forexample under ‘USD base’, the graph shows the correlation coefﬁcient between hedged EAFEand EAFE-weighted EAFE currencies.0.50.40.30.20.09
0.10.0−0.1
0.01−0.01
−0.03Negative correlation required for currencyto be diversifying
−0.2−0.3−0.4−0.5USD Base
JPY Base
DEM/EUR Base
GBP Base
Figure 8.1 Correlations between currencies and equities – correlation between hedged equities andcurrency surprise of the same market (market cap basket wieghts 1980–2002)1The currency series is the market-cap-weighted sum of the one-month currency surprises of three currencies versus the basecurrency. The equity weighting is from MSCI, and the currency data is from Record Treasury’s database. The equity return series arecountry indices from MSCI (including net dividends). The EUR is DEM prior to 1999.
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I have also shown the negative correlations that would be required for the addition of currencysurprise (i.e. holding the equity unhedged) to be diversifying.2 These are different for eachbase currency and international asset pair because the underlying volatilities are different. Ifthe currency and hedged equity volatility are identical, then the break-even is –0.5. The readercan see from the formula in the footnote that there is a linear relationship between this valueand the relative volatility of the currency and equity.8.1.3 Individual currency:equity correlationsFigure 8.1 shows the ‘rest of the world’ correlations for four base currencies. But what doindividual currencies:equities look like? Figure 8.2 shows the 12 relationships (four basecurrencies each with three ‘foreign equity markets’). It is notable that the individual countrycorrelations are more variable than the ‘World ex domestic’ baskets. In particular, the Germanequity market has a negative correlation with the DEM from two base currency perspectives –USD base and GBP base. As we saw above, this will mitigate the additional risk from holdingGerman equities unhedged, and reduce the impact of hedging. I will look into this more deeplybelow.0.5
US equities
0.4
Japanese equities
0.3
German equities
0.2
UK equities
0.1
US JAP GER UK
0.0−0.1−0.2
Minimum negativecorrelation required forcurrency to be diversifying
−0.3−0.4−0.5USD Base
JPY Base
DEM/EUR Base
GBP Base
Figure 8.2 Correlations between currencies and equities – correlation coefﬁcients between hedgedforeign equities and same-country currency surprise for each base currency (1980–2002)
In Figure 8.2, two examples of break-even values for currency exposure to become diversifying are included. For EUR equities/currency from a GBP base, the value is signiﬁcantly lessnegative than –0.5 (at –0.23) because this currency relationship is less than half as volatile asGerman equities. In contrast, the value for US equities and currency is –0.38 from a JPY base.The dollar is nearly as volatile a market as the hedged US equity market when looked at froma Japanese point of view.2For the mathematically minded, currency exposure becomes diversifying (i.e. reduces volatility) when the correlation coefﬁcientis more negative than −(SD currency surprise)/[2 × (SD hedged equity)].
