The Kelly criterion - is it good...or bad?
- Thread starter thenmmm
- Start date
Nothing wrong with using fractional Kelly for multiple trades. My point is that arbitrary fixed position sizing is woefully suboptimal as a money management strategy.
Just off the top of my head, I would divide each individual Kelly fraction by the total number of simultaneous trades. There's probably a better way to solve this problem and hopefully someone else more expert on Kelly will contribute.
Since no one has advocated using arbitrary size, you're arguing against a straw man. For example my own posts advocated size based on keeping drawdowns within a certain tolerance level, and using Monte Carlo analysis to estimate what is the maximum amount to risk based on a given risk tolerance.
When you say "if you can risk a little more via fractional Kelly and still be reasonably safe", you miss the point that it is NEVER reasonably safe to exceed your desired risk tolerances. I you can tolerate a 1% per annum chance of a 20% drawdown, and no more, then increasing your size from a level which risks exactly a 1% chance of a 20% drawdown, is now going over your risk tolerance. It is therefore not reasonably safe, by definition.
Kelly itself is arbitrary guesswork because you do not know your win rate or your risk/reward. It is only as good as the odds estimates - garbage In, Garbage Out. And, since Kelly requires TWO separate estimates - win rate %, and risk/reward ration, it is far more likely to have input errors than the drawdown/Monte Carlo method, which only requires one input, the % win rate. This is where trading differs from blackjack, roulette, and other fixed-odds games where you can be highly confident (but not certain, due to rigged games, biased wheels/decks etc) in the odds. Because of this odds uncertainty, you can never be sure that your method is still sound.
You are also overlooking several other risk factors. First, exceeding comfort level reduces returns while simultaneously increasing risk, the exact opposite of a trader's goal. The reason is that uncomfortable traders are weak hands: they are much more likely to get squeezed out of individual positions during market tests against them, and to lose confidence in a system during drawdowns. Both these things reduce returns; and the greater size increases risk. Lower returns with higher risk = bad news.
Secondly, black/grey swans always punish excessive size far more than insufficient size, with things like increased correlations across unrelated markets during panics/crashes, normal spread relationships breaking down or inverting, and so on.
Taking more risk therefore actually increases risk even more than the original decision to increase risk, because the risks of being squeezed out, losing conviction during drawdowns, and being battered by black/grey swans, increase exponentially with increased size.
Since higher but robust returns at lower risk, is what we are after, it is clear that all sizing decisions should always err on the size of caution.
To sum up: a method which focuses on minimising the risk of excessive losses is superior to one which focuses on maximising profit. A method which requires only one difficult estimate is superior to one which requires two difficult estimates. A simple method is superior to a complex one.
Therefore, Kelly is inferior for all risk-constrained traders. Kelly is only superior for traders who are not concerned with drawdowns at all, and are instead interested in maximising profit in the long-run. For example, someone who has a 50k account and has to pay the mafia 1 million within a month or get killed, would do better with the Kelly approach since blowing up is a lesser loss than being blow up, so to speak. Someone who is willing to risk a 75% chance of blowup, to maximise their chance of entering the billionaire list, may also care more about profit potential than risk. Kelly is for those people, and for people playing fixed-odds games where they don't have issues with systems losing their edge.
This is solved by my point made earlier, where you work out how much capital you could lose until hitting your 'uncle point', and then input that as your total capital into the Kelly equation. E.g. if you can only lose half your account before falling below the effective amount of $ needed to trade, then you input half your account value as the total account value in the Kelly equation.
You get trade odds whether you 'need' them or not. They are the probabilities of your present and future positions making or losing money at various % frequencies and with various risk to return payoffs. I am surprised you don't understand them because they are the two main inputs into the Kelly equation: % win rate on the trade, and payoff ratio on the trade. Without knowing those odds you can't even calculate the Kelly size.
Your Kelly fractions are not based on trade returns, because you do not know what your present and future trade returns will be. Rather, they are based on your estimates of future trade returns.
If your trade odds don't turn out to have been positive, then you will not make money trading.
That's true for all traders. Everyone gets squeezed out at a certain uncle point, even the most risk-neutral trader has a margin limit beyond which they can't go before becoming a weak hand (in this case, a forced weak hand). Every fund manager, even if they have ice-blood in their veins, has a point at which redemptions will close their fund, every trader has a point at which they get fired or lose heart, or just get margin-called into blowup.
Trading beyond comfort level is always a mistake, it reduces returns whilst simultaneously increasing risk. The difference with experienced traders is that their comfort level is higher. However, drawdown limits are still a hard cap on sensible risk levels - a risk-loving trader who bets 99% of his account on every trade is still over-trading, even though he is not beyond his comfort level.
So, it is essential to trade within both your comfort level and the mathematically optimal maximum size - it is always a mistake to exceed the Kelly position size. And, because of the difficulty calculating trade odds, it is almost always a mistake to consistently trade anywhere near the Kelly size.
Quote from kut2k2:
If you bothered to look at the Kelly equation, you'd realize that it is not static. Ergo, the Kelly solution is not fixed, it is adaptive.
