Against the Gods by Peter Bernstein

In the last few months, I read two books about the history of finance: Against the Gods by Peter Bernstein and The Ascent of Money by Niall Ferguson (there is a very watchable DVD version, as well).  My first thought, when I decided to read up on finance and money, was to dive into the deep end with one of the subprime mortgage crisis books. But I found that there were so many, each claiming to know the reason for the  meltdown, that I decided to table that effort. I decided to start, instead, with a couple of broader-perspective historical books. These choices, I have to admit, were a matter of laziness and convenience rather than careful and deliberate selection. Still they did the trick. Though they were somewhat random starting points, both books are pretty good, and they got me thinking about money in productive and stimulating ways. Let’s tackle the first one,  Against the Gods.

Against the Gods

Bernstein’s book suffers from a major flaw that almost makes it worthless: it was first published in 1996, with a second printing in 1998. The infamous Black-Scholes-Mertens Long-Term Capital Management (LTCM) fiasco and 1998 bailout by Clinton didn’t make it into the book. Instead, we only get a treatment of the early Black-Scholes options pricing work which won them the Nobel prize and made their reputations.

For those of you who are even less educated in matters financial than I am, the only reason I bring this up is that the timing of the book’s publication lends it a surreal age-of-innocence quality. The book is about the history of money, risk and finance all the way up to the point when most thinking adults completely lost faith in Santa Claus Wall Street (the laggards who missed the 1998 sneak preview lost faith in 2008). Ferguson’s 2009 book, which I will review later, has a very different paradise-lost quality to it.

What saves the book is a general tone of rather old-fashioned caution, and respect for the subject and its pioneers. Some days, when you are watching Jon Stewart interview yet another smug 20/20 hindsight author, with a  me-too “how we got screwed” book to pitch, it is easy to forget that the invention of modern finance is a major accomplishment. For all its flaws, it is possibly the most important invention in history. Peter Berstein, who died in 2009, had the ideal background to approach the subject in this respectful way. He was both a solid (and perhaps stolid) conservative investment intellectual, and a practitioner of the black arts, as a manager of large funds. You don’t get the sort of irreverent polemic you get with say, Nicholas Nassim Taleb (Fooled by Randomness and Black Swan are both must-reads for anyone interested in finance; you should finish them even if you find yourself itching to wring Taleb’s smug neck by page 3).

The book is billed as a history of risk, but it is really a history of money and financial risk, not risk in general. There is no complex, textured blending of multiple unstable narratives. Bernstein has no messy doubts about who the heroes are. For him, the history of finance is basically the history of applied mathematics, with minor supporting roles being played by the bankers, investors, and the like.  The background too, is set up in straightforward, almost 19th century ways: the story is painted on an unexamined Greeks-to-Renaissance-t0-Modernity canvas. It is an example of the sort of approach to history that makes more (post)modern historians want to throw up.

But for all these flaws, this is an interesting and valuable book, if only because risk is a very good lens through which to view the history of money.

Part I

The book is chronologically organized (another element of its extreme traditionalism). Part I is the history of risk up to about 1200 AD, and has a good deal to say about Diophantus, the early renaissance, Arab contributions, and the story up to the beginnings of modern European mathematics with Fibonacci in Liber Abaci. But much of this part of the story is really the history of mathematics in general, and if it interests you, you are much better off reading something like Edna Kramer’s The Nature and Growth of Modern Mathematics (a truly stupendous book, one of my top 10).

Part II

Bernstein’s story gets more interesting with Part II, which covers the period 1200 to 1700 AD. This is the era dominated by the early Italian and French pioneers of probability, who drew their inspiration from problems in gambling.  The stars of this section are Cardano, Pascal and Fermat, who, among them, built a theory of probability starting with cute little gambling brainteasers. This is perhaps the most interesting story in the book, since it is also the story of how modern institutionalized science began, through informal gatherings such as the ones organized by Abbe Mersenne and extended correspondence amongst collaborating mathematicians (the drawing room gatherings of Mersenne eventually led to the emergence of institutions such as the Royal Society).

Fermat attacked the subject through algebra, while Pascal attacked it with innovative methods drawn from geometry.  The correspondence between them is one of those legendary stories in mathematics, and Bernstein tells it well.

