John walks into a deli and asks what sandwiches are available. The counter guy responds that there are two choices: A turkey hoagie or pastrami on rye. John replies that he will have the turkey sandwich. A minute later the counter guy says “oh yeah, we also have a chicken salad sandwich to which John replies, you know what, I will have the pastrami on rye. This seems very illogical. John was presented a choice between item A (turkey) or B (pastrami) and chose item A. Conceptually, he was then provided a choice between A and C (chicken) – yet decided to choose B!
Uncertainty, also known as ambiguity, has a crippling effect on us humans generally. It keeps people from making the right choice from a probability standpoint in all aspects of life – switching a job, dating, which supermarket to go to and where to live are just some examples. As a group we would like to believe that we are hyper logical despite overwhelming evidence to the contrary (e.g., Illusory Superiority, Anchoring, Herd Behavior). The subject has been on my mind given the dramatic effect it has on both the way people think about and invest in the financial markets and the fact that most investment strategies, especially hedging strategies, tend to heighten uncertainty of returns rather than mitigate them. It is worthwhile examining the cost to this uncertainty, a cost that has still not been well defined in the financial markets. The best duo to begin this examination is with Daniel Kahneman and Amos Tversky, pioneers of Behavioral finance.
Obvious illogical decision-making happens with surprising frequency in life as has been illustrated by Daniel Kahneman and Amos Tversky in their groundbreaking psychological work on uncertainty and human reason beginning in the 1970s. This illogic was illustrated equally within populations with perceived high IQs (college professors) and the less educated (prison populations).
Brain Teaser: An example of a question asked by Kahneman and Tversky
All families of six children in a city were surveyed. In 72 families the exact order of births of boys and girls was G B G B B G. (G = Girl; B = Boy)
What is your estimate of the number of families surveyed in which the exact order of births was B G B B B B?
Additionally, they found that people, including professionals, are very quick to leap to conclusions and to draw a narrative on very small pieces of data. They went on to illustrate this by creating a statistical study with statisticians as the cohort (!) – a group that is trained to understand the odds as well as when a sample size is statistically significant. For example, a group of trained experimental psychologists were asked to guess the mean IQ of a sample of kids in which the first kid was found to have an IQ of 150. This group would often guess a mean IQ of 100 which is the mean of the larger population. The group generally assumed that this large high IQ outlier would be counter-balanced by one with an extremely low IQ – an easy and orderly story – when in reality the mean IQ based on the sample would be 101 according to a relatively well known mathematical theory (and one they all knew or should have known) – Baye’s theorem.
The element of uncertainty that Kahneman and Tversky so brilliantly teased out within their life’s work (Kahneman is still active while Tversky unfortunately died of cancer in 1996) is surprisingly absent from the formula driven/quantitative aspect of Wall Street. Probabilities are constantly assessed and variables inputted, both with knowledge that these are best estimates of professionals (or at least the inputters!), yet there are no real measurements of the variance or uncertainty of these estimates. As a result, there is no gauge of what this uncertainty cost the end-user generally or whether this cost is currently high or low, meaning whether there is more or less uncertainty at the current time. There is also no appreciation of whether a strategy adds or reduces uncertainty! For example, investors understand very well whether a strategy adds or reduces volatility and this factor is an important input into their decision making. It should be the same for uncertainty, also known as ambiguity. I for one believe investors would incorporate the cost of ambiguity into their decision process.
Did You Know
The Capital Asset Pricing Model (CAPM) developed by William Sharpe, for which he was awarded a Nobel Prize, and John Lintner, which is consistently used as a bedrock of finance has never been empirically proven!
Here is a rather detailed academic article on the subject authored by Eugene Fama and Kenneth French.
One of Exceed’s business advisors, Professor Brenner, and a colleague of his, Professor Izhakian, is working on a measurement (or cost) of ambiguity. Professor Brenner had also authored some academic papers that contributed materially to the creation of The Volatility Index, or VIX – a widely used market measure of forward volatility expectations of the S&P. The gauge of ambiguity measures the degree of uncertainty investors have in the probabilities used to make investment decisions. It is an exciting concept that hopefully will be available in the near future as it will provide a sense to the investor of both how much uncertainty is priced in the market and therefore what the potential cost is to them.
These elements of market behavior and potential measurements of uncertainty have been on my mind for a number of reasons primarily due their tremendous impact on the markets generally and due to the ways they provide material insight into both retail and professional investors approach to the market, with all their human foibles. I had recently picked up Michael Lewis’s The Undoing Project which simply reinforced the effect of these human characteristics (A very good and quick read, I highly recommend it). The book introduces the reader to Daniel Kahneman and Amos Tversky and their ground breaking work as detailed above. It is relevant on a number of fronts and is a good companion to the best-selling book Thinking, Fast and Slow by Daniel Kahneman, which is a bit more dense and technical but nevertheless very enjoyable and readable.
Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
(C): Cannot be determined
Defined Outcome investing was developed with these behavioral tendencies in mind. Individuals have been illustrated to have an aversion to ambiguity which is a key feature in the markets. Yet, most strategies in the market and especially within the hedged equity solutions sector, tend to exacerbate this ambiguity! Believe it or not, there is a real cost associated that is simply not taken into account when investing decision are being made. Defined Outcomes look to mitigate ambiguity by providing a clearer expected performance outcome based on market returns. Exceed Investments wrote a white paper on Defined Outcomes and its beneficial qualities as related to ambiguity a couple of years back which I believe is still very relevant today.
 Why? Because if he preferred B (pastrami) over C (chicken salad) then he already stated his preference of A (turkey) over B (pastrami).
 Neither myself personally or Exceed have any involvement in this work
 Original puzzle and answer from: https://www.theguardian.com/science/2016/mar/28/did-you-solve-it-the-logic-question-almost-everyone-gets-wrong