Understanding risk is essential to successful investment management, yet most common measures, like beta, capture only risk within markets – disregarding systemic risk of the markets themselves. Fortunately, new research is now shining light on “fragility” or systemic risk – how fast and how severely an unanticipated event will propagate through the markets.
These studies were pioneered by Mark Kritzman, who recently shared a “Top Ten” list of the most systemically crucial companies and industries today. But before I channel David Letterman to relay those rankings, let’s review the theory behind this new research.
Though it may be futile to try to beat the market through security selection, Kritzman – the prominent quantitative manager, educator, and author who is currently managing director and chief investment officer of Windham Capital Management – nevertheless believes that the stock market, or any market taken as a whole, can be priced incorrectly. In a recent issue of Financial Analysts Journal, Kritzman admonished readers to “respect the micro-efficiency of markets” but also to “Manage the macro-inefficiency of markets.”1
Kritzman has been researching how best to follow his second imperative for some time. In 2010, in the same journal, he published a paper on how to measure financial turbulence, which he defined as “a condition in which asset prices, given their historical patterns of behavior, behave in an uncharacteristic fashion, including extreme price moves, decoupling of correlated assets, and convergence of uncorrelated assets.”2 He noted there that in periods of financial turbulence, returns poorly compensate for risk, and that, although such periods arrive unexpectedly, they tend to persist. His measure, he suggested, could be used to stress-test portfolios and to adjust their composition to make them more resistant to turbulence.
On Tuesday, December 20, Kritzman spoke to the Boston chapter of QWAFAFEW (Quantitative Work Alliance for Applied Finance, Education, and Wisdom) about his latest research, which examines the large-scale fragility of equity markets. The subject, complementary to his previous research, was systemic risk and the sensitivity of sectors, industries, and individual companies to that risk. His talk was a summary and update of a recently published
paper of his. (At the outset, he acknowledged his collaborators, William B. Kinlaw and David Turkington, both of State Street Associates/State Street Global Markets.)
1. Mark Kritzman, “Post-Crisis Investment Management,” Financial Analysts Journal, January/February 2011, Vol. 67, No. 1:4-8.
2. Mark Kritzman and Yuanzhen Li, “Skulls, Financial Turbulence, and Risk Management,” Financial Analysts Journal, September/October 2010, Vol. 66, No. 5: 30-41.
Measuring fragility
Kritzman began by defining and distinguishing two terms: systemic risk and systematic risk. Systematic risk is that which a security takes from its exposure to the market (or other broad explanatory factors). This form of risk is better known as “beta.” Systemic risk, by contrast, is risk inherent in the market as a whole. It is the risk that a narrow shock will propagate through the entire market.
For some decades, investors (at least those who heed financial economics) have concerned themselves with systematic risk. But in the aftermath of the recent global financial crisis, investors and policy-makers have turned their attention to systemic risk.
Kritzman’s presentation divided into two main parts: first he identified his measure of the “fragility” of markets, and then he identified a separate measure of the linkages of any entity in the market (companies, industries, and sectors) to other entities, and thence to their sensitivity to the market fragility. The more that, say, one company is linked to other companies, the more sensitive it is to shocks to the system. For example, he asked, if anyone had known before the recent financial crisis of the extent of the linkages between AIG and other financial companies, would he have continued to rely on AIG to underwrite insurance?
Because of the difficulties inherent in trying to estimate systemic risk through fundamental analysis, Kritzman and his associates have come up with a measure of fragility that relies solely on historical prices. The obstacles to fundamental analysis of systemic risk include:
- Securitization obscures the connections among stockholders
- Private transactions obscure connections among companies
- Complexity reduces the clarity of the connections
- “Flexible accounting” hides financial linkages
- Even if we could identify the relevant linkages, they do not remain constant
Kritzman and his associates term their measure of fragility the “absorption ratio,” which is the fraction of the total variance (in its statistical meaning) of the return to an asset or set of assets that is explained or “absorbed” by a finite and fixed number of factors.3 Kritzman calculates these factors from price history, using principal components analysis. Recognizing the finite patience of his audience, Kritzman skimmed over the precise details of his mathematical formula, but for those who may be interested, he and a different set of coauthors derived the formula in a paper first published in 2010 and updated in 2011.) For those concerned with the current pertinence of a calculation based on historical prices only, he explained that he uses the most recent 500 days of data, with an exponential decline in the weights placed on them.
Kritzman’s measure reflects the degree to which markets are “coupled.” When markets are tightly coupled, they are fragile, and shocks propagate through them with greater rapidity and consequence. When the measure is low and the markets are not tightly coupled, they are more resilient.
Kritzman and his associates have found that changes in the absorption ratio, rather than the absolute level of the ratio, best capture turning points in market fragility. An illustration plotting, over time, both changes in the absorption ratio and the level of the stock market helped to make his point. It showed that there were instances, following a rise in the absorption ratio, when nothing dire happened to the markets. But although not all rises in the absorption ratio were followed by market “draw-downs,” as he termed them, nearly all market draw-downs were preceded by rises in the absorption ratio. This is a reminder that the absorption ratio is not a forecasting tool; it captures only the fragility of markets. If, when the markets are fragile, there are no severe shocks to the system, then the level of the market will not be affected.
