thismakes currency benchmarks particularly difﬁcult to understand and to maintain an intuitivegrasp over.7.1.3 Benchmark mechanicsWhat the investor can do is eliminate the effect of spot exchange rates by hedging the currencyrisk – selling currencies forward using forward contracts. What this does is to divide the twocomponents (currency, equities) on quite different lines – hedged return (instead of local return)
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and currency surprise (instead of spot return). These two components are investable, and theywill form the basis of a currency benchmark construction.Currency differs from equity in two further important ways. Firstly, an equity investor willwish his manager to broadly replicate an equity index, while an international investor is morelikely to ask his currency overlay manager to neutralise currency surprise – in effect holdinga currency hedging portfolio exactly opposite to the underlying currency portfolio. Secondly,currency exposure comes ‘by accident’ along with holding international assets, it is almostnever constructed deliberately.Going back to the equity analogy. The investor who wishes to know his returns from currency can calculate a ‘currency only’ benchmark (see below). This will set out accurately the‘voluntary’ exposure to currencies that the investor is accepting, and make no reference in itsreturns to the underlying asset returns. However, the ‘currency only’ benchmark is almost always calculated in the context of some hedging activity. It is possible (although rarely done) tocalculate a ‘currency only’ benchmark without any associated hedging programme or currencyoverlay.Of more practical interest is to deﬁne a benchmark in terms solely of the currency hedgingactivity rather than a combination of the underlying currency and the hedging activity. I willdeﬁne a benchmark which looks only at the hedging activity as a ‘currency overlay only’benchmark, and that which looks at strategic currency exposure as an ‘embedded currencyplus currency overlay’ benchmark (and this will include both the strategic currency returnsand any ‘contribution from hedging’ from overlay. I will discuss the concept of ‘contributionfrom hedging’ in more detail below.Alternatively, the investor may want to know how his underlying international investmentswould perform if currency exposure were eliminated, but the exposure to international equities(or whatever his chosen asset class) is retained. In this case we can deﬁne the benchmark asan ‘asset plus currency overlay’ benchmark (see below).
7.2 INVESTABILITYThe investability of a benchmark is one of its most important characteristics. Currency benchmarks rely on forward contracts for their execution, and these have certain characteristicswhich make the investability test a little different from most asset class benchmarks.The two key points about investability are that the calculations performed are:
r On instruments which are available in the quantities requiredr At prices which are available in the market to investors at the date/time speciﬁedTo enable us to examine benchmark investability, we need to understand the investment processthat currency benchmark construction implies. Section 7.3 will spell out the full detail, but thesteps below illustrate the issues we have to contend with.7.2.1 Forward currency pricesMost published benchmarks have now adopted WM/Reuters London Close as the pricingsource. This source is calculated at 4pm London time from the screen quotes of a pre-selectedrange of money centre banks.
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7.2.2 WM/Reuters rates17.2.2.1 WM/Reuters closing spot ratesSince 1993, WM has calculated daily standardised spot rates for global foreign exchangetransactions, using rates provided by Reuters. The service covers quotes for 103 currenciesagainst the USD, GBP and EUR. Bid, offer and mid rates are available.7.2.2.2 WM/Reuters closing forward ratesSince January 1997, the WM/Reuters closing forward rates have been calculated and publishedto complement the WM/Reuters closing spot rates. Nine time periods (ON, TN, SW, 1m, 2m,3m, 6m, 9m and 12m) for 41 currencies are quoted against the USD, GBP and EUR. Bid, offerand mid rates are available daily and are used in portfolio valuations, index compilation andperformance measurement.7.2.2.3 WM/Reuters intraday spot ratesIn June 2001, the WM/Reuters intraday spot rates service was launched. This service provideshourly spot rates from 6.00am to 10.00pm (UK time), covering Asia close throughout theglobal day to US close. 103 currencies against the USD, GBP and EUR are quoted. Bid, offerand mid rates are available.7.2.2.4 Cross ratesThe WM spot rates reconcile when crossed, as long as the ‘direction’ of the cross is correct,i.e. the rates used to cross are the ‘primary market’ rates. For example, crossing JPY/USD withUSD/GBP gives exactly the same JPY/GBP cross rate as quoted by WM. The primary marketfor JPY and GBP is USD.However, crossing DKK/USD and USD/EUR to obtain the DKK/EUR cross rate producesa spread on the DKK/EUR spot rate that is much greater than the DKK/EUR rate quoteddirectly, but crossing DKK/EUR and USD/EUR gives exactly the same DKK/USD cross rateas quoted by WM. This concurs with the fact that the primary market for DKK is EURbased.The forward rates do not reconcile exactly to cross forward rates, but the difference isusually no more than a fraction of an FX point and can be attributed to rounding in thecalculations.7.2.2.5 Bank holidaysWM rates are published on every day where at least two from the following four ﬁnancialcentres are open: UK, US, Japan, Germany. In practice, this means that the only days on whichWM rates are not published tend to be Christmas Day and New Year’s Day.1The interested reader can ﬁnd out more about WM/Reuters rates on https://www.wmcompany.com/page.php?pageid=market data currency service&cat=vrmds.
