Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.14 Volatility reduction from hedging – market cap international equity weights (1980–2002)
The results are ringingly clear – currency exposure is always risk-increasing,8 and currencyhedging is always risk-reducing. The volatility reductions available from eliminating it arelarge, and in line with the theoretical predictions based on no correlations between equitiesand currencies. The result is robust over different time periods. Figures 8.15 to 8.18 show thethree 5-year and one 7-year time periods 80–85, 86–90, 91–95, 96–02.The only exception to the risk-reduction hypothesis from all the time periods is the USDbase for 1996–02. The evidence we have already seen shows that the dollar has becomeincreasing positively correlated with German and UK equity markets (we have earlier calledthis ‘embedded currency’). This means that the DEM/EUR is negatively correlated with theGerman equity market, and the pound is negatively correlated with the UK equity market, bothfrom the US dollar perspective.If this relationship persists, it may prove an argument against the risk-reduction propertiesof currency hedging these markets from a dollar perspective. In the absence of a satisfactoryexplanation for the ‘embedded dollar’ phenomenon, we cannot be conﬁdent of the stability ofthis relationship.8I have shown the F-test results in Figure 8.14. An F-test shows the likelihood that the two samples (unhedged returns and hedgedreturns) are not drawn from populations with the same variance. The results in Figure 8.14 are very signiﬁcant indeed; i.e., it is proofthat hedging reduces risk.
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Currency Overlay20.0%
Unhedged vols for international equitiesTheoretical vols for hedged international equitiesActual vols for hedged international equities
18.0%16.0%14.0%12.0%10.0%8.0%USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.15 Volatility reduction from hedging – market cap international equity weights (1980–1985)30.0%Unhedged vols for international equities
28.0%
Theoretical vols for hedged international equitiesActual vols for hedged international equities
26.0%24.0%22.0%20.0%18.0%USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.16 Volatility reduction from hedging – market cap international equity weights (1986–1990)
8.1.11 Effect of hedging on portfolio riskFinally, we can add the reduction in international equities’ volatility to domestic equities togive the effect on portfolio volatility. Figure 8.19 the average (across all four currency bases) ofequity portfolio volatility as the proportion of international equities (hedged and unhedged) intotal equities rises. The X-axis of the graph is the proportion of international in the total (0% =fully domestically invested; 100% = fully internationally invested, with no domestic equities),and the Y-axis of the graph is equity portfolio volatility. The graph illustrates two non-basecurrency-speciﬁc ﬁndings: that the risk-reduction properties of hedging are disproportionatelyvaluable at high international allocations, and that hedging moves the optimum percentage
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22.0%Unhedged vols for international equities
20.0%
Theoretical vols for hedged international equities
18.0%
Actual vols for hedged international equities
16.0%14.0%12.0%10.0%8.0%6.0%USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.17 Volatility reduction from hedging – market cap international equity weights (1991–1995)24.0%Unhedged vols for international equitiesTheoretical vols for hedged international equities
22.0%
Actual vols for hedged international equities
20.0%18.0%16.0%14.0%12.0%USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.18 Volatility reduction from hedging – market cap international equity weights (1996–2002)
allocation to international up about 20%. In the four-base-currency average, the optimummoves up from about 55% to about 75% international. However, the absolute levels of theoptimum proportions of international are very dependent on the base currency, as we shallsee.Expressed in words, the graph shows that, on average, hedging is immaterial at internationalallocations of less than 10% – although note that the proportion is international equities/totalequities. For an Anglo/American pension fund with a typical equity allocation of, say, 60%,this is an international equity allocation of only 6% of the fund – much lower than both theUS and UK averages.
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20%
Hedged
Vol %
19%18%17%16%15%14%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% International
Figure 8.19 Portfolio volatility versus % international equities average, all bases – domestic equities,international equities unhedged and 100% hedged (1980–2002)
8.1.12 Base-currency-speciﬁc graphsAll the individual country graphs of this design have the same basic shape as the average –indeed it is a universal ﬁnding for every base currency and target investment currency. However,the scale of the risk reduction from hedging, and the optimum mix of international and domestic,are highly country-speciﬁc.8.1.12.1 US baseUSD-based investors have a large, well-diversiﬁed and low-risk equity market in the domesticUS market. The arguments for international investing are therefore signiﬁcantly less than forother base currencies. The USD-base graph is given in Figure 8.20.The ‘optimum’ international mix for US investors investing in hedged international equitiesis about 48%. Not coincidentally, this residual domestic weight (i.e. 52%) is reasonably inline with the weight of the US in the global equity market (currently 59%; 20-year average45%). Hedging shifts the optimum proportion of international about 15%, from around 33%to about 46%.
