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Predicting the credit crisis

This is a must-read paper from John Taylor of Stanford University and John Williams of the San Francisco Fed. The gist of it, is that the US Federal Reserve’s Term Auction Facility (TAF) - the market saving plan announced in December - didn’t work.

…we put forth the hypothesis, based on a simple financial market model, that the Term Auction Facility would not reduce the spreads between Libor and the federal funds rate when correcting for term expectations, contrary to the purpose of the facility.

We show that increased counterparty risk between banks contributed to the rise in spreads and find no empirical evidence that the TAF has reduced spreads.

Such conclusions, of course, go some way against the grain of received wisdom at the Fed.

But perhaps the most interesting thing is a corollary of the research, rather incidental to its main findings about the TAF.

The graph below is an attempt at isolating the “expectation risk” of interest rates from lending and so capturing “pure risk” in interbank lending. It measures the Fed’s favoured metric for interbank lending risk - the OIS to Libor spread:

OIS Libor spread

Looking at spreads going back to December 2001 illustrates just how unusual this episode has been… the spread on August 9 was 25 basis points above the pre-August 9, 2007 average. That is 7 times the standard deviation before August 9-more than a 6-sigma event. The mean through March 20 was 16 standard deviations above the old mean, which under normality would have been an extraordinarily improbable event.

Statistically speaking, a six-sigma event should occur every 2,500,000 days - or once every 6849 years. Notwithstanding the fact that markets have experienced six six-sigma events in the past 20 years (what’s the probability of that?) they note that the OIS-Libor spread puts the current financial crisis as a sixteen sigma event.

Such perhaps, is the folly of stochastics. Even so, it’s the accepted line: statistically the credit crisis was shocking, sudden, and unexpected. Viz. there was a massive jump in market risk in August 2007.

Which is why taking a longer view is so arresting. Taylor and Williams also provide a graph going back to 1991 of 3 month Libor (unsecured) against 3 month treasury-backed interbank repos (secured). Although it’s more “fuzzy”, the authors do say it’s probably an even better measure of “pure risk” than the OIS-Libor proxy.

3 month Libor less 3 month Repos

Over the full sixteen year period, there are several spikes corresponding to past financial blips, of which the current is far and away the largest. What’s clear though, is that by any standard-deviation or measure of volatility over the longer period, the current crisis is nowhere near a six-sigma event.

So - extrapolating in lay terms here - while the current crisis was unlikely, it was historically predictable.

Unless of course, you succumbed to the seductive logic of the boom: just like the first, post 2000 OIS-Libor graph, the repo-Libor graph looks very different if you take it from the beginning of the current cycle:

Libor repo spread
We’re back again in the realm of six-sigmas.

Which, to some extent, seems to validate the oldest risk rule of them all: it wasn’t different this time.

This entry was posted by Sam Jones on Friday, April 11th, 2008 at 11:52 and is filed under Capital markets, People. Tagged with , . You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.

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Comments

  1. Apr 12   10:53 Posted by N Not Set [report]

    http://en.wikipedia.org/wiki/Chebyshev’s_inequality

  2. Apr 11   20:42 Posted by S Jones [report]

    by sb - do correct me if i’m wrong, as I’m no quant. But rating agencies as I understand things, used Guassian copulas in a whole range metrics. VECTOR, CDOROM etc, typically all use(d) them to model spread/default correlations.

  3. Apr 11   18:10 Posted by sb [report]

    While it is true that the normal distribution is often (sometimes legitimately) used for simplicity, you would never (in finance) use it to calculate the probability of a six standard deviation event, although of course in any model such an event is unlikely.

    The ratings agencies did questionably use normal based models (Gaussian copula) to estimate low probability events and assign AAA ratings, they did not use it in this way.

  4. Apr 11   16:32 Posted by burnt quant [report]

    It’s not hard to make a better stab at the model either - you could say that there are two market states, when risk spreads are high and when risk spreads are low and nothing in between. Then the volatility of the spreads are proportional to their level - which is Geometric Brownian motion a.k.a. Normal distribution of returns.

  5. Apr 11   16:27 Posted by pegnu [report]

    I think the crisis was predictable in the sense that people just can’t go on with lax and reckless lending forever without there being a day of reckoning. However, there is clearly a qualitative change in behaviour of those spreads during this crisis and previous behaviour and it is not just random noise even if you consider data back to 1992.

  6. Apr 11   16:20 Posted by pegnu [report]

    they use geometric brownian motion i believe.

