Book Review: Fischer Black

The book is by Perry Mehrling and the full title is Fischer Black and the Revolutionary Idea of Finance.

I loved this book. I read it like a textbook--marking up my Kindle with extensive highlights, reading several chapters multiple times, and writing detailed notes so I don't forget so much. I was even inspired to look up a couple of Mr. Black's original papers.

It's not for beginners--I've read a couple econ textbooks, which seems sufficient. A little math background will be helpful--if you know what a random variable is you'll do just fine. That said, Mr. Mehrling writes extremely well, and a close reading will be rewarded.

Fischer Black (1938 - 1995) is most famous for the Black-Scholes equation for pricing options, in collaboration with Myron Scholes, following on work by Robert Merton. In 1997 Scholes and Merton were awarded the Nobel Prize in Economics, an honor Mr. Black would surely have shared had he lived long enough.

The mechanics of his life are not dramatic. He graduated in physics from Harvard, and then went to MIT to study computer science/statistics/economics, etc. He was sufficiently smart that they let him hang around without making much progress toward a degree, but eventually he settled on a thesis in operations research, for which he had already done the work. He graduated with a PhD within a year of formally entering the program.

He was married three times and fathered five children.

The first third of his career was spent as a consultant for Arthur D. Little. The second third was in academe, initially at the University of Chicago, and then at MIT. For the last decade he worked at Goldman Sachs. He died of throat cancer.

Mr. Black became interested in finance while still a grad student, during which time he met the founder of the modern discipline, Jack Treynor, who became his muse and colleague. Unlike Mr. Treynor, however, Black saw a deep connection between finance and economics. The result is he was always the odd man out--too much of finance guy for economists to take him seriously, and too much of an economist to fit in with the finance community.

The enormous progress in finance made during the 1960s was due largely to the newly available computer technology. Prior it had been impossible to test financial theories--investing was done on the basis of a hunch and hot tip. But computers demonstrated that stock prices moved randomly around a mean, and sometimes the variance was large. A lot of people traded on the noise, confusing it with the signal. Noise trading is never profitable on average, and including transaction costs it's a guaranteed loser.

Mr. Black asked why people persisted in noise trading--and that got him interested in behavioral economics.

Three themes dominated Mr. Black's thought: 1) the Capital Asset Pricing Model (CAPM), 2) the efficient market hypothesis, and 3) equilibrium.

CAPM, inherited from Jack Treynor, is summarized by this equation,
                                     ,
where E(Ri) is the expected return on the investment in an individual stock i, and E(Rm) is the expected return on some market index (e.g., the S&P 500). The equation tells you how you should price an individual stock with respect to the market index. It can be generalized to include assets other than stocks, such as real estate, precious metals, etc.

The equation contains two parameters that Mr. Black considered to be of central importance to all economics. Rf is the risk-free interest rate, i.e., the interest rate you will receive for the safest investment you can imagine (e.g., the Fed funds rate). is the volatility of stock i compared to the volatility of the index. Very risky (noisy) investments have a large beta, while safe (less noisy) investments have a very small beta. Beta is a measure of risk, and can be measured by calculating the variance (or variation) of price over time. CAPM says that the higher the risk, the greater the return on investment.

The efficient market hypothesis (EMH) claims that market always prices stocks in a way consistent with CAPM. That is, the price of share i will be E(Ri) + noise. If EMH is true, then it will be impossible to profitably trade stocks, since all you could do is trade on noise.

Or, to paraphrase Warren Buffett: if EMH is true, then how come I'm so rich? Mr. Buffett--who got rich by trading stocks--did not have much use for EMH.

That brings us to equilibrium, which is a funny word. In chemistry, a system is at equilibrium when it no longer changes over time. I think Keynesian economics views the concept in a similar way; they always talk about the natural rate of interest or the natural rate of unemployment. The goal of policy is to achieve that nirvana of natural rates where (absent external shocks) the economy will be stable, i.e., in equilibrium.

Mr. Black thought about equilibrium in a completely different way. In his view, equilibrium existed when there were no arbitrage opportunities. In other words, if assets were always priced by CAPM, and markets were invariably efficient, arbitrage would be impossible. There would only be noise, but never would there be time-independent stability as predicted by Keynesian models.

But EMH isn't always true. Markets are often out of equilibrium, and that leaves the door open for traders to make money. The effect of trading will be to pull the market back to CAPM and EMH.

In some cases disequilibrium arises from human nature. In particular, human intuition about risk is not accurate: we underestimate the risk of driving a car, and overestimate the risk of flying on a commercial airline. It's the same with stocks. We tend to be loss averse, which means we overvalue safety and undervalue risk.

That's precisely the disequilibrium that made Warren Buffett's fortune. He bought low risk stocks (calling it "value investing") instead of high risk stocks. Because people consistently underestimated the risk, he got them for cheap, which means he made a killing. He arbitraged our psychological biases.

I don't think that trick works as well anymore--sophisticated program trading is all over it. The arbitrage pushes the market back to CAPM, thus minimizing trading profits.

The biggest source of disequilibrium comes from government. The IRS taxes This and doesn't tax That. For Mr. Black that's a perfect trading opportunity--go long on This while going short on That, and pocket the delta (i.e., take money away from the IRS).

Armed with these concepts, Black and Scholes derived their famous options pricing formula--something that could never have happened prior to the computing age. An ability to price options has led to a whole zoo of derivatives and hedges, but in their day the only available option was the warrant. A warrant was an option to buy a stock at a particular price at some date in the future.

