A Review of Richard Zeckhauser’s (2006) Investing in the Unknown and Unknowable (UU)

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What did you take away from it ?

What are you doing differently ?

--What I Learnt on Wall Street

Thank you What I Learnt on Wall Street for probing and inspiring this write up. Without which the probability was nil to have gone through this deep dive.

The humorous and embarrassing thing is that at the time I was asked the above questions, I had thought about how interesting Zeckhauser’s article was but had not thought about how to systematically do things differently after enjoying the intellectual high it always gave me each time I read it.

So naturally, the right thing to do was to go back to the paper and read it over again but this time with two things in mind: See if I can teach it through active recall method and secondly to exert deep work on it to annotate what can be systematically extracted and introduced permanently into my analysis process.

For years, I’ve heard Charlie Munger say in Poor Charlie’s Almanac, “The right way to think is how Zeckhauser plays bridge. It’s just that simple.” I’m happy to report that my ignorance state today is far more amplified than the ignorant state you found me in the day you presented me the questions. I never gave it a second thought to ask, who the heck was Zeckhauser, nor did I have any presumptions. It just sounded right, and Zeckhauser was a cool name that went with “…Zeckhauser plays bridge…”

Until a few days back, I neither could tell you who Zeckhauser is nor could I tell you if he was contemporary and alive, or from a past era. So, getting to know Zeckhauser as a professor at the Kennedy School with tremendous contributions to finance, economics was eye opening. Richard Zeckhauser is the Frank Plumpton Ramsey Professor of Political Economy at the Kennedy School, Harvard University. He is a master negotiator. He has won multiple national championships in contract bridge. The world I was diving into was Decision Theory and Behavioral Finance. A world where you have to use Rational Analysis and Learn to think Probabilistically. The two big things that are important when you’re making a decision are your Preferences and your Probabilities.

If you’re like me, you’re going to cherish the work of Zeckhauser for a very long time. You’re going to start to think probabilistically rather than giving one answer to a question. This is going to impact the way you analyze companies and how you determine weighted allocations. It’s going to impact the amount of time you spend on emails and the amount of resources you invest proportionally on ideas. Your estimation of time, your expectations of people and investments. “The right way to think is how Zeckhauser plays bridge. It’s just that simple.”

Zeckhauser’s paper is broken down into six parts. This is how he describes them.

Part I of this essay talks about risk, uncertainty, and ignorance, the last carrying us beyond traditional discussions. Part II looks at behavioral economics, the tendency for humans to deviate in systematic ways from rational decision, particularly when probabilities are involved, as they always are with investments. Behavioral economics pervades the UU world. Part III addresses the role of skilled mathematical types now so prevalent in finance. It imparts a general lesson: If super-talented people will be your competitors in an investment arena, perhaps it is best not to invest. Its second half discusses a dispute between math types on money management, namely how much of your money to invest when you do have an edge. Part IV details when to invest when you can make more out of an investment, but there is a better informed person on the other side of the transaction. Part V tells a Buffett tale, and draws appropriate inferences. Part VI concludes.


People think the immediate is too important, that is invariably wrong. We’ve seen this bias referred to as Hyperbolic Discounting. People conclude either with false hope or false pessimism looking and overweighting immediate events. The world is much more uncertain. Zeckhauser asks us to consider when thinking of any problems in the finance world, particularly problems we’ve not seen before, to spread out the probability distribution as to what might be happening. It’s a very different way of thinking.

There are few places in the world where objective probability exists. They exist mostly in casinos. But in the real world of investing and finance, it’s subjective probabilities that we are dealing with.

People are highly averse to situations where probabilities are ambiguous. They will pay to avoid ambiguity. Here Zeckhauser recalls the experiment of the two urns. One with 50 red and 50 black marbles, and the second with yellow and green marbles but unknown composition. When asked which one students would like to choose from, they invariably choose the 50/50 urn. But as the payoff is increased on the other urn and the indifference point is met, people are willing to choose from the urn with unknown composition. Zeckhauser here claims that if people are able to change the probability of the urn with unknown composition by using a coin flip rather than guessing, they’d have changed the probability of the urn with unknown composition to 50/50 odds exactly as the red/black urn without having to overpay for the ambiguity.

One of the interesting characteristics of a bell-shaped curve in statistics is that far-out observations are exceptionally rare. One of the major findings of behavioral finance, a behavioral decision in far out outcomes are not unbelievably rare.

In the world of finance, markets and security prices move often dramatically beyond fundamentals. Currencies swing widely. Successful speculators/investors exist beyond expectations. I’ve read that winning at gambling registers at the same part of the brain as taking heroine.

The main premise of Zeckhauser’s paper is that in finance if you wish to play against the giants, it is impossible to win BIG playing the efficient markets (NYSE, TSX, LSE) or playing against institutional investors or playing against hedge funds using tools from traditional finance.

