Against the Gods: the Remarkable Story of Risk. Peter L. Bernstein. John Wiley & Sons, Inc. 1996. 383 pages
review by Otto Steinmayer
Against the Gods, with that juicy word “risk” in the subtitle, promises a series of thrilling stories of desperate ventures that paid off, or maybe didn’t. Open it up, you see that it’s about probability and statistics. Nonetheless, there are two activities in life where numbers go to the gut as well as the brain: when we count our money, and when we reckon our odds. Look at the lines outside the 4-D shops, the crowds at Genting. The placing of a decimal point on the stock pages can decide whether Broker X buys another Mercedes or jumps off a twelfth-floor ledge.
Peter Bernstein is a rare bird, an investor/scholar who understands both the head- and (so to speak) the bowel-approaches to risk. His analysis is simple in essence. We have to make decisions, and the future is unpredictable. However, the probability of an event can be estimated. By a constant refining of our understanding of probability and of the range of uncertainty, we can reckon our risks ever more precisely, and thus manage them. That means calling in the help of number.
Probability theory has a long history, which Bernstein traces in engaging style.
In the Renaissance, academics did not just stab each other in the back figuratively; they were wild enough to stick it in literally, and, true to the times, even professors of mathematics could be obsessive gamblers. Dice was a favorite addiction, and money aside, the problems dice pose are neat and abstract. Mathematicians began studying probability by calculating the combinations, odds, and what it would take to win.
Games of chance are at best an entertainment.
Their risk is the spice of play, and your average gambler plays to win;
losing is not an option.
Businessmen, however, must calculate their odds more soberly. Insurance, the best example, is as old as trade, and risk is its business. Insurers aim not merely to gamble and win—maybe. Ships arrive safe; ships also go down. The underwriter must face the fact that he’s going to win some and lose some. But by determining what odds he’s got, how many ships sink for how many that come to port, the broker can, much of the time, fix a premium that will both attract the purchaser and make a profit for himself.
To determine odds, one needs statistics. As early as the 16th century, the English government attempted to raise money by selling annuities. These were sold at a fixed price, regardless of the age of the buyer, and paid back their purchase price in seven years. Naturally, the government lost, for the life-expectancies the deal was based on were a mere guess and gross underestimate.
Then John Graunt and Edmond Halley (he of the comet) in the 17th century took the trouble to analyze actual parish records. For the first time people had a scientific view of the chances they had of living to any age, and insurers had something better than a guess on which to run their business.
The great discovery bodied out in the science of statistics was that with investigation and method number can be assigned to the probability of any event you care to name. Early statisticians felt that only a very large sample, and preferably a sample that included every instance, was necessary for data. Later mathematicians such as Abraham de Moivre demonstrated that even a random sample will give a clear picture how the whole field lies. This led to the concepts of distribution around the mean, pictured in the famous Gaussian curve or “bell curve”—familiar to anybody who has taken an examination—and standard deviation.
Meantime Daniel Bernoulli introduced the Law of
Diminishing Returns with a parable of two people playing a coin tossing
Peter will pay Paul one ducat if heads comes up on the first toss, two ducats if heads comes up on the second toss, four ducats on the third, and so on. With each additional throw the number of ducats Peter must pay Paul is doubled. How much should someone pay Paul—who stands to rake in a sizable amount of money—for the privilege of taking his place in the game?
Although Paul’s prospects are theoretically infinite, Bernoulli declares that no one would be prepared to pay more than a moderate sum for the chance to play. To put it simply, this so-called “Petersburg Paradox” is a mathematical demonstration of the saw that “a bird in the hand is worth too in the bush,” or as Francis Bacon said: “Hope is a good breakfast but an ill supper.” The corollary is that any mathematically fair game is a loser’s game, eventually even for the winner, for the utility of the money he may win is much less than what he stands to lose.
My grandfather, who played the market in the 20s and did shrewdly enough to remain solvent after the Crash, told my father: “I’ll bet, [viz., on a sure thing] but never gamble.” The successful entrepreneur may be bold, enterprising, aggressive; he tolerates risk, but according to Bernstein he is not foolhardy. People are rightly and naturally risk-averse, and prefer a sure thing, even though modest. There’s always risk; if you want to profit, you must hazard losing. But the Lady Or The Tiger—if accepted willingly—is a madman’s bet—you stand to lose more than you could ever possibly gain. All these emotional approaches are supported by the maths.
Economics, however the media protray it, is not a game, though chance and uncertainty operate largely within it. With the complications of global trade and interdependence of economies in this century, it has become clear that decisions on financial risk cannot be based either on emotion and guess or on an over-rational model such as the Victorians favored. Yet the world cannot afford another Great Depression, and the goal of such economists as Keynes, Arrow, von Neumann, and Markowitz, has been to find out how to get the most performance out of the market while keeping risk to an acceptable level. Along the way they have contributed largely to the study of probability in both the abstract and the practical senses.
Bernstein brings his story goes quickly on to the
present day, and he discusses the dynamics of investment in detail.
Here, I lacked the experience to compare Bernstein’s theory to
practice, for I have never played stocks and bonds. But, I am sure that
engaged investors will find plenty to relish.
At my level what I got was this strategy, a development of Game Theory. When information about the next move is scant and uncertain, don’t play to win, play not to lose. This is the rationale of diversification. (It’s interesting that this advice is exactly the opposite of what you must follow in games of chance or of skill, but then the stock market shouldn’t, ideally, be a game.)
As an instance, I spoke to a friend of mine who manages clients’ investments. He said that anybody could do what he does, if they had 20 hours a week to spend on research and business. Problem is, he continued, people who need to make money by investment don’t have 20 hours a week to give to investing. So, rather than take your capital, quit your job and take a big one-shot risk, it’s better to let someone (such as him) to manage it for you.
I especially enjoyed Against the Gods as
a most clear introduction to economic concepts I knew nothing about
before. For me, the historical approach works best. The mysterious
surface of economic jargon hides some very plain concepts and much
human feeling. The “derivatives”, for example, we’ve heard so much
about operate on a principle of futures, which is as old as commercial
I (and John Kenneth Galbraith) recommend that
even professional investors read Bernstein carefully, so they may see
how intellect and passion, and the awe of uncertainty have shaped the
business they ply.