currencies in that currency.Rebalancing in passive overlay, unlike rebalancing in asset allocation, is not a ‘strategic’decision. Let me explain.Suppose a fund has determined a strategic asset allocation process of, say, 60% equities and40% bonds. Let us also suppose that equities outperform bonds over a particular period, sothat the fund proportions change to 65:35. The design of the process by which the proportionsare rebalanced back to 60:40 is of strategic importance, and will have a material impact onthe performance of the fund. Asset rebalancing limits the compounding, or ‘convexity’ (seeBox 5.1), in a portfolio by selling highly performing assets, and buying lower performingassets with the proceeds. At the asset allocation level, it is a form of ‘value’ investing (i.e.selling ‘expensive’ stocks and buying ‘cheap’ ones). Rebalancing in passive currency overlay,however, does not have this effect, nor the same cause. The engine of currency overlay rebalancing is the performance of the underlying asset expressed in the foreign currency, not theperformance of the foreign currency (and therefore the overlay). We can conduct a workedexample on the basis of the portfolio shown above (which is a USD base). Table 6.3 takes theoriginal portfolio asset mix (from Table 6.1) and shows an example of its development overtime.Table 6.3 UK asset valuations over timeUK assets(one period = one month)End period 0End period 1End period 2End period 3
Asset value (£)
Spot rate (foreigncurrency per dollar)
Asset value (USD)
20.0022.0022.0019.00
0.62500.62500.64520.6061
32.0035.2034.1031.35
Suppose overlay starts at the end of period 0, with (as mentioned above) a hedge ratioof 100%. The ﬁrst thing to note is that consideration of the passive hedge is an individualcurrency-speciﬁc question, and that (with the exception of any proxy hedging) each currency’shedging is entirely independent of the others’.So, concentrating on the pound sterling hedge, at the end of period 0, the overlay managerwill sell £20m versus dollars one-month forward. I have not included the forward rate inTable 6.3, as it is not relevant to this discussion. If the rebalancing frequency is monthly,then at the end of period (month) 1, the overlay manager will increase the hedge from £20mto £22m because the underlying asset has increased from £20m to £22m. The calculation isalways performed with the amount of the foreign currency (in this case pounds sterling) asthe determinant of the size of the forward contract, and any proﬁts or losses that might ariseon the forward contract when it is closed will be paid or received in the home currency (inthis case US dollars). Attempting to calculate the size of the hedge required by reference todollar amounts (rather than foreign currency amounts) creates a series of complexities whichare completely avoided if we always use the foreign currency amount as the size determinant.Note that between period 0 and period 1, the spot exchange rate did not move. In the nextperiod, we have the opposite effect – the spot rate moves, but the asset value in sterling does
112
Currency Overlay
not. In this case, at the end of period 2, no rebalancing is necessary. The hedge remains at£22m, despite the movement of the spot rate. Note that the dollar valuation of the sterling assethas gone down in period 2 – this is not relevant for rebalancing, and indeed the hedge willhave thrown up a proﬁt to offset this loss. Finally, at the end of period 3, the asset valuationhas fallen to £19m. This would require a reduction in the hedge to this amount.What is clear from this example is that strong performance from an asset class is not‘penalised’ (as it would be in a conventional asset rebalancing exercise) by a sale of thestronger performing asset and a purchase of the weaker performing asset. At the end of period1, when the UK asset is strong in sterling terms, it is not the asset that is sold, it is an increasedamount of currency. The currency has been neither strong nor weak in period 1. In period 2,the dollar is strong (vs. the pound), and the overlay will have produced a proﬁt to offset theloss of dollar value resulting from this, but because the asset value of the UK asset has notchanged in sterling terms, the size of the currency hedge is left unchanged at the end of period2. This illustrates the mechanics of rebalancing, and shows that it does not act as an inhibitorof ‘convexity’.6.2.1 Frequency of rebalancingOne of the key decisions to be made is the frequency of rebalancing. There are competingpressures (for both higher and lower frequency), which makes the question a pragmatic one.The ﬁrst point to note (as made in Chapter 3) is that the value of foreign assets expressed indollar terms is a