The concept that you’re going to invest in IBM or Coca Cola and make 10X or 100X is highly improbable since the market players are all after mispriced opportunities. So rather than congregating at the feet of the giants to gather morsels on the floor, Zeckhauser has an empowering thesis for those that are brave to follow and that are not blame averse. He explains that if blame aversion is a prime concern of yours then DO NOT READ ON and use the EXIT iMMEDIATELY. On the other hand unknown and unknowable (UU) situations are idiosyncratic and present the greatest potential for significant excess investment returns.

A side note, Zeckhauser worked alongside Thomas Schelling – a scholar in Game Theory and Strategic Thinking at the Kennedy School, and Howard Raiffa a scholar in Bayesian Statistics and Subjectivism.

The main theme is, “Make Ambiguity your friend and wealth and success will be your reward”.

The nature of Unknowable events

  • Many unknowable events arrive in a thunderclap. Once they arrive, do not seem so strange. Dangers of hindsight, and Monday morning quarterbacking 9/11.
  • Some take place over time, but still remarkable. January 1996 – January 2001 NASDAQ rose five fold, then fell by two thirds in three years. Contrary to finance theory.
  • Warren Buffett “Virtually all surprises are unpleasant”

Zeckhauser starts with defining three main concepts with dealing with uncertainty:

Risk Probabilities Known Idea outcome is not known, outcome probabilities and distribution are well known Portfolio Optimization


Probabilities Unknown Distributions of returns conjectured Portfolio optimization, Decision Theory


States of the World Unknown Distributions of returns conjectured, often from deductions about other’s behavior, Complimentary skills often rewarded alongside investment Portfolio Optimization Decision Theory Complimentary Skills (Ideal) Strategic Inference

In the world of UU, unknowable situations are inevitable.
In the world of UU, most investors have little idea of how to deal with the unknowable.
In the world of UU, unknowable situations are associated with powerful investment returns.
In the world of UU, there are systematic ways to think about unknowable situations.

Although the net expected results even after allowing for loss aversion will be strongly, positive, prepare to have substantial losses – they are inevitable and prepare to be blamed after the fact. As we traverse this paper, Zeckhauser affirms that the opportunity to get 10 or 100 multiple on your investment as often as you lose virtually all of it is tremendously attractive.

Three-Prong Test for Big Positive Expected Value Bets – UU investments have 3 characteristics: (1) UU underlying features, (2) complimentary capabilities are required to undertake them, (3) unlikely other party on the other end is better informed.

Also, note that these three-pronged investments will not come every day. Not common, but not rare. Will not scale up like NYSE stock. Top-flight investors are always on the lookout. Warren Buffett trolls for them. You have to become UU-sensitive constantly on the lookout for new opportunities. Now remember these opportunities are not like any other opportunities you’ve seen. Guess who are your competitors: Warren Buffett, Charlie Munger, Todd Combs, and Ted Weschler.

Then Zeckhauser introduces the third U for Uniqueness. Notice he’s trying to sail where no one else would dare sail. He contends that arbitrageurs – who like to have considerable experience to guide them – will steer clear. So too will anybody who would be severely penalized for a poor decision after the fact. An absence of competition from sophisticated and well-monied others spells the opportunity to buy underpriced securities. The characteristics of these Unique are as follows:

  • Standard players stay away
  • Drive off speculators. Like to have a history (as with corporate takeovers).
  • Drive off people in organizations. Worried about blame
  • Fat tails. 1987 would never happen

Becoming a star in ordinary stock investment, requires unusual judgement. Those who can sensibly determine when to plunge into and when to refrain from UUU investments gain a substantial edge, since mispricing is likely to be severe. Very few others possess the complementary skills for UUU investments.

Also, Zeckhauser introduces the “Sidecar investments” in cases where we have confidence in the investor. The premier sidecar investment ever available to the ordinary investor was Berkshire Hathaway, many decades back. If you could have identified Warren Buffett in 1960 you would have been in a UU privileged situation.

Maxim A: Individuals with complementary skills enjoy great positive excess returns from UU investments. Make a sidecar investment alongside them when given the opportunity.

One of the examples is Gazprom 2006. Investments are fiercely profitable, selling below world price, instruments of government policy, bloated and terribly managed, Russian elite investing.

Behavioral Decision Traps – How to avoid falling prey to behavioral biases and decision traps in UU situations?

  • UU situations are those where our experience is likely to be limited
  • UU situations where we will not encounter similar to other situations that have helped us hone our intuition.

Consider the following traps: Overconfidence, recollection bias, and misweighting differences in probabilities and payoffs.

Overconfidence: Before getting into the details of overconfidence, try Assessing Quantities below.

1st %ile
99th %ile
Democratic Votes MT 2004 Pres election      
Length of Congo River      
Number of subscribers to Field & Stream          
Area of Finland (sq miles)      
Birth rate in France per 1000      
Pop. of Combodia      
Rev. of Wal-Mart 2003      
% Yields on
30-Year Bonds, 1981

When individuals are assessing quantities about which they know very little, they are too confident of their knowledge (Alpert and Raiffa, 1982). Zeckhauser clearly explains what to do with this exercise. For each of unknown quantities, such as the area of Finland, you are asked to provide your median estimate, then your 25th and 75th percentile estimates (i.e., it is one quarter likely the true value will be more extreme than either of the two), and then your 1st and 99th percentiles, what are referred to as surprise points. In theory, an individual should have estimates outside her surprise points about 2% of the time. In fact, even if warned about overconfidence, individuals are surprised about 35% of the time. Quite simply, individuals think they know much more about unknowable quantities than they do. And I also failed with flyign colors – I was overconfident.

