The Turkey Problem

"Take advantage of Wall Street’s handicap by seeking out low-risk, high-uncertainty bets." - Mohnish Pabrai
This is the first articles of my "Low-Risk, High-Uncertainty Betting" article series. This article dives into the Turkey Problem and how it relates to entrepreneurship and investing. Summary: Never be the turkey!

Before I read the book Antifragile by Nassim Nicolas Taleb I thought the world converges to an equilibrium smoothly with small bumps on the way - like a common vision the society wants to achieve (peace, wealth, love) and achieves it by walking its way directly towards it.

After I finished the book I think the world converges to a common vision but not smoothly. The bumps on the way change the route to that goal in massive ways - even reverse the direction society is going for some time. I think of the Cuban Missile Crisis: if one warship-captain on any side would have lost his mind, the world now would be in a very different shape - humanity cut by half (at least), global trade collapsed, ... Its not important how long few or small bumps appeared. Focus on the big bumps - they determine the direction we are going!

Taleb argues that the big bumps are all important. You either be prepared for big bumps or, if you can, increase the number of small bumps so that the big ones occur less often. This is essentially why I am so interested in Antifragility.

An example Taleb begins with in Antifragile is the turkey problem. In one sentence, the turkey has the most confidence in the butchers kind-heartedness the day before thanksgiving.

Lets think that through. On day 0 the turkey is hungry, the confidence in the butchers kind-heartedness is 0. On day 1 the turkey gets food and the confidence in the kind-heartedness increases. With every day of feeding the confidence of the turkey increases a little more. On thanks giving the confidence falls to 0 again.

From a naive standpoint I understand the turkey. As a turkey I do not think of the butchers ulterior motives. The turkey with all his information and mental capabilities is completely rational! Lets model this the naive way:



The red line is the actual confidence of the turkey, the blue line is a linear regression based on the data from day 1 to 5 (its shifted a little bit upwards, so that both do not overlap). If the turkey uses the regression as a predictor for day 6 the turkey encounters a black swan event.

The next graphic shows a linear regression from day 1 to 6. Even at time the total loss occurred, the regression has still 50% confidence at day 6.



That might explain why in market crashes many investors loses their head within hours or days. The prediction of the their model predicts something which does not match with reality in any way.

The slope of the linear regression needs many days after thanksgiving to get 0 or negative. 0 or negative slope essentially means do not trust or dis-trust the butcher even if he feeds you.

Lets investigate the slope of the turkeys confidence. We have to assume that the turkey lived a happy life before it was caught by the butcher. At day 1 and the days before its confidence in the butcher was all the time 0, therefore the slope was 0. From day 1 to day 5 the butcher feeds the turkey and the confidence grows 0.2 points per day. At day 6 the turkey is eaten and the slope is -0.8 downwards to 0. Technically the turkey is dead and has no confidence, therefore we might assume the confidence is and keeps being 0. In short: 0 -> 0.2 -> -0.8 -> 0.

On day 1 the confidence shows an acceleration of confidence from 0 -> 0.2 - the turkey is positively surprised that the butcher feeds it. On day 6 a de-acceleration from 0.2 -> -0.8 - the turkey is negatively surprised of the butchers knife. And an acceleration from -0.8 -> 0 as the confidence of the turkey cannot go below 0 - that is an assumption and should be discussed by a theologian, as the turkey is in turkey-heaven.

The change in acceleration cannot be explained by a linear regression and therefore another model has to be used to fit the regression with the actual confidence of the turkey. We might use a GARCH model, but I skip this, because it distract from the core message.



The above graphic uses for the linear regression data from day 1 to 9 (thanksgiving is on day 6) so that the slope of the regression is less than 0, which meets our rational thought, that a turkey should dis-trust a butcher. This means essentially that a regression only works if you have enough data, including bad days too!

But sometimes the bad days lie in the future. Take the perspective of the turkey. It never met a butcher before, so it does not know what will happen on thanksgiving. How could the turkey adjust for the missing data? The turkey might add a bias to its assessment of the butcher, which is do not trust a predator.

With the bias the turkey is able to create a good assessment with few data. This comes at the cost of having a bias, which should be chosen wisely. But its better to know that a prediction is biased as trusting an "unbiased" regression which has too few data points and therefore is biased with respect to the data points available at the time.

Biases allow us to deal with uncertainty through too few information. Biases are the first tool in our mental tool box to deal with "Low-Risk, High-Uncertainty Betting". In future we model biases explicitly as proof-able assumptions. Biases are an essential part of heuristics, which are part of future articles of this series.

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