Devil-Free Indexes

April 01, 1999

Constructing an index to include the correlations you want and exclude those you don't want can be more complicated than it seems. Individual stocks may fit the right categories for inclusion objectively, yet show strong correlations to unwanted influences. The author describes a process for identifying such mis-correlation and weeding it out from your index.

Tracking an index may be hard. Mis-tracking it -methodically and reliably - can be harder yet, aside from selling it short. But then, why should portfolio managers want to mis-track an index?

For some very good reasons, it turns out.

At heart an index is just a bundle of exposures. Apre-set bundle. With exposures come returns - hopefully the biggest returns for assuming these risks, if it is to be an 'efficient' index. But exposures are not just what you see, which stocks belong and how much they weigh. Each stock carries with it some hidden luggage, some covert links to other exposures -other stocks, other assets, other markets, here and abroad. Pick an index, any index, and chances are you'll get more than you bargained for. Your index may have hidden exposures to exactly what you don't want.

To date, index construction has focused on picking the 'right' stocks to capture the 'market', the sector, the style etc. Liquidity, float, accessibility to all investors: these are some of the key issues that take up most of the index designers'time. In some ways index construction is eerily reminiscent of drug research in times past. Up till a few years ago all sorts of substances and compounds were studied and checked against other findings. They were then clinically tried, until their effect against some ailment, some condition, had been firmly established. In our post-DNA world, things have become far more focused. With the mapping of the genome comes the hope of major breakthroughs: finding what causes the condition, pinpointing where the genetic code has erred, and what faulty message it is sending. Eventually custom-designed drugs may be built on this knowledge.

To progress, index design - like quantitative management - must follow a similar path: Here's a sample road map.

DESIGNER INDEXES FOR EVERYONE

Investors heeding the advice of the diversification gospel often go global. Alas, as they discover, salvation doesn't come so cheap, and brings far less than they'd hoped for. The demons of single market investing aren't so easily exorcised.

The message is right. But the messenger is wrong.

Going global doesn't just mean buying foreign stocks. It means buying the 'right' foreign stocks; and in the right proportions. In practice investors who want global exposure simply pick a 'global' index and go from there. But in global investing as in much else the devil's in the details. Ignore the details, lose the game. A 'foreign' index may well contain stocks that move in close concert with the 'domestic' trends you're trying to avoid or offset. A 'true' global index takes a lot of work to get those devils out and keep them out. Popular global indexes often fall far short.

Ideally a global index will mis-track a domestic one. In fact a good global index will mis-track methodically, reliably and maximally. You likely adopt it, after all, because you want diversification.

So to design such an index we must first single out what drives a domestic index - map out its genetic structure. Armed with this knowledge we can scan nondomestic stocks and gauge how far they depart from the domestic ones - how far their genetic code diverges from their domestic siblings'. Arbitrage Pricing Theory ('APT') shows how.

Here, for instance, is how we built a US-free index.

WILL 'REAL' US STOCKS PLEASE STAND

The first step is to pinpoint and map out the genetic structure of US assets. In practice, what does this mean? This is where common parlance leads us astray. To be sure, US stocks are typically issued by US-incorporated companies. But this is hardly helpful. Many a US company derives significant earnings from foreign operations - well over 50% in some cases. Conversely a 'foreign' company may be 'American' in all but name. So legal and geographical characteristics may be of little help here. What then makes a stock a US stock? It can only be what performance it shares with other 'US' stocks -and doesn't share with 'non-US' ones. It is more important to focus on price moves - returns - than on country affiliation. What differentiates US returns from 'US-free' returns? It is whatever US stocks share that foreign stocks do not. The key then is to single out and measure what 'drivers' propel their returns - and only their returns.

Imagine for a moment we could run the following experiments: starting from today's conditions (today's interest rates, inflation, exchange rates, industrial production, etc.), 'shock' each of these variables one at a time and observe how asset prices adjust to the new market order. Record this information and do it again. And again. And yet again. Pretty soon we have a palette of alternative histories. What could have been, had the stars lined up suitably that day.