8.1.12.2 Japanese baseThe same graph from the Japanese perspective is given Figure 8.21.Here the effect of hedging is immaterial up to the comparatively high proportion of 30% ofinternational. However, hedging becomes very important for risk reduction at higher levels ofinternational, and the optimum for hedging international equity is about 72%. This implies aweight of domestic (28%) again quite close to the average 20-year weight of Japan in globalequity market cap (24%).
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22%21%
Unhedged
20%
Hedged
Vol %
19%18%17%16%15%14%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% International
Figure 8.20 Portfolio volatility versus % international equities, USD base – domestic equities, international equities unhedged and 100% hedged (1980–2002)22%Unhedged
21%
Hedged
20%
Vol %
19%18%17%16%15%14%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% International
Figure 8.21 Portfolio volatility versus % international equities, JPY base – domestic equities, international equities unhedged and 100% hedged (1980–2002)
8.1.12.3 German/euro baseThe story is now reasonably self-explanatory (Figure 8.22). Hedging is very valuable at almost all proportions of international, and the optimum proportion of international is around95% – again implying a proportion of domestic (5%) close to the 20-year average Germanequity market cap weight (4%).
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Currency Overlay26%Unhedged
24%
Hedged
Vol %
22%
20%
18%
16%
14%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% International
Figure 8.22 Portfolio volatility versus % international equities, DEM/EUR base – domestic equities,international equities unhedged and 100% hedged (1980–2002)
8.1.12.4 GBP baseFinally, the GBP-base graph (Figure 8.23) is much as we would expect. Hedging is very valuableat almost all proportions of international, and the optimum proportion of international is movedsigniﬁcantly from about 50% to about 78% through hedging. The implied optimum domestic20%
Unhedged19%
Hedged
Vol %
18%
17%
16%
15%
14%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% International
Figure 8.23 Portfolio volatility versus % international equities, GBP base – domestic equities, international equities unhedged and 100% hedged (1980–2002)
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177
allocation (at 22%) is a little higher than the long-term UK market cap (10%). There is noimmediately obvious explanation for this. Nevertheless, for all the base currencies, the ruleof thumb that equity market investment should be in proportion to market caps if currencyhedged, but home-biased if unhedged, is attractive and plausible.
8.2 HEDGE RATIOSOptimisers have a particular use in strategic asset allocation. They are very good at handlingmultiple, interrelated and simultaneous asset allocation decisions (how much in equities?, howmuch in international?, how much to hedge?). However when all of the variables can move,it can be difﬁcult to pin down what is moving and why. I therefore propose to abandon theoptimiser approach in looking at the last question in this chapter – that of hedge ratios.8.2.1 Current debateThere is a live debate on the general question of an ‘ideal’ hedge ratio for internationally investedportfolio. Different commentators have drawn different conclusions. Summarising the rangeof opinions, Perold and Schulman (1988) have concluded that passive currency hedging offersa ‘free lunch’ in reducing the volatility of returns, even though the expected long-term returnfrom currency hedging is nil or marginally negative (transactions costs). Following on from thisconclusion, Perold and Schulman recommend a 100% hedged benchmark for non-domesticequities.Taking the middle ground, a number of commentators have sought to deﬁne optimal hedgeratio benchmarks at values between 0% and 100%. One approach has been to deﬁne an efﬁcient(in mean/variance terms) hedge ratio. Black (1989) proposes a ﬁxed ratio (a universal hedgeratio at less than 100%); both Nesbitt (1991) and Jorion (1994) link hedge ratios to wholeportfolio risk, not just international exposure. All conclude that hedging is justiﬁed undercertain combinations of international allocation and hedging transaction cost, and at hedgeratios of less than 100%. By contrast, Gardner & Wuilloud (1994) approach the problem fromthe point of view of minimising ‘regret’. This approach favours a 50% hedge ratio, which, notsurprisingly, turns out to minimise regret. Some writers, although the minority, have concludedthat currency hedging is sub-optimal at observed transaction costs, and therefore to be avoided.All researchers in this area agree, however, that empirical evidence is in general inconclusivein determining ﬁnal or ﬁrm answers. Correlations between currency movements and otherasset classes are highly unstable over time, exhibiting alternatively positive, insigniﬁcant andnegative correlations.In the limited space available, can we make an assessment of