
94
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Figure 8.35 Five-year rolling correlations, GBP base – correlation between hedged foreign bonds andforeign currency
currency (i.e. for the USD base the ‘Japan’ line is the rolling correlation between monthlyJapanese bond returns fully hedged into US dollars and the Japanese yen’s currency surpriseversus the US dollar; a strong yen gives a positive currency surprise).The USD base graph (Figure 8.32) shows that the overall positive correlations shown inFigures 8.29 and 8.30 do not translate into a systematic effect. Indeed, the most recent 5-year
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period has correlations on average negative. Similar stories of instability apply to the otherbase currencies (Figures 8.33–8.35).All of these correlations exhibit instability in both size and direction. Since we have established above that there is no chance, even in theory, of negative correlations undermining therationale for hedging international bonds, then we can move on to look at the historical datain relation to risk reduction.8.3.3 Volatility reduction from hedging bonds – the historical evidenceIn Figure 8.36 I have compiled the effect on hedging on the volatility of international bondsbaskets from the four currency bases we have been dealing with. There is no doubt whateverthat currency hedging of international bonds is massively risk-reducing. I have conducted anF-test on the two series (monthly unhedged returns and monthly hedged returns); the F-testtests whether two series are samples drawn from a population of the same variance. The F-testresult for all four of the base currencies is 100% – namely we can be 100% conﬁdent thatthe samples are drawn from different-variance populations. The 100% remains at 100% evenif we expand it to 46 decimal places! I think we can be conﬁdent that hedging reduces bondvolatility.14.0%Unhedged vols for international bonds
12.0%
Actual vols for hedged international bonds
Volatility
10.0%8.0%6.0%4.0%2.0%0.0%USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.36 Volatility reduction from hedging – market cap international bond weights (1985–2002)
8.3.4 International diversiﬁcationSimilarly to our equity analysis above, we can look at the effect of diversifying a bond portfoliointernationally, with both hedged and unhedged international bonds. Figures 8.37 to 8.40 showthis from the four main base currencies’ perspectives. These graphs are similar in axes toFigures 8.20 to 8.23 and, to recap, they show the effect on bond portfolio volatility (Y-axis) ofincreasing the proportion of bonds in international (X-axis). The two lines are for unhedgedinternational bonds and fully hedged international bonds respectively. It is immediately clearfrom the graphs what we have already discovered earlier in this section, namely that without
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Figure 8.37 Bond portfolio volatility versus % international bonds, USD base – domestic bonds,international bonds unhedged and 100% hedged (1985–2002)13%12%11%
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Figure 8.38 Bond portfolio volatility versus % international bonds, JPY base – domestic bonds, international bonds unhedged and 100% hedged (1985–2002)
currency hedging, international diversiﬁcation of bonds has no attraction. With hedging, theattraction is varied – for UK investors, diversiﬁcation is very valuable; for DEM/EUR investors,less so.There are two reservations I would have about these graphs. The ﬁrst is that bond investmentfor pension funds and insurance companies is in many cases designed to match liabilities –obligations to pay ﬁxed amounts of pensions for long periods. Many will therefore regard along bond exposure in their assets as the least-risk asset, and may even measure volatilityagainst long bond straight or index-linked returns. Under these circumstances a reduction innominal return volatility may not be an attractive goal.
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10%9%Unhedged
8%
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7%6%5%4%3%0%
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Figure 8.39 Bond portfolio volatility versus % international bonds, DEM base – domestic bonds,international bonds unhedged and 100% hedged (1985–2002)
Vol %
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Figure 8.40 Bond portfolio volatility versus % international bonds, GBP base – domestic bonds,international bonds unhedged and 100% hedged (1985–2002)
The second reservation is that these graphs only show the effect of diversiﬁcation in thegovernment bond universe. Sovereign debt (at least from OECD countries) is as near risk-freeas possible, and indeed is treated as completely ‘risk-free’9 for most purposes. Under risk-free9The academic literature generally refers to risk-free interest rates as those with zero volatility (and therefore zero volatility withother asset classes). By contrast, the practitioner community usually refers to risk-free as meaning sovereign debt of any maturity(which may or may not be zero volatility, depending on the horizon of the analysis). Note that only the sovereign debt of a countryissuing debt in the currency of its own denomination is generally accorded risk-free status. The case of the euro and its constituentcountries is currently puzzling the more thoughtful practitioners.