Of course markets aren't so obedient. Yet if we drill down into the daily price swings of all assets, including interest rates, exchange rates, sectors, styles etc., we can in fact recover the basic drivers and map out their contributions to each asset. In short we can draw the genetic map of US (and non-US) assets. And tag each one according to its 'US-free-ness.'

Without going into the details of the mathematical construction, which can be arcane, we can get a glimpse of the process with a simple illustration. Take a set of hypothetical returns on six different, hypothetical assets. Figure 1 displays their time-series realizations.

For each time period on the horizontal axis we record the synchronous returns of each asset - its return on that day, that week, that month. Examining the graph reveals 'like' patterns amongst some of the assets, and not others. This analysis is reminiscent of the kinds of observations we read in market commentaries: 'Today, oils rallied sharply as Brent crude shot up on the announcement of massive military buildup near the Saudi-Iraqi border; market participants blamed the disappointing performance of airlines and utility stocks, in spite of strong earnings reports, on these Mideast developments;' 'As minutes of last month's Fed meeting were released, long Treasury yields sank over fifteen basis points, its largest drop in the last two years, as prospects for a rate hike at the next Fed meeting dimmed further; bank stocks and utilities also moved sharply, while the yen rallied against the dollar reaching a three month high.'

While we cannot 'shock' the markets at will and run experiments as scientists would, we do have access to a treasure trove of data like these. Data which, arbitrage pricing theory suggests, is indeed 'linked' by traders' efforts to boost performance and steer through treacherous waters. By carefully sorting through these massive databases with the help of powerful mathematical tools, we can indeed single out and measure the common drivers shared by different assets. As Figure 2 illustrates this is like finding and pulling the common threads running through various fabric samples.

As we carry this analysis forward a clear map emerges in which each asset is mapped into its own genetic code: a precise description of its exposure to the common drivers which together define what a US asset is - and what it's not. Think of these codes as the universal bar codes adorning the price tags of any product we buy today. While it takes many readings on lots of exposures (e.g. interest rates, exchange rates, inflation, industries etc.), we summarize each stock's bar code with a simple bar chart made up of a couple dozen bars. The height of each bar is proportional to that stock's sensitivity to each common driver. Graphically shared exposures translate into different bar codes.

Consider for instance two technology stocks: Microsoft and Sun MicroSystems. Figure 3 compares their shared exposures to common drivers of returns. There is a strong family resemblance between them. Indeed as we leaf through the family album to pick lookalikes we find other individual stocks, sector indexes and mutual funds with real family resemblances to Bill Gates' little company (Figures 4-6).

As we scan through the charts, the resemblance is striking. Yet the 'assets' we have chosen are clearly disparate: a sector index, a mutual fund and a foreign stock - Nokia. This last example underscores the challenge of designing a true US-free portfolio, to achieve effective diversification: Microsoft, a US company, has far more in common with a Finnish company, Nokia, than with another US company, even in the same sector, Tektronix (Figure 7).

Here we have two technology stocks both in the S&P 500 Index, Microsoft and Tektronix, with less in common than a US and a Finnish stock! The moral is clear: buyer beware.

But all is not lost. For these findings actually give us the road map to design a US-free index - an index sharing as little as possible with US stocks or their foreign siblings.

IN SEARCH OF A US-FREE INDEX

We first map the US market APTprofile just as we mapped individual assets (Figure 8). This is effectively our version of the genetic structure of the US market. As we take samples of other asset returns, we can test how well they match that of US assets. While the method is quite general, it is easy to customize it to one's own index. For instance, if a manager's view of the US market is the S&P 500 Index, we can narrow down our search around that index structure. Conversely, if his view is the broad US market, such as the Wilshire 5000, we can use its map as our reference map. Clearly the method handles any other view of 'US-ness' just as easily - for instance, style-based views, such as 'growth' or 'value.'