hedge ratios and their impact onportfolios? We have already done so for limited hedge ratios (0% and 100%) but we can extendthis analysis to the full range of hedge ratios. I will concentrate on the effect of hedging onequity portfolios. I choose to ignore (at least in this section) the impact on whole portfolios (i.e.including bonds, property, alternatives) because the range of possible portfolio combinationsbecomes too numerous to handle. Domestic ﬁxed income returns are not highly correlated witheither equities or currency returns, and so most of the conclusions drawn from an equity-onlyanalysis are likely to apply to whole portfolios.The methodology I will use is identical to that just conducted on four base currency perspectives above (USD, EUR, JPY, GBP), but both the hedge ratio and the proportion of international
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equities (as a percentage of total equities) will be varied simultaneously. As a start, we can pickan arbitrary domestic:international mix, say 50:50, and show the effect of varying the hedgeratio from 0 to 100%. Figure 8.24 shows the effect on equity portfolio volatility of this varyinghedge ratio from the four different base currency perspectives.19.5%
USD BaseJPY BaseDEM/EUR BaseGBP Base
19.0%18.5%
Vol %
18.0%17.5%17.0%16.5%16.0%15.5%15.0%0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% Hedge ratio
Figure 8.24 Equity portfolio volatility versus hedge ratio (MSCI indices, 50:50 domestic: intenational,1980–2002)
The graph shows clearly that raising the hedge ratio from zero is always risk-reducing inthis 50:50 mix of domestic:international equities. For all of the base currencies except USD,the fall in volatility as the hedge ratio is raised is continuous. For the US, the fall stops at ahedge ratio of 86%, and then rises very slightly. It is likely that this is because of the ‘dollar’content that we identiﬁed in German and UK equities, which means that at high hedge ratiosthe USD investor is selling too many euros and pounds.This graph could be construed as a two-dimensional representation of a ‘cross-section’ ofa three-dimensional surface. We have ﬁxed the proportion of international equities in totalequities (i.e. 50%), and varied the hedge ratio from 0% to 100%. In theory we could varyboth variables, and represent the result in a three-dimensional ‘surface’ graph. Although threedimensional graphs are quite difﬁcult to read, I have nevertheless completed this exercise forthe four base currencies, and Figures 8.25 to 8.28 show the results.8.2.1.1 USD baseThe graph for the USD base is shown is Figure 8.25. Firstly, how to read this graph? Thevalues on the ‘back wall’ of the graph are the values in the unhedged line from Figure 8.20.The values at the front of this surface are the same as the ‘100%’ line from the same graph.The USD line hedge ratio graph (Figure 8.24) shows the ‘slice’ going from back to front inthe middle of Figure 8.25, starting at the 50% point on the back wall. To ‘see’ it as shown in
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21.00%
20.00%
19.00%
18.00%
Equity portfoliovolatility
0%17.00%
20%40%
% Hedge ratio
16.00%
60%80%100%0%
20%
40%
60%
80%
15.00%100%
% International
Figure 8.25 USD base ‘hammock’ (MSCI indices, 1980–2002)
Figure 8.24, you would have to look from the left-hand side at this cross-section. Note thatthe ‘front’ axis shows the proportion of international equities in total equities, not in the totalfund. For a fund with 50% of its assets in bonds, and the rest in equities, the 40% internationallevel would be an asset allocation of 20% international in the fund.In summary this graph tells us that international diversiﬁcation with unhedged foreign equities can reduce equity portfolio volatility by about 1.25% (and that the optimum internationalproportion is about 30% in international). If a full hedging policy is adopted, the optimuminternational mix rises to about 45%, and the volatility falls about a further 0.5%. The beneﬁtsof international diversiﬁcation and hedging for US equity investors are there, but they are notoverwhelming. In particular, the strategic beneﬁts of hedging are modest. As we shall see, theUS is a special case. The other three base currencies that we look at display very strong riskreductions from both international diversiﬁcation and from hedging.Why is the US special? The evidence points very strongly to two causes: the ‘embeddeddollar’ content in the UK and German (European) equity markets, and the sheer size anddiversiﬁcation of the US market in comparison with the international alternatives.Let’s look at the other base currencies.
8.2.1.2 JPY baseThe JPY base shows a very different pattern (Figure 8.26). For the yen investor, internationaldiversiﬁcation is hugely risk-reducing (by a nearly 5% volatility reduction), with the unhedgedoptimum at about 55% international, and the hedged optimum at about 70%. Hedging is alsovery strongly rewarded, with a nearly 2% further fall in portfolio volatility.
