### Risk Aversion

Think of your wealth as a pile of bricks with large bricks as the foundation and with smaller bricks the higher you go. A brick that is removed from the top will be larger than the next brick you can add to the pile. The pain from losing a brick is greater than the pleasure of gaining a brick.

Bernoulli gives the example of two men, each worth 100 ducats, who decide to play a fair game like tossing coins. There is a 50-50 chance of winning, with no house take. Each man bets 50 ducats on a throw, so each has an equal chance of earning 150 ducats or ending up with only 50.

Would it be rational to play the game? The mathematical expectation of each man’s wealth is 100 ducats (150 + 50 divided by 2). This is the same value as what they would each have if they chose not to play the game. The rational decision is to not play.

Bernoulli’s theory of utility reveals an asymmetry that explains why this game is unattractive. The potential of losing 50 has greater utility than winning 50.

Bernoulli uses this example to warn gamblers that even in a fair game (which is never the case in gambling), they would lose utility if they played. This depressing conclusion is a sign of nature’s admonition to avoid the dice altogether. We are what psychologists and economists call “risk-averse.”

### The Stock Market

Imagine your stockbroker recommends a mutual fund that invests a selection of the smallest stocks in the market. In the last 69 years, the bottom 20 percent of the stock market gave a capital appreciation that averaged 18 percent a year. This is a generous return, but the volatility was high – two-thirds of the returns swung between -23 percent and +59 percent. Negative returns over yearly periods happened one-third of the time and averaged 20 percent. This implies that the outlook for any year is highly uncertain, regardless of the long-term average returns of these stocks.

Now imagine that another broker told you to invest in a fund that buys and holds the S&P 500 Index. The average annual return on these stocks over the last 69 years has been around 13 percent, but two-thirds of the annual returns vary between -11 percent and +36 percent (a narrower range), and negative returns have averaged 13%.

If the future looks like the past, and you don’t have 70 years to find out how well you did, is the higher expected small-stock fund enough to make up for its greater volatility? Which mutual fund would you invest in?

### Regression to the Mean

The sayings “What goes up must come down,” “Pride goeth before a fall,” and “From shirtsleeves to shirtsleeves in three generations” should sound familiar. They are all informed by once principle: regression to the mean (Galton’s idea).

Joseph had this preordained sequence of events in mind when he predicted to Pharaoh that seven years of famine would follow seven years of plenty. It is what J.P. Morgan meant when he observed that “the market will fluctuate.”

It is the motto of the so-called contrarian investors, when they think that stock is “overvalued” or “undervalued.” They mean that either fear or greed has encouraged people to drive the stock’s price away from it’s real value, from which it will return. It is what motivates the gambler’s fantasy, that a long series of losses will give way to a long string of winnings.

Regression to the mean is religiously followed on the stock market. “Buy low and sell high” is the accompanying folklore, as well as “You never get poor taking a profit,” and “The bulls get something and the bears get something but the hogs get nothing.” They are all variations on the same idea. But many investors violate this rule every day because they find it emotionally difficult to follow. They are haunted by either greed or fear and run with the crowd instead of thinking clearly.

It is not easy to stay calm since we don’t know what the future holds – it is easier to think that the future will be like the present than to admit that it will change. A stock that has been going up for a long time seems like a better buy than a stock that has been falling for a while. We assume that a rising price means that the company is doing well and that a falling price means the company is in trouble. Why should we take a risk?

History tells us that many legendary investors made fortunes by betting on regression to the mean, buying low and selling high. They include Bernard Baruch, Benjamin Graham, and Warren Buffet. This contrarian position is confirmed by significant academic research.

But we only hear of the successful stories. We don’t hear of the investors who tried the same thing and failed, because they acted too soon, or didn’t act all.

Consider the investors who had the nerve to buy stocks in early 1930, right after the Great Crash, when prices had fallen about 50% from their previous highs. Prices would fall another 80 percent before they hit bottom in the fall of 1932. Or think of the cautious investor who sold out early in 1955, when the Dow Jones had finally regained their 1929 highs and tripled over the next six years. In both cases, the anticipated return to the “mean” failed to occur, and normal found a new location.

### Chaos Theory

Chaos theory says that what seems like chaos is truly the product of an underlying order, in which

insignificant events are often the cause of inevitable crashes and lengthy bull markets. The New York Times of July 10, 1994, reported an elaborate version of chaos theory by a Berkeley computer scientist, James Crutchfield, who “estimated that the gravitational pull of an electron, randomly shifting position at the edge of the Milky Way, can change the outcome of a billiard game on Earth.”

Proponents of chaos theory reject the symmetry of the bell
curve as a description of reality. They

have contempt for linear statistical systems that
assume the magnitude od the expected reward is the same as the magnititude of
the expected risk. They reject conventional theories of probability, economics,
and finance. They would call Galton a fool, and Pascal’s Arithmetic Triangle a toy
for children, and the bell curve is a caricature of the real world.

The most popular example of chaos theory is that the flutter of a butterfly’s wings in Hawaii that is the ultimate cause of a hurricane in the Caribbean. To chaos theorists, there are no such things as norms. The idea of a symmetrical deviations from the norm is nonsense since the mean is always in flux.

### Portfolio Theory

Markowitz thought that variance was the key method of measuring risk. Diversify your risk, and you minimize variance. If faced between a choice of investing in the S&P 500 or a 30-year Treasury bond, the investor should go with the latter because bonds have a lower standard deviation. But a higher return can compensate for greater volatility if the total stock return is sufficiently high.

One of the risks of timing the market is being out of the market when it has a big upward move. If a market-timer was in cash instead of stocks for only the five best days in the market (between May 26, 1970 to April 29, 1994) then his investment would have doubled instead of tripled during that period.

The annual standard deviation of monthly returns on the S&P 500 was
17.7% from the end of 1984 to the end of 1990; but decreased to 10.6% a year
for the next four years. Similar abrupt changes

have occurred in bond-market volatility. If this kind of
variation can develop in broadly diversified

indexes, there is a large probability that it will appear
with individual stocks and bonds.

### Irrationality

The world irrational is a controversial term, but it does not mean craziness. Richard Thaler observed that people are neither “blithering idiots” nor “hyperrational automatons.”

The pioneers of behavioral economics were Kahneman and Tversky. They came up with Prospect Theory.

If you want to understand what Prospect Theory is about, you only need to understand what it is against. And it is against the assumption that human beings act rationally in a competitive environment, and that any deviation from rationality in the market would lead to chaos.

Instead, they say that most people can survive in a competitive environment while being vulnerable to the quirks of their behavior that makes them less than perfectly rational. Tversky adds that the evidence of their studies on human decision making suggests that human choices are orderly, but not always rational (as Bernoulli would define it, for example).

“The failure of the rational model is not in its logic but in the human brain it requires. Who could design a brain that could perform the way this model mandates? Every single one of us would have to know and understand everything, completely and at once.”‘ Kahneman points out. He was not the first to understand the rigid constraints of the rational model, but he was the first to explain the consequences of that rigidity and how normal people constantly violate it. If investors tend to violate the rational model, then the model is probably not a good description of how capital markets work.