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0.600JapanGermanyUK
0.400
0.200
0.000
− 0.200− 0.400− 0.60085
86
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Year
Figure 8.3 Five-year rolling correlations, USD base – correlation between hedged equity and foreigncurrency
0.600USGermanyUK
0.400
0.200
0.000
− 0.200− 0.400− 0.60085
86
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00
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Year
Figure 8.4 Five-year rolling correlations, JPY base – correlation between hedged equity and foreigncurrency
8.1.4 Stability of correlationsFigure 8.2 shows that equity:currency correlations are close to zero, and certainly far from thelevel of negative correlation required for currencies to be diversifying. Is this a stable ﬁnding,
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0.600
0.400
0.200
0.000USJapanUK
− 0.200− 0.400− 0.60085
86
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Year
Figure 8.5 Five-year rolling correlations, DEM/EUR base – correlation between hedged equity andforeign currency0.6USJapanGermany
0.4
0.2
0.0
− 0.2− 0.4− 0.685
86
87
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92
93
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98
99
00
01
02
Year
Figure 8.6 Five-year rolling correlations, GBP base – correlation between hedged equity and foreigncurrency
or do correlations vary? Figures 8.3 to 8.6 show the 5-year rolling correlations for the same20-year period for each of the currency bases.It is clear that correlations are not very stable over time, and we should be wary of constructingmodels, hypotheses or strategies which are sensitive to speciﬁc correlation assumptions. One
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observation is notable in USD and GBP base currencies – namely that Germany has displayedquite a strong negative correlation between its equity market and its currency over the 1990s.We will investigate this further.8.1.5 Summary on correlationIn summary, all the available evidence points to there being no systematic bias (with thepossible exception of Germany) towards either positive or negative correlation between equitiesand currencies.3 This supports the no-correlation assumption made earlier in the book, andmeans that currency exposure does not have a natural place on grounds of negative correlationin international (or indeed any) portfolios. The time-speciﬁc variability of correlations alsomeans that we should be wary of spurious claims for correlation on the basis of limited-perioddata.8.1.6 Embedded currencyBefore reviewing the historical evidence of currency exposure on international portfolios’volatility, I want to turn to the correlation evidence cited above on embedded currency exposurein international equities – what has been coined the ‘BP’4 problem.8.1.7 Firm level analysisWe have two choices for examining the role of currencies in the performance of a company:(a) To attempt an individual corporate income/expenditure and balance sheet analysis brokendown by currency, or(b) To tease it out at equity return level using statistical measures.While the former may seem the ‘best’ or ‘pure’ route, there are two fatal objections to thisapproach.The ﬁrst is that the ‘corporate cash ﬂow analysis’ suffers from the same problems as theassumption that a UK-quoted equity is a GBP risk, or a German-quoted company is a EURrisk. A signiﬁcant number of corporate cash ﬂows occur in one currency, but are stronglyinﬂuenced by the level of another currency. Car manufacturers, hotels, downstream oil andchemical processors, commodity and food manufacturers and processors, utilities, telecomsand even farmers fall into this category to a greater or lesser extent – all may appear to havelargely local currency payables and receivables, but are affected by currencies. So just analysingthe currency of denomination in payables and receivables is likely to confuse rather than clarifythe corporates’ currency exposure.5If one fatal objection wasn’t enough, the other is that even if a company is transparentlyexposed to a particular currency or currencies, it is irrelevant if the market valuation of the3The other exception is Canada. In Canada, there is sufﬁcient negative correlation between non-domestic (i.e. US equities) andUSD/CAD to render hedging USD from a CAD base ineffective for volatility reduction.4So called because of the uncertainty as to whether BP is a sterling-based company (currency of accounts, head ofﬁce, mainquotation) or a dollar-based company (head ofﬁce of two large acquisitions, Amoco and Arco, and currency of denomination of oil,its dominant product).5The author has over 20 years advised many multinationals on these issues, and indeed pioneered in the early 1980s the hedgingof ‘invisible’ exposures not accounted for by foreign currency payables and receivables.
