An Illustrated Guide to the Structure of Global Markets

There was a Copernican revolution in 2008 in our understanding of finance and economics. There was, of course, the rediscovery of the non-neutrality of money. Macroeconomists had pretended for a half century that whatever finance was supposed to do in the economy could be captured by the money multiplier that related the quantity of money in the economic system to central bank policy. The entire edifice of modern macroeconomics was build on the premise that bracketing finance was an effective simplifying assumption; that what banks did was intermediate between savers and borrowers; that what really mattered were real quantities behind ‘the veil of money’. This paradigm mattered in the detail. Eg, Bernanke explained the failure of long-term rates to rise, despite Greenspan’s clockwork hikes in the mid-2000s, as a result of ‘a global savings glut’.

What was rediscovered in 2008 was that developments endogenous to the financial system had real consequences. They could generate financial cycles and asset price booms that could cause extreme dislocations in the real economy. That fluctuations in the risk-bearing capacity of market-based intermediaries drive fluctuations in asset prices. That banks, or non-banks performing banking functions, did not just respond to monetary policy innovations, but could and did create money out of thin air; that global financial intermediation was not a straightforward matter of intermediating between savers and borrowers; that funding was not saving; that the financial economy was not simply superstructure on top of the real economy. Finance mattered. And one simply had to pay attention to it, if one did not want to get things badly wrong.

The shock of the global financial crisis led to an intellectual revolution. Under the broad rubric of macrofinance, there appeared three highly-productive research agendas in what we may call the New Empiricist paradigm. The first, which came out of the Bank of International Settlements, especially Claudio Borio‘s work, paid attention to the financial cycle. This captured the slow-moving build-up of financial imbalances in the form of the coupled movement of private sector debt aggregates and property prices. It was shown that financial/credit cycles are much longer than business-investment cycles; that they are invariably coupled to housing and property prices via the collateral feedback loop; and that they can cause extremely destructive financial crises followed by long-lasting balance-sheet recessions. I documented the reemergence of the US financial cycle after a thirty year long period of financial repression — the 2000s were a replay of the 1920s, in the sense that both involved the coupling of housing finance and the financial cycle.

Farooqui (2016)

A second strand, led by Hélène Rey, sought to explain long-term fluctuations in real rates and risk premia — investor compensation for bearing financial risks. Here too, the explanandum was slow-moving variation, but in terms of prices rather than the quantities of credit. It was discovered by Rey that the consumption-to-wealth ratio contains predictive information about long-term fluctuations in the basic price of credit. I found that the consumption-to-wealth ratio also predicts property returns over a 10-year horizon. Research in this direction was greatly aided by the publication of the Jorda et al. macrohistory dataset.

Farooqui (2016)

These two New Empiricist research agendas were both focused on slow-moving or low-frequency fluctuations in macrofinancial quantities or prices of interest. Something quite different was going on in financial markets; which seemed to be populated more by short-horizon, inpatient investors rather than patient investors interested in long-term returns. We can define a patient investor as one with a net worth so large that they can ride out any cyclical downturn in asset price valuations, no matter how brutal. In practice, patient investors are what are called “real-money investors” in industry parlance — large institutional investors who are not much interested in leverage, speculation or risk arbitrage, but do have deep risk-bearing capacity. The problem for patient investors is the problem of long-term risk. This is a hard problem that we shall revisit another day. But how relevant is long-term risk to financial markets, which seem to live at a much higher frequency?

The third New Empiricist research agenda, intermediary asset pricing, concerned itself with the workings of asset markets. The discovery of intermediary asset pricing was that the marginal investor in securities is not your regular Joe — neither as a retail investor himself, nor indirectly via a patient intermediary. Rather, the marginal investor in asset markets was a market-based intermediary — hedge funds and other leveraged asset managers on the buy side and broker-dealer Wall Street banking firms on the sell side. Investment banks were intermediating not between savers and borrowers, but between money market intermediaries, who supplied the funding, on the one hand, and capital market intermediaries, who demanded funding to make leveraged bets, on the other — with the dealers making the market by taking the other side of the bet without immediately looking for an offsetting trade. So, dealers supplied both leverage and liquidity to risk arbitrageurs. In other words, global financial intermediation turned out be centered around a very specific market-based intermediary — it is a dealer ecosystem. What intermediary asset pricing, pioneered by Erkko Etula at Harvard and Tobias Adrian at the New York Fed and their coauthors, discovered, was that fluctuations in the risk-bearing capacity of the broker-dealers drove fluctuations in asset prices. The shadow price of dealer balance sheet capacity could be extracted from information contained in asset prices. More recently, I have shown how to isolate the signal for risk appetite at arbitrary frequencies from the term-structure of VIX futures.

