The author covers the topic in considerable depth but fails to understand the key points.
Mandlebrot makes serious criticisms of the standard models of stock and other valuations - these boil down to saying that the "tails" of market changes are going to be larger than the current models.
The simplest example is CDO's. If you believe in short-tailed, uncorrelated stock market changes, you can argue that the stocks of five different tripple-A rated major corporations have a zero percent chance of simultaneously declining. And you similarly combine together even poor quality bonds to create a "synthetic" bond which also supposedly has a nearly 0% chance of failure.
If you believe in long-tailed, correlated stockmarket changes, you believe that the chances of such bonds failing is much higher.
Guess what actually happened?
I would criticize Taleb, however, for not bringing the issue of complex random processes to the fore. I think he wants to make his ideas very accessible but the problem is that he looses the key difference between short-tailed and long-tailed distributions, since short-tailed distributions DO exist in reality, especially physics and so we're not talking generic randomness when looking the problems of understanding markets and uncertainty.
the problem is that he looses the key difference between short-tailed and long-tailed distributions
Isn't this basically what the entire "Black Swan" book is about? The difference between what he calls "Mediocristan" and "Extremistan", and that physical reality is in Mediocristan, is the basic concept he starts out with.
> saying that the "tails" of market changes are going to be larger than the current models
The claim is that people using the models are well aware that the gaussian distribution is only an approximation, and that substituting fatter tailed distributions into the models don't actually affect the outputs very much.
Do you think that, perhaps, the massive collapse of the financial system in the past year might at least cast a bit of doubt on whether that "awareness" translates effectively to behavior?
This is a not a very solid claim. The difference in calculations using a distribution with a finite variance versus one with an infinite variance could not be more different.
The approximation is not done for closeness, because they are not close at all, but for convenience and simplicity. Probability theory is amazingly difficult when you are dealing with infinite variance.
Mandlebrot makes serious criticisms of the standard models of stock and other valuations - these boil down to saying that the "tails" of market changes are going to be larger than the current models.
The simplest example is CDO's. If you believe in short-tailed, uncorrelated stock market changes, you can argue that the stocks of five different tripple-A rated major corporations have a zero percent chance of simultaneously declining. And you similarly combine together even poor quality bonds to create a "synthetic" bond which also supposedly has a nearly 0% chance of failure.
If you believe in long-tailed, correlated stockmarket changes, you believe that the chances of such bonds failing is much higher.
Guess what actually happened?
I would criticize Taleb, however, for not bringing the issue of complex random processes to the fore. I think he wants to make his ideas very accessible but the problem is that he looses the key difference between short-tailed and long-tailed distributions, since short-tailed distributions DO exist in reality, especially physics and so we're not talking generic randomness when looking the problems of understanding markets and uncertainty.