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Box 8.1
163
Embedded currency exposure
Currency exposure conventionally arises from investment in securities of different currencydenomination from the home currency. So UK pension fund investing in US Treasury bondsis unequivocally a denomination-based exposure.Let us suppose, however, that a UK pension fund invests in a US oil company. Ostensiblya US dollar investment, complete with currency exposure. If this company is taken over bya UK oil company, and the denomination of the share quote changed to sterling, has all thecurrency risk been eliminated?The answer is more complicated than at ﬁrst might appear. It is possible to determinehow much ‘foreign currency’ content any security has by analysing the ‘elasticity’ of theprice (expressed in the home currency) with respect to currency movements. A ‘pure’ dollarinvestment (say US T-bond) would show 100% elasticity of sterling price movement withrespect to the dollar. However, the oil company in the example above might show 50%elasticity with respect to the dollar (reﬂecting the strong US dollar earnings stream).This exercise can be conducted at index level, rather than at individual security level, andcan determine whether classes of equities have any foreign currency exposure embeddedin them. A 20-year study (Diversiﬁcation – op. cit.) shows that the UK equity market hasabout 19% US dollar content. The German equity market has about 40% US dollar content,and rising. The US equity market has no foreign currency content. Bond markets have noforeign currency content.This raises the questions of whether, for example, German investors in their domesticequity market should hedge their embedded currency exposure, and whether US investorsinvesting in UK stocks should hedge only 80% of their value. In practice, the concept ofembedded currency exposure has only been adopted by isolated investors and corporations,and not generally.business does not respond in a systematic way to changing currency values. There is littleevidence that valuation processes are that consistent – and anyway the way to test this is toconduct a statistical test on equity market returns, which is what we will do – i.e. option (b).At the company level, it means that there are businesses which are notionally UK- andsterling-based, such as BP, which deal in international markets (mainly priced in dollars), whichin the BP case are comprised of signiﬁcant portions of fully US businesses (Arco, Amoco).It is reasonable to assume that these businesses will have a positive correlation between theirproﬁts (expressed in sterling) and dollar returns versus sterling. Strong dollar, higher proﬁts;weak dollar, lower proﬁts.From an investment perspective, however, the level of proﬁt is not a direct determinantof equity returns. In determining hedging strategy, we must concern ourselves with equityreturns, not with corporate proﬁts. So the question is: is there positive correlation betweenequity returns for BP expressed in sterling, and dollar returns versus sterling? If there is acorrelation, how much of BP proﬁts are ‘really’ dollars?We can test this proposition, and the rolling 5-year correlation graph of Figure 8.7 is theresult. This shows a surprisingly stable result, and implies that there is a consistent (but quitesmall) ‘dollar content’ in the BP sterling share price.We can test the same data series using a different approach, which will indicate the proportionof BP returns that are dollar-denominated (rather than the proportion of the volatility which
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0.6
0.4
0.2
0.0
− 0.2− 0.4− 0.693
94
95
96
97
98
99
00
01
02
Year
Figure 8.7 Five-year rolling correlation between BP £ share price returns and dollar surprise(1988–2002)
is explained by exchange rate volatility). Firstly, we hypothesise the existence of a particularcurrency embedded in an equity’s return. For example, we would hypothesise quite naturallythat BP £ equity returns had USD embedded in them. We then apply an overlay to neutralisethis currency exposure, and we can examine a range of hedge ratios from 0% to 100%. Forthe avoidance of doubt, the overlay in this example would be for the UK investor to sell USDvs. GBP forward, the amount being a proportion (between 0% and 100%) of the value ofthe UK equity valuation. This forward sale, in common with all passive currency overlay,would be rolled at the maturity of the forward contract. This process would produce a seriesof proﬁts and losses, or ‘currency overlay returns’, which would be added to the returns of theunderlying assets. The question of whether there is any embedded USD exposure could thenbe observed by measuring portfolio volatility (the portfolio equals UK equities plus overlayreturns) in relation to the ‘hedge ratio’. Note that this process is applied if our hypothesis isthat BP earn USD net; we might think that other UK companies, for example, pay USD (oranother currency) net.The ‘low point’ of the curve in the graphs that follow will indicate the optimum proportion ofdollars to be hedged from a UK perspective, and therefore give an indication of the proportionof ‘embedded dollars’ in the equity return series.Figure 8.8 shows that the optimum hedge ratio is around 40% – implying (very loosely)that 40% of BP’s investment returns are dollar-denominated. It should be emphasised thatcurrency surprise only accounts for some 2.5% of the total volatility of the BP share price, sothe importance of this effect should not be overestimated.There is an interesting question (although largely academic) as to whether the key driver ofthe ‘dollar content’ (or any other currency) of equity prices is:(a) The equity-market-wide response to exchange rate moves(b) The domicile mix of ownership
