Topic for discussion in the Village of the Darned

I’ve been reading Nassim Taleb’s(Black Swan guy) books lately, as well as some of the work of Kahneman & Tversky (behavioral economics guys). They have lots of interesting ideas that apply to economics but also more broadly to all interactions among humans, including politics.

Here’s an outline of the two related topics I wanted to talk about and get everyone’s thoughts:

Assumption of rational actors (Nassim Taleb)

  • predictability/chaos
  • mathematical tractability
  • game theory (ludic fallacy)

Intuitive vs. rational thinking (Daniel Kahneman)

  • heuristics (System 1)
  • reasoning (System 2)

 

Please see comment below for a discussion of the figures.

Linear plot:

linear

Log plot:

log

drlorentz

About drlorentz

photon whisperer and quantum mechanic
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7 Responses to Topic for discussion in the Village of the Darned

  1. BrentB67BrentB67 says:

    Respectfully, I do not understand the question (a recurring problem).

  2. AdministratorAdministrator says:

    Actually had a great conversation on the topic!

  3. drlorentzdrlorentz says:

    Sorry if the topic was unclear. The post was not meant to be self-explanatory. They were just notes to go with the discussion.

    Tomorrow, I’ll post a followup to something that BDB brought up during the call.

  4. drlorentzdrlorentz says:

    There was some discussion on the Village call yesterday about fat tails in movements of the stock market. I said I’d put some data as follow up so here goes.

    A couple of years ago I analyzed the one-month changes in the S&P 500 from 1871 to the present time. (Data courtesy of Robert Shiller). Since I don’t know how to post graphics in comments, I’ll be putting them up in the OP.

    I tallied the frequency of various upward and downward movements in the market: a histogram. The data points are black squares. For example, there were about 150 upward and 500 downward fractional changes of about 5%, shown as points at +0.05 and -0.05, respectively on the graphs. The lines are various model functions.

    The top graph is plotted with a linear vertical scale. The blue curve (Gaussian or normal) looks pretty decent with the exception of one point. From this you might conclude that Gaussian statistics are a reasonable representation of the market.

    The bottom graph is exactly the same information, except displayed with a logarithmic vertical axis. This plot reveals the nature of the very unlikely events: market movements of 10% or more (up or down). A couple of things jump out:
    1. The data is skewed negative. Big one-month market drops are more likely than big rises.
    2. The blue curve is a terrible approximation and greatly underestimates the probability of outlier events. The chance of a 20% drop is underestimated by 100,000 to 1 by the normal probability function.
    If you assume normal statistics, they will give you a false sense of security. This, in a nutshell, is Taleb’s thesis about Black Swans.

    Since the data set is asymmetric, you can’t use any one symmetric function to model it. Since risk management is about the left-hand side of the graph, the cubic power law is the most pertinent. This isn’t quite as misbehaved as the Cauchy (or, as I prefer, Lorentz) function, but it’s pretty bad.

    I’m assuming that my editing of the OP will be successful. If not, this comment will look really stupid.

  5. drlorentzdrlorentz says:

    Related, from Taleb, yesterday:

    Something I learned today: The SP500 is Fat Tailed because of serial dependence. pic.twitter.com/zJFZLEdgma— NassimNicholasTaleb (@nntaleb) July 29, 2017

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