Kelly Criterion & Risk Of Ruin As Risk Management Tool

[nonlinear5]

Ok, I never do this anymore, but I am in this case for the sake of clarity. Using the parameters of hte six scenario "game" you provided in this thread a few posts earlier:

Note that at a horizon of 15 periods or plays (the minimum number given teh parameters of your game, for an inflection point to appear) the inflection point is at about 1.5%. At twenty games, then quit, it is at 7.1%.....and on. Ultimately, as the number of plays or periods until you quit approaches infinity, the inflection point approaches the peak.
But this is the more conservative of the two risk-adjusted return maximizing points. (Incidentally, disregard the other rows on the sheet, they are for a different exercise on a different data set. The only relevant rows here are "Horizon" and "Inflection Point.")

Okay, let's take the inflection point for the 50 year horizon, which is 0.196. This means that you'd size each trade at 19.6% of the account size, correct? For example, if your account size is $100K, and the stock XYZ is trading at $10/share, then your position size would be:

size = 0.196 * (100,000 / 10) = 1960 shares

Is that right?

 

[rvince99]

10/.196 = 51.02
So I would trade one share for every $51.02 in equity, so
100,000 / 51.02 = 1960 shares, yes

 

[nonlinear5]

10/.196 = 51.02
So I would trade one share for every $51.02 in equity, so
100,000 / 51.02 = 1960 shares, yes

Okay, thanks. With accordance to my own risk-adjusted growth calculations, the position size should be about 8 times larger. I'll see what you have in your papers, and perhaps we could continue this discussion after that.

 

[rvince99]

Incidentally, the calculation for 1 market/system is pretty straigthforward, and i have it on a spreadsheet. For multpiple, it gets considerably more involved and you would have to go to the paper I posted with LoPrado & Zhu and myself.

An easier paper to understand inflection poitns for 1 market/system is:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2230874

You can use the enclosed spreadsheet which implements this. You put your outcomes and probabilities in B13 and C13, copying on down, including the working rows E,F & G.
Depending how many rows you are copying down, you will have to amend the formulas in Col B, specifically B4, B7 and B9.
Then you;re ready to solve. Make sure you have the Solver addon in installed in Excel. The Data-Solver, and set the parameters of the Solver dialog as follows:

To determine the inflection point and set it in B6. If you cant solve for it, it is because the Horiaon you specified in B2 is too low and you must increase it for an inflection point to begin to show.

To determine the f value and growth function answers for the rest of Col B, set your solver parameters like this:

Good luck with it and PLEASE remember, I'm trying to trade the markets too, I'm not a software company, I make no representations about anything, I don;t support anything and I don't do homework for others.

 

[ironchef]

For a small mom and pop retail trader, your discussions are way over my head.

For me, once I know I have positive expectancy, my first priority is to avoid the risk of ruin, so I can live to fight another day. I would follow nonlinear5 and trade a small fraction of Kelly or growth optimal fraction or whatever. I survived 2000 and 2008 and now instinctively trade much smaller sizes.

So, what is the equation for determine trade size needed to avoid risk of ruin?

 

[rvince99]

So, what is the equation for determine trade size needed to avoid risk of ruin?

Risk of ruin is minimized by not trading! The smaller size you trade in, the less your chance of ruin.

Your criteria is certainly not just to minimize risk of ruin, that's only part of it yes?

 

[rvince99]

For a small mom and pop retail trader, your discussions are way over my head.

Actually, they are NOT too complicated. I have tried to simplify things. I find people implementing things like Elliott Wave or all sort of esoteric technicals and such who are retail traders. It;s not that this stuff is too complicated or over anyone's head, rather, it is that it is dry. Vital, but dry.

 

[murray t turtle]

"reality is what your brain tells you it is"!

if you think that you need to know all about position sizing..optimal leverage..black scholes..kelly criterion..fibonacci retracements..stochastics..and so on..and on..and on..and on..and on..then..you might want to think about how it is your brain is telling you that you need all this information in order to carry out the simple acts of buying and selling

%%
Stochastics look fine in some charts;
but i seldom use them, because they can get commission intensive, but mainly= i may not be out @ end of day. I tend , because of trends, to get in @end of day. Not a prediction I dont think markets are like taking quarters[00.25/+ half dollars] out of a pool hall, even though i did that when younger.LOL. But a [half] 50 % off sale can get plenty of attention.LOL

 

[nonlinear5]

An easier paper to understand inflection poitns for 1 market/system is:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2230874

Okay, I read your paper, and now I understand why your inflection point of 0.196 is so low compared to my inflection point of 1.7 for the trade distribution that I posted earlier.

The reason for this difference is that you assume that it's possible to lose the entire allocated amount in one trade, and you re-scale the risk to account for this possibility. This throws the entire curve very sharply to the left, yielding very low leverage.

I personally don't think that this assumption is reasonable. To illustrate my point, consider an (almost) Holy Grail system, which gives you a 99% probability of a 10% gain, and a 1% probability of a 1% loss. Without calculating anything, it's quite clear that one should borrow money to trade this system on margin, i.e. use leverage. But your optimal f is bounded to 1 on the right, which basically does not allow any leverage at all. That looks to me like an artificial restriction which affects the calculated risk/reward profile for a large set of trade distributions, including the one that I referenced earlier (the six-outcome distribution).

 

[ironchef]

Risk of ruin is minimized by not trading! The smaller size you trade in, the less your chance of ruin.

Your criteria is certainly not just to minimize risk of ruin, that's only part of it yes?

I want the maximum trade size that can avoid risk of ruin.