Hélène Rey showed that fluctuations in the risk-bearing capacity of global banks explain fluctuations not only in asset prices quoted in New York, but globally. Specifically, she showed that a single global factor accounts for the bulk of the variation in global asset markets — the comovement of international markets is such as to constitute ‘a global financial cycle’ driven by the risk appetite of Metropolitan banks. Roughly speaking, the tide of banking flows lifts all boats on the way in, and lowers them all on the way out. This tidal motion, this ebb and flow of global finance, powerfully structures the returns of national stock markets. The structure that is revealed by paying attention to the joint fluctuations of global markets is more than economic. In particular, the comovement or otherwise of stock market indices contains information on the shape of global markets — a function of how the world’s nations are differentially-situated with respect to global finance. Put another way, the joint variation of national stock market indices contains information on the core-periphery structure of the world. For there is a natural way to define center and periphery with respect to global financial intermediation.

Here we look at the joint variation in the stock markets of 51 nations. All national stock market index data is monthly and obtained from Haver Analytics. As a first pass, we document the usefulness of a familiar financial market practice — distinguishing between advanced economies and emerging markets. We obtain developed market and emerging markets return factors from Kenneth French’s website. With these two features, there exists a separating hyperplane/support vector that classifies national stock markets with near-perfect accuracy.

Image

There are data availability issues. The number of countries for which we have index returns is low in the 1990s, and there are always holes in the dataset.

We therefore use Jakob Verbeek’s probabilistic PCA algorithm to extract the first principal component from when we have less than 10 missing observations (from a basket of 51), which we do from 1997. This is Rey’s global factor. This is probably the strongest signal we have of risk appetite at the monthly frequency.

PC1 of 51 national stock market indices.

The sensitivity of national stock market returns to the global factor tells us how close or exposed they are to global finance; that is, to fluctuations in the risk-bearing capacity of global banks. Low global factor beta means that the national stock market is more autonomous, autarchic, or peripheral; high beta means it is closer to the center. The barometer may not be perfect, but the signal is extremely strong. Note how far China is from the center of global financial intermediation. This should change as and when China removes financial repression and opens up its financial markets to global intermediaries. Although Wall St banks have gained a foothold in China, we are still very far from full-scale liberalization.

The sensitivity to the global factor measures distance from the center of global financial intermediation.

If we look at how potential center countries are correlated with the global factor, China is immediately revealed as peripheral.

If we throw out autarchic China, Japan appears as an outlier. The center of gravity of global markets is clearly in the Atlantic. The correlation of the global factor with the SP500 and the FTSE is 0.97; that with China is 0.26.

Global markets are still centered on the Atlantic.

Forget the global factor for a second. One of the most revealing graphs is a simple scatter plot of national stock market betas with the US and Chinese stock markets respectively. Even if we restrict the data to the 2010s, there is no competition between the US and China. Only Hong Kong has moved into China’s orbit a little bit. (See my tweet storm here.)

Image

So there is a whole lot of structural information in this dataset. How can we extract it and visualize it to get a handle on the shape of global markets? One way to summarize the large amount of information contained in data is to use hierarchical clustering. That allows us to represent an astonishing amount of information in a single “phylogenetic tree.” What we need for hierarchical clustering is a notion of pairwise distance between national stock markets. There are two ways to go about this. One is to obtain these distances from pairwise correlations, via the familiar formula, d_{ij} = \sqrt{1-r_{ij}}, that we can normalize by diving through by the square root of 2. This yields the following tree. Distance along the tree is a function of the correlation of markets — the closer, the more in sync. UK and US flock together, although not as much as the Netherlands and Germany. There is a lot more going on in this graph and it pays to stare at it for a while.

Tree representation of hierarchical clustering model using the UPGMA algorithm and correlation based distance metric.

Another way to go about this is to choose a small set of features that capture essential dimensions of variation in market returns, and compute the distance in this (suitably normalized) space. Here we use five features: the global factor, French’s AE factor, French’s EM factor, returns on the VIX, and returns on oil price volatility (OVX). We project national stock market index returns on these five factors separately, all robustly rescaled, and obtain the standardized slope coefficients or betas. Then we feed the pairwise distances between national stock markets in the space spanned by these betas into our hierarchical clustering algorithm. Again, it pays to pay attention to the graph — which contains an awful amount of information! The differences between the two trees are small. Which is more reliable? It is not clear. What is clear is that we can be certain about points of agreement between these two pictures of the shape of global markets — such as on China’s peripheral position — as opposed to where they disagree. Note that we have documented the pattern for global stock markets. But there is no reason to believe that the shape is any different for other securities; although property and other highly illiquid assets may be more autarchic.

