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Predictions are irrelevant in risk management. You don't want to know what will happen, you want to know the worst thing that could possibly happen. What you ne

by zupatol 18y ago

Predictions are irrelevant in risk management. You don't want to know what will happen, you want to know the worst thing that could possibly happen. What you need is a theory of probability for price movements. Financial theory uses the normal distribution, which underestimates the likelihood of big crashes. Mandelbrot says fractals give a better picture of market behaviour. They can be used to generate scenarios of price movements which give you different values for your portfolio. This is the probability distribution of your portfolio. It tells you how much debt you can take if you want to be able to pay it back 99.99% of the time. He makes an interesting analogy with the likelihood of a storm. Ships are built to survive waves of a certain height, and the highest probable wave is also calculated with a probability theory. The theory of waves had to be revised because a lot more ships were sinking than was thought to be likely. Someone came up with a better theory, and now safer ships can be built. In the same way, fractals could help build better portfolios.

niels_olson 18y ago
========================= First, a bit of context ========================= This article was written shortly after the spectacular collapse of Long Term Capital Management in late 1998. At the core of LTCM were Robert Merton and Myron Scholes, who shared the 1997 Nobel Prize in Economics for the Black-Scholes model. The Black-Scholes model was inspired by some calculus developed for rockets. Rockets have to constantly recalculate their trajectories, constantly reassuming certain assumptions about the path ahead. It didn't take much to see how similar math could be very useful for trading: it's simply a matter of choosing the right space and the right projectile (eg, imagine the space of all stocks and your portfolio as the projectile). The Black-Scholes model is at the core of what Mandelbrot calls "portfolio theory". That is what collapsed in late 1998, what would prompt Mandelbrot to write an article or motivate some editors to ask him to write an article. Keep in mind, the one of the claims the fractals guys make is that fractals help explain turbulence, which is very related to, again, rockets. Interestingly, from 1947 to 1949, Mandelbrot studied aeronautics at Cal Tech (which gets huge USG and DoD money for aeronautics). Shortly after returning to France, his focus appears to have sharpened on what would become the seeds of his fractal theory. He started publishing papers in applied fields, like fluid dynamics and economics. So, just based on history, without thinking about the content of the theories themselves, I think it's reasonable to assume that Mandelbrot would have some professional interest and awareness of the Black-Scholes model. Now, considering that the Black-Scholes model is quite competitive with fractal theory in the big-money arenas of fluid dynamics and economics, and considering the bells of Stockholm have not yet tolled for Mandelbrot, it is little wonder he would be keenly interested in discussing the merits of his theory in the context of the competing theory's recent and spectacular failure. Scholes et al claimed to provide predictive power with their model at work in LTCM's computers. It is worth noting, in the current recession, the Black-Scholes model remains at the heart of the false confidence all those "Quants" on Wall Street gave their bosses, which is what led to their bosses feeling comfortable with 30:1 leverage positions. I couldn't agree more with Anon84, except to extend the analogy further: no mathematics can explain the markets in a predictive way such that people don't loose money. If that were the case, everyone would make money and then you'd have, oh, wait, a bubble. Here's a direct analogy: Black-Sholes trading : Russian Financal Crisis of 1998 Rocket on infinite trajectory : Giant black obelisk appearing in the flight path right in front of the rocket There are things that can be done in markets that are not possible in the space-time continuum. Buyer be warry. -------------- Quant, btw, is a pun. It's quantitative economics, sure, but it's also "Quantum", because it has been, since I was an undergrad in the '90s, the easiest place for a physics grad to get a job. To see how tight the relationship is, Google for quant and search the first article you find for "Black-Scholes". The two are inextricable. =========================================== Second: portfolios target 95% and neglect the 5% that makes us human =========================================== You see, the markets aren't the space-time continuum. They are full of nasty discontinuities, legal, psychological, and otherwise. Thus hedge funds are always looking for 'smart people motivated by curiosity', which translates roughly to "We find these damn discontinuities in our trades, and we need someone who can just focus on the math and not worry about how much the fund is leveraged and whether or not our seed money came from Russian mafiosos and how much return we promised to the sovereign wealth fund of Ethiopia (if you'd rather keep race out of the argument, please replace Ethiopia with Iceland)" And that over-the-top quote points out the issue: the mathematical descriptive theories make assumptions, but the real world contains the entire, real space and the real consequences, and real people and the real environment will bear those consequences. If you wipe out Ethiopia's national wealth, then they have no money until they dig up some more gold. Little babies die, fathers abandon their families looking for work, homes are lost. But, hey, at least the price of gas went down. Good thing America has so well insulated itself from the consequences of its actions.