The counter-intuitive result was that the warrant price did not depend on the price of the underlying stock at all. It depended only on its volatility, i.e., its beta value.

Two things need to be said about Black-Scholes. First, it assumes a simplified, cartoon model of reality. For example, it supposed that the inflation rate was zero. In doing so it revealed a basic truth about the nature of things, but one had to be careful about its application to any particular problem. Second, suitably adjusted, Black-Scholes can be applied to any option--and even to things that aren't options but behave like them.

The quants enthusiastically adopted Black-Scholes, and completely forgot that it was too simple by half. They fell in love with their computers and took the results as good coin no matter what. The outcome--much to Mr. Black's dismay--was that Black-Scholes was increasing noise rather than decreasing it. It inspired him to write an essay entitled The Holes in Black-Scholes, in an attempt to reverse the trend.

I found Mr. Black's understanding of money to be exceptionally interesting, and I now describe it here in my own words. For simplicity we imagine a cartoon world.

Consider Germany and Italy back in pre-Euro days when the Germans counted their Marks while the Italians spent their Lira. Imagine also that Germans ate bratwurst every day, for breakfast, lunch and dinner. They bought bratwurst for Marks, and because the market was so large and so steady and so liquid, the price of a bratwurst hardly changed at all. The volatility was very low. A German in Berlin, spending Marks, could buy bratwurst at the risk-free price.

Similarly, our cartoon Italians are addicted to spaghetti, which they eat every day for breakfast, lunch and dinner. They pay for it in Lira, and for identical reasons an Italian in Rome, spending Lira, can buy spaghetti at the risk-free price.

Occasionally, however, Helmut and Hilda, feeling adventurous, instead of eating bratwurst for dinner they go to an Italian restaurant to eat spaghetti. The market for spaghetti in Berlin is much smaller, less liquid, and therefore much more volatile. Sometimes spaghetti is cheap, and other times it's expensive. Unlike bratwurst, spaghetti is a risky good--on bad days the restaurateur will lose money, while on good days he'll make a killing.

Likewise, back in Rome, Mario and Maria hire a babysitter so they can go out for some bratwurst. They hope it will be cheap that day, because like spaghetti in Berlin, bratwurst in Rome is a risky good. The price varies by a lot.

In Germany, bratwurst is a risk-free good, while spaghetti is a risky good. In Italy it's the other way round. When a German uses his Marks to buy Lira, what he really is doing is purchasing an option to buy spaghetti at the risk-free price. And likewise, when an Italian buys Marks, she is really purchasing an option to buy bratwurst at the risk-free price.

Please read that last paragraph again to make sure you understand it.

Thinking of currencies as an option to buy risk-free goods means that the Black-Scholes formula (suitably modified) applies to currency transactions as well. That is, the exchange price between Marks and Lira depends on the volatility of spaghetti prices in Berlin and bratwurst prices in Rome. That is, it will depend on the price of risk.

To make the model less cartoonish, substitute for "bratwurst," a market basket of items typically purchased by German consumers in Berlin, and for "spaghetti," a market basket of items typically purchased by Italian consumers in Rome. Both of those are risk-free goods, but move them to the opposite capital they become risky. The exchange rate between Marks and Lira is proportional to the cost of that risk.

Note that this way of thinking about currencies puts the gold bugs out to pasture. The cost of bratwurst in Berlin is incommensurate with the cost of spaghetti in Rome. And if you reverse the capitals the prices are equally incomparable. There is no single price of gold that's going to measure both of them meaningfully.

The Euro won't work, either, and for the same reason. Since market baskets in Germany and Italy really are different, I think the Euro project is doomed. It's an attempt to take the risk out of risky goods by fiat.

So I really like Mr. Black's model (and kudos to Mr. Mehrling for explaining it to me). But I'm skeptical, and here's why.

Note that, in Mr. Black's model, currency fluctuations depend on different consumption baskets in different countries. So I used to live in Buffalo, where we spent greenbacks. Forty miles away is the comparably-sized city of Hamilton, Ontario, Canada, where they buy stuff with Loonie coins. For the life of me, I can't see much difference in what we consumed in Buffalo vs. what they consumed in Hamilton. We eat the same food, live in the same houses, drive the same cars, speak the same language, attend similar schools, get the same haircuts, etc. There may be small differences, but no spaghetti/bratwurst distinction.

That implies that the exchange rate between dollars and Loonies should remain about constant. So I'll remind you that in 2014 the Loonie bought US$1.05, while today it only fetches $0.76. That's a big delta for what should be a near risk-free exchange!

The common reason given for fluctuations in CAD/USD exchange rates is the price of oil--Canada is dependent on oil exports to the US. In 2014 oil cost about $100/bbl--today the price hovers around $55, which seems to explain the drop in the Loonie. And maybe that's true, but it's inconsistent with Mr. Black's model. In his account currency exchange rates are established by differences in consumption patterns, not production patterns.

That aside, Fischer Black had lots of other thought-provoking ideas, and Perry Mehrling's book explains them clearly. I highly recommend Mr. Mehrling's biography of Fischer Black.

(Apologies for exceeding my self-imposed word-count limitation. I just had too much to say.)

Further Reading:

• Book Review: Tomorrow 3.0
• Crypto as a Global Currency
• What Marxists Don't Understand About Economics