I have wanted to do a blog post on this topic for some time, and now I feel confident enough in this approach to position sizing that I can discuss it. I am going to be talking about the Kelly Criterion today. I was first exposed to this idea from playing online poker over a decade ago, although not by name. It was really my foray into advantage blackjack where I became intimately familiar with the Kelly Criterion.

First here is my current profit chart.

The first thing you might notice is I am having a massive drawdown right now. I recently linked my Venom/IB account with my direct IB account and now I'm having issues importing some of my trades, so my profitly account is not up to date with all of my trades. If those problems continue much longer I will have to manually add the trades which are not being imported. I was feeling extremely discouraged after a big loss in $ZFGN and my insanely supportive girlfriend snapped me out of that with one word, "Variance." And that brings us back to the Kelly Criterion.

What does my drawdown have to do with the Kelly Criterion? Everything, so let's get started. The Kelly Criterion is a formula you can use to calculate how much of your bankroll you can bet on a game given an edge in order to maximize the long term growth of your bankroll while at the same time minimizing your risk of ruin. It works by maximizing the period by period expected utility of wealth with a logarithmic utility function. The formula essentially can be boiled down to betting a portion of your bankroll equal to your edge divided by your odds. This leads to increasing your bet or position sizes proportionally with your account as your account grows. Because of that, it also leads to some fairly big drawdowns in the short term. 

A good example of those drawdowns are presented in the book Fortune's Formula by William Poundstone. "You might ask what game or investment is being charted. It doesn’t matter much. Kelly betting is a way of making all gambles and investments interchangeable. Given any gambling or investment opportunity, the Kelly wager converts it into a capital-growth-optimal gamble/ investment."

"This jagged mountain range can be a landscape of heartbreak. Suppose you found yourself at the top of the peak to the right of the center of the chart. Maybe that represents your first million. In this particular scenario, you are just about to lose most of it. The bankroll fluctuations in Kelly betting obey a simple rule. In an infinite series of serial Kelly bets, the chance of your bankroll ever dipping down to half its original size is… ½. This is exactly correct for an idealized game in which the betting is continuous. It is close to correct for the more usual case of discrete bets (blackjack, horse racing, etc.). A similar rule holds for any fraction 1/ n. The chance of ever dipping to 1/ 3 your original bankroll is 1/ 3. The chance of being reduced to 1 percent of your bankroll is 1 percent. The good news is that the chance of ever being reduced to zero is zero. Because you never go broke, you can always recover from losses."

Because the short term drawdowns can be so drastic, many people use fractional kelly bets, perhaps betting one-half of the amount Kelly prescribes. This will lower the volatility, but also the total expected returns. I've mostly come to term with the short term fluctuations, also known as variance, from my extensive exposure to them while counting cards playing blackjack. So I like to focus on the long term and take the path that will maximize my long term account growth which means I try to bet full Kelly whenever possible. And part of betting full kelly means that I will have to endure some large drawdowns. I had days playing blackjack where I would lose 1/3 of my total bankroll in a single day. Those were hard to endure, but the math told me I was playing correctly and that the more I played, the closer my results would come to match my expected value. 

I was actually very surprised during my recent win streak, with how consistently straight up my profit graph was going. That was nothing like blackjack, which in general was much more choppy and looked more like the graph of the Kelly Criterion above. This current drawdown in my trading profits actually has made me more comfortable in how I am sizing my positions because this is really more like how I expected my profits to grow. I did have a problem cutting losses on about 5 recent trades, and I think that was due to sizing up my positions too quickly. With the Kelly Criterion, your position size will change after every bet, because your bankroll changes as you win and lose each trade or bet. But as Tim G has mentioned in various webinars and probably in Trading Tickers, if you size up too fast, you won't be comfortable cutting a loss at your predefined risk level. This is what I am running into, so I am going to size down temporarily and then start increasing my risk size at a slower rate. 

But in general, I think this drawdown is just variance. My stats are still showing the right numbers, and my overall win rate is at an all time high as of my last trade. My setup specific stats are still right in the area I want them to be, which is 70%+ win rate with 2-1 risk/reward ratio. I have to keep in mind one of my trading rules, which I took directly from blackjack, and that is "Short term results are meaningless." I'm in this for the long run, and I have no control over the short term random distribution of wins and losses. All I can do is continue taking good trades and managing my risk well, and the profits should take care of themselves as long as I have an edge and continue applying that edge over a large number of trials.

This was a very high level overview of Kelly betting. If you have specific questions please leave them in the comments, or send me a message and I will try to answer them as best as I can.

Cheers!

 

 

 

Poundstone, William. Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (pp. 227-229). Farrar, Straus and Giroux. Kindle Edition.