A “systemic vulnerability index”: Measuring risk in the asset generation chain

Leonardo Felli, Luca Anderlini

22 August 2009

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Civil aviation is remarkably safe. IATA numbers put the probability of death at roughly one in 7.7 million passenger/flights in 2008. This makes air travel about 120 times less dangerous than car travel in the US, although the numbers are hard to compare.

Suppose you didn’t care about time or other airport hassles, only about survival, and had to go from New York to Los Angeles. If you fly non-stop you face a probability of one in 7.7 million of dying. If you stop over in Chicago O’Hare, you face the same risk twice, since flight-cycles are what count. That turns out to be a one in 3.8 million chance of dying. If you stop six times en route, you will die with a probability of one in 1.1 million. (This is still way safer than driving your car and less likely than being struck by lightning.)

The reason no-one thinks of layovers as dangerous is that flying is very, very safe. If each individual flight gives you a one in 25 chance of dying, then stopping six times en route increases it to a probability of one in four that you will be dead before touching down at LAX. Most people would think pretty carefully at this point.

At the end of the day, financial securities are no more than claims on some (combination of) underlying economic activity. Just like flights, securities can be non-stop (direct claims) or they can involve (sometimes many) intermediate stops (indirect claims). This is obvious but its importance has, in our view, been seriously under-appreciated in recent times.

Say you want to buy some Bunds (German government bonds). You have two means of purchasing them. The first is to have your bank buy the Bunds and have them in your name, with perhaps the bank acting as custodian. The second is that the bank buys the Bunds, which it holds in its name and issues a “mirror contract” to you that mimics the Bunds. The first is a non-stop flight; the second involves a layover. If each leg of the trip is really safe, then why should you care about the difference?

Now suppose that the date is 15 September 2008. Lehman has just gone to the wall; the financial equivalent of a disastrous storm progressively hitting all US airports, and quickly engulfing the whole planet. Each flight is quite dangerous. Suddenly the mirror contract looks quite different from the non-stop flight. In the latter case, it’s between you and the German government. In the former, for your piece of paper to perform as promised, both the bank and government must be solvent.

Measuring systemic vulnerability

Counting the number of stops or “contractual layers” that are between a security and the underlying economic activity, in most cases, is a relatively simple affair. We think that an index – just a single number, counting stopovers – of this kind is a reasonable gauge of the systemic vulnerability of a financial instrument (Rochet et al. 1996; Kiyotaki and Moore 1997; Allen and Gale 2000).1 A high SVI (“Systemic Vulnerability Index”) means that during a systemic storm, the security may not perform as intended or may not perform at all until bankruptcy proceedings are well under way. In fair weather, what matters is not the SVI of a security, but its letter rating and other standard measures. The letter rating of a security is, one hopes, already the letter rating of the weakest link (the most dangerous of the flights involved) in the chain.

The currently available financial vocabulary lacks words like the SVI that describe the “stress attributes” of financial instruments. This is a problem in more than one way.
Regulations, such as Basel II, often invoke standard letter ratings to determine whether and in what way various instruments may fulfil capital requirements (See Bolton et al. 2009 for the analysis of how standard letter ratings fail in stormy weather). But capital requirements are precisely designed to ensure the viability of financial institutions through bad weather.

This is by no means a new discovery, but recent events are a sharp reminder that financial storms can become systemic – and pretty quickly too. So, why should a AAA security with an SVI of 1 be treated by capital requirements regulations in the same way as one with the same AAA rating but an SVI of, say, 5? The latter is not at all uncommon by our count.

If something is of interest to regulators, it must be of interest to investors. If regulations were perfectly watertight then maybe investors could simply ignore systemic risk. But 15 September 2008 comes back to mind pretty quickly again. A security’s SVI is clearly not a measure of its volatility, and this is not why investors would ever be interested in it. A Bund with two mirror contracts instead of one has an SVI of 2. A “call on call” composite option on a volatile stock has an SVI of at most 2 (the SVI is actually 1 if the call and the call on call are “written” by the same player). Bunds never have been and never will be as volatile as that.

What if one layer of a security is made up of many “diversifying elements,” as in the case of mortgage-backed securities? If all the elements were sufficiently small (one can envisage a threshold level on the overall value – perhaps 5%?) and not highly correlated (these are the statistical requirements for actual diversification to take place), then the entire layer would be counted as increasing the SVI by 1. If the mortgage-backed security were then pooled with others into a CDO, the SVI would increase again.

At least until very recently, the Italian Post Office was marketing to the general public structured obligations that contained a substantial exposure to Merrill Lynch bonds. It is somewhat surprising that SVI indices are not already available. Perhaps the 79 years of relative systemic calm between 1929 and 2008 explain why. We think now is the right time to have a simple way to tell your grandmother that her life savings may disappear into thin air. Perhaps she would not have embarked on the plane trip in the first place.

References

Allen, Franklin and Douglas Gale (2000) “Financial Contagion,” Journal of Political Economy, Vol. 108.
Bolton, Patrick, Xavier Freixas, and Joel D. Shapiro (2009) “The Credit Ratings Game” Working Paper, January 1.
De Bandt, Olivier and Philipp Hartmann (2000) “Systemic Risk: A Survey” ECB Working Paper No. 35, November.
Kiyotaki, Nobuhiro and John H. Moore (1997) “Credit Cycles,” Journal of Political Economy, Vol. 102.
Rochet, Jean-Charles, Jean Tirole, Raghuram G. Rajan (1996) “Interbank Lending and Systemic Risk,” Journal of Money, Credit & Banking, Vol. 28.


1 The literature on financial vulnerability and systemic risk is relatively recent. See the survey by De Bandt and Hartmann (2000).

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Topics:  Financial markets

Tags:  systemic risk, bonds, systemic vulnerability index

Professor of Economics, London School of Economics

Professor of Economics, Georgetown University

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