:FV (future value) option premium means the amount payable contemporarily with the payoffvalue, i.e. at maturity and not up front. The up-front premium payable would be the FVdivided by the 1-year interest rate, but then to compare with the payoff value we would have tomultiply by the interest rate (because the option writer holds the money for one year before it isneeded).
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Annualised daily
16%
Annual
Volatility % p. a.
14%12%10%8%6%4%2%0%JPY/ USD
JPY/ DEM
JPY/ GBP
DEM/ USD
DEM/ GBP
USD/ GBP
Figure 10.3 Volatility measured at different horizons – volatility of currency surprise (1981–2002),daily volatility annualised and annual volatility
0.796 is the multiple applied to volatility (standard deviation) to calculate the absoluteaverage outcome of a normal distribution (see footnote 2 in Chapter 6); /2 because half thetime a call/put expires out-of-the-money and gives zero payoff value.Volatility is calculated from the log of currency returns(i.e. currency surprise), annualised√by calculating daily volatility and multiplying by 262. I will convert log values back topercentages after all the algebraic manipulation required.Using exactly the same logic, and formula, we can also calculate the average expected payoffvalue. This will have all the same elements of the previous formula, except that the volatilityis the average 1-year volatility.Average historical outcome: If we take the history of DEM/EUR against the USD (I will callit DEM/USD here) as an example, Figure 10.3 tells us the daily annualised percentage volatilitycalculated from the logs is 11.69%. The average option premium under our assumptions istherefore:exp[(0.796/2) × log(1 + 11.69%)] − 1 = 4.50%The average annual volatility for DEM/USD (also from Figure 10.3) is 14.38%. It follows thatthe calculated average payoff value is:exp[(0.796/2) × log(1 + 14.38%)] − 1 = 5.49%So on the face of it, the trending behaviour observed may be a cause of ‘undervaluation’ ofoption premiums, and therefore render passive option buying a proﬁtable strategy.Implied volatilities – the real test: I have collected a nearly 6-year series of daily impliedvolatility quotes from a major currency option provider bank for DEM/USD. An example ofthese quotes is shown in Figure 3.5. However, we need to test 12m option quotes (not 3moption quotes as shown in the graph). I will use the 12m offer quotes, the implied volatilitythe bank is using to price its options offered to customers. Its bid volatilities average 0.25%lower than the offer volatilities over this period. Its volatilities are expressed as percentages,
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although as explained in Appendix 2, these are really logs (i.e. percentages in continuous time).Banks do not exponentiate their option calculations based on logs back into proper percentages.However, since they charge clients option premiums based on the quoted percentage multipliedby the option principal, I will treat the quotes as percentages.Applying the test: We are going to calculate option premiums, and the actual payoff valuesexperienced, for DEM/USD 1997–2002 daily:1. We can calculate the FVs of at-the-money option premiums from the implied vols withoutinterest rates using equation (10.1). Puts and calls will be the same price because of arbitrage(put + forward purchase = call, although this arbitrage only works at-the-money forward).This will give us a series of option premiums.2. We can double this cost, because in the ‘value for money’ test we are going to buy doubles(i.e. buying both a put and a call). This will take away any dependency on arbitrary directionof exchange rate moves from the assessment.3. Then we need to calculate the payoff values for one-year DEM/USD puts and calls. Notethat I have not distinguished the numerator and the denominator, and as long as we work in‘log space’, we do not have to – the results are the same.4. Payoff values are not guesswork or averages. They are fact. Here is an example. One-yearDEM/USD LHS forward rate on 2 Jan 1997 was 1.5009. This was the price to buy DEM,sell USD. One year later, on 2 Jan 1998, the LHS spot was 1.8042. The payoff in log termswas log(1.8042/1.5009) = 0.1841 for the proﬁtable option (in this case the DEM put/dollarcall), and zero for the DEM call/Dollar put. I take 4 bp off the proﬁtable log value to accountfor the fact that the put and call strikes will be marginally different, reﬂecting a 4 bp one-yearoutright bid/offer spread, and