Generalized Fixed Ratio MM

The three guys are all Tradestation "maestros" : Alex M in particular has a very interesting website with some excellent free stuff.

The 95% DD referred to was hearsay : it was about 87% .

http://www.traders2traders.com/papers/Ryan.Jones.MM.htm

Edit for mods : link posted for comment relevant to this thread. My further reference to Unicorn website also for very useful MM info.

With all respect, I believe you are incorrect.

On page 83 of the Trading Game, he gives an almost identical example to the one I posted above.

If you follow your example to its logical conclusion, at some point you will inevitably blow out your account as your risk actually INCREASES as your account balance grows.

I'll check it out this evening, kore - I have to put on my cook's hat right now to feed the family ...

Thanks for the link, I found DH Dennis' post hit the nail on the head (and good for some laughs), this is essentially what I'm aiming for with this "generalized" fixed ratio...

Interesting material.

Will read it at ease during the weekend.

Thanks for posting this.

Here is a quote from the web page jtrade posted, that outlines some common arguments against fixed ratio:

"I think this is flawed for 2 reasons: first, it relies much too heavily on the size of the contract. The entire leverage structure he computes would be totally different for, say, $250 SP's vs. $500 SP's. But the big flaw is his use of additive growth instead of percentage growth. Moving from 1 contract to 2 isn't equivalent to moving from 100 to 101; it's like moving from 100 to 200! I think simple fixed-fractional approaches handle the position sizing much more logically."

1. I agree, and have brought this point up already. Fixed ratio will have vastly different performance if you consider a standard, or mini, or micro lot as the basic unit. Ideally you should be able to set this to any size contract that makes sense for your account balance, goals, appetite for risk and relative value of said contract. This is one way in which fixed ratio needs to be generalized. I use true leverage instead of an arbitrary contract size, to get away from this altogether.

2. I disagree on this point, as long as the above point is taken into account and you "tune" your MM formula to suit your account size and goals. If I had a million dollar trading account, I would be fine with having to make another million before increasing from 100 to 101 lots, or whatever (just an example). To still be obsessed over exponential account growth at that point seems silly; capital preservation becomes more and more important as your account grows (in my opinion).

well... after a delicious desert of fresh mango with whipped cream and brandy, I now have to eat my rather less delicious cook's hat : you're quite right, kore, and I apologise for posting total rubbish .

Pass the brandy... and have a great weekend.

Hi Kore,
thx for starting this very interesting thread, I tried to study Ryan Jones's MM but I wasn't able to apply it into my real account, maybe you can help me on this matter.
For example let suppose I have a 30000 euro account , how much should be the initial lot to be used (I use normally a 100 pips stoploss for all my trades with a 2% fixed fractional MM) ?

Cheers,
Skyline

Ok one more post for now... At the risk of jumping ahead a little... There is one more oddity about fixed ratio that I was dissatisfied with, although I liked the overall premise.

If you look at the fixed ratio progression again, you may notice that your risk actually peaks around (starting balance + delta) and drops off in either direction. Your risk at $10k is the same as it is at $40k. This goes against the whole logic of the strategy, and until you reach $15k the MM is actually doing the opposite of what it's supposed to(!)

$10k - 1 lot (1 lot for every 10k)
$15k - 2 lots (1 lot for every 7.5k)
$25k - 3 lots (1 lot for every 8.3k)
$40k - 4 lots (1 lot for every 10k)
$60k - 5 lots (1 lot for every 12k)
....

Therefore instead of using a starting balance, I pinned the formula to 0. As your balance approaches 0, your risk will approach 2x your target leverage. However it will never be more than 2x your target leverage.

In essence this is fixed ratio with a "starting balance" of 0, and a delta equal to the target balance.

So to create an analog to our above examples, set the target balance to $5000, and target leverage 20. This results in the following position sizes:

$0k - 40:1 leverage (theoretical)
$5k - 20:1 leverage (1 lot, 1 for every 5k)
$15k - 13:1 leverage (2 lots, 1 for every 7.5k)
$30k - 10:1 leverage (3 lots, 1 for every 10k)
$50k - 8:1 leverage (4 lots, 1 for every 12.5k)

(Note: I do not recommend these settings, they are just for illustration relative to previous examples.)

Hi Skyline, this is a question you'll need to answer for yourself, because it depends on factors that are different for each person.

The basic feature of fixed ratio-style MM is rapid (higher risk) growth at the beginning, and slower (lower risk) growth as your account builds up.

Maybe you can think of your trading account(s) like a human life, there is a childhood phase where you grow up very quickly, an adult phase where you grow more slowly but still pick up new tricks along the way, and a retirement phase where you collect your pension

If you trade 2% of your equity for the entire lifespan of your account, you are cutting off your childhood IMO.

