Investment psychology
The emotional tail wags the rational dog
Today’s post presents some key insights that investors can learn from behavioral psychology. They revolve around the notions of risk averse behavior and risk seeking behavior.
In the early 1970s, Amos Tversky and Daniel Kahneman, two Israeli psychologists, started working together on the subject of people’s attitudes to risky choices. The standard theory in psychology at the time, indeed in all social sciences, including economics, was the ‘expected utility theory’. In 1979, they published their results in a paper titled “Prospect Theory: An analysis of Decisions under Risk.” (Emphasis added)
Prospect Theory
Kahneman says: “Our theory was closely modeled on utility theory but departed from it in fundamental ways. Most important, our model was purely descriptive, and its goal was to document and explain systematic violations of the axioms of rationality in choices between gambles.” (Kahneman, Thinking, Fast and Slow 2011) p271 (Emphasis added)
What I have just quoted is quite a mouthful. It can be put more simply. Kahneman quotes the psychologist Jonathan Haidt who said: “The emotional tail wags the rational dog.” (Kahneman, 2011) p140
This was the beginning of the study and application of behavioral psychology to decision making. Ultimately Kahneman, following the death of Tversky, became a recipient of the Nobel Prize in Economic Sciences. Tversky would undoubtedly have shared the prize had he been alive. Today their ideas have become an important adjunct to economics and finance; witness behavioral economics and behavioral finance.
Ideas about ‘violations of rationality’, ‘decision making’, ‘risky choices’ and ‘emotional tails wagging rational dogs’ are naturally of great interest to investors. The field was called Prospect Theory.
Critical to understanding all this is the definitions of the expressions risk seeking and risk averse.
By Kahneman’s definition, risk aversion does not have the hazy meaning of somehow not liking to take risks. Risk aversion is specifically an unwillingness to take on a risk in spite of the fact that the reward amply justifies the risk taken. That is, the gamble or investment has a positive ‘expected value’.
Warren Buffett explained ‘expected value’ at the Berkshire Hathaway Annual Meeting in 1989: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”
Similarly, risk seeking has a specific meaning. Risk seeking is taking on a risk in spite of the reward not justifying the risk taken. That is, the gamble has a negative expected value.
Both risk averse and risk seeking behavior can almost be thought of as pathological, although tails wagging dogs sort of sums it up.
Fourfold pattern
Kahneman and Tversky’s work identified four situations in which human decision makers are likely to overweight an improbable outcome.
Kahneman tells us: “The fourfold pattern of preferences is considered one of the core achievements of prospect theory. (Kahneman, 2011) p317
Kahneman explains: “A similar analysis applies to each of the cells of the fourfold pattern: systematic deviations from expected value are costly in the long run – and this rule applies to both risk aversion and risk seeking. Consistent overweighting of improbable outcomes – a feature of intuitive decision making – eventually leads to inferior outcomes.” (Kahneman, 2011) p321 (Emphasis added)
Beyond the fourfold pattern
As an aside, we need to remember that the fourfold pattern is only one of many things investors can learn from behavioral psychology. Others include short term thinking, confirmation bias, overconfidence, crowd think and herding and several others.
What is the fourfold pattern?
Kahneman looks at four situations where humans are making decisions involving risk. In each of the four situation humans tend to consistently overweigh improbable outcomes.
Here are the four situations. Humans tend to:
1) Miss-weight high probabilities of gains by risk aversion
2) Miss-weight high probabilities of loss by risk seeking
3) Miss-weight low probabilities of gain by risk seeking
4) Miss-weight low probabilities of loss by risk aversion
I’ll give examples below that will make it easier to understand. Kahneman’s figure 13 illustrates the fourfold pattern (Kahneman, 2011) p317
Kahneman writes: “A similar analysis applies to each of the cells of the fourfold pattern: systematic deviations from expected value are costly in the long run – and this rule applies to both risk aversion and risk seeking. Consistent overweighting of improbable outcomes – a feature of intuitive decision making – eventually leads to inferior outcomes.” (Kahneman, 2011) p321
The best way to get comfortable with this is to look at examples. Kahneman uses bets. We can use well known investment situations.
1) Miss-weight high probabilities of gains by risk aversion
Kahneman illustrates this one by two sets of choices.
- 61% chance to win $520,000 or a 63% chance to win $500,000
- 98% chance to win $520,000 or a 100% chance to win $500,000
Kahneman writes: “If you are like most people, you preferred the left-hand option in problem A and you preferred the right-hand option in problem B. If these were your preferences; You have just committed a logical sin and violated the rule of rational choice.” Kahneman, 2011) p313
This is the certainty effect. Outcomes that are almost certain but are not completely certain, are given less weight than their probability justifies. We are biased to certain compared to almost certain.
