Reading Notes: Antifragile by Nassim Taleb

Books

Author

Eliott Kalfon

Published

December 21, 2024

What if you could separate people and ideas by their reactions to disorder? Some break, others thrive. We notice this every day around us. Some institutions collapse in times of crisis, others triumph. Antifragile is an inquiry into this distinction, becoming more and more relevant in our chaotic world.

This is the first of my reading notes. When people ask me for advice, I would usually write things down in a Google Doc and share that with them. It allows me to better structure my thought process and spares a 5-minute voice note. I now tend to put things on this blog.

A friend of mine who was struggling with Taleb’s style asked me to summarise the main ideas from the book Antifragile. This list of ideas is my best attempt so far, a personal attempt only.

Iatrogenics: Being sceptical of intervention

The concept of iatrogenics is described as the harm done by a medical treatment. Taleb expresses scepticism with regards to medical intervention with a small known gain and large possible unknown negative side effects.

This applies in many domains in which there is often a drive to “do something”. Generally, these interventions on complex systems have known small gains and large possible losses.

Systems such as human bodies or the economy are complex; it is difficult to predict the exact consequences of interventions. One should therefore be sceptical towards the new, the intervention, the addition.

Hormesis: The virtues of stressors

The concept of hormesis describes the benefits from an organism’s response to minor stressors.

As an example, the human immune system is strengthened by fighting viruses and infections. The skin on climbers’ hands develops calluses with training. Caloric restriction (fasting) has been shown to extend the life expectancy of lab animals ¹.

Removing these stressors could have negative consequences on an organism’s or institution’s fitness. For example, the excessive use of antibiotics has been shown to lead to the development of antibiotic-resistant bacteria. The over-sterilisation of our environment is one of the possible causes of the development of autoimmune diseases ².

Tested by time: The Lindy effect

It is said that in Florence, during the Renaissance, the price of insurance was the same for a 20-year-old man and a 50-year-old man. A 50-year-old man had already survived many years and had the same probability to live an additional year as a younger man.

This also applies to institutions such as restaurants and shops. Imagine a scenario in which each shop has a fixed probability of failure every year (e.g. 1%), negatively correlated with its quality. The higher the quality of the shop, the less likely it is to fail each year.

The more robust and resilient these businesses are, the less likely they are to fail. An old restaurant is much more likely to have a low probability of yearly failure than a new restaurant, hence, more likely to be good.

Bringing books back into the picture, this would mean that books having survived the test of time, such as the works of Seneca, Marcus Aurelius, Plato and many others, are more likely to be good than the books found in the Novelty section.

We can tie this back to the restaurant example by imagining that each book/author has a fixed probability to be forgotten every century, negatively correlated with its quality. Books which have not been forgotten are much more likely to be good.

Taleb leverages this idea to make predictions about the future, arguing that concepts and institutions that have existed for thousands of years (such as wine, restaurants, art…) will most likely stick around for another few years.

Concavity of hurt

Why would being thrown 1000 pebbles of 10 g hurt us less than being thrown a single stone of 10 kg? Why can cats and mice fall from several times their heights and keep running while elephants cannot? Why does driving into the same wall ten times at 10 km/h do less damage than running into the wall once at 100 km/h?

The same can be applied to many other domains such as alcohol consumption or traffic control in large cities.

For example, the disturbances generated by increasing the car traffic by 20% in London are much higher than twice the disturbances generated by increasing traffic by 10%.

This links to the concept of non-linearity and concavity of hurt, which is one of Taleb’s definitions of fragility: “Shocks bring higher harm as their intensity increases (up to a certain level)”.

Using the example of the elephant or of complex systems, size seems to make organisms and institutions more fragile, more sensitive to increases in disturbance/volatility.

Harm increases more than linearly with respects to size

Code used to generate the plots

import numpy as np
import matplotlib.pyplot as plt

# Generate x values from 0 to a positive value
x = np.linspace(0, 10, 400)

# Define the concave polynomial function with maximum at x = 0
C = 0  # Maximum value at x = 0
y = -x**2 + C

# Plot the function
plt.figure(figsize=(8, 6))
plt.plot(x, y)
plt.xlabel('Size', fontsize=14)
plt.ylabel('Hurt', fontsize=14) 
plt.title('Concavity of hurt as a function of size', fontsize=16)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)  
plt.grid(True)
plt.savefig("concavity.png")
plt.show()

Moving beyond size, a system with two critical components, each with a probability of failure of \(10\%\), has a combined probability of failure of \(1-0.9^2 = 19\%\). A similar system with three critical components has a combined probability of failure of \(1 - 0.9^3 \approx 27\%\). The more components or points of failure a system has, the higher its probability of failure. This one of the main reasons in favour of building redundancy in systems.

The One-way effect of delay

Because travel time cannot be negative, delays tend to accumulate. Trains and planes rarely arrive early, or only by a few minutes; and tend to be late, sometimes by several hours.

To link this point with the previous one (size and concavity of hurt), the expected delay (\(\text{probability} \cdot \text{size of delay}\)) increases more than proportionally with the number of transport methods/connections a journey includes.