You need to consider not only the lot size (leverage amount) but also the "delta" (or target balance in my spreadsheet). The delta will determine how quickly the MM kicks in and starts to reduce your risk. If you make the delta too small, your "childhood" will be too short and the account will not grow as much or as quickly as it could otherwise. If you make it too large, you will be exposed to higher risk for longer amounts of time, perhaps unnecessarily (depending on your goals). Then you turn into the 45 year old beach bum who still thinks he's 21.

I suggest you play with different values and see how they translate to the lifetime of a trading account, either using my spreadsheet, or just writing them out on paper. You need to know in general how much you are willing to risk, and what you consider to be a mature trading account -- it will be different for everyone.

I'll try my best to answer any questions you have but cannot advise you on what your position size "should" be. If in doubt, stick with your current MM.

If I have understood this correctly, this sounds is very similar to what I have experimented with.

I have two ranges, percentage range and account balance range instead of one fixed risk ratio per trade.

Let's say that percentage range is from 5% to 1% and balance range is from 10k to 100k. Note that the previous numbers are totally fictional and not based on any tests or real data.

So to calculate risk, I reduce the risk linearly from begin balance to end balance, before the begin balance (10k) the risk is 5%, after the end balance (100k) risk is 1%. Between the 10k to 100k the risk is 5%-(account balance-10k)/(100k-10k)*(5%-1%).

Here I updated the spreadsheet, this should be the last change, unless anyone has ideas for improvement.

I changed the formula for both "shifted power" and "base lots" to eliminate errors when you use an offset, and current account equity is below the offset amount.

Those looking for settings can try playing with

Target Balance in the range $5,000 - $50,000
Target Leverage in the range 5 - 20.

Enter in different values for Equity, and see what your position size would be, and what this translates into for risk...

Let me know if you find any errors.

Hi mikkom - yes that sounds very similar and sticks to the "childhood - adulthood - retirement" idea. The main difference I think is if you plot fixed ratio positions, it is not linear with defined start and end points, but a smooth curve.

I think methods like yours make so much more sense than the whole "risk 2% per trade" advice... Thanks for sharing... Have a great weekend!

I'm really glad to see more in depth analysis of position sizing.

Markets change from sideways periods to trending periods and from low volatility to high volatility and all permutations of these scenarios.

I like the idea of increased risk during early stages of a small account and scaling out as time goes on and the account grows. Unfortunately without paying attention to the the market conditions mentioned above, one can expose oneself to some serious volatility in account balance.

I was wondering if anyone is varying risk based on market conditions given the systems being traded.

Trading is based on a constantly evolving sample and if one is unable to understand the conditions leading to drawdowns on a particular system, a position sizing model based on a fixed lot size for different account balance targets will not help minimize drawdowns. I think the application of this kind of model and also applying a varying risk based on market condition can be even more beneficial to growing an account.

Just my 2 cents.

Maybe I misunderstand your concept of a "dollar working." To me, the measure of how hard a dollar works is the percentage return I get on the risk. If I risk $200 and gain $200 on that risk, then my dollars have "worked" at the rate of 100%.

By using a fixed 2% risk (and assuming for clarity that our hypothetical trader Joe is always spot on with his trades), the dollars never have to work any harder at any level than at any other, as shown by this example:



Notice in the example that the deltas in balance size are NOT the same however, and maybe this is the rub. You seem to use an arbitrary "delta" value; i.e. a minumum value by which your account must increase before you are willing to increase the risk. Just set that delta value to zero and the problem goes away.

Just so that my above example isn't misunderstood to mean that Joe (who IS Joe anyway ) isn't "willing" to increase position size until the gains in the account are $200, then $204, then $208, etc., I'll provide a scenario in which Joe's gains are variable.

1. He starts with $10,000, makes a trade with a risk of $200, and ends up taking a profit of $20.

2. He now has $10,020. So at 2% he is willing to risk $200.40. So he makes a trade with a risk of $200.40 and let's say his gain this time is $50.

3. His balance is now $10,070. So at 2% he is willing to risk $201.40. So he makes a trade with a risk of $201.40.....

And so on.

Also, position sizes are a funtion of risk amount and stop distance, so it doesn't really make sense to talk about when to "increase position size." If I have $10,000 in an account, and my MM rule is to risk 2% on a trade, that means I risk $200, but it tells me nothing about what position size to use. To find position size, I need to know (based on chart analysis) where I'm going to be placing my stop. Note that the following examples are based on USD base pairs with the "standard" $10/pip for a "round lot" of 100,000 units.

