wilmott.com

I know it's well researched subject in the field of economics. But I wonder how many people use it on real world trading decisions?thanks...

I sometimes use it, but you have to do your analysis before doubling down. It's not automatic, but rather discretionary. Most of the time this works well.

You've read Poundstone's Fortune's Formula? That tells who! (And, more tellingly, who doesn't!)P

QuoteOriginally posted by: PaulYou've read Poundstone's Fortune's Formula? That tells who! (And, more tellingly, who doesn't!)PI have heard of it, thanks to article by Dr. Thorp.Also, the title itself overrates the Kelly criterion, it's not a "fortunes formula" in the sense that it doesn't tell you how to make money - it tells you how to manage money so that not to lose it. No Kelly criterion will save you in a game with negative expectation and unfaroble payoff. Speaking of unfavorable payoffs - it was unnoticed until September 2008, that the Kelly criterion as originally formulated - leads to ruin. It's now called the Proebstring paradox. Some guy with that name, e-mailed Thorp about the strange fact that one loses money when she/he bets in a game with non-constant odds. For example, if one the first trial the odds are 2:1 and then on the second 3:1 - you will lose all your wealht in such game. A very clear description is given even in Wikipedia: " For example, if a 50/50 bet pays 2 to 1, Kelly says to bet 25% of wealth. If a 50/50 bet pays 5 to 1, Kelly says to bet 40% of wealth.Now suppose a gambler is offered 2 to 1 payout and bets 25%. What should she do if the payout on new bets changes to 5 to 1? She should choose f* to maximize:"because if she wins she will have 1.5 (the 0.5 from winning the 25% bet at 2 to 1 odds) plus 5f*; and if she loses she must pay 0.25 from the first bet, and f* from the second. Taking the derivative with respect to f* and setting it to zero gives:So f* = 0.225.The paradox is that the total bet, 0.25 + 0.225 = 0.475, is larger than the 0.4 Kelly bet if the 5 to 1 odds are offered from the beginning. It is counterintuitive that you bet more when some of the bet is at unfavorable odds.Now consider this formula:"For example, given the original example of a 2 to 1 payout followed by a 5 to 1 payout, in this formulation the bettor first bets 25% of wealth at 2 to 1. When the 5 to 1 payout is offered, the bettor can sell back the original bet for a loss of 0.125. His 2 to 1 bet pays 0.5 if he wins and costs 0.25 if he loses. At the new 5 to 1 payout, he could get a bet that pays 0.625 if he wins and costs 0.125 if he loses, this is 0.125 better than his original bet in both states. Therefore his original bet now has a value of -0.125. Given his new wealth level of 0.875, his 40% bet (the Kelly amount for the 5 to 1 payout) is 0.35."So, simply put - the Kelly criterion is NOT wrong as long as you knwo the odds being given on each trial. But there is one option of Kelly which is still unresolved until present day, from what I know: It assumes that the capital is unfinutely divisible. Of course if you reach 0,0000$ in your trading experienc, then you are either multibillionaire who likes to test the criterion on practice or just drunk . Now, I am thinking on applying the Kelly critetion together with Parrondo paradox in something that I am calling "complete market". I will explain in better detail in other thread...And...by the way, I wrote one code to show the immense power of the Kelly criterion some time ago. The code is in PHP. Below is the code + SQL database code. You can test it and see if you change some variable HIGHER than the allowed from Kelly - you will lose money . If you lower the variable - you win - but slowly...