by zupatol 18y ago

niels_olson 18y ago

========================= First, a bit of context ========================= This article was written shortly after the spectacular collapse of Long Term Capital Management in late 1998. At the core of LTCM were Robert Merton and Myron Scholes, who shared the 1997 Nobel Prize in Economics for the Black-Scholes model. The Black-Scholes model was inspired by some calculus developed for rockets. Rockets have to constantly recalculate their trajectories, constantly reassuming certain assumptions about the path ahead. It didn't take much to see how similar math could be very useful for trading: it's simply a matter of choosing the right space and the right projectile (eg, imagine the space of all stocks and your portfolio as the projectile). The Black-Scholes model is at the core of what Mandelbrot calls "portfolio theory". That is what collapsed in late 1998, what would prompt Mandelbrot to write an article or motivate some editors to ask him to write an article. Keep in mind, the one of the claims the fractals guys make is that fractals help explain turbulence, which is very related to, again, rockets. Interestingly, from 1947 to 1949, Mandelbrot studied aeronautics at Cal Tech (which gets huge USG and DoD money for aeronautics). Shortly after returning to France, his focus appears to have sharpened on what would become the seeds of his fractal theory. He started publishing papers in applied fields, like fluid dynamics and economics. So, just based on history, without thinking about the content of the theories themselves, I think it's reasonable to assume that Mandelbrot would have some professional interest and awareness of the Black-Scholes model. Now, considering that the Black-Scholes model is quite competitive with fractal theory in the big-money arenas of fluid dynamics and economics, and considering the bells of Stockholm have not yet tolled for Mandelbrot, it is little wonder he would be keenly interested in discussing the merits of his theory in the context of the competing theory's recent and spectacular failure. Scholes et al claimed to provide predictive power with their model at work in LTCM's computers. It is worth noting, in the current recession, the Black-Scholes model remains at the heart of the false confidence all those "Quants" on Wall Street gave their bosses, which is what led to their bosses feeling comfortable with 30:1 leverage positions. I couldn't agree more with Anon84, except to extend the analogy further: no mathematics can explain the markets in a predictive way such that people don't loose money. If that were the case, everyone would make money and then you'd have, oh, wait, a bubble. Here's a direct analogy: Black-Sholes trading : Russian Financal Crisis of 1998 Rocket on infinite trajectory : Giant black obelisk appearing in the flight path right in front of the rocket There are things that can be done in markets that are not possible in the space-time continuum. Buyer be warry. -------------- Quant, btw, is a pun. It's quantitative economics, sure, but it's also "Quantum", because it has been, since I was an undergrad in the '90s, the easiest place for a physics grad to get a job. To see how tight the relationship is, Google for quant and search the first article you find for "Black-Scholes". The two are inextricable. =========================================== Second: portfolios target 95% and neglect the 5% that makes us human =========================================== You see, the markets aren't the space-time continuum. They are full of nasty discontinuities, legal, psychological, and otherwise. Thus hedge funds are always looking for 'smart people motivated by curiosity', which translates roughly to "We find these damn discontinuities in our trades, and we need someone who can just focus on the math and not worry about how much the fund is leveraged and whether or not our seed money came from Russian mafiosos and how much return we promised to the sovereign wealth fund of Ethiopia (if you'd rather keep race out of the argument, please replace Ethiopia with Iceland)" And that over-the-top quote points out the issue: the mathematical descriptive theories make assumptions, but the real world contains the entire, real space and the real consequences, and real people and the real environment will bear those consequences. If you wipe out Ethiopia's national wealth, then they have no money until they dig up some more gold. Little babies die, fathers abandon their families looking for work, homes are lost. But, hey, at least the price of gas went down. Good thing America has so well insulated itself from the consequences of its actions.