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conditions, what diversiﬁcation of risk is being achieved by investing internationally? Theanswer is clearly not credit diversiﬁcation, since there is no credit to diversify. In fact what ishappening is that each foreign bond is substituting exposure to the long maturity interest ratecurve domestic country with the long maturity curve foreign country. This happens becausethe currency hedge is one-month rolling – i.e. very short maturity. Whether this is the intendeddiversiﬁcation, I doubt.Box 8.2
Duration
The expression ‘duration’ is a technical term used in the bond investment world to expressthe point (i.e. years ahead) on the yield curve that any particular bond or portfolio of bondsexposes the investor to. This is not the same thing as the maturity of the bond, which is thedate on which the principal is repaid. Why are maturity and duration not the same thing?The answer is because, except for a zero-coupon bond, some of the money from a bondwill come earlier than maturity, in the form of coupon payments.There are two main deﬁnitions of duration – we will start with an intuitively appealingone called ‘Macaulay duration’. This (in words) is the average number of years ahead of allthe cash ﬂows, with the cash ﬂows weighted by their present value using the current yieldto maturity of the bond as the discount rate.Let’s take an example. A USD bond pays 6% p.a., say semi-annually, for 10 years fromtoday’s date, and then repays the principal at $100 per $100 face value. Let us also supposethat the current yield curve is 6%. The reader might like to ascertain that the Macaulayduration is 7.67 years. This maths leads us to see that the higher the coupon, the shorter theduration relative to the maturity. The following graph illustrates this trade-off, showing thecurves at both 6% discount rate and 1% discount rate:Macaulay duration vs. coupon(10 year semi-annual bullet bond)
10.06% Discount rate1% Discount rate
Duration (years)
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A small modiﬁcation to Macaulay duration leads to a deﬁnition called ‘modiﬁed duration’.Modiﬁed duration equals Macaulay duration/[1 + (discount rate/number of coupon payments p.a.)], where the discount rate is the yield to maturity of the bond. The appeal of themodiﬁed duration measure is that even though its unit is years, it is used as an elasticity – amodiﬁed duration of 7 means that for every 1 bp change in the yield curve, there is a 7 bpchange in the value of the bond.
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For those investors who wish to hold the long end of the domestic yield curve, it is possible,although rarely done at the moment, to extend the maturity of the foreign exchange hedge usinginterest rate and/or currency swaps. It is possible (indeed straightforward given the certaintyof bond maths and the liquidity of the swaps) for, say, a UK investor to eliminate the (say)US yield curve inherent in US bonds, fully hedge the currency risk, and ‘go up’ the UK yieldcurve as far as at least 30 years. The diversiﬁcation argument for this structure becomes strongwhen the bond portfolio contains credit, not just sovereigns.
8.4 PROPERTYUsing currency overlay for property portfolios is rare, but not unheard of. However, very littleof the foregoing analysis which we used for equities and bonds has any application to property portfolios. The reason is simple: property cannot realistically be marked-to-market everymonth with prices that are either traded or tradeable. This means that the size of the currencyhedge needed is likely to be a crude ‘current value’ approximation, or another alternative, likecost.However, just because valuation prices are not easy to obtain, or frequent, does not mean thatcurrency exposure has gone away, or is irrelevant. Foreign property portfolios generate currencyrisk without any expected return, and therefore the same arguments that can be demonstratedin support of currency hedging in the case of marketable assets apply here. Where property isheld corporately (for example in property investment companies or investment trusts), then itis quite likely that part of the initial cost would be ﬁnanced by borrowing. Many companieswould borrow in the currency of the residence of the property to hedge the currency risk and,incidentally, give the lender better security.Interestingly, some years ago, one large UK property investment company with substantialforeign property holdings, Hammerson, polled its large investors as to whether they wouldprefer the company to currency hedge their non-sterling assets and income, or not. Surprisingly, a majority of the larger investors (presumably professional institutional fund managers)responded by saying that they would prefer the company to remain unhedged, supposedlyto retain the diversiﬁcation of foreign currency exposure. Perhaps they would have answereddifferently had they read this book!