  7. Apr 11   16:20 Posted by burnt quant [report]

    I’m afraid I am a bad writer - what I was really trying to say is that the conclusion about how “exceptional” these events have been is just more excuse making from the Fed for their own part in encouraging speculative excess. It sounds like it’s from the same hymn sheet as “you can’t predict bubbles before they burst”.

    I know it’s hard to predict a bubble, but really, if I turned up at work in the morning saying it’s too hard blah blah then I would fully expect to be shown the door.

  8. Apr 11   16:13 Posted by burnt quant [report]

    (1) Of course it’s not normally distributed. And as has been said this is one problem with VAR. You could try other distributions that have more area in the tails like T-dist or Pareto/Levy. They are much harder to work with which might explain why people try to shoe horn the Normal distribution in there. Alternatively you could say risk mgmt faces the difficult problem, viz you have a lot of broadly average days from which you want to estimate the highly improbable days. That is why so much of quantitative finance is like banging your head against a wall.

    (2) Does anyone else find the idea of starting this series in Dec 2001 fishy? I mean what is that like 6.5 years? There were two other significant liquidity events prior to then, around Dec 1999 (the Millenium) and Sep 2001 during which banks were less willing to lend to one another. By excluding these it makes the conclusion: “Looking at spreads going back to December 2001 illustrates just how unusual this episode has been” stronger. If you were setting out to prove something, like how unusual this is and how it could not have been foreseen, then I would take issue with this choice of period.

    (3) On more careful reading I now see that this is the point that Sam Jones is making. If you subscribe to the “seductive logic of the boom”, which of course the entire group-think Fed appear to do, and if you haven’t got a mind of your own and you exclude other bits of data that don’t fit in with “the spin” then you’ll be really surprised about once in a generation.

  9. Apr 11   15:45 Posted by S Jones [report]

    On meaningless statistics -

    Fully aware that 6-sigmas, 2.5m days etc. is a fairly meaningless number. It’s illustrative of the point, however, that it’s all too easy to say there’s no way we could have seen the credit crisis coming. Looking over a 15 year period, the mean volatility is far far more meaningful, than in a five year period.

    Also - re. normal distributions… I gather they crop up rather a lot in rating agency models.

  10. Apr 11   15:11 Posted by maximus [report]

    It is an excellent piece of research, regrettably despite the efforts of the Fed and the far less effective interventions by the ECB and BoE, the problem is going to persist until Governments actually act to create a market mechanism by which counterparty risk can be reduced. In his short article Luigi Spaventa from Rome University refers us back to Brady Bonds-remeber them, in the Latam crisis banks were similarly mired in debts that could not be priced or traded until Bradys allowed the often deeply discounted debt to be traded and gradually the system stabilised with the indebted countries relieved of the immediate debt burden to begin to grow again. Quite rapidly Brady bonds became highly liquid instruments and unblocked the arteries - they also were redeemed way prior to maturity and replaced with sovereign debt. The US Govt had to step in to suport these bonds but theey did the trick. It is not by any means a perfect correlation but unless similar types of mechanisms are in place I can see that the TAF or similar efforts will not work. The US Government despite the cries of moral hazard - we had that too- and bailing out reckless lenders needs to act along these lines to unblock this confidence problem amongst banks. We have been here before just in a different part of the globe

  11. Apr 11   15:06 Posted by Carlomagno [report]

    @sb: “Since no one with a basic understanding of statistics ever though that it was normally distributed, that number is completely irrelevant.”

    Doesn’t just about every VaR model assume a normal distribution?

  12. Apr 11   14:54 Posted by kt [report]

    Nice pick, this paper is a must read.

    But when is the financial world (including our esteemed FT corespondents) going to stop using meaningless statistics?

    Surely the significant information is that there have been six periods of large scale market movements in the last 20 years.

  13. Apr 11   14:09 Posted by Carlomagno [report]

    Sam, you are a geek. BTW, nice post! ;-)

  14. Apr 11   12:51 Posted by sb [report]

    Interesting article.

    However, when you say,
    “Statistically speaking, a six-sigma event should occur every 2,500,000 days - or once every 6849 years. ”

    What you mean is

    “Statistically speaking, if the spread is normally distributed, a six-sigma event should occur every 2,500,000 days - or once every 6849 years. ”

    Since no one with a basic understanding of statistics ever though that it was normally distributed, that number is completely irrelevant.

  15. Apr 11   12:09 Posted by pegnu [report]

    nice post.

    3M LIBOR less 3M Repo, I would say they are both possibly more than 6 sigma as the spreads have never been this elevated for this long. By which I mean, the longer it remains at this elevated level, the more statistically significant it becomes surely?

This post is closed to further comments.