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26.0%
Vol %
25.5%
25.0%
24.5%
24.0%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% Hedge ratio
Figure 8.8 Volatility of BP share price versus hedge ratio – BP £ returns ‘hedged’ with a short dollaroverlay versus sterling (1988–2002)
(c) The trading ‘weight’ in different share listing environments (e.g. UK listing vs. NYSElisting), or(d) The genuine economic impact of exchange rates on a business.Because the question is interesting rather than critical, I will not devote a signiﬁcant amountof time trying to ascertain the importance of each of these elements. However, we can conducta couple of simple tests which might help to eliminate one or more of these elements.I will examine the behaviour of a widely held, large cap UK stock, but this time with noostensible US dollar income or expenditure. I have chosen Tesco, a UK supermarket chain withlittle international activity. Figure 8.9 shows the same measure as that above: the volatility ofthe ‘hedged’ return series versus the hedge ratio (remember that the hedge is to sell dollarsvs. sterling – eliminating any ‘embedded dollar exposure’ if there is any). The result is pleasingly intuitive. The graph shows that Tesco shows no embedded dollar returns in its equityreturns – any addition of a dollar ‘hedge’ increases the volatility of the Tesco equity returnseries.These two graphs might lead us in the direction of thinking that it is the underlying economics of a business that are the main determinant of the equity returns’ sensitivity to exchange rate movements. However, if we look at a third stock, HSBC – the banking group –we get a confusing message. Using the same analysis and graph design, we get Figure 8.10.This shows a continuous reduction in equity volatility with increasing hedge ratio. It impliesthat all of HSBC’s proﬁts (and more (actually 150%) if we extrapolate the curve) are derived from dollar-based sources. It may be plausible that a signiﬁcant proportion of HSBC’sproﬁts are dollar-related, but given its substantial interests in the UK and non-dollar locations elsewhere, it is implausible that it is exposed to the dollar to more than 100% of itsproﬁts.
166
Currency Overlay28.0%27.5%27.0%
Vol %
26.5%26.0%25.5%25.0%24.5%24.0%0%
10%
20%
30%
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50%
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100%
% Hedge ratio
Figure 8.9 Volatility of Tesco share price versus hedge ratio – Tesco £ returns ‘hedged’ with a shortdollar overlay versus sterling (1988–2002)
40.0%
39.0%
Vol %
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36.0%
35.0%0%
10%
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100%
% Hedge ratio
Figure 8.10 Volatility of HSBC share price versus hedge ratio – HSBC £ returns ‘hedged’ with a shortdollar overlay versus sterling (1988–2002)
It seems more likely, therefore, that some of the explanation of this apparent exposure to thedollar lies in the other three reasons. We could continue the exercise ad inﬁnitum, with eachstock generating a different proﬁle. But of more value for our purposes is to move on to theequity returns at the country level.
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8.1.8 Country index equity returnsI would remind the reader that we assumed that all these companies earned USD net. As itturned out from the result, it was not an unreasonable assumption to make. However, we mightthink that there are UK companies (say net importers) which pay USD net. In this case wemight like to test an overlay which had rolling purchases not sales of USD against GBP.We should perhaps allow for this eventuality by allowing the hedge ratio to vary from–100% (100% purchases of USD vs. GBP) to + 100% (100% sales of USD vs GBP). We haveconducted this test on the UK, and Figure 8.11 shows the UK market/embedded USD exampledescribed tested over 22 years (1980–2000).25%24%
No hedging23%
Vol %
Lowest vol hedge ratio20%22%21%20%19%18%−100%
−80%
−60%
−40%
−20%
0%
20%
40%
60%
80%
100%
Hedge ratio % (+ = sell dollars)
Figure 8.11 Hedging embedded currency, GBP base – volatility of UK equity market versus hedgeratio of USD overlay (1980–2002)
It shows a small reduction in overall portfolio volatility (compared to ‘unhedged’) with theminimum volatility at around 20% hedge ratio. This might be thought of as the amount of theembedded net USD exposure in the UK equity market being around 20%,6 or alternativelyit might well be a spurious result (particularly given the small volatility reduction achieved).How can we tell the difference?One way is to look at stability. Figure 8.12 shows the same graph for four non-overlapping5-year periods (I have normalised the absolute start level of volatility to make the graph morereadable). This shows a signiﬁcant apparent increase in the ‘USD’ content over the past 20years. In the last 5-year period, the low point of volatility is at a hedge ratio of 74%, comparedwith a ‘lowest volatility’ hedge ratio of −15% for 80–85. There is probably not much point‘overmodelling’ beyond what we have. We can easily ex post rationalise that the world has gotmore ‘global’; that the USD has increasingly become the numeraire of international business;that the US pension fund perspective dominates global equity market behaviour; that the UKbusinesses that now dominate the UK indices (TMT, oil, ﬁnancial) are global in nature, and‘dollarised’ in outlook. However, I suggest that however plausible all these are, they are still expost rationalisations, and the ﬁrm evidence supporting a large USD content in the UK market6
It also implies that the optimum hedge ratio for hedging UK equity exposure from a USD perspective is 100% − 20% = 80%.