8.5 OTHER CLASSESIt is possible for currency overlay to overlay any asset, assuming it has some foreign currencycontent. Possible candidates include private equity, hedge funds, commodities, synthetic assetsconstructed with swaps, futures and options, rights of various kinds (copyright, media rights),non-bond monetary obligations such as cash, deposits, T-bills, commercial paper, mortgagesand bilateral debt.For liquid assets, the investor determines the optimum policy for currency hedging usingsimilar analysis to that shown in this chapter. Illiquid assets cannot be analysed using quantitative methods; the decision of whether to hedge, and the benchmark hedge ratio, must betaken on general policy grounds.
9Is the Currency Market Efﬁcient?For an active manager to make money consistently over time in a particular market, then thatmarket must be inefﬁcient. The use of this word originated in academic ﬁnancial theory,1 andmeans only that the market price does not always reﬂect the information then available. If, bycontrast, a market price does always represent all the information available, then it is called‘efﬁcient’.
9.1 TYPES OF INEFFICIENCYThe academic literature2 has highlighted three (rather arbitrary) levels of efﬁciency.Weak form efﬁciency is where past prices are not predictors of future prices. This means thatany model (equation, chart, mechanistic trading process) that uses past prices of that marketas the only input will not be found to have predictive power – i.e. future price movements willnot be provably different from random for any price-only-based model.Semi-strong form efﬁciency is where all public information about a market is already in theprice, and models that use public information to predict that market’s future prices will nothave predictive power.Strong form efﬁciency is where all information about a market, private and public, is alreadyin the price. Under this, strongest, form of inefﬁciency no model, process, information, expertise, insider status, or indeed anything can improve the predictability of prices above random.Strong form efﬁcient markets would not reward active managers, or hedge funds, with addedvalue, however expert they were.I mention it elsewhere, but it is vital that the reader understands that calling the currencymarket ‘inefﬁcient’ is not the same thing as questioning the efﬁciency of its operation. InChapters 3 and 4, I have explored in some detail the extraordinary size, diversity and liquidityof the foreign exchange market, and in Chapter 6 I have shown the extremely narrow bid/offerspreads (i.e. transaction costs) that can, and have, been achieved in executing currency contracts.All of this information, and comparative information from the other main ﬁnancial markets,leads us to conclude that the foreign exchange market is the most transactionally efﬁcientmarket in the world. This meaning of the word ‘efﬁcient’ is not related in any way to thequestion I want to address here.Concepts of efﬁciency are very ‘pure’ concepts, and in reality markets are the result ofconstant human activity, motivations and necessity, and these are not ‘pure’ processes. Thereare probably no markets in the real world that correspond to the strongest efﬁciency model,although this is a highly contentious subject. I will stick to the currency markets, and arguebelow that currency markets are certainly not efﬁcient in at least one sense.
