Stochastic Bookmark

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Interesting times, timing interest

Attention conservation notice: A swerve into career history, plus wonky financial (and economic) speculations.

This being a hobby-blog, mostly on literature, I've only obliquely touched upon professional concerns (which are considered somewhat sensitive in the banking biz), but being sidelined for over a year now, I guess it qualifies as a hobby for now. Per my prior post, I've been upskilling on my own, which served me well once before, ten years ago. But expertise that I acquired well prior to that may be relevant to the shape of things to come, particularly the shape of the yield curve (beyond battered).

As a model-maker for market-makers before "financial engineering" was codified, I did pioneering work on the term structure of interest rates, e.g. in '86 on the application of principal component analysis (though the meteorologist I teamed with called them empirical orthogonal functions), or in '93 on the application of tension splines, for on-the-run Treasuries (in the latter case, replacing my funky very-high-degree polynomial method based on holding forward rate acceleration constant between knots, and paired with more conventional splining to price off-the-runs real-time; the former case represents my only brush with publication, a piece in a special advertising supplement in the June '87 Scientific American called "The Science of Making Money"). While yield curve dynamics are no longer my principal interest (sorry), under the circumstances I can't help but be drawn to the topic. But this being a low graphics blog, I'll paint word-pictures instead. (When college composition required a description of a physical object, I essayed a tesseract. You've been warned.)

Basics: The yield curve plots the annualized internal rate of return for recently issued (on-the-run) government securities (as if all the coupons returned or were reinvested at the same rate) against their term to maturity. To begin with, the three widely accepted configurations are "normal" (yields monotonically increasing with term to maturity), "inverted" (decreasing likewise), and "humped" (increasing to a maximum, then declining). This last generally has an inflection point after a hump (itself often around 2 years out), as rates level off for longer maturities; the normal yield curve may or may not have an inflection point early on, usually within one year to maturity. The current yield curve, while "normal" in shape, is abnormal not only in being so low (though Japan's has long been lower), but also in that its inflection point occurs farther out (2-3 yrs). The idealized flat yield curve is not considered a stable configuration (others can explain stuff like the market price of [interest rate] risk), but an unstable equilibrium, a transition state between the others. So, why did an essentially flat curve persist through '06 to the beginning of the credit crunch in Aug'07?

The shape of the curve is often taken as a harbinger for more than just future rates: for the economic forces that drive them, and for forecasting economic conditions (see Baum's May commentary). For example, an inverted curve is supposed to signal impending recession. (Contrarywise, even for signalling future rates, the curve retained a normal shape through most of the Great Moderation.) This is not something that is much under the control or influence of government intervention. The Fed traditionally sets only the shortest term rate, and the Treasury determines how much it needs to issue at what maturities; these actions, and market anticipations thereof, filter through the term structure. Current conditions being what they are, there's been fiddling with bits of the off-the-run curve even in the midst of massive new issuance, ostensibly to prevent localized distortions from affecting the whole market, but managing the curve itself to some extent as well.

Back to that flat curve preceding the financial crisis: There was a lot of ambiguity about whether it represented a true inversion; by one oversimplified measure, the 2-10yr spread oscillated between positive and negative. But viewed as a flat curve (which was resisted since it didn't fit the paradigms), the persistence was itself an indicator of something big in the works (like a monkey-wrench): The longer that a dynamic system spends in an unstable state, the more likely it is that the departure from it will be profound. And so it was ...

Principal component analysis derives modes of movement, daily changes in yields across the curve[1], that correspond to long-time practitioners' understanding. The primary mode is a parallel shift, in which all yields move up or down the same amount across all maturities (though a tad more in the middle ranges), and explains the bulk of yield variation; the second is slope change, steepening or flattening (again more pronounced in the center of the curve); the third is a bowing (or humping) of the curve (though the related trade is called a butterfly); the rest is noise.

The combination of these modes of movement in proper proportion give rise to all of the yield curve shapes described above. Plus one more: just as a normal curve can be inverted, so too can a humped curve, but an inverted humped curve was not thought to occur in nature, until it did in Germany in early '94. (NB: I'm working from memory here as I no longer have data access to be more precise.) Yields reached a minimum about 3 yrs out before increasing again. This was the result of a confluence of two historic events, the work-out from the reunification of Germany that preceded it, and the absorption of the Deutschesmark into the Euro that followed. This is not the sort of state of affairs that seems likely to recur, except that the U.S. faces the prospect first of exiting its extraordinary monetary stimulus, and second, of its reserve currency status being supplanted by something like Special Drawing Rights (SDRs) of which it would be the largest component. So, perhaps four years down the road, the U.S. bond market could experience the same inverted humped curve, but with an impact on derivative markets well beyond the previous German episode.

So, what does this add up to now? Well, one more attraction to Thursday's Treasury auction of 7-year notes, that step-child among the on-the-runs ...

[1] It would be too obtuse to link it up there, but for a daily pulse on the bond market, Across the Curve is unmatched.

Other readings:

Larry Wasserman, All of Statistics & All of Nonparametric Statistics: another recommend gleaned from Cosma Shalizi (his weblog also where I picked up the attention conservation locution); among other virtues, reconciles statistical and machine-learning perspectives.

Rick Perlstein, Nixonland: political history of the 60s, before I came of age.

Marcel Proust, Swann's Way: I thought that this would be a departure from financial topics and here I find it's a long segue about a stockbroker's son ...

On deck: Quantitative Finance and Risk Management: A Physicist's Approach, by Jan Dash, a fellow Merrillumnus whom I once had the pleasure of working with, and, who knows, may once again.