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7.2.3 Contract rollingMany asset class benchmarks are calculated on mid-prices. For a static basket of securitiesin a benchmark, the benchmark would not outperform a live static portfolio, since little orno transactions are required – only valuations. Currency benchmarks are different. Forwardcontracts are for ﬁxed maturity dates, and in the benchmark, as in the actual portfolio, theymust be closed out for cash settlement, and re-opened for a new maturity date. This process isknown as ‘rolling’.Rolling forward contracts requires regular transactions in the currency market – and formost published benchmarks, this is monthly.7.2.4 Scale of contractsThe author’s ﬁrm has conducted surveys over the years of the quoted prices for various sizes ofcurrency contract. It is clear that Reuters/WM prices are applicable to individual contracts ofaround USD50m or less – larger contracts will suffer wider bid/offer spreads. While USD50mis substantial in most market contexts, for currency benchmarks we have the whole portfolioto contend with – and for many overlay clients this can be a billion dollars plus.The relevance of scale is not that the FX market is illiquid – far from it – but that violationof the ‘no-cost’ assumption for most benchmarks becomes less important with time, howeverlarge they are. This is because there are only two material deals in a typical equity portfolio –buying at the start and selling at the end. In FX, this buying and selling happens every month.This means that a large portfolio ($100m+) is likely to show signiﬁcantly more drift from boththe costed and costless benchmark than a small one.7.2.5 RebalancingAt the end of each reporting period, the size of the currency contracts needed to hedge aninternational portfolio will need to be changed, because the size of the assets, expressed in theforeign currency, will have changed. This process is known as rebalancing, and in practice (aswell as in benchmark assumptions) it requires that not only are existing contracts rolled, but inaddition a spot (reducing the size of the hedge) or forward (increasing the size of the hedge)deal is executed to bring the new hedge size in line with that required. These may be calculatedeither from the relevant bid or offer prices (costed) or mid-prices (costless).7.2.6 Geometric linkingIt is now universal to link period returns geometrically (i.e. by multiplication rather thanaddition – see Appendix 2 for details). For currency benchmarks, this requires the assumptionthat, whether or not the benchmark currency prices are costed or costless, the underlying assetscan be costlessly dis- or reinvested in the underlying (international) securities to neutralise thecash ﬂow arising from the settlement of maturing forward contracts. The mathematics of thebenchmark methodology makes this assumption implicitly, as we shall see.The practicalities of the market mean that this is likely to be by far the worst violatedassumption in benchmark construction since the bid/offer spreads and other transactions costsof the underlying securities are an order of magnitude higher than that of the currency markets.This is fully explored in Chapter 6.
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In theory, a benchmark could be constructed which included an allowance for this costdrift. I have never seen this done, and I regard it as unlikely to be done in the future. Thisdrift is also largely invisible. The very act of geometric linking – applied to both the liveportfolio and the benchmark portfolio – excludes it by assumption. However, just becausestandard methodology does not highlight a cost does not mean the that cost disappears. Cashﬂow management and sensible investment guidelines are two of the key skills required of theoverlay manager and client to minimise this cost.