the cost of closing the proﬁtable option at spot. This leavesus 0.1837 in log terms as the double proﬁt.5. Converted back to percentages, the payoff was exp(0.1841) − 1 = 20.16%.6. The premium for a single option from the volatility quote in this case was 3.52%, or 7.04%for the double. The proﬁt on this observation (i.e. a double bought on 2 Jan 1997) was20.16% − 7.04% = 13.12%, or 6.56% for the single equivalent.Figure 10.4 shows the net value of the single option equivalent payoff values minus optionpremiums for the purchase periods Jan 97–Nov 2001 (maturing Nov 2002). We can clearly seethat this net payoff is quite volatile, but that it delivers +44 bp of value added over the period.This is not a spurious ﬁnding – it ﬁts in with the trending nature of data we have studied, andwhat we know about how banks price option premiums. Table 10.8 gives summary information.Table 10.8 One-year DEM/USD options,averages 1997–2001 (purchase dates)Average option premium (FV)Average (put + call)/2 payoff valueAverage gain per option %Max gain %Max loss %
4.38%4.82%0.44%11.93%−5.61%
This result arises from one deﬁnitive value (payoff) and one less transparent value (optionpremium). How can we be more conﬁdent about how option premiums are quoted? I havecompared the option premiums (from implied vols quoted by a major bank) with historicalvolatilities calculated from spot rates on a rolling backward-looking 6-month period. So for
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Average = +0.44%8.0%
Net profit %
6.0%4.0%2.0%0.0%−2.0%−4.0%−6.0%−8.0%
1997
1998
1999
2000
2001
Figure 10.4 One-year DEM/USD put + call options – payoffs less premiums ($/DEM (latterly EUR)options, 97–02, 12m maturity)
2 Jan 1997, the log of the spot changes 2 Jul 1996–2 Jan 1997 would be the source data,and this sample’s standard deviation would be annualised, and used as the source to calculatethe ‘historical’ option premium using equation (10.1). The graph of the implied (quoted) andthe historical rates is shown in Figure 10.5. Quoted premiums are clearly closely based onhistorical volatilities, over this period they have averaged 4.38% vs. 4.21% for the historicallycalculated – a difference of 17 bp.All of the above is an example; it covers one particular period, for one currency pair, neitherthe most trending nor the least on the basis of Figure 10.3. It does illustrate, however, that thereis a potentially interesting opportunity for overlay managers in this area of ‘passive’ optionbuying.10.3.3.2 ‘Active’ option tradingThe Black–Scholes formulation assumes constant volatility. If this assumption is relaxed, as itplainly is in real markets, then there is a premium placed on successful prediction of volatility.10.3.3.3 Volatility forecastingVolatility, more speciﬁcally implied volatility, has become a recognised market in the worldof option trading. Option traders, when asked what they do, will often reply that they ‘tradevolatility’. Indeed several banks offer OTC products which allow their customers to buy and sell‘volatility’ directly. There are several issues that surround volatility trading. The ﬁrst is that whatis traded is implied volatility, not historical volatility. In a sense this makes the market peculiarlycircular. Implied volatility is, in effect, a forecast of future volatility. Any manager wishing tosuccessfully ‘trade’ volatility is being required to forecast future changes in the forecasts of
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% Premium
6.50%
6.00%
Quoted premiums
5.50%
Calculated historical premiums
5.00%
4.50%
4.00%
3.50%
3.00%
2.50%Jan 97
Jan 98
Jan 99
Jan 00
Jan 01
Jan 02
Figure 10.5 Quoted and historical volatility option premiums (DEM (EUR)/USD, 1997–2002, 1-yearoptions, ATMF, FV premiums)
volatility. Actual volatility may not come into the equation at all! The second point is that volatility is an artiﬁcial construct, predicated on (almost certainly violated) assumptions. ‘Volatility’is traded because the Black–Scholes formulation assumes a lognormal random walk for the underlying markets, and volatility is the annualised standard deviation of these changes. However,as we have seen above, violation of the Black–Scholes assumptions (in particular uncorrelatedrandom changes) can radically affect even the straightforward calculation of volatility.Turning to implied volatility forecasting, there is very little academic literature on this area,particularly in foreign exchange. There have been no systematic studies of implied volatilityforecasting