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22.00%
21.00%
20.00%
19.00%
18.00%
Equity portfoliovolatility
0%20%
% Hedge ratio
17.00%
40%60%
16.00%
80%100%0%
20%
40%
60%
80%
15.00%100%
% International
Figure 8.26 JPY base ‘hammock’ (MSCI indices, 1980–2002)
8.2.1.3 DEM/EUR baseThe DEM/EUR investor (Figure 8.27) shows a similar pattern to the yen investor, exceptthat the optimum domestic equity proportion is much smaller, and the gain from hedgingis greater. Here the optimum mix of international is even higher (70% unhedged), and fullyhedged is about 90%. The combination of international diversiﬁcation and hedging is, again,extremely risk-reducing, with the combination reducing overall equity portfolio risk by amassive 9%. Euro investors ignore both international diversiﬁcation and hedging at theirperil.8.2.1.4 GBP baseFinally, the graph from a UK investor’s perspective is shown in Figure 8.28. Again, bothinternational diversiﬁcation and hedging are very risk-reducing for the UK investor. Hedgingis particularly valuable – diversiﬁcation and hedging contribute equally to the nearly 4%reduction in portfolio risk.It is worth re-noting an observation that I remarked on earlier – namely that the proportionof domestic equities which gives the lowest risk when combined with hedged equities is, forall base currencies, very close to their average historical weight in the world market caps. Thisis not true where the equities are left unhedged: unhedged international equities are underrepresented in optimising any equity portfolio from the historic data, and such portfolios willdisplay home bias and higher-than-necessary volatility.It is possible that this is one area where ﬁnancial theory and actual outcomes match. Inthe world of classical markets, all equities, whatever their base currency, will be arbitraged
Overlaying Different Asset Classes
25.00%24.00%23.00%22.00%21.00%20.00%19.00%
0%20%
18.00%
40%
% Hedge ratio
Equity portfoliovolatility
17.00%
60%16.00%
80%100%0%
20%
40%
60%
80%
15.00%100%
% International
Figure 8.27 DEM base ‘hammock’ (MSCI indices, 1980–2002)
19.00%
18.50%
18.00%
17.50%17.00%0%
16.50%
20%
% Hedge ratio
16.00%
40%60%
15.50%
80%100%0%
20%
40%
60%
80%
% International
Figure 8.28 GBP base ‘hammock’ (MSCI indices, 1980–2002)
15.00%100%
Equity portfoliovolatility
181
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by mobile capital to deliver returns commensurate with their risk. If the market cap of equityindices is a proxy for diversiﬁcation of risk (either within large corporations, or with a multitudeof small companies), then the riskiness of different countries’ equity markets will be inverselyproportional to their market cap. This is what comes out in the analysis of portfolio behaviouronce currency risk is eliminated.
8.3 BONDSWe can conduct a similar exercise to that conducted with equities above. I have chosen toconcentrate on government bonds in the examination of the data. I have done this for tworeasons:1. Government bond prices represent a ‘pure’ ﬁxed income asset, i.e. they reﬂect only thedomestic interest rate curve, and not credit pricing.2. Credit pricing is based on an individual corporate or other asset-related element (e.g.mortgage-backed securities). We have examined the behaviour of equity prices in some detail in the ﬁrst half of this chapter, and to include credit in an examination of non-governmentbond prices and returns runs the risk of re-examining some of the same elements embeddedin equity pricing.Much of the analysis of currency:asset correlations (particularly with individual stocks),however, will be superﬂuous. Accordingly, I will concentrate on national bond indices, andlook at the four main countries examined in the equities section – the US, Germany, Japan andthe UK.