7.3 DESIGNThe AIMR Report speciﬁes, amongst other things, that effective benchmarks should be:
r Investabler Constructed in a disciplined and objective mannerr Formulated from publicly available information (i.e. transparent), andr Consistent with underlying investor status (e.g. regarding regulatory restrictions, time horizons, etc.)AIMR also speciﬁes that when reporting actual portfolio results against benchmarks, returnsshould be calculated to include both realised and unrealised gains/losses; that rates of returnshould be time-weighted, with revaluations at least at every ‘cash ﬂow’ (created, inter alia, byforward contract maturities – see more on this below); and that returns in one period shouldnot be affected by returns in another period, or by the start date of the analysis.The following section sets out three possible benchmark methodologies which are in linewith AIMR principles, and based on essentially the same philosophy and mathematics. Theseare the ‘asset plus currency overlay’, ‘embedded currency plus currency overlay’, and ‘currencyoverlay only’ methodologies.As its name suggests, the asset plus currency overlay methodology produces a benchmarkwhich is made up of changes in underlying (unhedged) asset values and a contributionfrom currency hedging. Periodic returns of this benchmark can be geometrically linked tocreate multi-period and/or annualised returns of hedged assets. These can be compared with2 the out-turns from an overlay programme (based on the same underlying asset returns as thebenchmark) to assess the effectiveness of the currency management, whether passive or active.In addition, the volatility of this benchmark and of its unhedged ‘underlay’ can be comparedwith that of the overlay programme to assess the effectiveness of overlay as a risk reductionstrategy.The embedded currency plus currency overlay methodology produces a full ‘carve-out’ ofall the currency exposures incurred (and hedged) by an international investor.The currency overlay only methodology produces a benchmark without underlying assetreturns, and is made up of the same contribution from currency hedging as is used as an inputinto the asset plus currency overlay benchmark. Currency overlay only period returns cannotbe geometrically linked without a ‘carrier asset’, but are not inﬂuenced by the returns on theunderlying assets. They can be used to assess the effectiveness of currency management bylooking at the average periodic performance of the benchmark and overlay, and by looking atthe tracking error of the overlay relative to the benchmark.22‘Tracking error’ is throughout deﬁned as the annualised standard deviation (volatility) of the difference between two return series(usually between a benchmark and actual returns). All these measures are calculated via logs (see Appendix 1).
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The algebra of each of these methodologies are set out below: numerical worked examplesare shown in Section 7.5. We also set out below brief details of certain other methodologies,and the reasons why these have been rejected as models for benchmarks.7.3.1 Asset plus currency overlay methodologyThe asset plus currency overlay methodology deﬁnes the benchmark return for each period tas:Benchmark returnst % = Hedged returnst %
(7.1)
Hedged returnst % = Unhedged returnst % + Contribution from hedgingt %
(7.2)
where
where all these terms are expressed as % of the unhedged asset value at the start of the period.The hedged return is in other words the return of the hedged asset expressed in the investor’shome currency.Regular period returns calculated in this way are then geometrically linked to create an indexover time, as follows:Hedged indext = Hedged indext−1 × (1 + Hedged returnst )
(7.3)
For the purposes of this example, I will assume that the investor is USD-based and the investment is denominated in EUR. The component pieces of this structure are derived as follows:Unhedged returns% =
Foreign currency portfolio valuet × Spot ratet−1Foreign currency portfolio valuet−1 × Spot ratet−1
(7.4)
where the spot rate is expressed as USD/EUR.Contribution from hedgingt % =
Contribution from hedging USDtUSD amount of exposuret−1
(7.5)
whereContribution from hedging USDt = [Hedge valuation USDt + Cum cash ﬂow USDt ]− [Hedge valuation USDt−1 + Cum cash ﬂow USDt−1 ](7.6)andUSD amount of exposuret−1 = Valuation of overlaid international assetst−1converted to USD at spot ratet−1
(7.7)
Hedge valuation USD is the marked-to-market valuation (MMV) of all the outstanding unmatured forward contracts (or other instruments) in the benchmark hedge structure, and Cumcash ﬂow USD is the simple cumulation over time (with no allowance for interest or return oncapital) of the realised cash from maturing benchmark hedges.
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7.3.2 Special case – monthly benchmark calculationIf the hedge maturity is equal to the reporting period (i.e. if the benchmark hedges are put inplace at point (t − 1) with a maturity at point t), the hedge MMV is zero and the end-monthcash ﬂow is the contribution from hedging.3 Under these particular circumstances we canexpress the contribution from hedging in exchange rate terms. In this equation, we deal withone currency (say EUR) for a USD-based currency:Contribution from full hedging EUR %(EUR portfolio valuet−1 × Fwd ratet−1 ) − (EUR portfolio valuet−1 × Spot ratet )=EUR portfolio valuet−1 × Spot ratet−1
(7.8)
where the exchange rates are expressed as USD/EUR and the ‘Fwd rate’ is the one-month forward. Note that if the foreign currency is the denominator of the exchange rate (say JPY/USD),then the portfolio values are divided by the exchange rates, not multiplied.We can eliminate the EUR portfolio value from the equation, to get the neat:Contribution from full hedging EUR% =
Fwd ratet−1 − Spot ratetSpot ratet−1
(7.9)
The sharp-eyed reader will note that this is the negative-signed currency surprise (see Chapter3). If the benchmark hedge ratio is less than 100%, then the value from equation (7.9) will bemultiplied by the BHR.This formula determines the ‘contribution from hedging’ from one currency (EUR). Thetotal contribution from hedging all the currencies in the portfolio is therefore simply:n
Total contribution from hedging % =
wi (Contribution from hedgingi %)
(7.10)
i=1
wheren = no. of currencies hedgedi = currencywi = weight of currency i in the total international portfolio (all measured at t−1)Note that it is quite possible that the sum of the weights (w) add up to less than 100%. Theresidual will be unhedged or unhedgeable currencies. The denominator of the percentage onthe LHS of equation (7.10) is the total international portfoliot−1 , which is also the denominator of the asset return calculations for the portfolio. This common denominator means thatpercentages can be added across each period.