Without delving too far into the rather complex mathematics of 'DNA-testing' of stock returns, we can illustrate the basic approach graphically. Taking, for instance, a large cap Japanese stock, Nippon Yusen, we ask: (1) How much of its performance can be traced to US market-defined exposures; and (2) of thatpor-tion traceable to US market exposures, how closely does the exposure pattern fit the US code? We find that about 27% of Nippon Yusen's behavior is US market-driven and that its exposure code differs sharply from the US code (Figure 9). Nippon Yusen is clearly a good candidate to include in a true US-free Index.

Now pick another foreign stock, UK-based Danka Business Systems. Nearly 60% of its performance is US market-driven and unlike Nippon Yusen its 'code' is far closer to the US one (Figure 10).

Note in particular that while the bar code is systematically more stretched out than the US market one, its overall direction is broadly in sync with it. In the previous case, the overall directions were typically reversed. The stretching of the bars is simply the graphical signature of the greater volatility of that asset. Amore volatile asset that maps closely the reference (US) asset provides no US-free-ness since, by simply holding that asset in the proper hedge ratio (less than one in this case: for instance 1/3 Danka to 1 US) we can expect similar performance, and thus no effective diversification from US assets. In fact, without such hedging, Danka might actually increase the ' US-ness' of your index or portfolio.

As we map a broad universe of foreign stocks, an interesting picture emerges.

HIGHLIGHTS OF A US-FREE INDEX

Consider first the universe of the top capitalization 'foreign' stocks - the ones typically included in the popular global indexes. We started with a sample of 1,700 stocks drawn from the major sectors and the major equity markets of the world.

Mapping each of these stocks and code-testing them against our US market code shows an average shared US market exposure of 18%. Figure 11 depicts the distribution of these exposures across the whole sample. By way of comparison, note that the average US stock has a shared exposure with the US market that is near 50%. In this sample a 'foreign' stock averages well below half that. The average, however, masks sharp differences between different countries.

Taking each major national equity market separately and repeating the test yields a rather different picture (Figures 12-14).

The last chart is in many ways emblematic of the general pattern: at the US-free end are many Japanese stocks, while at the US-like end we find lots of Australian stocks. In between we find the European equity markets and some of the large emerging markets (e.g. Brazil). We also find the exception of Mexico, which is clearly in the US market orbit in spite of its emerging market status. This convergence towards the dominant trading partner economy is a general phenomenon. Our historical calculations show the accelerating magnet-like effect of the senior trading partner (United States) for Mexico and Canada. In the European Union the effect is even stronger, and accelerating with the launch of the Euro.

Traditionally economists have viewed 'optimal currency areas' in terms of some optimal distribution of production factors. In the new world economic order it may well be that initial factor endowments matter far less than the capital market structures and relationships of these economies.

Is such a US-free universe tradable, though? Taking for instance the bottom 50% of the universe in the distribution of Figure 11 ('Most US-free'), how much capitalization would we in fact capture? The fear of course is that we might effectively pick the 'foreign small-caps' to the exclusion of the large world-class companies. But this capitalization effect, as we note below, is primarily linked to sector effects, especially the massive capitalization of the oil companies and their worldwide reach and outlook. In this universe the bottom 50% - the most US-free equities - still account for nearly 40% of the total capitalization.

What about the Wall Street-bound US manager? The manager who wants to invest globally right in the US? For him ADRs (American Depositary Receipts) and other market instruments seem ideal. Yet, will his Wall Street focus deprive him of what he's really looking for - effective global diversification?

Taking the universe of US ADRs with sufficient trading history to yield a reliable map for code-testing against the US market, we find 851 stocks. To be sure in this ADR universe US exposure is more pronounced - 31% on average, rather than 18% for the top 1,700 foreign stocks.

But, as Table 1 shows, the distribution is not all that different.

TABLE 1
SHARED US EXPOSURE (%) TOP 1700 ADR'S
Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . 31
Median. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . . . 31
Min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . 1
Max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 . . . . . . . . . . . . . . . . . . 72
Stdev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . . . . . . . . . . . . . . . . . . 13

The capitalization effect of the world major oil companies is striking: oil companies make up over half (56%) of the top 50 US-exposed ADR's capitalization. Oil is truly a world business. Energy exposure is a globally shared exposure. While also emerging world businesses - and thus global exposures - telecoms and banking come a distant second and third, with capitalization shares of 24% and 13% respectively (Table 2).

