Investment psychology
What we can learn from a jar of marbles
This post will look at some Anomalies in finance that investors, with some knowledge of behavioral psychology, can take advantage of.
For the last 50 years, the conventional wisdom in investing has been that the stock market is very efficient and that stock prices are essentially always right. This conventional wisdom pooh poohs Benjamin Graham and Warren Buffett’s belief that smart investors always buy with a Margin of Safety.
Such ‘wisdom’ parallels academic economics and academic finance in which models and schools of thought have been built on the premise that people are selfish and rational optimizers. In this way of thinking, people are homo economicus. I coin the term homo investorus to describe economicus’s investing and finance blood brother. In the real-world people are simply human. Humans are neither fully rational nor fully selfish.
In the last 35 years behavioral economics and its sister, behavioral finance, have made their mark. This history is told in a fascinating new book The Winner’s Curse by Richard H. Thaler and Alex O Imas (Thaler and Imas, 2025). Thaler received the 2017 Nobel Prize in economic sciences and is a professor at the University of Chicago Booth School of Business. His co-author Imas is a chaired professor of behavioral science, economics and applied AI at the same school.
The book describes a dozen or so Anomalies in economics and finance that make clear the world does not operate in accordance with conventional economic or finance theory posited on the notion that people are both rational and selfish.
In this post I will look at three Anomalies in finance. The first, described in the book, is the Winners Curse in auctions and bidding; The second, which I have noted from other sources, is the Behavioral Gap, an Anomaly in which investors consistently earn less than the aggregate total returns of the funds they hold; and third, also from other sources, the Anomaly of the excessive Equity Risk Premium.
The Winner’s Curse
This Anomaly was recognized when Atlantic Richfield and other oil companies were bidding in government auctions for drilling rights in the Gulf of Mexico. The successful bidders consistently found that the amount of oil found at the sites was less than the successful bid assumed. They lost money consistently because their bids exceeded the value of the oil found.
The oil companies were seriously expert in bidding and drilling. They had teams of geologists and other trained professionals advising them. And, they had experience in high level bidding processes. Of course, it was difficult for them to predict what oil would be found. But that kind of uncertainty is just like what is faced by business people and investors every day.
In a rational utility-maximizing world you might expect the successful expert and experienced bidder in these auctions would sometimes overbid and lose money. But, to do it consistently is a puzzle only explained by behavioral psychology.
The prime psychological culprit seems to be overconfidence in a competitive bidding environment. It happens all the time in competitive corporate take-overs. These big-time, but flawed, corporate decisions are taken by higher up executives who relish the action and the exercise of power and authority.
It’s a good lesson for the little guy. Wall Street is filled with these kinds of movers who have a very high opinion of their skills. The street is littered with overconfident tycoons who have crashed and taken investors with them.
The Behavioral Gap
This Anomaly is about investors who invest in ETFs and Mutual Funds. The evidence over many decades is that Investors consistently earn less than the aggregate total returns of the funds they hold. We might think of it as The ETF and Mutual Fund Investors Curse!
This is a serious and well documented Anomaly showing a gap between Homo Investorus and humans. Finance theory built on the utility maximizing actions of Homo Investorus suggests their returns should match the funds they invest in.
The two most recent reports documenting this are Morningstar and Dalbar.
This from Morningstar: “We estimate the average dollar invested in US mutual funds and exchange-traded funds earned 7.0% per year over the decade ended Dec. 31, 2024. The 7.0% annual dollar-weighted return is about 1.2 percentage points per year less than these funds’ 8.2% aggregate annual total return (which assumes an initial lump-sum purchase) over the 10 years ended Dec. 31, 2024.”
“Investors in sector equity funds saw the largest shortfall to the funds’ total return, as the average dollar gained 7.0% per year compared with the funds’ aggregate 8.5% annual total return.” This 1.5% means the investors earning 7% could have earned some 20% more per year on their investments, absent the Behavioral Gap.
According to the reports, the primary cause of the gap is the timing and magnitude of investors’ transactions. Investors tend to buy funds after they have performed well (buying high) and sell them after they have performed poorly (selling low), missing portions of market rallies. The largest single factor I can see is the development and sales of theme and sector ETFs. They are an invitation to practice market timing and sectoral rotation which are deadly to performance. The main problem for ETF investors is that they are price acceptors. You can’t compare the fair value vs price of an ETF unit in the same way you can with common shares.