At this point, the whole story takes a more practical turn, and elements of modern finance start to appear. Chapter 5 hops across the English Channel and covers the birth of empirical statistics and modern actuarial science, through the work of John Graunt, who took on the project of tabulating statistics on births and deaths in London. That work eventually led to the emergence of one of the pillars of the modern  finance industry: insurance.  Much of modern insurance began in England, and Graunt’s work was among the triggers. Scottish Widows invented modern life insurance, and it began as an effort by mathematically-minded priests looking to take care of actual widows in their parish (the modern models in Scottish Widows ads represent a bit of a departure from those beginnings). Lloyd’s organized the insurance business in shipping (which may have had quite a bit to do with how Britain overtook the continental maritime powers, despite a somewhat later start), and laid the foundations for the business of insuring against risks in the enterprise of capitalism.

Part III

In Part III (1700-1900), we head back across the Channel, this time to yet another colorful chapter in the history of mathematics, one that revolves around the family Bernoulli. I can never keep the many Bernoullis apart in my head, but among them, they managed to take the basic axiomatic probability theories of Fermat and Pascal, the empirical work in England, add ideas about what we know today as utility theory, and synthesize the beginnings of a recognizably modern edifice. With the work of the Bernoullis in place, humans could now properly use the past to reason about the future, and samples to reason about wholes. This was probably the moment of birth of all modern financial weapons of mass destruction, as Warren Buffet calls them. The assumption that the future will be like the past, essential to most models, is probably the root of every problem in finance, since it is so easy and tempting to forget that it is in fact an assumption.

The dangers did not go unnoticed, and were spotted in the earliest days. In one of the quotable bits, Bernstein notes that Leibniz took  “a dim view” of the Bernoullis’ approach to modeling empirical realities with theoretical models. Leibniz reportedly wrote to Jacob Bernoulli,

“[Nature has established patterns originating in the return of events, but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary.”

The quote seems surprisingly modern and Taleb/Black-Swan like, and to be fair to the recipients of the warning, the Bernoullis and others never forgot Leibniz’ warnings. It is mostly their lesser disciples who did the convenient forgetting.

From the Bernoulli family in Europe, we move back to England, another priest, Thomas Bayes, and an expat Frenchman, De Moivre. Bayes invented the methods we use today to factor the past into decisions about the future, while De Moivre figured out standard deviation.

Two foundation stones remained. The first was the work of Gauss, who finally systematized the familiar toolkit of today: the normal (bell curve) distribution, error functions and ways of measuring the significance of deviations in trend data. Through this work, another big assumption underlying many statistical models, the idea of “independence” of statistical variables, was built into the foundations of financial mathematics. The assumption that one thing does not affect another thing is so useful in modeling that it is easy to throw it in and forget it, just to simplify complicated things. It is so tempting to do so in fact, that Nobel prize winners did it, with multi-billion dollar consequences (this is the Black-Scholes-Mertens fiasco which I mentioned earlier).

Thinking about such basic things — future-is-like-the-past, things-are-independent and the infamous correlation-is-not-causation — is really scary in a way. Contrary to what a lot of people seem to be saying, the big flaws, the spectacular collapses, don’t occur because the experts got something enormously complicated wrong. We’d like to believe that; that very complicated Quant Black Magic went wrong. It would be reassuring if that were so. But no, in most cases I’ve read about, people forget about basic sanity checks on modeling assumptions. This is basic stuff that gets taught very early, and reinforced repeatedly, in any mathematics-based discipline. But that’s the problem. We get so used to ritual graduate school incantations that begin “assuming that x(t) is independent and identically distributed…” that we forget that they are not mere rituals. They are boring checklist items (I need to read Gawande’s Checklist Manifesto)  that you need to get out of the way before you get to the cool stuff. And sometimes, in the excited rush to the cool stuff, we don’t do these modeling safety checks. I hate to admit it, but I’ve made these mistakes too (though never with billion-dollar consequences).

Anyway, back to the book.  Part II ends with one last foundation stone: the innovations inspired by the theory of evolution, and pursued by Darwin’s cousin, Francis Galton. Galton of course, is responsible for sparking off eugenics thinking, but he also made legitimate contributions to the foundations of finance, through his development of the idea of regression to the mean. I really enjoyed this Galton quote describing this subtle idea:

The child inherits partly from his parents, partly from his ancestry…[T]he further his genealogy goes back, the more numerous and varied will his ancestry become, until they cease to differ from an equally numerous sample taken at haphazard from the race at large….This law tells heavily against the full hereditary transmission of any gift…The law is even-handed; it levies the same succession-tax on the transmission of badness as well as of goodness. If it discourages the extravagant expectations of gifted parents that their children will inherit all their powers, it no less discountenances extravagant fears that they will inherit all their weaknesses and diseases.