Step 1: Estimate the Median

Step 2: Estimate the ¼ likely more extreme than either of the two

Step 3: Estimate Surprise points – about 2% of the time

If you are overconfident of your knowledge, you will fall prey to poor investments in the UU world. Indeed, they are green plants in the elaborate ecosystem of finance where there are few lions, like Bill Miller and Warren Buffett; many gazelles, like you and me; and vast acres of grass ultimately nourishing us all.

Recollection Bias. Know thyself and avoid the natural tendency to judge hypotheticals from the past. Would I have sold out of the NASDAQ in 2001?

Misweighting probabilities and preferences: The two critical components of decision problems are payoffs and probabilities. Effective decision requires that both be carefully calibrated.

Consider the following lottery choice:

  • $2000 payoff 0.01 probability
  • $1000 payoff 0.025 probability

According to Zeckhauser, past experiments have shown that many individuals choose the first choice since they do not distinguish sufficiently between two low probability events (in accordance with prospect theory).

Now let’s get closer to the spectrum of UU events as possible and subject to the limitation that they must be named.

  • 10,000-ton asteroid passed within 50,00 miles of Earth within past decade
  • More than a million mammals crossed the border from Tanzania to Kenya last year

We ask a random sample of people to guess the likelihood of these contingencies. We then alter the asteroid distance until the median answer is 0.03.

  • $2000 payoff Draw a 17 from an urn with balls numbered 1 to 100
  • $1000 payoff 10,000-ton asteroid passed within 40,000 miles to the Earth

 Maxim C: When information asymmetries may lead your counterpart to be concerned about trading with you, identify for her important areas where you have an absolute advantage from trading. You can also identify her absolute advantages, but she is more likely to know those already.

Competitive knowledge, uncertainty and ignorance

Maxim D: In a situation where probabilities may be hard for either side to assess, it may be sufficient to assess your knowledge relative to the party on the other side (perhaps the market).

Daniel Ellsberg (1961) alerted us to ambiguity aversion long before he created a UU event by publishing the Pentagon papers. In an actual experiment, individuals preferred to win a prize if a standard coin flip came up heads, rather than

To win a prize if a mangled coin whose outcome was difficult to predict. Ambiguity aversion has a potential to exert a powerful effect.


“Make Ambiguity your friend and wealth and success will be your reward” —Richard Zeckhauser
UU investments will drive away all but the most self-directed and rational thinking investors. Allow me to conclude with a paragraph from Zeckhauser:
“Central concepts in decision analysis, game theory, and behavioral decision are deployed alongside real investment decisions to unearth successful investment strategies. These strategies are distilled into eight investment maxims. Learning to invest more wisely in a UU world may be the most promising way to significantly bolster your prosperity.”

Maxim A: Individuals with complementary skills enjoy great positive excess returns from UU investments. Make a sidecar investment alongside them when given the opportunity.

Maxim B: The greater is your expected return on an investment, that is the larger is your advantage, the greater the percentage of your capital you should put at risk.

Maxim C: When information asymmetries may lead your counterpart to be concerned about trading with you, identify for her important areas where you have an absolute advantage from trading. You can also identify her absolute advantages, but she is more likely to know those already.

Maxim D: In a situation where probabilities may be hard for either side to assess, it may be sufficient to assess your knowledge relative to the party on the other side (perhaps the market).

Maxim E: A significant absolute advantage offers some protection against potential selection. You should invest in a UU world if your advantage multiple is great, unless the probability is high the other side is informed and if, in addition, the expected selection factor is severe.

Maxim F: In UU situations, even sophisticated investors tend to underweight how strongly the value of assets varies. The goal should be to get good payoffs when the value of assets is high.

Maxim G: Discounting for ambiguity is a natural tendency that should be overcome, just as should be overeating.

Maxim H: Do not engage in the heuristic reasoning that just because you do not know the risk, others do. Think carefully, and assess whether they are likely to know more than you. When the odds are extremely favorable, sometimes it pays to gamble on the unknown, even though there is some chance that people on the other side may know more than you.

“Of all the ways of defining man, the worst is the one which makes him out to be a rational animal”—Anatole France


Capitalism and Society, Volume 1, Issue 2 2006 Article 5, Investing in the Unknown and Unknowable by Richard Zeckhauser

Distinguished Lecture Series

1/3 https://youtu.be/_7D11N6O22k

2/3 https://youtu.be/gd8mSPClI3A

3/3 https://youtu.be/Bmn2FTn7tCE

The Wisdom of the Crowds and the stupidity of the Herds


Behavioral Finance


Zeckhauser: How much would you pay for 50% chance of winning a hundred dollars?

Kahneman: I would pay 38 dollars. That’s what I truly think.

Zeckhauser: That’s preposterous


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