Tree representation of hierarchical clustering model with the UPGMA algorithm and distance metric based on 5-factor betas.

What we have documented here is a clear discordance between the shape of global markets and the Toozian China-has-already-emerged narrative; one based almost entirely on purchasing power parity economic size comparisons and China’s structurally central position in global value chains. The stunning gap between China’s position in global markets and China’s position in global value chains is probably an artifact of Chinese financial repression. As and when China liberalizes its financial markets, it will probably become a pole of the world’s financial economy. For how could global finance resist? And that takes us straight back to Braudel’s theorem on the agnosticism of capitalism, especially after the switch to finance. More on that another day.


Postscript. We have reported two trees. One based on the distance derived from pairwise correlations between stock market index returns; another based on the Euclidean distance in reduced dimensions spanned by the elasticities with respect to five selected features. Another natural notion of pairwise distance in a space of reduced dimensions is that spanned by the principal components. Here’s what the scatter looks like with two principal components. (Recall that the first principal component is Rey’s global factor.)

If we use the first five principal components, we obtain the following tree.

Which is the more reliable tree of global markets? I was a bit flippant to pretend that the question could be avoided. It cannot. We need to be more precise about the structure of global markets. The space of phylogenetic trees/hierarchical models grows very, very fast. Moreover, I am unaware of a naturally defined notion of distance on this wild space.

fast.png

What we do have, however, is a well-defined, natural notion of distance on the space of pairwise distance matrices — the inputs of the hierarchical clustering algorithm that gives us the trees. This is the natural distance metric derived from the Mantel test statistic. The null hypothesis of the Mantel test is that two distance matrices are no more similar than would be expected purely randomly. The Mantel test statistic has the same mathematical properties as the correlation coefficient, and as we have seen before, d=\sqrt{\frac{1-r}{2}}, is a mathematically well-defined distance metric derived from the correlation coefficient. So, what is the distance between the three pairwise distance matrices which we have used as inputs to obtain our trees? The following table reports our estimates.

Table 1. Mantel Tests.
CorrelationCorrelationPCA
SelectedPCASelected
d0.4060.4040.409
r0.6710.6740.666
Z7.0487.1288.326
Notes: r is the Mantel test statistic, d is computed as the square root of (1-r)/2, Z is the zscore for the Mantel test.

The Mantel test statistic for all three pairs of five factor, PCA, and pairwise correlation distance matrices is roughly r = 0.67, with the result that the distance between the three matrices are close to d = 0.40. The z-scores show that we can reject the null in all three pairwise tests with high confidence. P < 0.0001 for all three pairs and is not displayed. The implications are twofold. First, our selected features were very efficient in the sense that we cannot do much better at all by blindly choosing the five principal directions of variation. Second, and more importantly, it shows that there is a lot more information in the distance matrix based on pairwise correlations between stock markets than is captured by either the principal null directions or our carefully selected features. In other words, reducing dimensions throws out important information in the joint variation of international stock market returns. Unless we have good reason to do so, we should use the full set of information contained in pairwise correlations. The most informative tree on the structure of global markets is therefore the following.

Every single feature of this tree is noteworthy. We can use nested brackets to represented the purely cladistic information (only splitting order sans any notion of distance) displayed in the tree. The tightest knit block, in terms of patristic distance (ie distance measured along the tree) is between the center countries: Netherlands, France, Germany on the continent, with Italy not far, and, of course, the US and the UK offshore. The core can thus be represented cladistically as (((Netherlands, France), Germany), (US, UK)). The rest of the AE’s can be split into three clusters: (((Switzerland, Belgium), Ireland), Denmark), (Spain, Portugal), and ((((Norway, Canada), Austria), South Africa), (New Zealand, Australia)). (Hungary, Czech Republic) are right outside this ring. At a much greater distance is ((((Japan, Finland), Greece), Israel), Turkey). The EMs are broadly split into three clusters of very unequal size. One is a singleton, Venezuela. It is close to the outer cluster of relatively autarchic markets (we can tell because their branches are much longer): ((((Pakistan, Morocco), ((Sri Lanka, Jordan), Nigeria)), China), Slovakia). On the other hand, you have the EMs more exposed to the whipsaw of the global financial cycle, made up of an East Asian cluster, ((((Singapore, Hong Kong), Taiwan), South Korea), ((Thailand, Phillipines), Indonesia)), a central-Latin American cluster, ((Mexico, Brazil), Columbia)). Interestingly, India is closer to the Latin American cluster than the East Asian cluster. Then you have Russia classified with the southern-Latin American cluster together with Egypt and Malaysia, (((((Russia, Chile), Peru), Argentina), Malaysia), Egypt).

Do you see what I mean by the astonishing amount of structural information on global markets contained in the tree?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s