reliability or success, and the vast majority of the (mainly bank-sponsored) research in this area has concentrated on the relationship between historic volatility and impliedvolatility. But for forecasting purposes, this is of marginal use, since even a reliable impliedvolatility model based on historic volatility simply shifts the burden of forecasting to anothervariable – historic volatility.Historic volatility (a misnomer since the history may be only a few seconds old) is an averageof indeterminate length of the magnitude of changes in the underlying market. Historic volatilitycan be calculated as the observed standard deviation of a sample of changes in recent history,and this is in practice applied with the assumption that the true (underlying) standard deviationhas been constant throughout the sampling period. With increasing length of history, this wouldbe ﬁne if volatility were indeed constant (in line with Black–Scholes assumptions), but it is notﬁne if population volatility is either non-normal, randomly variable over time, or predictablyvariable based on other inputs.Over the past few years modellers have recognised that the underlying variance/volatility isnot constant and have contrived to use more sophisticated models to deal with this. GARCHmodels forecast underlying variance as a (complex) function of past values. This is a more
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realistic standpoint but unfortunately leads to an exponential growth in the number of parameters which need to be estimated (are they variable too?, when do we stop?), with all theattendant drawbacks.10.3.3.4 Other active option strategiesPutting aside volatility forecasting, what else can an active manager do with options to enhancereturns? Banks will trade options proﬁtably by making prices, not taking them. A currencymanager, without a customer-orientated dealing room, client base, brand and market positionand capital, cannot do this.A manager may use options as a downside-controlled way to take currency market betsin either direction, but this is not using option expertise so much as general currency marketexpertise to add value.10.3.4 Dynamic10.3.4.1 Option replicationVery early in the history of currency risk management, in the early 1980s, before currencyoptions became available, currency managers recognised that option-like payoffs were anattractive goal. We have seen in the earlier sections on option models that Black–Scholes’ 1973paper asserted that it was possible to exactly replicate an option position with a dynamicallyadjusted portfolio of the underlying securities (or forward contracts in this case). Variousassumptions violations mean that this assertion is not, in practice, true. Nevertheless, somesort of approximation is possible, and this section explores the various approaches managershave taken to this approximation.10.3.4.2 Dynamic hedging overlay styleAs the OTC option market in currency options started in the second half of 1984, so the moneycentre banks who were offering them began to more or less crudely hedge the resulting exposureusing dynamic, or ‘delta’, hedging techniques. The concept of delta hedging is broadly speakingto hold a position in the underlying market whose change in marked-to-market valuation persmall (1 bp) movement in the underlying market is equal and opposite to the change in markedto-market valuation of the option sold. A bank that sells a large portfolio of options in onecurrency pair can combine these to create a portfolio delta, which is the elasticity of the wholeportfolio of options with respect to a 1 bp movement in the underlying market. As an example,an outstanding option sold to a third party, say a $1m call against a third currency, could havea marked-to-market valuation which varies by $350 for a 1 bp movement in the exchange rate.Since a $1m position in the underlying market would have a $100 change in marked-to-marketvaluation per 1 bp move, this would be called a delta of 0.35 or 35%. Deltas will range betweenzero and one for ‘vanilla’ options, but can vary widely and wildly for exotic options. There isa common further measure of the shape of the delta curve with respect to the exchange ratewhich measures its instantaneous ‘curvature’, and this is called the gamma. There are a wholelot more Greek letters denoting the elasticities of the option valuation with respect to time,volatility, etc., but they are of interest more to bank risk managers than to the general currencyoverlay reader.