Homo Investorus would not suffer this gap. As a rational utility maximizing investor they would have bought and held and dealt with all our human failings and frailties. Why do humans with all our behavioral biases and cognitive errors not act like Homo Investorus. It’s because we are just humans.
Readers might wonder how they can learn about this. In the simplest sense we are seriously afraid of losing money but, at the same time, we are don’t realize how lacking in skill we are in dealing with money and investments. We are schizomaniac, swinging from Risk Averse to Risk Seeking behavior. The good news is that every investor can learn about this stuff and through trial and error become a skillful investor.
The main pitfalls for investors revolve around these subjects: The attractive trap of extrapolating the most recent past into the future; Control our animal spirits when faced with risky situations; The herd mostly gets it wrong; Our minds search for confirming evidence; We generalize from limited observations; Over-confidence and optimism bias; Jumping to conclusions; The problem of short-term thinking.
Readers wishing to dig deeper can take a look at this post. Investment psychology explainer for Mr. Market – introduction It will guide you to further reading if you wish.
The Equity Risk Premium Anomaly
The riskiness of stocks vis-a-vis bonds is priced by the stock market. The idea that you enjoy a premium return investing in stocks is a reflection of the common-sense idea that higher risk needs a higher reward. But risk is in the eye of the beholder. The premium return from stocks reflects investor Risk Aversion, information uncertainty and perceptions of macroeconomic risk. In the world of finance, it’s called the Equity Risk Premium.
But, the Equity Risk Premium of stocks is too high! It is too large based on the most reasonable assumptions. It always has been and looks like it always will be. And this is an Anomaly resulting from behavioral psychology.
The Anomaly has been identified through studies. For example, see research by Mehra, Rajnish, and Edward C. Prescott, 1985, The Equity Premium: A Puzzle, Journal of Monetary Economics, v15, 145–61. The researchers concluded that investors would need implausibly high Risk-Aversion coefficients to demand the premiums they identified.
One of the worlds leading experts on the Equity Risk Premium is Aswath Damodaran. He is a professor of finance at the Stern School of Business at New York University. His area of focus is corporate finance and equity valuation.
Damodaran looks at the latest evidence. Equity Risk Premiums (ERP): Determinants, Estimation, and Implications – The 2024 Edition by Aswath Damodaran :: SSRN
His conclusion is that “it is not quite clear what to make of the equity risk premium puzzle. It is true that historical risk premiums are higher than could be justified using conventional utility models for wealth.”
There is one explanation that makes sense to me. It is derived from behavioral psychology. It is called a cognitive error. The specific cognitive error we are concerned with here is that Humans tend to miss-weight high probabilities of gains by Risk Aversion. They do this through consistent overweighting of improbable outcomes. I discuss this in my post The price of risk in equity markets
This is the certainty effect. Outcomes that are almost certain, but are not completely certain, are given less weight than their probability justifies. As Humans, we are cognitively biased to certain compared to almost certain. We are biased to “Risk Free” compared to the S&P 500. That is, the Equity Risk Premium of stocks is too high based on the most reasonable assumptions.
High equity risk premia make stocks cheaper in relation to the discounted cash flow valuations. Blessedly, investors clued into this Anomaly, can take advantage of it.
We’ve looked at three Anomalies. I want to take a look at one other aspect of the Winner’s Curse.
Bidding on a jar of marbles
The Winner’s Curse Anomaly can be further tested by a bidding game based on a jar of marbles. This marble game is discussed by Thaler and Imas at p4 ff.
I have modified the game so that each marble is worth one dollar. Let’s say ten players bid for the jar’s contents. They don’t know how many marbles the jar contains. The jar actually contains 100 marbles. The highest bidder get’s $100 less their bid. A winner who bid $90 would receive $100 less $90, i.e. $10. If the winning bid is $110, the winner has to pay $10.
Because of the Winner’s Curse, typically winners end up paying rather than receiving money in the marble game!
Let’s look at the bidding by, and the end result for, the losers. Their bids were too low to win. As Thaler and Imas put it: “The average bid will be significantly less than the value of the [marbles}”
That is, consistently the research has shown that in bidding situations, if you take all the bids and average them, this average will be significantly less than the value in the jar. Of course, the average includes not only low-ball bids but also bids higher than the fair value in the jar including the winning bid.