1
See Fama, E.F., ‘Random walks in stock market prices’, Financial Analysts Journal Sept/Oct (1965).See also two surveys by Fama: Fama, E.F., ‘Efﬁcient capital markets’, Journal of Finance 46 (1991) 1575–1617 and Fama,E.F., ‘Market efﬁciency, long-term returns and behavioural ﬁnance’, Journal of Financial Economics 49 (1998) 283–306.2
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9.2 MAKING THE CASE FOR CURRENCYMARKET INEFFICIENCYTo make the case that active currency management with a well-founded expectation of successis possible, I ﬁrst have to demonstrate that the currency markets are inefﬁcient at some level.Fortunately, I do not have to enumerate all the myriad possible ways in which inefﬁciency mayexist; I only have to describe or demonstrate one convincingly, and I will have disproved theefﬁciency hypothesis. I will start with a somewhat anecdotal description of one of the functionsof currencies and exchange rates, and go on from there to test a hypothesis that ﬂows naturallyfrom the description.9.2.1 Cyclical behaviourCurrency exchange rates perform a fundamental function in the global economic system – thatof a negative feedback loop for the current account performance of individual countries. Letme elaborate.Suppose an individual country, for whatever reason, begins to run a current account deﬁcit –i.e. its imports are greater than its exports (including invisibles). This means that there is anexcess supply of that country’s currency which will have to be mopped up by capital accounttransactions – foreign borrowing, asset sales to foreigners or inward foreign investment. Whilethe capital accounts of most advanced economies are well developed enough to cover manyyears of normal deﬁcits, in the end the appetite for this ‘surplus’ currency will run out. Whenthis happens, the currency will fall as sellers of excess currency fail to ﬁnd buyers, and theypress the need for sales by offering the currency at lower prices. A falling currency will raise thedomestic price of imports, and cheapen exports when viewed from abroad. This will stimulatethe latter and inhibit the former, although with a potentially long and variable lag.3None of these adjustments happen quickly, and the depth of capital markets now means thatthis adjustment process can be delayed for years. However, in extremis, currency weakness(or strength, the argument vice versa) is ultimately the author of a fundamental rebalancingof an economy back towards equilibrium. The buffer effect of the capital account is furtherstrengthened by the long lags in the real economy in response to price changes. As an example,the US steel industry, decimated by the strength of the US dollar in the mid-1980s, startedseriously closing plant and cutting capacity in 1984/5, almost at the high point of the dollar,and ﬁve years into the dollar bull run. Two years later, the dollar had fallen far enough to makeUS steel competitive again – but too late.This is what engineers call a negative feedback loop with a lag. Any competent schoolphysics student will tell you that negative feedback loops with lags (and without dampers) cancreate oscillation. The evidence is that the frequency of exchange rate oscillation is variable,but measured in years not months.9.2.2 Lack of statistical arbitrageOscillations which evolve over time with smooth price adjustments create proﬁtable opportunities for active currency participants. Under these conditions, simple trend-following modelswill be proﬁtable – but the behaviour of these proﬁt-seeking participants will tend to eliminate3
The lag is the origin of the ‘J’ curve of economics textbooks.
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such trends. They will buy appreciating currencies (and vice versa), which will tend to increasetheir price and reduce the expected gain. In a market which is dominated by proﬁt-seekingparticipants, such behaviour would be expected to completely eliminate any opportunity forconsistent gain. This is what happens in most securities markets where inefﬁciencies begin toemerge.But the currency market is not dominated by proﬁt-seeking participants, and therefore thisarbitrage is not fully eliminated. The currency market is dominated by highly constrained(but active) players like the ICCs, fund managers, portfolio investors and central banks (seeChapter 4). To exploit this particular inefﬁciency, proﬁt-seeking participants need to have akey characteristic: a long horizon. A long horizon because the inefﬁciencies I have describedare likely to emerge over a full currency cycle, and may be unreliable at shorter horizons. Thehorizons could be ﬁve years or more.There is a shortage of long-horizon risk capital for this arbitrage, and not surprisingly.The opportunity is not self-evident; the appropriate method of exploiting it is not universallyagreed; many former active participants have failed to capture the opportunities because ofoverconﬁdence and a misunderstanding of the nature and role of modelling in this context (thehedge funds ‘yen-carry trade’ of 1998 stands out). And, most importantly, it is a zero-sumgame in a world where the creation of wealth through equity appreciation is positive-sum. Thismakes it a poor cousin of the simple expedient of taking long (not necessarily active)-positionsin equities.
9.3 EMPIRICAL EVIDENCE FOR MEDIUM-TERM TRENDSIf the currency market is inefﬁcient by the nature of its structure, do we have ﬁrm evidenceof this in the evolution of prices over history? The answer is yes, and Figure 9.1 illustratesone particular way of presenting the evidence. The vertical axis shows the volatility of the
18%
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 9.1 Volatility measured at different horizons – volatility of currency surprise 1981–2002, dailyvolatility annualised and annual volatility
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historical series. The hatchedannualised volatility4 calculated from daily prices,√ bars show the5annualised by the standard 262 multiple. The black bars show the annual volatility calculatedfrom observing the one-year forward price on one day, and the spot price (for delivery on thesame day) one year later. This test is repeated daily for the 22 years of historical data (i.e. 5455times, ignoring the ﬁrst year of daily vols to avoid possible data bias), and the volatility of theresulting return series is measured using standard statistical techniques.We can present the same data in a different way. For each currency, the annual volatility canbe represented as a ratio to the annualised daily volatility. Because all the annual volatilitiesare larger than the annualised daily, all the ratios will be higher than one. Figure 9.2 shows thedata presented in this way.1.401.35
95% Significance level
Ratio of Volatilities
1.301.251.201.151.101.051.00JPY/ USD
JPY/ DEM
JPY/ GBP
DEM/ USD
DEM/ GBP
USD/ GBP
Figure 9.2 Volatility ratios measured at different horizons – ratio of annual volatility to daily volatilityannualised (1981–2002).
