Thread by @carefullycnsdrd

Black Swans don’t happen on a schedule. We can’t predict when they’ll happen.

But we can predict our vulnerability to them.

Thread based on @nntaleb's lectures at #RWRI17

1. We’ll use three building blocks to understand how to predict vulnerability to Black Swans:

• Fragility
• Nonlinearities
• Modeling under uncertainty

2. Fragile things don’t like volatility.

Consider three levels of shock to a coffee cup:

• Level 1 shock: cup doesn’t break
• Level 2 shock: cup maybe breaks
• Level 3 shock: cup definitely breaks

3. Now think about two different sequences of events.

• Scenario 1: Five shocks of level 0, then one shock of level 3.
• Scenario 2: Six shocks of level 1/2.

In both cases, the average shock level is 1/2. But the cup breaks in the first scenario and doesn’t in the second.

4. This is because the cup is fragile.

It prefers to take the response to the average shock (1/2) and erase any volatility.

In math terms, we say that the cup’s response to shocks is concave in the region where it breaks.

5. Everything fragile has this property: in the phases where it breaks, it has an accelerated response function.

In other words, the response is nonlinear.

6. Being nonlinear to harm is an essential feature of being alive.

Humans (or financial institutions) that are linear to harm are already dead. Intermediate daily fluctuations in x (which are common) have killed them.

7. Take a look at the graph below.

The Black Swan event leads to a much worse response in the concave function (curving downward).

This is why financial institutions blow up in the tail. Daily volatility doesn’t hurt them, but the accelerated response kicks in during a crisis.

8. With these two concepts, we’re ready to tie things together with modeling under uncertainty.

Our motivating example will be modeling deficits as a function of unemployment.

9. Let’s say our model makes the following predictions:

• 8% unemployment => $75B deficit
• 9% unemployment => $200B deficit
• 10% unemployment => $550B deficit

10. We know that our model is prone to error and uncertainty. For example:

• What if the deficits would actually be 20% worse under each scenario?
• What if the worst-case scenario isn’t 10% unemployment, but 12%?

11. How can we get useful information out of any model under so much uncertainty?

The key is to look for nonlinearities in the tail.

12. The model says that f(9%) = $200B. But the average of f(8%) and f(10%) is worse: it’s $312.5B.

This nonlinear acceleration in the response function reveals fragility in the tail.

13. An analogy is using an inaccurate ruler to measure the height of a child. It won’t tell you the child’s height, but it will tell you if he or she is growing if you keep using it over time.

We don’t know if our model is accurate. But we can still get information out of it.

14. Recap (technical - can be skipped):

We took the parameter and multiplied a point value (9%) by (1+a) and (1-a). Here a=1/9, so the perturbations yield 10% and 8%. We then found that the response was fragile to volatility.

This is why Nassim refers to this as the 1+a method.

15. Even under considerable uncertainty, our model revealed vulnerability to Black Swans via nonlinear acceleration in the tail.

We can’t predict Black Swans. But this is how we can predict our vulnerability to them.

16. This is a high-level view of predicting vulnerability to Black Swans. But there are important nuances.

For example, the model has to meet certain conditions for the method to work.

I recommend reading this article to better understand these nuances:

imf.org/en/Publication…

17. If you’re interested in diving deeper into fragility and antifragility, here's a thread:

https://twitter.com/carefullycnsdrd/status/1494774246660263949

18. I hope this thread helps in understanding how to detect vulnerability to Black Swans:

• Fragile things don’t like volatility
• Nonlinearities are everywhere
• Even under uncertainty, models can reveal fragility in the tail

Thanks to @nntaleb for sharing these lessons!