Equally noteworthy is the US exposure of individual foreign markets when traded as single baskets ('WEBS'). Unlike Figure 13, which draws on a stock by stock mapping, if we take each market as a single asset - a 'WEB' - its exposure to the US market is very large as evidenced at the bottom of Table 2. In other words, while picking individual foreign stocks carefully, mindful of their US-free-ness, will limit exposure very effectively, picking a pre-packaged bundle will fail miserably. Global asset allocators beware! Indeed, this is precisely what global managers experienced in the last round of global market volatility in 1998: when diversification is most needed, correlation across markets climbs to 1! This need not be the case, though, as we have shown here: don't blame the message (diversification); blame the messenger (the index).

What we have just done for a US-free index applies everywhere, and to every category of index for which you might want an anti-index. Building 'Asia-free', 'Euro-free' 'growth' or 'value' indexes through their genetic APTcode offers the only sure way to achieve the best tracking - or mis-tracking! S

TABLE 2
COMPANY CAPITALIZATION SHAREDEXPOSURE (%)
Bp Amoco Spn.Adr . . . . . . . . . . . . . . . . . . . . . .175837.75 . . . . . . . . . . . . . . . . . .66
Shell Tran.Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76855 . . . . . . . . . . . . . . . . . .54
Vodafone Group Spn.Adr. . . . . . . . . . . . . . . . . . . .60971.5 . . . . . . . . . . . . . . . . . .58
Barclays Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48158.47 . . . . . . . . . . . . . . . . . .53
Nokia Spn.Adr. . . . . . . . . . . . . . . . . . . . . . . . . . . .40861.41 . . . . . . . . . . . . . . . . . .52
Elf Aquitaine Spn.Adr. . . . . . . . . . . . . . . . . . . . . .40504.83 . . . . . . . . . . . . . . . . . .54
Ing Groep Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . .38430.7 . . . . . . . . . . . . . . . . . .55
Koninklijke Phil.Eltn. Spn.Adr . . . . . . . . . . . . . . .34071.13 . . . . . . . . . . . . . . . . . .52
Total Sponsored Adr. 1 . . . . . . . . . . . . . . . . . . . .28592.07 . . . . . . . . . . . . . . . . . .52
Alcatel Alsthom Spn.Adr . . . . . . . . . . . . . . . . . .23153.85 . . . . . . . . . . . . . . . . . .51
Stmicroelectronics Adr . . . . . . . . . . . . . . . . . . . . .19704.15 . . . . . . . . . . . . . . . . . .58
Bnc.Santander Cent Hispano Adr . . . . . . . . . . . .14435.96 . . . . . . . . . . . . . . . . . .56
Ypf D Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13414 . . . . . . . . . . . . . . . . . .52
Bass Pub Spn.Adr. Adr . . . . . . . . . . . . . . . . . . . . .11629.16 . . . . . . . . . . . . . . . . . .55
Mitsui & Co.Adr. . . . . . . . . . . . . . . . . . . . . . . . . .11104.38 . . . . . . . . . . . . . . . . . .52
Brierley Invs.Adr . . . . . . . . . . . . . . . . . . . . . . . . . .7308.34 . . . . . . . . . . . . . . . . . .55
British Airways Adr . . . . . . . . . . . . . . . . . . . . . . . .6815.14 . . . . . . . . . . . . . . . . . .55
Enter.Oil Spn.Adr. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3157 . . . . . . . . . . . . . . . . . .52
Amvescap Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . .2484.49 . . . . . . . . . . . . . . . . . .70
Indosat Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . . .2019.22 . . . . . . . . . . . . . . . . . .57