When the annual volatility is greater than the daily, then the volatility of currency returns ata one-year horizon is greater than would be expected from a lognormal random walk series,and the series is exhibiting positive serial correlation of returns, or annual trends. When theannual volatility is less than the daily, then the volatility of currency returns at a one-yearhorizon is less than would be expected from a lognormal random walk series, and the seriesis exhibiting negative correlation of returns, or annual mean reversion. Is this a statisticallysigniﬁcant ﬁnding?The annual data is overlapping, so standard tests for signiﬁcance would be suspect. Instead,we can apply a Monte Carlo simulation, in which the identical calculations as described aboveare performed on a lognormal random number series generated using the observed average22-year daily historic volatility. We have recorded the distribution of ratios (daily annualisedto annual), and derived a standard deviation of these ratios. The signiﬁcance level shown in4Volatility is the standard deviation of price changes. We have used log-transformeddata to eliminate additive approximation√errors. [Using Excel notation: if r = ( pt / pt−1 ) − 1, then annualised vol = Exp( 262(Stdev(ln(r + 1)))) − 1, where pt is the FXmarket rate on day t.]5262 is the number of weekdays in the year. The Central Limit Theorem tells us that we annualise volatility using the root function.
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the graph is the 95% conﬁdence level from this distribution. Figure 9.2 tells us that all of thecurrency pairs shown have exhibited annual trends over 20 years of data, and all but one areindividually signiﬁcant at the 95% conﬁdence level. But taken together, are these results reallystatistically signiﬁcant?Using the Central Limit Theorem, we can test whether the average of the sample of sixcurrencies lies outside the range contemplated by a random generator. The average ratio of thesix currencies is 1.26. The SD of the average of six randomly generated ratios is 0.052. Themean ratio of randomly generated series is 1.00. This makes the average of the six currencies(1.26 − 1)/0.052 = 4.99 SDs away from the mean. This is signiﬁcant at the 99.99997% level.I will refer to the most obvious hole in this analysis – the choice of currencies. The ﬁrstpoint is that the reader will recognise the four main currencies (USD, JPY, DEM, GBP) fromBox 9.1
Trends
It is commonly asserted, and not only in relation to the currency markets, that there are‘trends’ in markets. But what are trends, and how can we identify them?Let’s start by stating what kinds of markets do not exhibit trends. These are the theoreticalconstructs of classical ﬁnance theory. Under these assumptions, markets exhibit ‘lognormalrandom walk’. This means (roughly) that the percentage change in the market each period(say one day) is normally distributed, with a mean of the expected market return. (For theexact description, see Appendix 2.) Under these assumptions, each daily (weekly, monthly)movement is independent of every other, and indeed independent of any other variable.This market will not exhibit trends.If, then, we can establish from the historical record sufﬁciently consistent data to rejectthe classical hypothesis, we can say that a market exhibits trends. Mathematically, we canexpress period return with the equation:Returnt = α + β(Returnt−1 ) + εwhere ‘Return’ is the currency surprise in the period and ε is a random normal variate.If we can demonstrate that β is positive and signiﬁcantly different from zero, then wecan reject the ‘no trend’ hypothesis. If β is negative and signiﬁcantly different from zero,then the market can be said to be mean-reverting. Note that in reality, relationships may beunstable, and changing the periodicity of the data (daily, monthly) may change the resultsof the tests. This test is conducted in Chapter 10.There are other, more sophisticated and sensitive ways of establishing trending behaviour.One of these is the volatility/horizon analysis conducted here.all the other chapters in the book. These currencies were chosen not because they ‘trend’, butbecause they are the largest in the world. The six pairs are just all the possible pair combinationsof the four.The other possible attack from a statistical point of view is that currency pairs are notindependent (i.e. USD/GBP is not statistically independent from USD/DEM), and thereforeif one or more are trending, it is more likely that they all will be. There are two points here.The ﬁrst is that while returns from the two pairs (like the two cited) may be correlated, thatdoes not imply that the ratios of daily annualised to annual SD must be correlated. Secondly,since we are trying to identify inefﬁciencies, the fact that these inefﬁciencies arise in a group
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is largely irrelevant – if they are there they can be identiﬁed and exploited. However, whilethe scale of the conﬁdence (99.99997% level) is undoubtedly overstated by my simple maths,even if there was 100% correlation between currency return series, the average ratio of 1.25would still be signiﬁcant at the 98% level. The truth is somewhere in between.While it is possible for a purist to pick these kind of holes in this ‘proof’, the length ofthe data, and the strength and consistency of the effect, must force us to abandon the efﬁcientmarket hypothesis. But we will not have to rely on this observation alone.