multiplicative relationship between the asset and the spot foreign currency,and also between the asset returns and the spot foreign currency returns. Simply put, this meansthat a 10% increase in both the value of an asset in foreign currency terms, and a 10% increasein the foreign currency spot, will mean a 21% rise in the asset value in dollar terms, not a 20%rise.For currency overlay to replicate (and therefore fully neutralise) this multiplicative relationship, the size of the passive hedge must be continuously adjusted. ‘Continuous adjustment’means just that – the adjustment has to happen in inﬁnitesimal size, inﬁnitely frequently. If therewere a ‘no-cost’ trading environment, then in theory (although not in practice, since how doesone trade inﬁnitely frequently?) it would be possible to completely neutralise all the impactfrom currency exposure. However, the trading environment required for this is the ‘classicalmarket assumptions’ – exactly the same behaviour as is assumed in the Black–Scholes modeland in Chapter 3. I have taken some time and effort to argue that these assumptions mustalways be materially violated in practice. Human beings, and indeed computers, respond andoperate in discrete time, not in continuous time. If the ‘ideal’ is to be approached, it will be anapproximation in which rebalancing takes place at very high frequency.In passive hedging in the real world, approaching the ideal (continuous rebalancing) has to beweighed up against the transaction and other costs associated with high-frequency transactions.This calculation is heavily inﬂuenced by the observation that rebalancing is created by themovement of underlying assets, not the movement of currency, and so the strong presumptionis that higher frequency adjustment will not improve (or reduce) returns, only marginallyreduce the residual currency error inherent in the asset valuation.There is a further, and important, point. A manager is generally required to minimise tracking error versus the benchmark, other things being equal. As we shall see below, any goodbenchmark must have a transparent calculation methodology, and this will include a discrete
Passive Currency Overlay
113
rebalancing period (since continuous rebalancing is not replicable and uninvestible). If thebenchmark has a rebalancing period of t, what incentive is there for a manager to deviate fromthat, except on grounds of cost? Certainly there is no incentive to attempt higher frequencyrebalancing than the benchmark; there may be some incentive to adopt a lower frequency ifthe costs of dealing are material.Can we make some estimate of rebalancing costs at different frequencies? If we assume alognormal random walk distribution for (equity) asset returns with 16.3% annual volatility1(and remember it is the asset volatility, not the currency volatility, which is the ‘generator’), andassume a 6.5 bp bid/offer spread (the average of the 1m outright spreads from Table 3.3), wecan estimate the annual cost of rebalancing at each frequency using a statistical property (notderived here) that the mean absolute outcome of a normal distribution with SD = x is 0.796x.2(This means that (speaking loosely and not adjusting for the log element) a 10% annualised volsreturn series has an average absolute annual movement of 10% × 0.796 = 8.0%.) Since meanabsolute movements are the determinant of rebalancing costs, and the properties of lognormalrandom walk returns allow us to calculate these for any horizon, we can produce an (amusing)theoretical table (Table 6.4).Table 6.4 Rebalancing costs at various frequenciesFrequency of rebalancing1/1000000th sec1/1000th sec1/100th sec1 sec1 min1 hr6 hr1 day2 days1 week2 weeks1 month3 months6 months1 year
Average size of deal(% of exposure)
No. deals per year
Total cost p.a.(bp)
0.0000025%0.00008%0.00025%0.003%0.020%0.152%0.37%0.75%1.06%1.68%2.39%3.5%6.2%8.9%12.8%
2.26368E + 1322 636 800 0002 263 680 00022 636 800377 28062881048262131522612421
1 858 61358 77418 58618582393112.66.34.492.842.021.380.810.580.42
This tells us that rebalancing frequencies of anything less frequent than 1 day are manageableif measured purely in terms of annual transactions costs. If we try to go close to the theoreticalcontinuous-time model, the costs explode out of control.In practice, rebalancing is unlikely to be less frequent than once a month, and is virtually certain to be no more frequent than once a day, since virtually no benchmark will havehigher than daily frequency. This puts the cost range between 0.7 and 3.2 bp p.a. on theassumptions.12
The 22-year historical hedged average of four: US, UK, Germany, Japan – a close approximation to the local return vols.Brenner & Subrahmanyam, Financial Analysts Journal 45 (Sep/Oct 1988).