This is interesting because Galton did not want to discover this phenomenon, since it made the foundations of eugenics suspect. That’s another story, but the idea of regression to the mean is, today, a big part of the theology of markets, the theory of business cycles, and “what goes up must come down” thinking in general. Bernstein has a very thoughtful discussion of how regression to the mean influences Wall Street thinking. It shows up everywhere from gut-instinct trading strategies to the assumptions buried inside complicated algorithmic trading strategies. But the validity of a lot of this is somewhere between murky to downright idiotic.

Part II ends with a quick chapter on the developments in utility theory after the Bernoullis, through the work of Jeremy Bentham and his followers, and connects the dots to early “Political Economy” (mostly, but not quite, what we understand today as macroeconomics).

Part III

Part III, which covers 1900 to 1960, is very appropriately titled “Clouds of Vagueness and the Demand for Precision.” That describes exactly how I feel about modern finance: maddeningly precise treatments of frustratingly obscure and suspect foundational ideas. This part of the story is home territory for Bernstein and the book changes tone from historical to op-ed like.

The modern story begins, in Chapter 12, with Louis Bachelier, a student of Poincare, who wrote a dissertation titled “The Theory of Speculation” which, though underappreciated at the time, laid the foundations of modern options pricing theory (and predated Einstein’s work on random walks, which is more generally viewed as the inspiration for theories of price movements). The story moves on, in Chapter 13, to Keynes and his less well-known contemporary and nemesis, Frank Knight, who eventually ended up at the University of Chicago where he founded what is today the “Chicago school” of economics.

Next, in Chapter 14 we get a treatment of the development of game theory by Von Neumann and Morgenstern (like I said, the book tells the unsurprising version of the story; there are no big surprises in what’s included, and in what order). What was new to me though, was the details of the story told from the perspective of the history of finance and economics (since I am more familiar with the physics/engineering aspect of the story).  Particularly interesting, for those of us who learned game theory through rock-paper-scissors examples, is a detailed discussion of an economic game suggested by Alan Blinder, a Vice Chairman of the Fed from 1994-1996. The game is a “Politicians versus Federal Reserve” situation that models how the two sides fight over interest rates and budget surpluses (the objective, as modeled in the game, is that each side wants the other to make the unpleasant decisions).  It was an entertaining and illuminating example (I’ll skip the details, but the moves in the game are do nothing, contract spending, expand spending).

Chapter 15 tells one of the stories that was completely new to me: the origins of portfolio theory in the work of Harry Markowitz, a Chicago grad student in the early fifties. Markowitz was the first to properly think through the idea that you needed to look at both risks and returns, and recognize the implication: that you needed to invest in portfolios. This seems like common sense, and to a certain extent it is, but the contribution was to work out exactly how a bundle of investments with variable risk/return expectations ought to be put together. In other words, he worked out the basic mathematics of diversification, which is why you and I invest in mutual funds today, rather than individual stocks. Markowitz’s work has since become controversial, but the basic ideas seem to have endured anyway.

The book has an extended technical discussion of the strengths and flaws of portfolio theory, the most significant of which is that volatility is not a good measure of risk. Which means that Markowitz’ methods manage the wrong thing in many situations. That’s a complicated point, but there is a cute, user-friendly anecdote, credited to portfolio managers at BZW Global Investors, that kinda explains it (or at least, leaves you with an illusion of comprehension):

A group of hikers in the wilderness came upon a bridge that would greatly shorten their return to their home base. Noting that the bridge was high, narrow, and rickety, they fitted themselves out with ropes, harnesses, and other safeguards before starting across. When they reached the other side, they found a hungry mountain lion patiently awaiting their arrival.

The point (as in Taleb’s Black Swan) is about the effects of what gets left out of models of risk management (Bernstein’s comment on the anecdote: “I have a hunch that Markowitz, with his focus on volatility, would have been taken by surprise by that mountain lion.”) There is a limit to the value of managing known unknowns.

Chapters 16 and 17 provide a discussion of behavioral economics (an early take, and one that seems dated given the truckloads of books on the subject that have appeared since). Chapter 18 finally gets to the black magic subject: derivatives.  Though I’ve called the book an age-of-innocence book, it isn’t entirely innocent. There is a short but thoughtful discussion of the dangers of the murkiness of derivatives. You’ve probably heard the Buffet phrase I used earlier (“financial weapons of mass destruction”) and the book offers two similar thoughts:  “Are derivatives a suicidal invention of the devil or the last word in risk management?” and a quote attributed to James Morgan, a Financial Times journalist: “A derivative is like a razor. You can use it to shave yourself… or you can use it to commit suicide.”

It would appear that we’ve chosen to commit mass suicide.

The book ends, rather appropriately, on a pensive, doubtful note, in a concluding chapter titled “Awaiting the Wildness.” Seems to me we are in the “Wildness” now.