by admin June 24, 2013 Comments Off

A free adjusted kelly criterion spreadsheet download link will follow the end of this article.

The kelly criterion is a mathematically and statistically based set of formulas intended to maximize an individuals long term return on bankroll using optimal money management. Optimal in this case assumes an unlimited amount of time and unlimited tolerance for risk such that the only goal is to maximize the long term growth rate on your bankroll. It also assumes certainty, and no fees or commissions which is much more detrimental to a more volatile strategy. As such what is optimal to most individuals in an uncertain, commissioned market will be a much less aggressive than optimal strategy.

Accurately and appropriately applying the kelly criterion to investing is very problematic because many people miss out on a lot of important details.

For starters, the kelly criterion is intended for a single bet at a time, where as a portfolio is best utelized using a variety of relatively uncorrelated bets.

Additionally, it is commonly developed into an all or nothing bet calculator. In reality strategies are made up of bets that may have an INTENDED stop loss and an INTENDED target, but at times you will have losses greater than the stop and greater than the target. If you dont use a target, and instead use say a trailing stop or discressionary based trading, your entire losses and gains will vary significantly and each will have a different probability of occuring.

This is where my spreadsheet comes in.

If you are considering stock trades, you may wish to factor in the slight possibility of maybe half a percent for the unexpected massive overnight liquidation of the company like Lehman Brothers, Enron, WorldCom, Bear Sterns, etc. If you are using options particularly as you farther out of the money and shorten the length of time on the contract, the possibility of losing it all is much greater.

Eventually I have some ideas on how I will even improve this spreadsheet for now, this is what I have.

The relationship is such that lower correlation is better assuming the same odds and edge, since its closer to an independent bet and thus each individual bet is closer to being able to use the full kelly percentage as a percentage of the REMAINING capital available averaged out over the number of remaining trades.

If you trade stocks, a very diversified stock portfolio will have a correlation of roughly 70%.

www.etfscreen.com/corr.php

You can look at the correlation of

xlb,xle,xlf,xli,xlk,xlp,xlu,xlv,xly as an example of around 70% average correlation between assets.

Now if you add in aggricultural commidity ETF (DBA) and oil etf (USO) and a gold ETF it currently is around a correlation of .5.

Add in bonds and some currency ETFs and you can get it down to maybe .3.

Add in a few individual commodity ETFs and individual country ETFs and corporate bonds and government bonds and various currency, hedge fund etfs and REITS and mortgage backed security ETFs and you can get it closer to zero correlation. If you use options the decay of extrinsic value is highly correlated with the decay of others, particularly if the expiration dates and strike price are all similar. This isnt properly measured using traditional correlation.

However, correlation is not all bad, particularly as you are able to forecast and EXPECT rotations of capital into these areas. Afterall, increasing your timing increases your chances of success and upside, boosting your kelly% and return. Being more strongly correlated with the areas that have the greatest expected growth rate is fine.

The point of it is to just understand the relationship that MORE bets have at a lower correlation. That relationship is MORE bets risking less per bet at a lower correlation is better, at least until fees and law of diminishing returns start to become an issue.

Additionally, this can help you structure out multiple strategies in one portfolio solving for the M% for each bet.

For example if you plan to have a portfolio with 10 trades on at the same time, strategy A at HALF the maximum F% or full kelly might say to risk 4% as M%.

Strategy B at the maximum F% may say the equivilent M% is 8%.

You then can take your overall portfolio of all 10 names and multiply it by the ratio of your bet size to the maximum M% times the percentage of capital allocated towards that opportunity. Repeat for entire portfolio and add it all up. This will give you your overall portfolio risk as a percentage of the total maximum adjusted kelly F%.

This is a bit confusing and difficult to explain since the M% is the adjusted kelly based upon the number of bets and given F%. The M% represents the adjusted amount per bet given the F%. The goal is to adjust the F% until the return per one bet is maximized. Based upon the given F%, the given average correlation and the number of bets the M% will adjust on a per bet basis to maximize return.

The M% is thus the important determiner of success once you have maximized the return based upon F over a set amount of time such as a year given the number of trades you have in a year. For example 1000 trades per year at half a percent gain that can compound again and again is better than 1 trade per year at 1000% gain. The primary function of the spreadsheet is on a per trade basis for multiple bets, but you first want to use the F% and N to solve for the maximum M^N over a year to ensure you have the best strategy and only then consider multiple bets at a given correlation with that strategy.

The adjusted M^N only is set to work at 1 trade to give you a return on bankroll on a PER trade basis.

Portfolio Management:

This tool is all about managing your portfolio, so you have to learn how to do it right.

I always aim for the total weighted M average as less than HALF the maximum amount allowed since some of the positions will grow before I sell it. I never want to be forced to sell or reduce a position before it reaches its target just because it has grown in value. That requires you allow for enough growth in your portfolio so as to not violate the solid money management principals. As such I have certain rules.

1)If the total M% average is equal to or greater than 1, sell immediately until its less than 1.

2)If M% avg is between .5 and 1 sell as soon as trade strategy allows it.

3)If M is greater to or equal to 1 immediately suspend ALL trades with a positive correlation to portfolio

4)If M is between .5 and 1 immediately suspend all trades with a correlation greater than .4 to portfolio, and greatly reduce the amount of trades made overall if you can help it without passing up a great opportunity

The trick is, when I say HALF the M I am actually talking about the M AT half the maximized F% (HALF the kelly). That actual amount may be entirely different.

The awesome thing is, the relationship between the kelly criterion and long term return and amount risked holds true across the M% as well.

For example, the full KELLY risked per one trade of 19% may correspond to 10 bets with 65% correlation at 3.88% per bet (38.8% capital at risk). HALF the full kelly of 9.5% will correspond to 10 bets with 65% correlation at 2.55% per bet (25.5% capital at risk). Although you have about 65% of the maximum at risk, this is still the equivilent to HALF a kelly at risk, and will still produce nearly 70% of the return or in the example calculated 5.6601% gain as opposed to 8.2755% or about 68% of the return at half the amount of volatility. Actually risking HALF the M% per bet and risking 3.88/2=1.94% per bet for 10 bets at 65% correlation will produce a return of 4.4% or around 53% of the return with significantly less volatility.

In One set of data I tested, a Half M% strategy was the equivilent to about 22% of the full kelly.