114
Currency Overlay
6.2.2 Rebalancing buffer (Y/N? size)For practical management, rather than the construction of a benchmark, it is possible, and maybe desirable, to insert a buffer into the rebalancing decision. Any transaction, however small,attracts a ﬁxed cost. This will consist, at the very least, of the labour involved in agreeing thedeal and the conﬁrmation process. This makes very small deals increasingly expensive, evenif that expense is not necessarily visible.To avoid very small deals, a buffer (expressed either as a percentage of the particular currencyexposure concerned, or as a percentage of the total currency programme) will reduce the volumeof transactions, and on average increase their size.We can rewrite Table 6.4, inserting a buffer of, say, 1% of the particular currency involved,and the results are given in Table 6.5. We can play with these variables endlessly; the maths forbuffers gets hard very quickly – Table 6.5 was calculated using Monte Carlo analysis. However,it is clear that buffers are useful where the rebalancing frequency is potentially very high.Table 6.5 Rebalancing costs with bufferFrequency ofrebalancing1hr6 hr1 day2 days1 week2 weeks1 month3 months6 months1 year
Average size ofdeal (% of exposure)
No. dealsper year
Total cost p.a.(bp) with buffer
Total cost p.a.(bp) without buffer(from Table 6.4)
1.113%1.266%1.548%1.786%2.389%3.043%4.155%6.720%9.236%12.702%
177.6132.286.262.033.319.19.83.61.80.9
6.435.444.333.602.581.881.320.780.550.39
3112.66.34.492.842.021.380.810.580.42
Finally, we can add in a de minimus ﬁxed cost per deal. I have used $8.33 per deal (basedon 10 min labour at $50/hour). Table 6.6 shows the effect of this on a $10m single currencyexposure (i.e. quite small). Assumptions are otherwise unchanged.Table 6.6 Rebalancing with a ﬁxed cost per dealFrequency ofrebalancing1 hr6 hours1 day2 days1 week2 weeks1 month3 months6 months1 year
Total cost p.a. (bp)(inc. ﬁxed deal cost)with buffer
Total cost p.a. (bp)(inc. ﬁxed deal cost)without buffer
7.96.545.054.112.862.041.400.810.570.40
83.421.48.55.593.272.231.480.840.590.42
Passive Currency Overlay
115
6.2.3 Buffer – ‘percentage of what?’Finally, in this section, the denominator of the buffer can be the total underlying currencyexposure of the overlay programme rather than the individual currency exposure. This wouldbe logical where there is a ﬁxed cost per deal, since it equalises the importance of each deal tothe fund – even if the buffer could be 10% of a very small currency, or 1% of a large currency.Just to elaborate on this point. A rebalancing buffer can be calculated on each individualcurrency, and expressed as a percentage of the currency exposure related to that currency alone.This is a common approach, that has the merit of making each currency’s hedge portfoliobehaviour independent from each other currency.But there is a signiﬁcant drawback to this approach. A European (euro-based) fund mighthave $100m in US dollars, and $1m in Swedish krone, both of which it is hedging passively.This means that the size of the buffer might be $10 000 in SEK, but $1m in USD, and that dealsin SEK are a hundred times less material than deals in US dollars. This creates an executioninefﬁciency – a common effort (dealing time, back ofﬁce usage) has a hundred times theimportance when applied to the US dollar compared to the Swedish krone.The solution is to base the buffer on a common denominator – say the total currency exposure.Under this example the buffer might be 0.25% – and let us suppose the total currency exposureoverlaid is $250m. This would mean that whenever there was a US dollar exposure changeof greater than $0.625m (0.2% × $250m), the amount of the US dollar hedge would bealtered to re-establish the hedge ratio back to benchmark. This equates to 0.625% of the dollarexposure, so this is a smaller buffer for the dollar portfolio. However, if the same criterion($0.625m exposure change) is applied to the SEK exposure, this represents 62.5% of theSwedish exposure. This could mean in theory that the SEK exposure could fall by 60% from$1m to $0.4m, and no action would be taken. A 100% SEK hedge ratio could become a$1m/$0.4m = 250% hedge ratio.Many investors would ﬁnd it hard to swallow a hedge ratio at such variance with the benchmark, and some operate in regulatory regimes where hedge ratios over 100% are not permitted.However under this regime, each deal will have the same economic impact on the overall portfolio, and virtually the same impact on tracking error.Some investors will adopt a combination of the two denominators, or impose a minimumdeal size on the single-currency denominator to eliminate spurious dealing. These choices area matter of expediency rather than of great strategic importance.