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The argument for currency overlay managers offering a dynamic hedging style of currencyrisk management runs like this. Buying currency options to protect against adverse currencymovements in the fund context is attractive for two reasons: it reduces volatility if correctlytargeted and benchmarked, and it satisﬁes the asymmetric risk-aversion utility curve that meanvariance analysis is poor at coping with. From the evidence presented above, it can also exploittrending markets to add value.But a manager has to buy currency options from banks. This is true whether or not theyare OTC or exchange-traded, since the market-makers on the major exchanges are the majormoney-centre banks. Banks sell currency options with the prospect of securing a proﬁt on thecombination of the premium received for the sale and their cost of covering their risk. Theycan cover their risk in one of two ways: buying options from third parties or running a deltahedge in the underlying market. Since there are no natural writers of currency options whowrite them without a delta hedge (in contrast to equity options where institutional holders maywell write ‘covered’ options), banks generally are the ultimate writers of currency options.One way or another, therefore, options written to customers will be matched by a delta hedgerun by a bank with the prospect of proﬁt to the bank. Delta-hedging currency managers (ordynamic hedgers) offer, at the least, a delta hedge run on behalf of the investor to reduce thecost of the option premium by the amount of the prospective bank proﬁt. They may also offerother advantages: ﬂexibility in tailoring speciﬁc option speciﬁcations; high liquidity of theforward market compared to the option market; cash ﬂow improvement (no up-front optionpremiums); and less sensitivity to market volatility in marked-to-market valuation.In a perfect Black–Scholes world these advantages would be unsullied by any disadvantages.The Black–Scholes model tells us that any option can be exactly and risklessly replicated bya portfolio of the underlying security (foreign currency or forward contracts in this case). Aswe have seen earlier in this chapter, however, Black–Scholes markets do not exist, and one ofthe effects of this is that option replication is not a riskless exercise.What is the effect of this in practice? To simplify the discussion, I propose to discuss thereplication of one vanilla option with the following speciﬁcation:Put currencyCall currencyPut amountStrike rateInitiation dateExpiry dateMaturity dateEuropean style(i.e. exercisable only at expiry)Premium (% dollar amount)Premium payment date
Japanese yenUS dollar1bn yen100 yen/$1 Jan 19961 Jul 1996 (date for exercise)3 Jul 1996 (date for payoff cash ﬂows)
3.02% (=$302 000)3 Jan 1996
Suppose that an investment fund wishes to ‘buy’ this option on 1 Jan 1996. If it wishes to buyit by replication and not in the OTC market, what will a typical dynamic hedging currencyoverlay manager do? At the moment when the ‘option’ is established, the overlay managerwill use a Black–Scholes model variant (a variant to cope with forward contracts with no yieldand no cash requirement), input the option speciﬁcation and current market data, particularlythe 6-months forward yen/$ rate and a volatility value. The volatility value may be current
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implied volatilities, historical volatilities or some model value from the manager’s volatilityforecasting model. The model will provide a series of outputs, the most important of which isthe sensitivity of the marked-to-market valuation (in effect the option premium) to changes inthe yen/$ exchange rate – the hedge ratio or delta. If this comes out at, say, 45.6% on the ﬁrstdata entry, then the overlay manager will sell 45.6% × yen 1bn = yen 456m against dollarsin the forward market. The manager may choose to sell at any forward date, but the obvious‘default’ value would be to sell for a maturity of 3 Jul 1996.What happens next is very much manager-speciﬁc, but Black–Scholes theory requires thatthe manager then conducts continuous monitoring of the exchange rate, and continually adjuststhe hedge ratio to stay in line with model output, which will vary as the exchange rate andvolatility changes and time passes. Black–Scholes require that this process is literally continuous, so that thousands of deals could in theory be conducted in the space of a second, or indeedin a nano-second. This requirement is clearly impractical, so the manager must embark on aseries of approximations to get as close to this as possible. Firstly, a manager must decide onmonitoring frequency and procedures. Does monitoring take place at ﬁxed frequency: once asecond, once a minute, once an hour, once a day, once a week? If monitoring is ﬁxed frequency,what about 24-hour dealing? What about illiquid times of day, when perhaps only a thin MiddleEastern market is available? What about weekends, what about Bank Holidays? If monitoringis not planned to be ﬁxed frequency, how is it conducted? If it is triggered by a certain levelof exchange rate movement, how is this movement monitored, continuously? If monitoring ishigh frequency, does this always trigger adjustments in the hedge position, even if these aresmall? Are there buffer exchange rate zones or buffer dealing sizes that keep dealing frequencyunder control? How is volatility monitored? Do market implied volatilities drive the hedgeratio, or historical or model output volatilities?The variety of answers to these and more questions provide ample material for managerdifferentiation – and many of the issues here have been dealt with in other contexts earlier in thebook. But there is a straightforward test that a customer can apply. Has the option replicatorsucceeded in replicating the payoff value of the option being replicated, and at what cost?The arithmetic of this is simple. Take the two possible states that an option can expire in:in-the-money and out-of-the-money. If the option expires out-of-the-money, then the payoffvalue is zero. In this case the cost of the dynamic hedge is the closed sum of the dollar valuesof all the forward contracts relating to the option. If the option expires in-the-money, thenthe payoff value will be positive. If the close-out spot rate on 1 Jul 1996 is 108, then thepayoff is $740 740.74 [=(1bn/100) − (1bn/108)]. The cost of the dynamic hedge is then thedifference between the closed sum of all the associated forward deals, and $740 740.74. Asan example, if the delta hedge yields $550 000, then the cost of replication was $190 740.74(=$740 740.74 − $550 000) or 1.91% of the dollar principal.The key question that arises from the process described is whether it consistently reducesthat cost below buying the equivalent options in the market, and how wide is the variability ofthe cost. The evidence is difﬁcult to ﬁnd, in particular since option replication either by banksor by overlay managers is a commercial undertaking not open to public scrutiny. Under somefairly rigid assumptions about the monitoring process, however, it is possible to simulate theresults of delta hedging using actual option premiums and underlying market rate histories.It appears from this slim evidence that delta hedging under these rigid assumptions is notmaterially lower cost than typical option premium offer prices, but nor does it have materiallyhigher cost variance. Any cost savings experienced by dynamic overlay customers are likelyto be the result of the managers’ proprietary reﬁnements.