8.3.1 CorrelationThe ﬁrst thing to establish is whether bonds and currencies are correlated. We can use thesame analytical tools that we used in examining equity:currency correlations. Again, we areinterested in establishing whether, from each base currency perspective, hedged bonds arecorrelated with currency surprise. The reader might like to remind him- or herself why thesetwo measures are the right ones to look at by reference to p. 215 in this chapter.Figure 8.29 (in the same format as Figure 8.1) shows the 17-year historical data between abasket of hedged international bonds and currency surprise in the same weights (the basket isroughly market cap weights, and is dominated by USD-denominated bonds until recently, whenJPY-denominated bonds show a strong weight increase). Note that currency surprise in thiscontext is the returns from holding the same foreign currencies as the bonds are denominatedin. If currency surprise returns are negatively correlated with (hedged) bond returns, then theymay have some diversifying effect. Although we did not ﬁnd this with equities, we did notethat there were, in theory, levels of negative correlation between currencies and equities belowwhich currencies would be diversifying, and these were marked on the graph. Why have I notmarked the equivalent levels on this graph?The answer is because in all four of the base currencies, the volatility of currency returns ismore than twice as high as the volatility of hedged bond returns. The ﬁgure ‘twice as high’ isimportant. I explain in footnote 2 of this chapter that the formula for calculating the negative
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0.50.4Correlation coefficient
0.30.2
0.15
0.10.0−0.1
−0.09
−0.2
−0.11−0.19
−0.3−0.4−0.5USD Base
JPY Base
DEM/EUR Base
GBP Base
Figure 8.29 Correlation between hedged bonds and currency surprise of the same market basket weights(1985–2002)
correlation required to make currency exposure diversifying is:−(SD currency surprise)/[2 × (SD hedged bonds)]It does not need more than a cursory glance to see that if the volatility of currency surpriseis more than twice the volatility of hedged bonds, then it would need a correlation of lessthan −1 to produce diversiﬁcation. Correlation coefﬁcients are bounded by −1 and 1, so itis impossible, under any circumstances, for currency exposure to be diversifying when thevolatility of currency returns is more than twice as high as the volatility of bond returns. Thisdoes make the case for currency hedging for international bonds rather compelling, if the casefor hedging international equities was not compelling enough!Just turning to Figure 8.29 for a moment. It is interesting that the correlations are, if anything,rather stronger both ways (i.e. more distant from zero) than in the equity case. I suspectthat this is for two reasons. Firstly, we know there is a relationship between bond returnsand domestic monetary conditions. There is a looser, rather unstable, relationship betweendomestic monetary conditions and currency returns. This implies that correlations might notbe zero between the two. Secondly, government bond indices are effectively one asset. Whilethere are typically scores (but not hundreds) of securities in a government bond index, they allmove in tandem as the yield curve moves, and only break away from each other when the slopeor shape of the yield curve changes. This makes the possibility of a common causal link morelikely.As well as the weighted average of bond and currency returns, we can show the correlations ofthe individual country indices (Figure 8.30 mirroring Figure 8.2). The pattern of correlations forbonds is quite different from the pattern for equities. In particular, it appears from the consistentpattern here in relation to the USD base that US dollar currency returns are negatively correlatedwith US bond returns, and that US bond returns are positively correlated with the other countrybond returns.
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Currency Overlay0.5US bonds
0.4
Japanese bonds
Correlation coefficient
0.3
German bonds
0.2
UK bonds
0.1
US JAP GER UK
0.0− 0.1− 0.2− 0.3− 0.4− 0.5
USD Base
JPY Base
DEM/EUR Base
GBP Base
Figure 8.30 Correlation between hedged foreign bonds and same-country currency surprise for eachbase currency (1985–2002)1.00.9
Correlation coefficient
0.80.70.60.50.40.30.20.10.0USD Base
JPY Base
DEM/EURBase
GBP Base
Average allcurrencies
Figure 8.31 Correlation between hedged bonds and domestic bonds basket weights (1985–2002)
The intuitive explanation of the ﬁrst point is that US bond returns are strong when US ratesare falling. When US rates are falling, this depresses, at least under this theory, US dollarcurrency returns – not just spot, but currency surprise. A falling Dollar means a rising foreigncurrency. But does a rising US bond market mean a rising foreign bond market? As for thelatter point, we can check it: Figure 8.31 shows correlation coefﬁcients between hedged foreignbond returns and domestic bond returns.Certainly it appears that there are quite strong positive correlations between the international government bond markets – perhaps surprisingly high. But this observation supports thecontention made above to explain the USD bond correlations.
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8.3.2 Stability of correlationsThe above explanation is not an attempt to provide a forecasting mechanism for the US dollar,and the following rolling correlation graphs show why. Figures 8.32 to 8.35 show the 5-yearrolling correlations (monthly data) of hedged bond returns and currency returns of the same0.600
JapanGermanyUK
0.400
0.200
0.000−0.200−0.400−0.60090
91
92
93
94
95
96
97
98
99
00
01
Year
Figure 8.32 Five-year rolling correlations, USD base – correlation between hedged foreign bonds andforeign currency0.600
0.400
USGermany
0.200
UK
0.000
− 0.200− 0.400− 0.60090
91
92
93
94
95
96
97
98
99
00
01
Year
Figure 8.33 Five-year rolling correlations, JPY base – correlation between hedged foreign bonds andforeign currency
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Currency Overlay0.600
USJapanUK
0.400
0.200
0.000−0.200−0.400−0.60090
91
92
93
94
95
96
97
98
99
00
01
Year
Figure 8.34 Five-year rolling correlations, DEM/EUR base – correlation between hedged foreign bondsand foreign currency0.6
USJapanGermany
0.4
0.2
0.0
− 0.2− 0.4− 0.690
91
92
93