6.2.4 Delay in rebalancingIn an ideal world, there would be no delay between the valuation of the underlying international assets, and the execution of hedging contracts to rebalance the hedging according to theguidelines agreed. In particular, any benchmark calculation will assume that there is no delay,and therefore delays will appear as a source of tracking error.In practice, however, an overlay manager will need to put in place, and agree with the client, atimetable for this process. This will give the manager a framework within which to operate, andthe client conﬁdence that the rebalancing process is timely and effective. A typical timetablemight go as follows for a monthly rebalancing procedure:Last business day of month (LBDM):LBDM + 3:
Date for asset prices to be collected by custodianAll prices required are captured by custodian
116
Currency Overlay
LBDM + 5:LBDM + 6:LBDM + 7:
Custodian produces asset valuationOverlay manager receives asset valuationOverlay manager conducts rebalancing trades
While in theory the price collection, capture and valuation could be virtually instantaneous,in practice new assets, erroneous prices, questionable prices, mistakes in data entry and so onmake the valuation process neither automatic nor particularly timely. In the above example,an overlay manager would plan to rebalance on LBDM + 7, and this will build in a small, butirreducible tracking error versus benchmark. We can quantify the tracking error that delays inrebalancing will create, and this is done in Section 7.6.6.2.5 Valuation ratesThe decision of which valuation rates to use is a matter of convenience and convention.Unlike other markets, where prices are of varying quality and liquidity, there is rarely anyissue over the liquidity or tradeability of prices in the major foreign exchange markets. Acommercial service provider – WM/Reuters – now provides a wide range of daily prices, spotand forward, for London closing prices, which are deﬁned as 4pm London time. These havevery quickly become the market standard in the investment industry, and are now the valuationrates of choice for custodians, investment managers and currency overlay managers. Theyare available in mid-price form (which is the arithmetic average of the bid and offer prices),and in bid and offer form. There is a range of forward horizons up to one-year maturity toallow the accurate interpolation of rates for intermediate forward contracts. Most custodiansuse mid-exchange rates in conjuction with mid securities prices for their valuations of pensionfund and investment trust portfolios, and while these are not strictly realisable values, the verynarrow bid/offer spreads make this approximation acceptable. For the valuation of unit trusts,bid and offer exchange rates are normally used in conjuction with bid and offer securities’price in an effort to obtain more exact Net Asset Values for dealing in the units.
6.3 CASH FLOWAll currency hedging and overlay produces cash ﬂow. This is the settlement, in cash, of theproﬁts and losses of the forward FX contracts that comprise the overlay or hedge. Cash ﬂowarises at the maturity of forward contracts.Let us ﬁrst examine the likely scale and pattern of cash arising from the model portfolioabove. Figure 6.1 shows the monthly cash ﬂows for a market-cap-weighted EAFE portfolioover the past 20 years: the asset weights shown in the model portfolio are quite close to marketcap weights, and rather than assuming ﬁxed weights, I have assumed these have changed inline with asset valuations over history.The ﬁrst thing to notice about Figure 6.1 is how large the monthly cash ﬂows are: the averageabsolute monthly value is 2.06%. Figure 6.2 shows the cumulative annual rolling cash ﬂow; itillustrates the scale of the cumulative cash ﬂow – the average absolute annual rolling averageannual cash ﬂow is 8.8%.Cash ﬂow is an inevitable concomitant of currency hedging or overlay. Changing the original maturity of the hedging contracts can change (and delay/advance) the cash ﬂow, butthe cumulative cash ﬂow over time will be very similar irrespective of the maturity of the
Passive Currency Overlay
117
8%6%
% International
4%2%0%−2%−4%−6%−8%82
84
86
88
90
92
94
96
98
00
02
Year
Figure 6.1 Passive hedging monthly cash ﬂow (USD base, EAFE weights, Sep 82–Sep 02, 100% hedgeratio)30%20%
% International
10%0%−10%−20%−30%−40%82
84
86
88
90
92
94
96
98
00
02
Year
Figure 6.2 Passive hedging 1-year cumulative cash ﬂow (USD base, EAFE weights, Sep 82–Sep 02,100% hedge ratio)
contracts. It is, after all, the cumulative cash ﬂow from hedging contracts which form one ofthe key contributors to the volatility-reducing properties of hedging/overlay – the other beingthe marked-to-market valuation of the unmatured forward contracts.