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Dynamic hedging can also be operated entirely outside the Black–Scholes model environment, and a subclass of dynamic overlay managers do this. Under their processes there is noassumption of lognormality, of continuous markets, or even of volatility levels. Their payoffoutcomes are identical to delta hedgers, but the composition of their costs is different. Theircosts will be higher or lower than delta hedgers, dependent on whether their models more orless effectively exploit market non-randomness. (Note that with pure lognormal random walkmarkets, all strategies are ultimately identical at zero net return less transaction costs.)Dynamic currency overlay managers (or option replicators) represent one of the largeststyle classes of currency overlay managers. Many overlay managers will not use this styleexclusively, but many rely on it as the core of their active process.
11Active Currency Overlay – Evidenceof PerformanceThis is a short chapter. There is now some evidence of the performance of currency managers,but much of it is proprietary, and it ages quickly. In summary, however, there is good evidencethat the universe of currency managers have on average delivered outperformance againstpassive benchmarks over the 14-year period 1989–2002. There seems to be some ‘reversiontowards the mean’, in that earlier studies showed higher outperformance than later studies, andas the universe has expanded.
11.1 SURVEYS11.1.1 Currency overlay performance surveysCurrency overlay as a recognised activity in the institutional investment market started in 1985,when this ﬁrm (Record Currency Management) secured a mandate to actively hedge the USdollar exposure of the Water Authorities Superannuation Fund – then a public UK fund. Severalmore mandates followed in the UK in that and subsequent years. The earliest US mandateswere 1988/9. The sector grew quite rapidly, largely on mandates from the larger US public andprivate sector funds. It began to spread to continental Europe, Australia and the Far East inthe mid-1990s. The UK is still relatively undeveloped in currency overlay, despite having thesecond largest pool of deﬁned beneﬁt pension assets after the US. Performance measurementof currency overlay managers is a relatively recent phenomenon, but there are now at leastthree sources from which we can draw data.11.1.1.1 The ‘Strange Report’In 1997, an ex-currency overlay manager, Brian Strange, then working in his own small consultancy, Currency Performance Analytics, persuaded 11 currency overlay ﬁrms to submitdetailed client-by-client data on their performance (vs. benchmark) for all their currency overlay accounts, live and terminated. A further three submitted composite data. The subsequentreport, published May 1998, showed that, on average, currency overlay managers had addedabout 1.9% p.a. in the period since 1989, the earliest data submitted. The average trackingerror in this study was 3.5%, giving an average information ratio of 0.54. The total numberof currency overlay accounts was 152, and from this client base 1783 client-quarters wereanalysed. A number of different ways of segmenting the data were illustrated, and in each astory of consistent manager behaviour and consistent value-added emerged.There was little in-depth analysis of why a universe of specialist managers could perform sowell en masse, but it was noted that a signiﬁcant proportion of the client-quarters covered the3-year 1995–97 period, when the dollar was broadly strong, the most popular benchmark wasunhedged, and the dollar was the most common base currency. Currency overlay mandates ofthis speciﬁcation would be expected to add value!