9.4 FORWARD RATE BIAS – ANOTHER INEFFICIENCYWhat is the forward rate bias (FRB)? The FRB is the name given to the collective observationthat, on average, the spot rate of a currency whose forward rate is at a discount (higher interestBox 9.2
Forward rate bias
The ‘forward rate bias’ is a theory rather than a fact. It hypothesises that where a pair ofcurrencies have a liquid forward market, the forward rate of higher interest rate currencyis a biased estimator of the future spot rate. The bias in this theory is one-way, the higherinterest rate currency is expected to show a positive currency surprise. In other words, theforward discount of the higher interest rate currency is too large: the spot rate will notdepreciate as much as predicted by the forward rate.The forward rate bias theory has ﬁrm support from the historical price record. We can,however, only reliably test about twenty years’ data. Longer periods of data run into problems of illiquid forward markets, and of ﬁxed exchange rates.There are three plausible explanations for its hypothesised existence. The ﬁrst is the ideathat the higher interest rate currencies are ‘less attractive’ or ‘lower quality’ than the lowerinterest rate currencies. Under this theory, these currencies would offer a ‘risk premium’to persuade international investors to hold them rather than lower risk currencies. The riskpremium cannot just be higher interest rates – international investors’ exposure to a currencyis a combination of the interest rate and the movement of the spot rate. Hence the forwardrate bias theory.The second explanation is the domestic monetary policy argument. High interest ratecountries are often those where domestic monetary considerations overwhelm all others.A high interest rate country’s government may choose to hold rates higher, and for longer,than international economic considerations may warrant.Finally, there is a school of thought that says that currency market participants sufferfrom ‘nominal price illusion’. This says that, for example, a period of price stability (i.e. thespot rate remaining unchanged) is seen by the market as just that, whereas in fact a periodof price stability for a high interest currency is a period of currency surprise appreciation,and vice versa.rate currency) does not depreciate as much as the forward rate predicts. This also means thatthe spot rate of a currency whose forward rate is at a premium (lower interest rate currency)does not appreciate as much as the forward rate predicts. Currency forward discounts and
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premiums are always relative to another currency – so the FRB phenomenon is always aboutcurrency pairs.9.4.1 What is the evidence for the FRB?Numerous studies have found evidence of bias. Simply presented, in the equation:Currency surprise = a + b (previous period forward discount/premium) + e (error term)we must reject the unbiasedness of the forward rate if we can show that b explains a signiﬁcantproportion of the currency surprise. We measure signiﬁcance with a ‘t-stat’ for the coefﬁcientb – over 1.96 means we are more than 95% conﬁdent that the forward discount/premium hasgenuine explanatory power for the currency surprise.If we take monthly data, Table 9.1 shows the extent of the bias based on 1980–2002 exchangerates. The row and column headers deﬁne the pairs of currency that relate to the t-stats, andthe ‘P’ value in brackets is the conﬁdence we can have that the effect is genuine. From thistable we can see that the FRB