Oce Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1643.18 . . . . . . . . . . . . . . . . . .53
Galicia Adr.'B' . . . . . . . . . . . . . . . . . . . . . . . . . . . .1634.32 . . . . . . . . . . . . . . . . . .53
Ptl.Geo Svs.Spn.Adr. . . . . . . . . . . . . . . . . . . . . . . . . .765.11 . . . . . . . . . . . . . . . . . .68
Aracruz Pnb Spn.Adr . . . . . . . . . . . . . . . . . . . . . . .614.57 . . . . . . . . . . . . . . . . . .57
Tamsa Adr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .606.99 . . . . . . . . . . . . . . . . . .69
Stolt Nielson Sa Spn Adr. . . . . . . . . . . . . . . . . . . . . .530.12 . . . . . . . . . . . . . . . . . .57
Coca-Cola Femsa Spn.Adr . . . . . . . . . . . . . . . . . . . .524.58 . . . . . . . . . . . . . . . . . .53
Desc 'C' Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347 . . . . . . . . . . . . . . . . . .54
Danka Bus.Sys.Spn.Adr . . . . . . . . . . . . . . . . . . . . . .319.36 . . . . . . . . . . . . . . . . . .58
Fletch.Chal.Forest.Divn.Adr . . . . . . . . . . . . . . . . . .230.95 . . . . . . . . . . . . . . . . . .57
Apt Sat.Hdg.Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . .213.28 . . . . . . . . . . . . . . . . . .55
Stolt Comex Seaway Sa Spn.Adr 'A' . . . . . . . . . . . . .210.21 . . . . . . . . . . . . . . . . . .59
WEBS Index Fd.Hong Kong . . . . . . . . . . . . . . . . . . . .98.51 . . . . . . . . . . . . . . . . . .53
WEBS Index Fd.Germany . . . . . . . . . . . . . . . . . . . . . .91.63 . . . . . . . . . . . . . . . . . .51
WEBS Index Fd.Uk. . . . . . . . . . . . . . . . . . . . . . . . . . .90.58 . . . . . . . . . . . . . . . . . .51
Menatep Bk.Spn.Adr. . . . . . . . . . . . . . . . . . . . . . . . . .89.43 . . . . . . . . . . . . . . . . . .60
Tmm L Adr.144a Adr . . . . . . . . . . . . . . . . . . . . . . . .74.77 . . . . . . . . . . . . . . . . . .52
Ceteco Holding Spn.Adr . . . . . . . . . . . . . . . . . . . . . .63.01 . . . . . . . . . . . . . . . . . .53
WEBS Index Fd.Australia . . . . . . . . . . . . . . . . . . . . . .60.41 . . . . . . . . . . . . . . . . . .53
WEBS Index Fd.France . . . . . . . . . . . . . . . . . . . . . . . .54.02 . . . . . . . . . . . . . . . . . .53
WEBS Index Fd.Neth. . . . . . . . . . . . . . . . . . . . . . . . . .27.32 . . . . . . . . . . . . . . . . . .52
WEBS Index Fd.Sweden . . . . . . . . . . . . . . . . . . . . . . .18.56 . . . . . . . . . . . . . . . . . .56
WEBS Index Fd.Canada . . . . . . . . . . . . . . . . . . . . . . .18.28 . . . . . . . . . . . . . . . . . .70
WEBS Index Fd.Mexico . . . . . . . . . . . . . . . . . . . . . . .17.05 . . . . . . . . . . . . . . . . . .57
Carulla Adr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.75 . . . . . . . . . . . . . . . . . .57
Djl Limited Adr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.77 . . . . . . . . . . . . . . . . . .72
Telecom Corp.Of Nz.Spn. Adr . . . . . . . . . . . . . . . . . . .0.02 . . . . . . . . . . . . . . . . . .62
Brahma Pn Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . . .0.01 . . . . . . . . . . . . . . . . . .56
Petsec Energy Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . . . .0 . . . . . . . . . . . . . . . . . .57
Telepartner A/S Spn.Adr . . . . . . . . . . . . . . . . . . . . . . . . . .0 . . . . . . . . . . . . . . . . . .55

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