If my stop distance is 100 pips away, then my position size will be $200/100 pips = 20,000 units (0.2 lots)

If my stop distance is 1000 pips away, then my position size will be $200/1000 pips = 2,000 units (0.02 lots)

If my stop distance is 25 pips away then my position size will be $200/25 pips = 80,000 units (0.8 lots)

The point I brought up at the end of the last post on position sizing is one with which a lot of new traders seem to struggle. Everyone seems to want to do it backwards, i.e. choose the position size first and then use that to determine the stop location. I wrote an article about this a few years ago, and this seems to be an appropriate place to bring up the subject. Here's a link:

http://market-geeks.com/articles/010...etterStops.php

Thanks for the replies capitalist, it gets me thinking.

What if you only use a stop loss as an emergency mechanism, and always close out based on PA... what is your risk then? On an individual trade, you will never know.

I like to size positions based on the expectancy of a trading method, even though this can only ever be a "best guess" based on probabilities and past performance. I also take into account maximum expected drawdown, and try to be prepared for 3-4 times this amount. But on an individual trade, I don't think the stop loss needs to have any direct relationship to the position size: stop loss is according to the trading method, position size is based on the expectancy (measured over many trades) of the method, allowing for maximum expected drawdown (and then some).

I agree that generally it makes more sense to gauge how our dollars are "working" based on raw returns. I was just trying to explain Fixed Ratio and the logic behind it, since my MM is based closely on that.

I'm not trying to prove anything to you or change your thinking. In fact it is more likely that my thinking gets changed as a result of all this.

Personally I'm willing to risk more than 2% when I have such a small account as I do, but as it grows I want to have a defined method of scaling back my risk. Sure I could arbitrarily reduce my risk whenever I felt like it, but I think it's better to be methodical.

All the arithmetical issues aside, I'm in complete agreement on what you're saying. It does seem kind of useless to stick to such a small percentage in a small account, because the entire account value might be negligible compared to the trader's overall financial situation. So why not take some larger risks? Not doing so just leads to frustration... as a super trade with a 300 pip win doesn't even cover the price of a happy meal. But as the account becomes larger and larger, it makes more sense to protect it by lowering the risk percentage.

Risk management/money management/trade management are something with which I've been going around in circles with in my mind lately. It can sometimes seem as complex a puzzle as the analysis of price behavior itself. There's the same sort of "combinatorial explosion" in the variables.

After testing my spreadsheet to death ( can a spreadsheet die? no it is still alive) I came to realize that my current formula is actually not fixed ratio at all. It is somewhere between fixed ratio and fixed fractional MM.

Seeing this, at first I tried to modify it to enforce a fixed ratio, but the results were highly unfavorable. Way too much risk with a low balance and/or way too small leverage with larger balances. This was a result of my attempt to eliminate the "hump" in the fixed ratio curve (risk increases before it decreases, as mentioned in a previous post).

So I've got a different curve here, and I'd better stop calling it fixed ratio. Or even "generalized" fixed ratio. Most of what I have written is still valid, and what I am presenting is much closer to fixed ratio than fixed fraction MM. But going forward I will be sure to be more accurate in my statements.

For the technically inclined

My "ratio" actually follows an exponential curve from 0.5 to 1.0. This is because I decided that as my balance approaches 0, risk should approach 2x the base leverage (so the first step of the MM has a ratio of 1/2 or 0.5). Then as the MM sequence progresses, it gets closer and closer to fixed ratio (1:1) -- without ever reaching it.

I don't know if this will make sense to anyone... Here are some figures to illustrate: these are the ratios between position size and profit required to increase position size.

Fixed Fraction
1:1
2:1
3:1
4:1
5:1

The above illustrates the "unequal achievement" of fixed fraction MM. Your position sizes increase much more rapidly as your account grows (because 5 lots can make "1" profit much more rapidly that 1 lot can).

Fixed Ratio
1:1
2:2
3:3
4:4

Fixed ratio speaks for itself, the main problem I have found is that when the sequence is getting off the ground, it has to start out with low risk and gradually increases risk up to a point (the delta), or else is forced to start out with excessive risk as I discovered in my tests today. I find both of these options unpalatable. So, with a tip of the hat, I am tossing fixed ratio out the window (actually I did long ago but just realized it today).

Kore MM
1:2
2:3
3:4
4:5
5:6

This is what my MM looks like, "something between" FF and FR. The rate at which positions are increased still rises along with growth in equity, but nowhere near as rapidly as with fixed fraction; also as the sequence unfolds it gets closer and closer to a 1:1 ratio (this is because the formula is based directly on the fixed ratio formula).

This was arrived at empirically mostly through trial and error (over the past year or two) while trying to eliminate the flaws in fixed ratio MM, but keep its benefits.

Posting this thread has forced me to think through and describe analytically what I had arrived at experimentally. Forgive me for fumbling a bit!