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Why didn’t people in finance pay attention to Benoit Mandelbrot?

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Re: Why didn’t people in finance pay attention to Benoit Mandelbrot?

#51

Earlier quoted context omitted.

I think the standard model also tells you that you cannot do much, no? Well, as a matter of fact... --- No, not true. The "standard model" predicts a kind of randomness which is fundamentally tractable. It comes down to Gaussian versus non-Gaussian stable distribitions. A Gaussian model predicts that total market changes mostly come from day-to-day, small incremental changes - ie, a Gaussian model is equivalent to Br…

No, he was right. The standard model does tell you you can't make money. You are addressing a completely separate issue (hedging risk) in the rest of your post.

If by the "standard model", one means the general model of Black-Scholes and modern mainstream mathematical finance, I stand by my original claim.

In practical terms, modern mathematical finance's modeling of market with the Gaussian distribution has the implication that it is possible to add together a number of risky items to get a product which is less risky. This was the basis of Long Term Capital Management and this was the basis of the "synthetic" Triple A bonds built out of sub-prime mortgages.

The "free money" comes of out the risk combining/hedging approach through the implication that by adding up supposedly uncorrelated risks, you can create a lower-risk financial "vehicle" that still delivers a rate of return somewhat comparable to underlying items. If a bank pays 1% interest and you can get a 5% "virtually risk free return", then you've got 4% profit. Now Black and Merton of LTCM went one step further. They were so mathematically impressive that they got a virtually infinite line of credit to borrow against to use in the risk-combining approach. The implication was they would be, again, getting a nearly-risk-free rate of return and so investment banks could lend to them nearly-risk-free too. Even their massive failure didn't convince people. The entire stable of CDO etc product sold on the same basis, the basis of providing risks no greater than the highest rated corporate bond but with significantly higher return. We can see how "risk-free" they really were.

Moreover, it is true that if you can find a bunch of small, uncorrelated risks with finite mean and variance, you can add them up to get a big, tractable Gaussian distribution with a very small variance (that's the mean-value theorem, in fact). So the synthetic bond approach rests firmed on the standard modeling of the market as akin to Brownian motion.

The problem with this approach is that, as Mandlebrot pointed out is that one doesn't actually wind-up dealing with distributions having finite variance. Adding up distributions without finite variance gets you a distribution in the L-stable family of distributions, which are in general much less tractable, not having finite variance themselves. In this light, it seems clearer why synthetic bonds turned not to be the free money they claimed to be.

One might argue that this mean that the "efficient market hypothesis" itself would imply that markets don't follow a Gaussian distribution. I'll leave that those who still some faith this formulation - I'd personally claim this "hypothesis" isn't even a coherently position.

Re: Why didn’t people in finance pay attention to Benoit Mandelbrot?

#52

Earlier quoted context omitted.

No, he was right. The standard model does tell you you can't make money. You are addressing a completely separate issue (hedging risk) in the rest of your post.

If by the "standard model", one means the general model of Black-Scholes and modern mainstream mathematical finance, I stand by my original claim. In practical terms, modern mathematical finance's modeling of market with the Gaussian distribution has the implication that it is possible to add together a number of risky items to get a product which is less risky. This was the basis of Long Term Capital Management and…

In practical terms, modern mathematical finance's modeling of market with the Gaussian distribution has the implication that it is possible to add together a number of risky items to get a product which is less risky.

Nonsense. Any Finance 101 textbook will tell you this is only true if the securities are uncorrelated. It will also tell you that assuming the EMH holds, people will buy into the lower risk index until returns are reduced to 1%.

As for LTCM, the thing that killed them is that they didn't have an unlimited supply of credit and they got hit by margin calls.

The entire stable of CDO etc product sold on the same basis, the basis of providing risks no greater than the highest rated corporate bond but with significantly higher return.

No, the entire stable of mortgage-backed products was backed by the assumption that housing won't go down crash, a factor exogenous to Black Scholes. Also, you seem to not understand how CDOs are priced - the Black Scholes style models are used for interest rates, which have not exhibited infinite variance. Default rates, which are included separately, also have not exhibited infinite variance (in fact, since they are bounded between 0 and 1 they cannot exhibit infinite variance).

No model works if you plug in the wrong parameters. To quote Babbage: ...I have been asked, – "...if you put into the machine wrong figures, will the right answers come out?"... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

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