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Book review: Fortune's Formula
Dec. 10th, 2008 07:05 amIf you are a gambler, or you invest actively in the stock market, read this book! This means you ![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
patrissimo and songmonk.
This book is Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone
It goes into a lot of background and colorful detail about gangsters and betting, mathematicians and economists, and describes why many respected economists don't like the risk structure called the Kelly Criterion.
The Kelly Criterion is basically this: it tells you how much to bet on any given wager to maximize your rate of return on capitol in the long run. How much you should bet is based on how much information you have. It minimizes your chances of going bankrupt. It draws a clear mathematical line between "aggressive" and "insane" betting. In the long run, an aggressive bettor does well. An insane better always bets that 1:1000 will never come up, and one day ends up bankrupt a la Long Term Capitol Management.
...
Take the example of a coin toss that pays you $1 if it comes up heads, and takes your dollar if it comes up tails. Let's say you know you're using a coin that comes up heads 55% of the time, and you have $100 to start with and you can keep making the bet. How much do you bet on each toss?
One way is to bet $1 on each toss. Then your money grows very slowly. Another way is to bet your entire bankroll on every toss -- if the first toss is heads, you now have $200. If the second toss is heads, you now have $400. If the third toss is tails, you now have $0 and can't make any more bets.
The Kelly criteria is to bet edge/odds as a percent of your bankroll, which in this case comes out to 55%. First toss heads, you now have $155. Second toss you bet $85.25, you win and now have $240.25. Third toss you bet $132, you lose and now have $108.25. In the long run, your money will grow exponentially, but it will have it's ups and downs. You can smooth out the curves by making a half-kelly bet.
Kelly gets even better when you're making multiple simultaneous bets. The book gave the example of tossing 100 coins with a 55% chance of coming up heads. In the rare case where only 45 of the coins come up heads in one round of tossing the coins, the Kelly better ends up with $90 of a $100 bankroll at the start of that round. The better who leveraged 30:1 and placed all their money on heads now owes 2 times as much money as they had at the start of the last round.
...
The author claims that LTCM wasn't so much guilty of bad strategies or even making the same bet all over the world, but they were guilty of overbetting, a problem sure to lead to ruin eventually, even if all the bets are "good".
The Kelly criterion is much-maligned in the economic academic circles for reasons the author attributes to prominent academics claiming that real people can't handle the Kelly losses and so mean-variance or other ways of valuing risk are much better. The author is clearly biased in favor of Kelly, and after reading the book I'd have to agree, but Jon and I are still actively reading. The other methods claim to be for investors who are less risk tolerant, but at the same time, those methods can expose them to more risk.
--Beth
patrissimo and songmonk.This book is Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone
It goes into a lot of background and colorful detail about gangsters and betting, mathematicians and economists, and describes why many respected economists don't like the risk structure called the Kelly Criterion.
The Kelly Criterion is basically this: it tells you how much to bet on any given wager to maximize your rate of return on capitol in the long run. How much you should bet is based on how much information you have. It minimizes your chances of going bankrupt. It draws a clear mathematical line between "aggressive" and "insane" betting. In the long run, an aggressive bettor does well. An insane better always bets that 1:1000 will never come up, and one day ends up bankrupt a la Long Term Capitol Management.
...
Take the example of a coin toss that pays you $1 if it comes up heads, and takes your dollar if it comes up tails. Let's say you know you're using a coin that comes up heads 55% of the time, and you have $100 to start with and you can keep making the bet. How much do you bet on each toss?
One way is to bet $1 on each toss. Then your money grows very slowly. Another way is to bet your entire bankroll on every toss -- if the first toss is heads, you now have $200. If the second toss is heads, you now have $400. If the third toss is tails, you now have $0 and can't make any more bets.
The Kelly criteria is to bet edge/odds as a percent of your bankroll, which in this case comes out to 55%. First toss heads, you now have $155. Second toss you bet $85.25, you win and now have $240.25. Third toss you bet $132, you lose and now have $108.25. In the long run, your money will grow exponentially, but it will have it's ups and downs. You can smooth out the curves by making a half-kelly bet.
Kelly gets even better when you're making multiple simultaneous bets. The book gave the example of tossing 100 coins with a 55% chance of coming up heads. In the rare case where only 45 of the coins come up heads in one round of tossing the coins, the Kelly better ends up with $90 of a $100 bankroll at the start of that round. The better who leveraged 30:1 and placed all their money on heads now owes 2 times as much money as they had at the start of the last round.
...
The author claims that LTCM wasn't so much guilty of bad strategies or even making the same bet all over the world, but they were guilty of overbetting, a problem sure to lead to ruin eventually, even if all the bets are "good".
The Kelly criterion is much-maligned in the economic academic circles for reasons the author attributes to prominent academics claiming that real people can't handle the Kelly losses and so mean-variance or other ways of valuing risk are much better. The author is clearly biased in favor of Kelly, and after reading the book I'd have to agree, but Jon and I are still actively reading. The other methods claim to be for investors who are less risk tolerant, but at the same time, those methods can expose them to more risk.
--Beth