The same applies to large engineering projects. The time it takes to build a feature is rarely negative. When a feature is delivered earlier than planned, it is generally by much less than when it is delayed (same as transportation above). This also shows how the expected delay increases more than linearly with project size and complexity.

This becomes even more dramatic in contexts in which delays in one train/feature are correlated with delays in other trains/features, or when there are dependencies between components of a system.

Where to go from there? Buffers, buffers, buffers… When working as a Data Science consultant, my workload only became manageable when I started to budget and sell my own projects. In other words, I was the one determining what we would deliver and how much time each item would take. Knowing that delays would always occur somewhere, I implemented buffers in practically every work item. This made delivery times more accurate (better for the client) and my work life much more enjoyable.

Dealing with transportation, as delays generally accumulate in a non-linear way, leaving 10 minutes earlier at rush hour will most likely make you arrive more than 10 minutes earlier at your destination.

The Virtues of optionality

Options and optionality are generally described by Taleb as low upfront cost (price of the option) with no other possible downside, combined with uncapped possible upside.

In financial terms, an option is the right to buy or sell an asset (such as the share of a company) at a given price.

If I buy an option to buy a company’s share at today’s price in two weeks, I pay a small upfront cost. If the share price increases, I make a profit by exercising my option and buying the stock at the old (lower) price and selling it at today’s (higher) price. If the share price decreases, I do not exercise my option and nothing happens; I simply lose the price of the option.

Putting this into numbers with a simple example:

A company named Tables & Chairs (also known as “T&Cs”), a large corporation selling home furniture, currently has a share price of €10. For €1, I buy an option to buy one share of T&Cs at €10 in two weeks.

If the price of the share increases to €13 after two weeks:
- I exercise my option, buy at €10, and sell at €13.
- Payoff: \(13 - 10 - 1 = 2\).
If the price drops to €5:
- I do not exercise the option.
- Payoff: \(-1\) (option cost).

Comparing that strategy with owning the share:

Price increases to €13:
- Payoff: \(13 - 10 = 3\).
Price drops to €5:
- Payoff: \(5 - 10 = 5\).

Payoffs of owning a share vs. buying a call option

Code used to generate the plot

import numpy as np
import matplotlib.pyplot as plt

# Define share prices from €0 to €20
share_prices = np.linspace(0, 20, 200)

# Parameters
purchase_price = 10   # Purchase price of the share
strike_price = 10     # Strike price of the option
option_cost = 1       # Cost of buying the call option

# Calculate payoff for owning the share
payoff_own = share_prices - purchase_price

# Calculate payoff for buying a call option
payoff_option = np.where(share_prices > strike_price, share_prices - strike_price - option_cost, -option_cost)

# Create a figure with two subplots, one on top of the other
fig, axes = plt.subplots(2, 1, figsize=(10, 12), sharex=True)

# Adjust the x-axis range from €0 to €20
axes[0].set_xlim(0, 20)

# First subplot: Payoff of owning the share
axes[0].plot(share_prices, payoff_own, label='Own the Share')
axes[0].axhline(0, color='grey', linestyle='--')
axes[0].set_ylabel('Profit/Loss (€)', fontsize=16)
axes[0].set_title('Payoff of Owning the Share', fontsize=18)
axes[0].legend(fontsize=14)
axes[0].grid(True)
axes[0].tick_params(axis='both', which='major', labelsize=14)

# Second subplot: Payoff of buying a call option
axes[1].plot(share_prices, payoff_option, label='Buy Call Option', color='orange')
axes[1].axhline(0, color='grey', linestyle='--')
axes[1].set_xlabel('Share Price at Expiry (€)', fontsize=16)
axes[1].set_ylabel('Profit/Loss (€)', fontsize=16)
axes[1].set_title('Payoff of Buying a Call Option', fontsize=18)
axes[1].legend(fontsize=14)
axes[1].grid(True)
axes[1].tick_params(axis='both', which='major', labelsize=14)

# Adjust layout to prevent overlap
plt.tight_layout()

plt.savefig("option_payoff.png")
# Display the plot
plt.show()

These graphs show that with the option, the maximum loss is limited to the option cost (€1), while the potential gain is unlimited as the share price increases. Options are antifragile as they only have a small potential downside, the price of the option, and a large potential upside.

Skin in the game

Of all the concepts described in the book, this one had the strongest impact on my worldview. Taleb highlights that many authors are not held accountable for their predictions, or sometimes do not even make these falsifiable predictions.

A writer explaining history or society after the fact faces much less risk than a writer predicting the future and being held accountable for their predictions. The book may have a stronger bias towards skin in the game as its ideas (antifragility, Lindy effect…) were “proven” or illustrated by Taleb’s own investment track record.

There is a link between optionality and skin in the game. Writers who can cherry-pick their successful predictions from a lifetime of predictions have optionality. They can choose whether or not to exercise their option of sharing their predictions to the world after the fact.

Final Thought

Taleb has a divisive style, sometimes openly criticising and labelling established economists and tradesmen as fragilista or other derogatory terms. Some find this style entertaining; others find reading his work difficult to read.

Regardless of this controversy, I believe that some of the ideas shared in Antifragile deserve some thought. If you haven’t read it, what about making your own mind about it?

As always, get in touch to discuss any of these!