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I was reading a cheat sheet about Day Trading on dummies site. There I encountered an interpretation of kelly criterion that says "In its simplest version, the percentage of your account that you trade is equal to the probability of the trade going up minus the probability of it going down."

I am not a day trader, and my accuracy is 70%, so according to their interpretation I should trade with 40% of my account size. What impact will following it have on my capital?

Dana
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    Small tip: If you are at the "For Dummies" stage of learning investing, do not day trade. It is a very high-risk activity, and you should be comfortable enough with your knowledge that you fully understand the risks involved. If you don't understand the risks, you are liable to make some poor decisions. Many people decide that day-trading is too risky for them, period, regardless of how comfortable they feel in their investing knowledge. – Grade 'Eh' Bacon Mar 08 '17 at 14:51
  • @Grade'Eh'Bacon - the OP specifically said they are not a day trader, so no need for your small tip !!! – Victor Mar 08 '17 at 23:03
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    @Victor In my opinion, it is specifically because the OP considers themselves 'not a day trader', and yet refers to using day-trading practices ("What impact will following it on my capital?"), that this advice is most critical. If someone displays a potential lack of knowledge over such a risky subject, I hope no one objects to a warning about it. Not to mention anyone who sees this question and would fall into a similar category. – Grade 'Eh' Bacon Mar 09 '17 at 13:54
  • @Grade'Eh'Bacon - that is correct, it is your opinion. Trading is not limited to only day trading, and as the OP has also mentioned their accuracy is 70%. So has it occured to you that the OP is already trading (but not day trading) and is asking about applying a technique to their situation. – Victor Mar 09 '17 at 22:25
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    @Victor I'm not sure why my comment seemed improper to you; my sole points are that (a) if someone mentions day-trading, they appear to be interested in day-trading; and (b) if someone mentions reading "for dummies" level of information, then they may have insufficient experience to understand the risks of day-trading. Please don't besmirch my desire to lay out what I freely admit above is my opinion, which is that the terms the OP is using indicate perhaps less experience than they realize, relative to the risk of the subject matter. – Grade 'Eh' Bacon Mar 10 '17 at 13:38
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    @Grade'Eh'Bacon - so all you do is read the words but not their context. So someone says "I am not a day trader", and all you see is "day trader" and you preach your opinion onto them. – Victor Mar 10 '17 at 22:43

3 Answers3

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Three important things worth remembering about Kelly when applied to real world edges:

1) Full Kelly staking is gut wrenchingly volatile. While it maximises the growth of the bankroll, it does so in a way that still leaves you very likely to experience massive (50%+) reductions in capital. Most long terms users of Kelly tend to stick in the 1/4 to 1/2 Kelly unit range to try and stay sane and retain a margin of error. See below for how large the typical swings can be with full Kelly:

enter image description here

2) Garbage in, garbage out. If you are making errors in pricing your actual edge, Kelly becomes very wrong very fast, easily leading you to a high chance of ruin if you are over estimating your true edge. As most people do massively over estimate their edges, Kelly simply pushes them far into territory where risk of ruin is high.

3) A Kelly user prefers to back likely outcomes over non likely ones, even to the point where they prefer a smaller % edge if the chances of winning are better. Compare the below comparison of growth between two betting scenarios (decimal odds, so for the percantage chances do 1/odds):

enter image description here

In this case, despite the percentage edge on the red bet being higher than that of the green, in terms of bankroll growth it ends up only being roughly as good to a kelly gambler as the smaller edge on the more likely event. This has an obvious effect on the types of edges you should be seeking out if given choices between liklihoods.

Philip
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  • Can you link to a source for the figure? – Nosrac Mar 08 '17 at 14:52
  • Which figure do you mean Daniel? – Philip Mar 08 '17 at 14:53
  • "Figure 2", the image embedded in your answer – Nosrac Mar 08 '17 at 14:54
  • Sure. Here: http://bethelp.haitco.com/index.php/site/page?view=principle – Philip Mar 08 '17 at 14:55
  • Thanks! I was curious about how constant betting was defined in the simulation. – Nosrac Mar 08 '17 at 15:03
  • The green wager has a compound growth rate of just under 0.001% per trial (wagering about 0.503% of bankroll).

    The red wager, has a compound growth rate of a little more than 0.099% per trial (wagering about 1.515% of bankroll).

    If you have to choose one to bet on, it's nearly certain that as the number of trials goes to infinity (remembering Keynes' dictum about the long run...), the chance of someone following any strategy much different from betting about 1.5% on the red wager having a bigger bankroll approaches zero.

     – Levi Ramsey Sep 13 '17 at 01:11
  • Of course, an even better growth rate can be had by betting on both, but the optimal strategy there is not 0.503% on green and 1.515% on red (which can be seen by, for instance, having 50 wagers on independent greens with the same true/offered odds and 50 wagers on likewise independent reds and noting that the hallmark of the Kelly strategy is that it avoids any staking which could possibly result in zero bankroll). With a little work, one can find that the Kelly allocation is 97.983% cash, 0.502% green, and 1.515% red, which has a growth rate of slightly over 0.1% per trial. – Levi Ramsey Sep 13 '17 at 01:22
  • It is true, though that Kelly is volatile. If wagering full Kelly, the probability (regardless of your bankroll), that there will be some future point where your bankroll will be at most half of your current bankroll is 50% (and by extension there's a 1 in 4 chance of seeing a cumulative loss to some point of 75%, 1 in 8 chance of losing 87.5%, 1 in 16 chance of losing 94% and so forth). – Levi Ramsey Sep 13 '17 at 01:40
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The goal of the kelly criterion strategy is to find a balance between preservation of starting capital and returns. One of extreme you could bet the entirety of your account on one trade, which would maximize your returns if you win, but leave you unable to further invest if you lose. On the other extreme, you could bet the smallest amount of capital possible over the course of several trades to increase the probability that you'll even out to 70% accuracy over time. But this method would be extremely slow.

So for your case, investing 40% each time is one way to find an optimal balance between these two extremes. Use this as a rule of thumb though, because your own situation and investing goals may differ from the goal of optimal growth.

Nosrac
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I don't know too much about the kelly criterion, but going by the other answers it sounds like it could be quite risky depending how you use it.

I have been taught the first thing you do in trading is protect your existing capital and any profits you have made, and for this reason I prefer and use Position Sizing (PS).

The concept with PS is that you only risk a small % of your capital on every trade, usually not more than 1%, however if you want to be very aggressive then not more than 2%. I use 1% of my capital for every trade.

So if you are trading with an account of $40,000 and your risk R on every trade is 1%, then R = $400.

As an example, say you decide to buy a stock at $10 and you work out your initial stop to be at $9.50, then our maximum risk R of $400 is divided by the stop distance of $0.50 to get your PS = $400/$0.50 = 800 shares. If the price then drops after your purchase, your maximum loss (subject to no slippage) would be $400.

If the price moves up you would raise your stop until your potential loss becomes smaller and smaller and then becomes a gain once your stop moves above your initial purchase price.

The aim is to make your gains be larger than your losses. So if your average loss is kept to 1R or less then you should aim to get your average gains to 2R, 3R or more. This would be considered a good trading system where you will make regular profits even with a win ratio of 50%.

Victor
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