(fractional kelly).The code that demonstrates the Kelly power is as follows: The program runs a series of games. Each game has 50% chance of winning/losing and 2/1 payoff. Acording to Kelly - we bet 25% of our capital. The program finally shows our wealth after the games it has played. It's ALWAYS positive. The program also assumes that the capital is inftinely disivible. Another option I have included is the option to show if ouw capital falls below certain limits. The code has some comments...but skip them...I am just lazy now to delete them...Here is a table from phpmyadmin generated by the program simulator following Kelly:So, as you can see - we weren't that lucky in our first 4 games . Starting with 1000 capita l -we have lost our first 25%(-250). Then our next 25%(-187.5). Then our next 25%(-140.625)...our next -105.46875. When the luck comes on our side - we win our 25% with the promised payoff of 2/1 - which is 2 times for every amount bet, meaning our 25% * 2. Hence the next time you don't see: 79.1015625 - expected from negative return of 2 - but you see 2 times the 25% - and namely: 158.203125Here is the code:1. Database:-- phpMyAdmin SQL Dump-- version 2.11.7-- http://www.phpmyadmin.net---- Host: localhost-- Server version: 5.0.51-- PHP Version: 5.2.6SET SQL_MODE="NO_AUTO_VALUE_ON_ZERO";---- Database: `xedema`---- ------------------------------------------------------------ Table structure for table `xedema2`--CREATE TABLE IF NOT EXISTS `xedema2` ( `result` varchar(20) NOT NULL, `capital` varchar(20) NOT NULL) ENGINE=InnoDB DEFAULT CHARSET=latin1;---- Dumping data for table `xedema2`--INSERT INTO `xedema2` (`result`, `capital`) VALUES('', '1000');Now the PHP code:<?$con = mysql_connect("localhost","root","linux");if (!$con) { die('Could not connect: ' . mysql_error()); }mysql_select_db("xedema", $con);for ($xxxy = 0; $xxxy <= 400; $xxxy++){$b = rand(1,2);/*$result = mysql_query("SELECT sum(x) FROM xedema1 where x <= 60000000"); if ($result)$query_data=mysql_fetch_array($result);$total=$query_data["sum(x)"];*/$result1 = mysql_query("SELECT sum(capital) FROM xedema2 where capital <= 60000000"); if ($result1)$query_data1=mysql_fetch_array($result1);$total1=$query_data1["sum(capital)"];if ($total1 <= 10){echo "capital has come to lower than $10";}if ($total1 <= 5){echo "capital has come to lower than 5$";}if($total1 <=1){echo "bancrupt...this should never happen though ";}$scalaro = 0.25 * $total1;//$scalaro = ($total+ $total * 0.5 - 0.5)/$total+$total;if ($b == 1){$jk = $scalaro * 2;//+ ($scalaro/2);//(0.5 * ($total1/4));mysql_query("INSERT INTO xedema2(result,capital) VALUES (1,$jk)");}if ($b == 2){$totaler = $scalaro - $scalaro - $scalaro;mysql_query("INSERT INTO xedema2(result,capital) VALUES (2,$totaler)");}}//echo $total;echo $total1;?>By the way, I feel sleepy now...friday night - so I can't even confirm if this is the very fight file with code. But...I am not joking...so it has to be the right file! Oncee again - don't read the php comments. Just create the database and execute it. The simulator as defined above will execute 400 games using the Kelly criterion. The games have 50% chance of success and 2/1 payoff - hence the bet is 25% of capital of 1000. If the values are incorrect or you don't like them - change them easily here:$jk = $scalaro * 2;So, aside from the nice code above - conclusion...Kelly works but:1. Capital is not infinitely devisible.2. Proebstring should be taken into account.3. Because of the fat tails and non-linearity it might take a long time until you go ahead.My advice is not to use any model which relies on price prediction. To quote Nills Bor again: "Prediction is hard, especially on the future".

P.S.Just by the way... I just discovered(not that it's my honer at all...) that Kelly criterion is wrong at least because of:- Parrondo paradox.- Will rogers phenomenon.I also have the hypothesis that it MIGHT be wrong or at least producing very different and non-stochastic results when the capital is divisible on special groups of numbers. Such as producing better results on perfect numbers and worse results on odd numbers. But this is very, very, very shy hypothesis. But...take a look at Parrondo...if someone here is not aware of it of course - it basically knocks down the Kelly criterion. Still, my advice is to use Kelly to price easy situations...but again - beware of fat tails.P.S.One interesting philosophical thing to ponder for the weekend - how to play a life game according to Kelly? Since the life itself is definetly a game with nagative expectation(100% chance to lose - one should kill himself and not live according to Kelly . OK, now I feel sort of satisfyed after I broke apart the Kelly criterion even without the need of formulas and code (still I really like the criterion though...). Now I have to find more spare time to do something useful and something producing high returns . happy 14th to everyone, though.