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28%26%
Vol %
24%
No hedging
22%20%
80–8518%
86–9091–95
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96–02
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−60%
−40%
−20%
0%
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Hedge ratio % (+ = sell dollars)
Figure 8.12 Hedging embedded currency – volatility of UK equity market versus hedge ratio of USDoverlay (1980–2002, 5-year tests)
is slim. I would also point to the very low explanatory power of the USD in the 20-year returnsof UK equities – a regression of the two variables shows an R 2 of 0.015 (i.e. that the USD‘explains’ only 1.5% of the total equity market variance) and a ‘just signiﬁcant’ t-statistic forthe USD of 2.03 (statistically signiﬁcant t-stats are higher than c. 2).This line of enquiry opens up a huge amount of potential empirical testing: what aboutall the other currency weights in the UK market? What about all the other markets and alltheir foreign currency weights. Regression, a (rather abused) statistical technique, allows us totest whether any number of independent variables (in this case currency returns) provide anyexplanation for one dependent variable (in this case domestic equity returns). The results ofthe regression can estimate both the size of the effect, and its statistical signiﬁcance. We haveperformed single regressions7 for each of our four major base currency equity markets (US,UK, Japan, Germany), and the results are summarised in Table 8.1.Regression results always need to be treated with caution, and these results particularly so.There appear to be only three currency:equity relationships with any explanatory power at all:(a) A weight of 19.5% of dollars in the UK equity market(b) A weight of −25.7% of euros in the Japanese equity market(c) A weight of 31.7% of dollars in the German equity market7In conventional (econometric) modelling, multiple regression is the standard approach to estimating variable signs, weightsand signiﬁcance. However, where the explanatory power of the independent variables (in this case individual currency surprises) islow, and the independent variables are signiﬁcantly correlated with each other (which they are in this case), multiple regression canthrow up spurious results. One way round this problem is to perform separate regressions for each single independent variable (singleregression), and I have chosen this technique. The reader may like to note that the (currency) weights of the variables in the regressionresults are very close to the hedge ratios that give minimum volatility (compare Figure 8.11 and the weight of USD in the UK marketin Table 8.1).
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Table 8.1 Embedded currency weight and sign(t-stats in brackets) – regression coefﬁcientsmonthly data (1980–2002)Equity market
Embedded currencyUSD
US
GBP
JPY
EUR
Neg
Neg
Neg
UK
19.5%(2.0)
Japan
Neg
Neg
Germany
31.7%(2.8)
Neg
Neg
Neg−25.7%(2.4)
Neg
Note: A t-stat greater than approximately 2 is statisticallysigniﬁcant. Where the regression that produces these valueshas an R 2 of less than 1%, I assign ‘Neg’ = negligibleimpact.