In a drawdown (aka a series of loses), the Kelly fraction will shrink, thus reducing exposure (aka risk).
In a series of wins, the Kelly fraction will grow, thus increasing profits.
It's as easy to use adaptive Kelly in a backtest as in live trading. It's all good.
You missed his point. His point is that if you make a mistake in estimating the % win rate and the payoff ratio of your trades, then your Kelly fraction will be off, potentially by a very large amount (e.g. a factor of 5 or 10).
Also, the Kelly *fraction* does not shrink or grow during drawdowns or winning streaks - the sole inputs into the Kelly fraction are the win rate, and the payoff ratio. Therefore the amount of drawdown or profit, and even the amount of capital, have no impact whatsoever on what % of capital you should bet, according to the Kelly formula.
Since the word "drawdown" means a series of losses, not a single loss, and since adaptive Kelly shrinks with each loss, your assumption that Kelly cannot address drawdowns is simply wrong.
Since my Kelly calculations require neither winrate nor a win/loss ratio, then by your own logic, my method is superior to yours.
Perhaps if you ever bother to read my Kelly threads already referenced, you can spare yourself further embarrassment.
Good link.
These things are indisputable:
1. Exceeding the Kelly fraction is always sub-optimal for generating returns. So, Kelly is always a hard maximum limit.
2. Exceeding your uncle point (whether on a single trade, or a drawdown, or investor/manager/self confidence) will always increase your risk of blowup and/or going on tilt to undesirable levels, and will usually reduce total trade, and career P&L. So, is usually a mistake to exceed your comfort level.
3. It is always impossible to know the exact trade odds. Future results can always differ drastically from backtesting or theoretical estimates of future returns. So, it's always a mistake to think you have precise inputs to your money management system. Estimates of trade odds, and thus of correct bet size, are always rather vague.
4. Calculating two difficult estimates is harder than calculating one difficult estimate. Since drawdown size is affected mainly by win rate (since your worst possible drawdown streak contains zero winning trades) and % risk per trade, rather than by win rate, and payout ratio, and % risk per trade, it makes sense to estimate correct position size by trying to estimate just the one variable, and make it the far more important one - % win rate.
5. Maximum size based on % win rate and drawdown tolerance will ALWAYS be less than Kelly. Therefore Kelly's main theoretical and practical use - limiting maximum bet size to the theoretical optimal level - is rendered irrelevant.
6. Black/grey swans can cause losses greater than anticipated on one or more positions simultaneously or in short order.
So, the best solution for traders in the real world is to do this:
i) decide on maximum drawdown tolerance - this should be NO BIGGER than the amount that would endanger your trading career, and ideally should be below the amount that would start to stress you out and affect your quality of life. Stressed traders are radically more likely to make mistakes that can end in blowup, theft/fraud, jail, divorce, suicide and so on.
ii) estimate the win rate and payoff ratio of each trade, being conservative with the estimates.
iii) Use Monte Carlo analysis to work out the % chance of a drawdown streak hitting your max drawdown tolerance. Include the possibility of each drawdown having one black/grey swan that causes a greater than expected loss.
iv) size your trades such that the chance of hitting your maximum drawdown tolerance is sufficiently small to live with. For example, there is no point reducing this risk to a % chance that is smaller than the chance of you dying or being crippled for life, or losing your life savings (e.g. to lawsuits, war, government confiscation etc). I would say 1% is sufficient.
If you do the calculations, you will find that the equation I posted here covers the most common trading situations. I set my drawdown tolerance at around 20% for these numbers:
http://elitetrader.com/vb/showthread.php?s=&threadid=231801&highlight=rule+of+thumb
High win rate trades e.g. 70% win rate, bet 2-4%
Medium win rate trades e.g. 50% win rate, bet 1-2%
Low win rate trades e.g. 30%, bet 0.5-1%
I would add a category of very low win rate trades e.g. 15%%. In this case bet 0.1-0.25% of capital.
That is all you need to know about position sizing. If your drawdown tolerance is higher than 20% then you can bet a bit more than those figures. If your trade payoff ratio is very favourable (e.g. 5:1 or higher) then you can bet a bit more than those figures.
However, simple arithmetic should show that even for very favourable trades, betting more than say 10-20% of capital (as Kelly recommends very often) will almost guarantee hefty drawdowns during your career.
Analysing Kelly to death or trading to optimise size based on random guesses about trade odds, or absurd faith that backtesting will work just as well going forward, will not do you any good. Position sizing is somewhat tricky to analyse at first, but luckily the solution to it is trivially easy. So, spend your time on working out how to find good setups with good trade odds - that is the hard part of trading. The risk management is fairly simple and a 1 paragraph formula covers pretty much all trading eventualities without any need for complex or lengthy calculations and backtesting.
I'm just point out that using Kelly as it is to place your bets is not mathematically correct for the real world. Perhaps people smarter than I have come up with a great modified Kelly strategy to trade with. However, the way Kelly is set up in it's original form implies that there's a 0% chance of going broke. If you are getting 1:1 and are going to right 75% of the time Kelly says risk half of your account.