3. Actually, eigenvectors.
A typical objection from his critics to this work, Kritzman said, is that averaging the correlations of returns among a large group of securities would be much simpler and work just as well. Kritzman, however, argued that correlations pay no attention to the relative significance of particular securities; they capture different information. He has found that the average correlation is of no help in the determination of market fragility. That said, he conceded that one might be able to tweak a measure of weighted average correlations to produce a useful measure.
Reinforcing his case, Kritzman said that he has applied his methodology to markets around the world – even to the Case-Shiller real estate index – and found that the absorption ratio works similarly in all.
Measuring systemic importance
In the second part of his presentation, Kritzman offered two new measures. One, which he called “centrality,” captures three characteristics:
- How broadly and deeply an asset is connected to other assets in the system
- The asset’s vulnerability to failure
- The riskiness of the other assets to which it is connected
The mathematical methodology behind the calculation of centrality, which Kritzman again briefly passed over, resembles that for the absorption ratio. To give an intuitive grasp of it, though, he pointed out that in its simplest form, with just one factor, his centrality calculation resembles Google’s PageRank algorithm, which places search results higher in the search engine’s results the more they are linked to and relied upon by other sites.
Centrality, as Kritzman estimates it, captures the degree to which an asset drives the market’s variance, he explained. What matters far more to an investment manager is the inverse: identifying the assets that are of most concern when market fragility is greatest. To determine this, he applies to a list of assets a statistical screen that is based on the deviation of their centrality at times of high market fragility from their long-term averages, and he ranks the results. This ranking, or screen, is his other new measure, which he terms “systemic importance.”
Kritzman presented two tables of systemic importance, of sectors (aggregated from industry scores) and of industries. (Both were calculated with respect to a baseline average of their centrality from December 1997 to June 2011.)
Top Sectors by Systemic Importance |
Average Percent Rank |
Energy |
85 |
Financials |
75 |
Telecommunications Services |
64 |
Information Technology |
62 |
Health Care |
46 |
Consumer Staples |
43 |
Consumer Discretionary |
39 |
Materials |
35 |
Industrials |
34 |
Utilities |
30 |
Top Industries by Systemic Importance |
Average Percent Rank |
Diversified Financial Services |
95 |
Capital Markets |
94 |
Software |
92 |
Commercial Banks |
91 |
Communications Equipment |
90 |
Oil, Gas, and Consumable Fuels |
90 |
Computers and Peripherals |
90 |
Real Estate Investment Trusts |
87 |
Pharmaceuticals |
85 |
Industrial Conglomerates |
85 |
When it comes to individual companies, Kritzman cautioned that his methodology is not the only way to estimate their systemic risk. Estimates of corporate systemic risk have been made by the Financial Stability Board (FSB), as requested by the G20, using fundamental data. But the FSB’s methodology is immensely time consuming. It took the FSB two years to produce its list of the 29 most systemically important financial institutions globally, which it released on November 4, 2011. In contrast, Kritzman and his associates, using their methodology based only on prices, were able to produce a comparable list in one week. Kritzman stressed that his methodology is not necessarily superior, only more timely, though he then went on to say that his may also capture information overlooked by the more labor-intensive approach.
The overlap between Kritzman’s list and that of the FSB was 80%, which suggests that they were pretty much capturing the same thing. And some of that 20% difference has a simple explanation: the FSB’s study did not look at insurance companies – AIG, for instance, is not on FSB’s list – whereas Kritzman et al. made a point to include insurers in their survey of the financial services sector.
Ranking the riskiest bets
Kritzman concluded his presentation with a top-ten list of the most systemically important financial institutions, calculated as of November 25, 2011. In true “Top Ten” fashion, here they are in countdown order:
10. |
Royal Bank of Scotland |
9. |
HSBC |
8. |
Barclays |
7. |
Lloyds Banking Group |
6. |
Santander |
5. |
BNP Paribas |
4. |
Wells Fargo |
3. |
JP Morgan Chase |
2. |
Citigroup |
1. |
Bank of America |
By his calculation, the market is especially fragile right now, which implies that if there is bad news, the market’s response will be much worse than it would be were it not in a fragile state. If you believe in Kritzman’s methods, then, any long-only portfolio containing these stocks, you should underweight them in comparison with the weights that you might otherwise give them.
It seems Kritzman’s approach to systemic risk is gaining recognition. During the question period that followed his formal presentation, Kritzman said that he had not yet applied his method to credit default swaps (CDS), but the U.S. Treasury had contacted him, and he thought that they might want to apply the method to the CDS of European financial institutions.
Adam Jared Apt, CFA, is a financial advisor and the owner of Peabody River Asset Management, based in Cambridge, MA.
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