Books off the queue and lodge securely somewhere behind my eyes: “A Mathematician’s Apology” by G.H. Hardy and “A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation” by Richard Bookstaber

- A Mathematician’s Apology by G.H. Hardy (with a foreword by C.P. Snow)

I was really looking forward to reading this classic, since mathematicians certainly have a lot to apologize for. Sadly Hardy instead writes a fairly depressing defense of mathematics from a fairly dogmatic view of the subject. Of course, he has every right to this view (unlike me, who barely deserves to be writing this parenthesis) seeing as how he produced such a fine quantity of the pure stuff. Highlights of the book, for me, were C.P. Snow telling us that precocious boys do long division when they are young, and Hardy lamenting how certainly the “theory of numbers” is of no practical use. Since our modern public key cryptosystems are based solidly on the “theory of numbers” I found that this part of the book made me the happiest. Not because he was wrong, but because it seems that even someone as brilliant as Hardy, cannot see the future and predict the usefulness of today’s obscure mathematics in tomorrow’s world.

- A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

Quantitative finance, risk, hedge funds, and lots and lots and lots of financial disaster as told from a front line witness. Bookstaber tells the story of many of the most famous financial crisis of our time (LTCM, 1987, etc.) and tries to bring some sense into why each of these events happened. Basically, Bookstaber argues that decreasing the complexity of financial instruments and breaking the coupling of transactions are key to decreasing the likelihood of future financial crisis. The book is an entertaining read, with a scattershot of stories centering around Bookstaber’s career, but also varying as far as feudal England property markets and Three Mile Island.

It has been a while since I read “Apology”, but from what I remember, Hardy didn’t lament that number theory had no applications, rather, he reveled in it. It would be interesting to see his reaction to modern cryptography and algorithms that make heavy use of the stuff.

It also makes me wonder… there are many areas of mathematics that I currently consider too “pure” (read: abstract) to be useful. Some of these have already found use in the hands of the right people (e.g. n-categories and John Baez). So clearly my opinion is under-informed. But, there must be mathematicians today that hold similar but better informed opinions about current mathematics. If they are as spectacularly wrong as Hardy was, then what amazing uses will these ideas have in another 50 years? One can but dream.

Is it that short-term rewards are significant enough for the financial analysts to overlook the long-term risks/instabilities?It would be interesting to look at this from the point of view of how financial analysts are paid. If my own personal money isn’t directly invested in a product, and I get componsated by how the product performs in the short term (and not penalized when things go wrong), it seems that I’m not really incentivized to properly analyze risk. But certainly there must be analysts who stradle this categorization and do invest a sizable portion of their own money in the instruments they analyze. So it should be possible to tease out whether the later outperforms the former in analyzing risk (of course it may be that the later are, by selection, larger risk takers, so there needs to be some way to control for this…doh.)

Bookstaber’s work fundamentally rests on a lack of transparency in the financial markets. Financial innovation of late has led to increased use of complex leveraging schemes in the markets, apparently leading to confusion about the level of risk in a particular investment portfolio. In today’s NYTimes Krugman argues that this kind of opaque investment strategy caused various institutional investors to take on more risk than they perceived, and in part precipitated the liquidity meltdown we’re seeing today.

The appropriate analogy would be the use of proofs and theorems in mathematics and physics. Imagine every scientist took as good faith that a particular theorem was appropriately supported and vetted. You can easily envision a proliferation of fragile lines of arguments, such that the eventual collapse of one insufficiently tested theorem produces a catastrophic collapse of numerous theorems downstream.

Of course, physics and math rarely work like this, but the financial markets, for all their quantitative analysts, seem to have fallen into the groupthink hole pretty easily. Why? Is it that short-term rewards are significant enough for the financial analysts to overlook the long-term risks/instabilities? Thoughts?

My understanding is that by and large, investment analysts earn most of their income through bonuses which reflect their individual performance and the firm’s financial position. They do not have remuneration tied into the long-term prospects of their portfolios.

A close associate in finance who will remain nameless has gruffly likened many financial analysts to “dumb jocks” who suffer greatly from groupthink – no one wants to be left out of a huge investment opportunity – and who rely on the claims of others to motivate their investment strategies. The widespread meltdowns of many financial houses and hedge funds over the subprime and other past crises seems to suggest there is a lack of independent analysis. Further, there have been many reported cases of analysts pushing a stock in order to benefit their margins in the short run, despite well-understood long-term problems with certain investments.

So even if analysts do invest in their own recommendations, they seem tied only to the short-term returns, and are hence disincentivized from worrying about the overall validity of their claims (so long as enough people jump on the wagon, the stock will go up!)

So if you don’t like the book, is it “off the queue and into the geraniums”?

Sorry, I couldn’t resist.