6.4 COSTSThe costs of passive hedging are a key determinant of the strategic decision of whether tohedge international assets or not. It is therefore important that we know, or can calculate, what
118
Currency Overlay
the expected costs are of a particular passive hedging policy and structure. There are threemain elements of cost in a passive hedge – two direct costs, and one indirect. The indirectcosts are less straightforward, but can be estimated with the additional assumptions below. Theassumptions for the costs are otherwise based on the example in this chapter.6.4.1 Direct costs6.4.1.1 Rolling costsIn Chapter 3 I looked in detail at the dealing costs of spot and forward FX contracts. We canuse this information to calculate the expected rolling costs of any passive hedging structure.I do not propose to differentiate between different base currency investors: I will use theunweighted averages of dealing costs in these calculations. The reader with a particular investorbase currency in mind can perform his own calculations based on the relevant currency pairsonly.Annual rolling costs are the product of half the swap spreads at the relevant maturity, andthe frequency with which that maturity has to be rolled in a year (i.e. 12 for monthly maturity).Using the WM/Reuters averages from Table 3.3, the rolling costs can be deduced (see Table6.7; the row in bold shows the assumptions made in this chapter’s model portfolio). From thisdata, it appears that there are marginal cost savings from dealing at 6 months, rather than 1month or 12 months.Table 6.7 Passive rolling costs versus maturityOriginal maturityof contract1m2m3m6m12m
No. ofrolls p.a.
Average WM/Reuters spreadfor each roll (bp)
Average costp.a. (bp)
126421
0.350.600.791.434.25
2.131.801.581.432.13
We can do the same exercise on live deal spread data, from Table 3.4. The results are shownin Table 6.8. With live data, 12-month original maturity contracts are just cheaper than 6months – 1-month rolling is twice as costly.Table 6.8 Passive rolling costs (live spreads)Original maturityof contract1m2m3m6m12m
No. ofrolls p.a.
Average live spread foreach roll (bp)
Average cost(bp) p.a.
126421
0.460.680.811.542.86
2.772.031.611.541.43
Passive Currency Overlay
119
6.4.1.2 Rebalancing costsRebalancing, as discussed above, is the process by which the amount of currency hedged isadjusted to remain in line with the valuation of the underlying assets. It can be conducted atany frequency, independently of the original maturity of the hedging contracts.Rebalancing requires outright deals, i.e. spot and forward, to increase or reduce the hedgein line with the new asset values. Table 6.9 is a cut-down version of Table 6.5, showing theeffect of the frequency of rebalancing on costs. The WM/Reuters cost column shown is the‘with buffer’ column in Table 6.5. I have also added a cost column which uses the live dealdata rather than the WM/Reuters data, to illustrate the cost savings possible by competitivequoting. Because the model portfolio in this chapter is one-month maturity contracts, I haveassumed that deals are conducted at one-month outright spreads.Table 6.9 Rebalancing costs-WM/Reuters vs live spreadsFrequency ofrebalancing1 day2 days1 week2 weeks1 month3 months6 months1 year
Total cost p.a. (bp)WM/Reuters
Total cost p.a. (bp)live deals
4.333.602.581.881.320.780.550.39
2.201.831.310.960.670.400.280.20
6.4.2 Indirect costsThere are some possible indirect costs associated with passive overlay. There is one – cashﬂow management – which has the potential to be high, higher than the costs shown in Section6.4.1. There is a second – overlay manager fees – which although apparently transparent, mayin some circumstances generate opaque costs (and income for the manager/manager’s bank)from the bid/offer spreads in the FX contract pricing.6.4.2.1 Cash ﬂow managementAs we have seen in Section 6.3, passive hedging produces cash ﬂow. This is not, of itself,a source of cost, but the consequential management of the cash can be. The management ofcash ﬂow is not directly the responsibility of the currency overlay manager, but the policiesadopted by the client can materially affect the costs they suffer. The key requirement is theminimisation of transactions in underlying securities.We can categorise (Table 6.10) the range of policies from most to least potentially costly.Option D is costless if it results in no changes in either asset allocation or any securitiestransactions. Option C will be very low cost if properly structured. The cost of option Bdepends on the size of the cash buffer. Finally, we can cost option A as follows:Annual cost% = Average cash ﬂow per maturity × Number of maturities × Underlyingsecurity transaction costs