3The inquiring reader may wish to understand why the cum cash ﬂow is cumulated without interest. Simplifying away somedetails, this is because the ‘contribution from hedging’ measure we need is the change in value of the currency overlay portfolio(expressed as a percentage of the end-prior-period international assets) assumed to be PV’d to the period end. In all major publishedbenchmark calculations, the cash ﬂow from the overlay is simultaneous with the period end. This means that outstanding MMVs arealways zero, and we do not need any cash cumulation, we can simply take the cash as the numerator in the ‘contribution from hedging’return calculation. However, if we chose to construct, say, a 3-month maturity benchmark, and value it monthly, we would need tocalculate the change in MMV plus (the PV of) any cash that has ﬂowed in the month (i.e. the change in the cum cash ﬂow). However,once the return calculation has been made, any cash that has ﬂowed will be caught up in the geometric linking process (which assumesthat all the currency overlay return in a period is then invested in the underlying asset in the next period). To uprate the cash with anyinterest or return would mean double counting returns on the cash.
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7.3.3 Valuation of unmatured contractsThe above case is the special (but common) case of monthly reporting and one-month hedging.In more general terms, the MMV of the hedges will be the value of the outstanding hedges,evaluated based on a publicly available pricing source. In a published benchmark, relevantforeign exchange rates would almost certainly be the relevant WM/Reuters closing prices(spot and forward points, with intermediate dates determined by straight-line interpolationbetween forward points). The question of whether the MMV should be calculated with orwithout discounting of future cash ﬂow is considered further below.7.3.4 Benchmark hedge ratioI have not until this point mentioned the benchmark hedge ratio in detail. This is a criticalelement in the strategic currency decision, but where does it ﬁt in the above maths? Theanswer is that the benchmark hedge ratio can be expressed as follows:Benchmark hedge ratio % (BHR) =
Contribution from hedgingtContribution from full hedgingt
(7.11)
And in practice, the size of the hedges to match the underlying embedded currency exposurewill be BHR% × size of underlying exposure.This approach to benchmarking currency overlay is widely used. Its advantages are thatit allows the investor to see the return of his underlying international assets with all or partof the currency returns removed. It can be geometrically linked without difﬁculty, and itallows the volatility-reduction properties of currency overlay to be directly observable in thebenchmark returns. The key disadvantage is that, for benchmark hedge ratios of 1–99%, whenthe benchmark returns are being increased by currency returns, there are negative returns andnegative cash from the ‘contribution from hedging’. While this is not a problem in principle,it does give investors a headache!A worked example (with numbers) of the asset plus currency overlay methodology is setout later (Table 7.3).7.3.5 Embedded currency plus currency overlay methodologyThis section deals only with the ‘embedded currency’ plus overlay methodology. The overlayonly methodology is set out in Section 7.3.6. The benchmark return is deﬁned as follows:Benchmark returnt % = Currency surpriset + Contribution from hedgingt %
(7.12)
This is because currency surprise represents the embedded currency return in an internationalportfolio. In what may seem rather a circular calculation, we reach the currency surprise asfollows:Currency surpriset % = Unhedged returnst % − Fully hedged returnst %
(7.13)
But we know from equation (7.3) that:Hedged returnst % = Unhedged returnst % + Contribution from full hedgingt %Therefore substituting:Currency surpriset % = −Contribution from full hedgingt %
(7.14)
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So the only way we can calculate the currency surprise is to take the negative of the contributionfrom full hedging. This leads us to:Benchmark returnt % = Contribution from hedgingt % − Contribution from full hedgingt %(7.15)If there is an overlay programme in place, then the returns of the combination of the embeddedcurrency and the overlay are the sum of the two. Taking the three main benchmark hedge ratios:Benchmark hedge Currency only benchmark (embeddedratiocurrency + overlay)0%50%100%
−100% × contribution from full hedging−50% × contribution from full hedgingNil