We have discussed item (a) at some length earlier. The effect is weak, but it is plausible. Weknow the relationship to be unstable, currently with rising dollar weights, and with a number ofdifferent possible explanations. My favourite explanation is that rising dollar weights indicatea combination of the internationalisation of some of the heavyweights of the UK indices (BP,Vodafone, HSBC), together with a rising weight of international (particularly dollar) investorsin the UK market. It is notable that on current (December 2002) market capitalisation andexchange rates, the UK is easily the largest equity market outside the US. This makes it thenumber one target of US investors, the largest group of international equity investors.Item (b) indicates that the Japanese equity market returns are negatively correlated with theDEM/EUR. This is a bizarre ﬁnding, implying, inter alia, that the companies making up theJapanese equity market are net importers of euro-denominated goods (which they are not).It is hard to ﬁnd other plausible explanations, and frankly I suspect that this ﬁnding may bespurious (i.e. chance). This feeling is supported by the split test: the relationship is strong forthe 1980–1991 period, and absent for the 1991–2002 period. I would therefore suggest that thenull hypothesis embedded in the assumptions for the theoretical case made above – namely nocorrelation - is maintained intact.Item (c) appears to be a more secure ﬁnding. It implies that there is a signiﬁcant weightof dollar returns in the German (and by association, European) equity market. The effectappears to have increased over the past 20 years, and it is highly plausible that this has comeabout through the same inﬂuences as the dollar impact on the UK market. The strength of therelationship, however, may be greater than the UK’s because there is little in the way of German(or indeed European) institutional investment; the dominant investors (and at the margin) inthe German equity market are US investors.8.1.9 International equity correlationsWe have spent a considerable amount of time examining the question of currency:equity correlation, since our theoretical model earlier in the chapter assumed a currency:equity correlation
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of zero. We have uncovered scant evidence to abandon that hypothesis. But what about thehistorical evidence as it applies to our theoretical analysis of international equity correlations?We set up a theoretical example above, in which we assumed that domestic equities hadan annualised volatility of 16%, unhedged international equities had a volatility of 16%, andcurrency surprise had a volatility of 11%. We assumed that domestic and unhedged internationalhad a correlation of 0.5, and we predicted that domestic and hedged international would have an‘apparently higher’ correlation of 0.69, despite the fact that the covariance was unchanged. Wesaw that this was due entirely to the reduction in volatility of the international assets throughhedging, and not through any loss of ‘diversiﬁcation’. How does this theoretical predictionmatch up with the historical evidence?In Figure 8.13 we show (for 1980–2002) the actual historical correlation for domestic:unhedged international equities for each of four base currencies versus the ‘World exdomestic index.’ From this information, we make a theoretical prediction of the expected correlation for domestic:hedged international equities, and show the actual observed correlationfor comparison. The graph also shows the average correlations for all currency bases.1.0
Correlation Coeff.
Unhedged international equities
0.9
Theoretical correlation for hedged international equities
0.8
Actual correlation for hedged international equities
0.70.60.50.40.30.20.10.0USD Base
JPY Base
DEM/EUR Base
GBP Base
Average allcurrencies
Figure 8.13 Correlations between domestic and international equities – international equities unhedgedand hedged (‘World ex domestic’ weights, 1980–2002)
The graph illustrates that the increases in correlation are close to what we would havepredicted. The middle (upward striped) bar shows the increase expected purely from historicalvolatility reduction, and the right (horizontal striped) bar shows the actual historical correlation.The average of all currency bases shows that there is little overall difference in the theoreticaland actual correlation values.8.1.10 Volatility reduction – the historical evidenceIn this section we will examine the volatility of portfolios containing international equities (bothhedged and unhedged), and compare theoretical expectations with actual observed. We haveestablished that, broadly speaking, equity:currency correlations are zero. We therefore expect
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that currency exposure will always increase volatility, and conversely that hedged internationalequities will always have lower volatility than unhedged international equities. On the basisof the historical volatilities of equities and currency, we can theoretically predict the volatilityincrease from taking currency risk (see Chapter 5 for the theory), or expressed another way,the reduction in risk for eliminating currency risk. Figure 8.14 shows the results for ‘Worldex domestic’ for the four base currencies and the average. Note that all the hedges are 100%,despite the fact that we have identiﬁed above that hedge ratios less than 100% may be optimallyrisk-reducing.22.0%
F-testsignificance
Unhedged vols for international equitiesTheoretical vols for hedged international equitiesActual vols for hedged international equities
Vol %
20.0%
18.0%
>99.5%>99.95%
>99.95%
>99.5%
16.0%
14.0%
12.0%USD