>>Selling a stock too soon is a logical sin
Many investors fear that stock market volatility and other unknown dangers will rob them of their gains. They forego future likely gains to lock in a small gain in the stock of a good company. The small gain is certain. The future return, while having a really good expected positive value is, well, uncertain. This is risk averse behavior. It’s like the bad advice that you can never go broke cashing in a profit. This is silly and takes you out of a good position, a winning stock, which is a logical sin.
>>Accepting a lower return to avoid uncertainty violates the rule of rational choice
Let’s look at another example. This is a big picture case. Accepting a penalty to avoid uncertainty in large measure explains the risk premium attached to equities (Equity Risk Premium) as against ‘risk-free’ United States Treasury bonds. That is, investors are willing to forego the higher return from stocks to avoid the uncertainty of stocks. In point of fact, this behavior is risk aversion in the sense we have defined it.
The following figure is a chart of the real total return on stocks over the long haul compared with other asset classes. It is on a semi-log plot and shows the situation properly. Jeremy Siegel writes, “The superiority of stocks to fixed-income investments over the long run is indisputable.” (Siegel, Stocks for the Long Run – The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies. 1998) p 22 I have read quibbles with Siegel’s numbers but never seen evidence that his big picture conclusion is not completely valid.
Stocks are not risk free. My point simply is that investors miss-weight the relative riskiness of stocks vs bonds because of the perceived certainty of bonds and fear of disappointment in stocks. This is the certainty effect again. Outcomes that are almost certain but are not completely certain (stocks), are given less weight than their probability justifies. We are biased to certain compared to almost certain.
But it violates the rule of rational choice.
As an aside, and not directly relevant to present discussion, the belief that UST bonds are risk free is mistaken because of inflation and interest rate fluctuations.
The interesting feature of this risk averse behavior is that the level of risk aversion and hence the Equity Risk Premium varies with market conditions. At times of low investor confidence Mr. Market becomes more risk averse and drives up the risk premium attached to equities, that is, equities become relatively less expensive. The irony is that, when the risk premium is higher, this is exactly when the risk of equities is lower and they can be purchased with a higher margin of safety.
The level of risk aversion moves markets. 2008 was a traumatic year. As reported by the Economist Magazine November 10, 2012, “According to EPFR Global, a data provider, bond funds have attracted…almost $1.1 trillion since the beginning of 2008. In contrast, equity funds and money-market funds have seen net redemptions of $467 billion and $793 billion respectively since the start of 2008.”
It should be remembered that 2008 was the year the U.S. subprime financial crisis struck and the stock market tanked and that through 2012 there was an unrelenting sovereign debt crisis in the Euro zone.
Mr. Market became more risk averse and shifted money away from the uncertainty of stocks and into the relative certainty of bonds. In point of fact, stocks could have been purchased in March of 2009 with a higher margin of safety than at any time in the last twenty years!
2) Miss-weight high probabilities of loss by risk seeking
This situation from the fourfold pattern is illustrated in a common investor quandary. It called facing Bad Options.
Regarding risk seeking in face of Bad Options, Kahneman explains: “This is where people who face very bad options take desperate gambles, accepting a high probability of making things worse in exchange for a small hope of avoiding a large loss. Risk taking of this kind often turns manageable failures into disasters. The thought of accepting the large sure loss is too painful, and the hope of complete relief too enticing, to make the sensible decision that it is time to cut one’s losses. This is where businesses that are losing ground to a superior technology waste their remaining assets in futile attempts to catch up. Because defeat is so difficult to accept, the losing side in wars often fights long past the point at which the victory of the other side is certain, and only a matter of time.” (Kahneman, 2011) p319
When a stock has dropped in price from a purchase price of $20 to $15, it’s not necessarily a bad situation. At $20, the stock should have been bought with a margin of safety. Also, a drop to $15 may simply reflect stock market volatility. What you paid is irrelevant. What matters is what the fair value of the stock is. If fair value is still $20 or higher, there is little to worry about.
But what is the situation if the stock bought at $20 drops below $15, say to $12? It’s time for a sober reassessment. Our investor is facing Bad Options. They can sell and realize the loss. They can hold and risk the stock going down further thus increasing their paper losses. Both are Bad Options. In face of Bad Options, they can also double down and buy more stock at $12. Doubling down in face of bad options is a common blunder. It is a high risk and likely desperate move. In face of Bad Options humans tend to be risk seeking.
For many inexperienced investors, and not just those who are risk tolerant and overconfident, this is what they will do. It is comparable to what is sometimes called ‘gamblers’ ruin’. This is where the gambler persists in making bets where the odds are against them hoping against hope to hit a jackpot. This is a classic example of risk seeking behavior.