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11.1.1.2 Watson WyattThe actuarial and investment consulting ﬁrm Watson Wyatt have picked up the mantle left byBrian Strange (Brian left the consulting business, and now works for an overlay manager).The US arm have continued collecting data on currency overlay performance, and have recently released1 their latest ﬁndings. Up to the end of 2000, the 5-year median value addedof currency overlay managers in their universe who are operating to a USD base and an unhedged benchmark has been 1.32% p.a. The equivalent ﬁgure for a 50% hedged benchmarkis 0.84%.11.1.1.3 Frank RussellFrank Russell is an investment consulting ﬁrm who have tracked and researched currency overlay managers for longer than any other consultant, and have built a database from contemporarydata (rather than ex post) supplied by the managers. They published a report in September 2001in which they analysed the performance data from 24 currency overlay managers. Their dataran from July 1995 to June 2001, and they found an average outperformance of 1.47% p.a.They analysed the data in somewhat more detail than the Strange Report, and reported valueadded of 0.94% p.a. for 50% hedged benchmark accounts. Unhedged benchmark accountsshowed 2.45% p.a. outperformance, and fully hedged benchmark accounts 0.20% underperformance. This data tends to conﬁrm the suspicion voiced in the Strange Report that time- andmandate-speciﬁc factors were distorting the ﬁgures in a favourable way.These reports are now uploaded quarterly.11.1.2 Performance summaryThe three surveys discussed above, and some other unpublished performance surveys, allpoint to there being identiﬁable value added in currency overlay when measured at the level ofuniverse of overlay managers. That this unusual ﬁnding is possible is explained by the natureof the FX market – that currency overlay managers have identiﬁed and are exploiting one ormore persistent market inefﬁciencies at the expense of the vast majority of the FX market whoare constrained in their behaviour and/or are not proﬁt- or price-sensitive.
11.2 WHO LOSES?Elsewhere in the book (Chapter 4, Chapter 9) I have described the mechanics and structureof the foreign exchange market in some detail. If the (small) universe of currency managershas made money on average over nearly 15 years, then the remainder of the FX market, notmeasured by investment consultants, loses. This is deﬁnitional.I have commented elsewhere that the possibility of consistent average outperformance bythe universe of overlay managers is a highly unusual position for a group of managers to bein, particularly where there is no real debate about the nature of the benchmark against whichthey are measured (this is not the ‘outperformance’ of bond managers holding credit measuredagainst government bonds). To be fully intellectually rigorous, however, I should emphasise1
Brian Hersey and Kurtay Ogunc, Watson Wyatt Presentation, 25 June 2001.
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again that there cannot be overall outperformance generated by the currency market in total.Taking all of the participants, including the market-making community, global outperformanceis zero. The observation we have made from the surveys, and from the evidence presented inearlier chapters, is that an identiﬁable class (overlay managers) has made money. This is anobservation about style, since the general style that overlay managers adopt (discounting thedifferences within the overlay universe) is more successful as a trading strategy than at leastone other of the groups that make up the total FX market.
12Implementing Currency OverlayIn this chapter I set out a ‘check-list’ for investors considering currency overlay – whetherdesigned to reduce risk, or add value, or both. I also cover some of the practical questions thatclients have asked when they establish currency overlay programmes. The answers I give reﬂectthe realpolitik of getting mandates started as well as the theoretical considerations covered inthe remainder of the book.Let’s start with the ‘check-list’.
12.1 SUMMARY CHECK-LISTI will raise and answer a number of practical points, which I will summarise in table form inSection 12.1.14.12.1.1 What mandate type?Currency overlay investors generally come in two categories:1. Those who wish primarily to reduce their existing international portfolio’s exposure tocurrency risk.2. Those who wish to tap a source of excess return from active management of currencies.These two aims may also co-exist, in which case answers to both halves of the question arerelevant.(1) Risk reduction: To reach the decision to implement a risk-reduction currency overlayprogramme, an investor would normally have conducted an asset allocation study, in which‘hedged equities’ was one of the categories included in the range of assets studied. As aresult of the study, the investor would generally be asked to choose (often with the help of aninvestment consultant) a benchmark hedge ratio for international equities. This is a fundamentalasset allocation decision, similar in strategic importance to the domestic:international equitiessplit, and second only to the equity:bond split decision. Many investors do not have a stronginstinct for currency and its implications, and therefore they often ﬁnd this decision difﬁcultto make. The author’s experience is that as a result this decision can be delayed for years, orindeed never properly addressed. It is a minority of investors who systematically analyse thestrategic role of currency exposure within their portfolio