120
Currency OverlayTable 6.10 Cash from management choicesMore costly
Less costly
A. Full acquisition/disposal of underlying securities each month(or cash ﬂow frequency) [assumed in benchmark]B. Acquisition/disposal of underlying securities only whencumulative cash ﬂow exceeds cash bufferC. No acquisition/disposal of underlying securities – sufﬁcientlylarge equitised cash buffer held [underlying securities’ returnpattern replicated with futures contracts]D. No acquisition/disposal of underlying securities – all cash ﬂowsabsorbed within fund’s existing cash buffer [easier for smallinternational allocations]
We know the ﬁrst two values for the model portfolio from the above data. Average transactioncosts for securities, however, are notoriously variable. Table 6.11 is a very rough guide (it isexpressed in ‘round trip terms’ (like bid/offer spreads) and so has to be divided by two to getthe single transaction cost).Table 6.11 Estimated asset transaction costsSecurity type
Transaction cost range
OECD government bondsLower sovereign + high qualitycorporate creditLarge cap OECD equities/lowerquality corporate creditSmall cap OECD equities/largecap emergingOther emerging equities, etc.
2–15 bp15–50 bp50–80 bp (+50 bp UK)80–200 bp200+ bp
From this data we can create a similar table (Table 6.12) of the overall expected cost ofhedging cash ﬂow management for the top three securities categories using the most costlyoption A. Again the costs are basis points of the international allocation. For a one-monthoriginal maturity passive hedge, the calculation is as follows (values from data given): annualcost % = 2.06% × 12 × underlying security transaction costs/2.Table 6.12 Estimate costs from cash ﬂowSecurity typeOECD government bondsLower sovereign + high qualitycorporate creditLarge cap OECD equities/lowerquality corporate credit
Estimated annual costs from cashﬂow transaction costs p.a. (bp)0.63.79.9
Passive Currency Overlay
121
Finally, we can show the effect of adding a cash buffer (option B). The maths is quitecomplicated, but Figure 6.3 shows the impact of adding a cash buffer with the following rules:
r A cash buffer deﬁned as ‘x%’ (say 2%) will be held initially.r When it falls to zero through cash outﬂows, securities disposals will be made to restore thebuffer to x%.
r When it rises above 2x%, security acquisitions will be made to reduce it to x%.r The acquisition and disposal rules are therefore symmetrical, and a 2% buffer can allow cashto move between 0% and 4% without underlying securities transactions.Figure 6.3 shows the transactions costs compared with the buffer (expressed as the x% above)for a buffer size of 0–40%. The base case transaction cost is 9.9 bp – ﬁnal row of Table 6.12 –i.e. buying and selling large cap equities.12
Transaction costs (bp)
10
8
6
4
2
00%
4%
8%
12%
16%
20%
24%
28%
32%
36%
40%
Buffer % international
Figure 6.3 Transactions costs from currency hedging cash ﬂow (1982–2002 data, USD base, 100%passive hedge)
The graph shows that there are signiﬁcant marginal cost savings for a buffer of up to 8% –thereafter the rate of marginal cost reductions begins to reduce.6.4.3 Summary on costsFrom this detail, we can summarise (Table 6.13) the expected total costs of a standard USDbase passive 100% hedging programme expressed as basis points of international exposurehedged. I have assumed that large cap equities are the main security class transacted to providecash.
122
Currency OverlayTable 6.13 Passive hedging costs p.a. (bp)Cost categoryRolling costRebalancing costCash ﬂow transactions costsTotal
No cash buffer
4% Buffer
2.11.39.913.4
2.11.36.39.8
6.5 POSTSCRIPT ON COSTS – CONFLICT