The right response in a situation of serious paper losses is to change the Reference Point to intrinsic value. It may also be time to carry out a Broad Framing analysis of the situation and make a dispassionate decision on that basis. The combined change of Reference Point and Broad Framing would consider purely the investment merits of the stock at $15 or $12 putting it in the context of the portfolio as a whole and the long-term picture.
A decision by an experienced investor to buy more at $15 or even $12 is not an easy one. At one time the investor might have concluded fair value was $26 per share. The original purchase at $20 was made at what the investor thought was a bargain price. Now with the stock trading at $15 or $12 the investor must naturally decide whether the original assessment of fair value was mistaken. The fair value figure has become a Preconception. All our efforts to research and then buy the stock at $20 mean we have a Sunk Cost in the position. The fact we own it Endows it with special value to use. These terms I have capitalized all have special meaning for behavioral psychologists.
3) Miss-weight low probabilities of gain by risk seeking
>>Lotteries and taking a flyer
The classic cases here are lotteries and flyers. Many people put their hard-earned money into buying lottery tickets. Often, they can’t afford it. They know there is virtually no chance of winning. But if they did win, the windfall would be enormous. Lotteries are a classic example of people being risk seeking when there is a small chance of a large gain. Based on the odds, the expectation of winning does not justify the ticket purchase price.
Investors do the same thing. In the 1990s they threw money into dot com stories knowing the chances of decent returns were remote. They were hoping to hit the next Microsoft. In the 2010s they invested in tech IPOs hoping to score the next Netflix or Facebook. During Covid there was a meme stock craze.
What motivates them is the feeling that the enormous potential returns justify the investment. Many investors allocate a small but still significant part of their portfolios for investing in flyers. It doesn’t make sense. Based on the expectation of return the investments are irrational. The investments are a classic case of humans being risk seeking where there is a low probability of gain. I have never bought a lottery ticket in my life. I avoid flyers like the plague.
Remember, risk seeking behavior is pathological.
4) Miss-weight low probabilities of loss by risk aversion
>>Faced with a small loss and wanting to avoid a larger loss
When our well bought (margin of safety) stock has dropped in price from our purchase price of $20 to $15 not long after buying it, the investor is facing a testing situation. The first reaction is to think the original decision to buy was mistaken. The investor has read advice to cut your losses and let the winners run. They can sell and realize the loss. This is a mistake.
First, the stock should have been bought with a good margin of safety. If the price drops, it’s entirely likely the fair value of the stock hasn’t budged. In fact, after you have bought a stock, the price paid is irrelevant. They only thing that matters is the fair value of the stock. If that hasn’t changed there is no reason to sell.
The proper rule is to sell losers. Losers are stocks where the company is losing its way. It is no longer the superb company you bought. So, sell losers.
Losses (not losers) are paper losses often caused by nothing more than stock market volatility. Volatility should be your friend not your enemy. Volatility gives us opportunities to buy at prices less than fair value.
Bailing out at the first sign of volatility is risk averse behavior.
To cope with the situation the investor needs to reframe investment away from price and in terms of intrinsic value. With proper reframing, an experienced investor might decide to buy more at this now better price.
>>Product warranty, low deductibles and other insurance silliness.
The miss-weighting of low probabilities of loss by risk aversion applies in other money situations.
Kahneman writes: “The bottom right cell is where insurance is bought. People are willing to pay much more for insurance than expected value – which is how insurance companies cover their costs and make their profits. Here again, people buy more than protection against an unlikely disaster; they eliminate a worry and purchase peace of mind.” (Kahneman, 2011) p318 (Emphasis added)
“When you take the long view of many similar decisions, you can see that paying a premium to avoid a small risk of a large loss is costly.” (Kahneman, 2011) p321
But there is a place for insurance. We put insurance on our houses protecting us against fire loss and other perils because a total loss of our house in a fire would be a financial calamity. Some insurance is a complete waste. Extended warranty insurance on consumer products is silly. Property damage insurance on cars make sense so long as you have a very high deductible. A deductible is called self insurance. This is a loss we can handle. Most travel cost (as opposed to travel health) insurance is a waste. One should self insure.
Conclusion
When Amos Tversky and Daniel Kahneman were working on Prospect Theory, they came to the conclusion that humans are neither fully rational nor fully selfish. They also came to understand that economics as a discipline and the models economists created, were largely founded on the idea that humans are perfectly rational. This rather undermined a lot of economic, finance and investment thinking. Investors would be wise to learn about violations of rational thought in risk averse and risk seeking behavior and keep the fourfold model in mind.
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For readers wishing to dig a little deeper into investment psychology, the following post offers a gateway:
Investment psychology explainer for Mr. Market – introduction
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