How much should you risk?

[bleau]

One of the better threads on elite. Thanks!

 

[globalarbtrader]

This is trivial stuff. Just use a black swan factor (BSF):

BSF == 0.9/max[ .0001 , X*max[ -Ri ]_i=1toN ]

BSF prevents your next losing trade from wiping you out even if it is X times as large as your current worst loss. Choose the smallest value of X that lets you sleep at night. Default: X = 2.

Use min[ BSF, your (fractional) Kelly estimate ] as your trading fraction.

That's a nice formula.

Of course my point still stands - the effect of the BSF on fraction level will dominate the choice of kelly sizing formula for negatively skewed trading returns.

GAT

 

[kut2k2]

So essentially you are adding new information (i.e. new trades) to your existing trading stats and recalculating Kelly? Would that be right?

Yes.

 

[kut2k2]

Yes, using a formula that accounts for higher moments is important (whether 3, 4, 5 or 6). But I still think that Kelly blowups usually happen not because of the wrong formula, but because of a poor appreciation of the uncertainty of returns.

I'm going to labour the point, in case there are people reading this thread without the same appreciation of the nuances that you obviously have.

The first order problem is that if are over confident about your mean versus your standard deviation (there I won't use the 's' word again); as I've already discussed. It doesn't matter how you update your estimate of optimal Kelly, you're going to need thousands of data points just to know that there is a 95% chance your optimal Kelly is somewhere between 2% and 4% (using more realistic numbers).

The second order problem is you have a negative skew / evil kurtosis, but don't realise you do, because you haven't yet had your LTCM moment. So you get a long string of small positive returns. Even the fanciest Kelly formula will be taking you to fill your boots.

Or if you prefer

There is a 95% chance that you win 1% of your bet ;
There is a 5% chance that you lose 10% of your bet
There is a 0.01% chance that you lose 100% of your bet

... comes out to around 97% (using excel solver, with rounding, for the avoidance of any ambiguity)

But if the true distribution is actually:

There is a 95% chance that you win 1% of your bet ;
There is a 4.8% chance that you lose 10% of your bet
There is a 0.2% chance that you lose 100% of your bet

... optimal comes in around 55%

But then is why we use half kelly, right? We'd just about get away with it.

But if the true distribution is actually:

There is a 95% chance that you win 1% of your bet ;
There is a 4.5% chance that you lose 10% of your bet
There is a 0.4% chance that you lose 100% of your bet

Then you should be using something more like 17%.

My question is does anyone really have a well calibrated idea of whether something has a 0.01%, 0.2% or 0.4% chance of happening? I refer you to the behavioural finance work on this, plus everything Taleb has written.

Even if the underlying distribution of returns is stable (a massively unrealistic assumption as I've already said), you'd need tens of thousands of trades to narrow down a sufficiently narrow window for that figure.

(this is a more long winded way of saying that having to estimate higher moments doesn't make your life any easier)

And in real life, as I've already said we don't have a stable distribution or enough data; nine times out of 10 we're LTCM in 1998 or the CDO guys in 2006 and the -100% currently has a realised probability of zero. So you have to guess what the odds of -100% are. If you're tied into a gaussian thought process you'd not bother assiging any probability, since even on the last set of numbers -100% is a 15 sigma event. Even if you manage to get yourself to confront the remote possibility of a total loss how do you know whether that possibility is 0.2% or 0.4%?

The only way out of this conundrum is to avoid trading anything with such evil skew (or anything that's likely to have such nasty skew in the future), or if you absolutely must do so then use an extremely conservative fraction of optimal Kelly. One Kelly formula might tell you that optimal is 90%, another might say 80%, but in certain situations you'd be insane to use more than 5%.

GAT

I disagree. First most Kelly blowups happen precisely because of bad formulae. I didn't write the Bad Kelly thread and the other threads for my health.

You're stuck on the fiction that there is some return probability distribution out there that you can reach out and touch, if only you could calculate its parameters with some certainty. I reject this fiction. My formulas prove that all you need are accurate recordings of the trade returns. The mean tells you if you have positive expectation. Beyond that, the standard deviation, the skew, etc. matter not a wit. You don't need any of that artificial stuff to figure out your betting fraction.

There is no uncertainty in the trade returns. There is only uncertainty in the phantom distribution you imagine they adhere to.

 

[botpro]

kut2k2, I doubt your equation(s), I mean your "New" Kelly stuff, will make an entry into any academic paper or book as it is not scientific what you do.

 

[kut2k2]

kut2k2, I doubt your equation(s), I mean your "New" Kelly stuff, will make an entry into any academic paper or book as it is not scientific what you do.

It's very scientific, it's just not revealed science. And I didn't do it for academia, I did it for me. Screw academia; what they know about trading generally doesn't amount to a hill of beans. What I figured out isn't rocket science, it's half rocket science. So how come the academics haven't figured it out?

Like Sherlock Holmes, I observed and I deduced. That's all.

 

[Visaria]

Yes.

So what is the need for new kelly or for proprietary kelly? Just recalc the new win rate and distribution, and stick it into excel...out pops the correct kelly fraction.

 

[botpro]

So what is the need for new kelly or for proprietary kelly?

That I asked myself too... ;-)

 

[kut2k2]

So what is the need for new kelly or for proprietary kelly? Just recalc the new win rate and distribution, and stick it into excel...out pops the correct kelly fraction.

What distribution? IRL there is no distribution. Just a long and growing string of trade returns. So what do you do?

 

[romik]

Here's a new puzzle for you optimal sizers.

Here's the scenario:

There is a 35% chance that you win 20% of your bet ;
There is a 25% chance that you lose 15% of your bet ;;
There is a 20% chance that you win 12% of your bet ;
There is a 15% chance that you lose 6% of your bet ;
There is a 4% chance that you win 50% of your bet ;
There is a 1% chance that you lose 100% of your bet.

What percentage of your betting account should you risk to maximize your potential gain?

These are like the shittiest odds ever. What I would recommend is to flip used vehicles adding 5% each time and compound each time you flip. Initial investment $5k, keep re-investing 100%.