Compounding My Interests by Elliot Turner

Nassim Taleb

Defining and Mapping Fragility

Black swans are not about fat tail events. They are about how we do not know the probabilities in the tail.
The absence of evidence vs evidence of absence is very severe
- Too much is based on non-evidentiary methods
Financial instruments (options) are more fat-tailed than the function suggests
- P(x) is non-linear
- Thus the dynamics of exposure are different than the dynamics of the security
- To that end law of large numbers doesn’t apply in options
“Anyone who uses the word variance does not trade options”
- The measure of a fat tail is a distribution’s kurtosis
There was a great chart of 50 years of data across markets
- In the S&P in particular, 80% of the kurtosis can be represented by 1 single day (1987 crash)
- This would not converge in your data studying a broad look at the S&P
- One can only talk about variance if the error coefficient of the variance is under control
- In Silver, 98% of its 50-year variance comes from 1 observation
EVT-extreme value theory is very problematic because we don’t know what the tail alpha is.
- In VAR, a small change can add many 0000s
- There is no confidence at all in the tails of these models
- The concentration of tail events without predecessors means that such events do not occur in the data. Tails that don’t occur are problematic.
A short option position pays until a random shock. Asymmetric downside to defined, modest upside. This bet does not like variability (dispersion), volatility.
Look at the level of k (believe kurtosis??) and see sensitivity to the scale of the distribution. This is fragility.
- Volatility = the scale of the distribution
- The payoff in the tail increases as a result of sigma
If you define fragility, you can measure it even without understanding the probabilities in the tail
- Nonlinearity of the payoff in the tail means that the rate of harm increase disproportionately to an instance of harm
- What is nonlinear has a negative response to volatility
Fragility hates 2nd order effects. For example: if you like 72 degree room temperature, 2 days at 70 degrees is better than 1 at 0 and the next at 140.
Lots of nature demonstrates “S” curves
- In the convex face of the s-curve, we want dispersion. In the concave face we do not (stability)
How to measure risk in portfolios: takes issue with IMFs emphasis on stress tests looking at a “worst” past instance, which is a stationary point in time.
- Dexia went out of business shortly after “passing” such a stress test
- Solution: do 3 stress tests and figure out the acceleration of harm past a certain point, as conditions get worse.
  - We should care about increasing levels of risk, not degree
  - Risk increases asymmetrically, so if the rate of acceleration is extreme, this is stress.
Praised Marty Liebowitz for “figuring out convexity in bonds”
“Convex losses, concave gains --->thin tials ---> robust”
Antifragile=convex, benefits from variability
Can take the past to see the degree of fragility. You get more information and more measurable data from something that went down and then back up in the past, than something that went down and stayed at 0.
Adding information is concave (N). Convex is when we add dimensions (D), spurious correlations increase.
- There is a large D, small N problem in epidemiology.
- NSA is one of the few areas that uses data well, but this is so because they are not interesting in many things, only the few that have value to what they’re trying to do.
PCA analysis, variations are regime dependent.
We can lower nonlinearity of a price (buying options)
- Hard to turn fragile into anti-fragile, but can make it robust (tea cup can put lead in it).
- Robust requires the absence of an absorption barrier – no O, no I in transition probabilities. Don’t stay or die in a specific state.
“Small is beautiful”
Q that “VAR is the best we have”:
- A pilot says on a flight to Moscow: “We don’t have a map of Moscow, but we do have one of Paris.” You get off that plane. We don’t take random maps for that reason, and same logic applies to VAR.
- Using VAR under this logic is troubling because it encourages people to take more risk than they really think they are taking. They anchor to the probabilities of VAR, not reality.
Liquidation costs are concave. There are diseconomies of scale from massive size.