The question is whether this average of all bids, being less than the value in the jar, is an Anomaly like the Winner’s Curse and other situations that break with conventional economic or finance theory posited on the notion that people are both rational and selfish.
Let’s hold that thought and for a moment look at another jar of marbles situation.
Estimating a jar of marbles
Before we decide whether the less than fair value average of bids on the marbles is an Anomaly, we should take a look at the so-called Wisdom of Crowds. In his 2004 runaway best seller titled The Wisdom of Crowds, James Surowiecki says that in 1906 a British mathematician stumbled on a “…simple, but powerful, truth that is at the heart of this book: under the right circumstance, groups are remarkably intelligent, and are often smarter than the smartest people in them.”
Surowiecki called it the Wisdom of Crowds, a riff on the Extraordinary Popular Delusions and the Madness of Crowds by Scottish journalist Charles Mackay, first published in 1841. (The Wisdom of Crowds, James Surowieckij, Vintage Books edition 2005) pxiii
In 1906 an English country fair was holding a contest to guess the dressed weight of an ox. Roughly 800 people guessed the weight. Some guessed very high and some guessed very low. Sir Francis Galton, a brilliant English statistician (amongst other things) was there. Galton got his hands on all the answers and averaged them. Remarkably the average was very close to the real weight.
What Galton had stumbled on was the statistical phenomenon known as ‘decorrelation of error’. When a large enough sample of people guess at something like the number of marbles in a jar, averaging shaves off the high and low guesses leaving an estimate very close to the actual number. Put another way, with a sufficiently large sample, the errors made both high and low tend to average out towards zero.
The critical thing to know about a crowd estimating the weight of a dressed ox or the number of marbles in a jar is not that “groups are remarkably intelligent”, as Surowiecki puts it, but that the accurate average estimate is a purely statistical phenomenon.
Surowiecki’s book, The Wisdom of Crowds also discusses the benefits of group collaboration. This is something entirely different and has nothing to do with guessing the weight of dressed oxen or marbles in a jar.
For present purposes, we simply need to know that a crowd estimating the number of marbles in a jar and getting it right is not Homo Economicus at work.
Comparing bidding on a jar of marbles with estimating a jar of marbles
In the bidding situation, the average of all the bids is consistently less than the value of the dollar equivalent marbles. In the estimating situation, the average of all the estimates is remarkably close to the real number.
The estimating situation is simple. It is simply a statistical phenomenon. The bidding for marbles is more complex. Thaler and Imas treat it as an Anomaly. They say the unsuccessful bidders are ‘risk averse’. I’m inclined to think not.
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.
Risk savvy
I like to think of the unsuccessful bidders, for oil drilling rights or marbles in a jar, as being risk savvy. That is, their assessment of risk is more or less spot on for the expected outcome. In an uncertain bidding situation, as with all stock market investment, one is making decisions in face of risk and uncertainty. One of the problems stock investors have, is coming up with a serviceable estimate of fair value. Price is what you pay. Value is what you get. Benjamin Graham and Warren Buffett are clear that buying with a Margin of Safety is at the heart of investing. One of the main reasons to buy with a Margin of Safety is to make allowance for the difficulty of making a good estimate of fair value in face of uncertainty. One also hopes to buy at a bargain price.
So, my thought is that the losing bidders for the jar of marbles and for the oil drilling rights in the Gulf of Mexico were being risk savvy rather than risk averse. They built a Margin of Safety into their bids.
The reason the estimates of the number of marbles in the jar and the bidding for marbles in the jar are different is that the bidders were acting in a bidding risk savvy exercise whereas the estimators of the marble in the jar were not making a decision in a risky situation.
Conclusion
The world of economics and the world of finance and investing are filled with Anomalies resulting from human behavioral biases and cognitive errors. In reality the stock market is fairly inefficient. See my posts The conventional view of market efficiency is badly mistaken and Market (In)Efficiency and beating the market
The good news is that we can learn about human behavioral biases and cognitive errors and develop the skills to not only avoid their pitfalls but also take advantage of the behavioral frailties of Mr. Market.
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