Generalized Fixed Ratio MM

I am opening a thread to discuss a Money Management formula which I call Generalized Fixed Ratio. I also call it Shifted Power MM because when I first curve-fitted the fixed ratio position sizes, it resulted in an equation called, you guessed it, shifted power.

I will work up to it over a few posts, to cover all the bases. It is based on Ryan Jones' book on MM, except my version of Fixed Ratio does not lock you to a particular lot size, which is an important improvement, especially when you are dealing with mini or micro lots.

Comments and criticism are welcome here, just try to keep it on topic, and please let me complete my first series of posts (it will be obvious when I'm done, I'll include an excel spreadsheet at the end).

Note: the attachment in post #11 is out of date, the one at the top of page 3 is current and I am attaching it here also.

The simplest kind of MM is no MM, in other words fixed position sizing. You decide to trade one standard lot per trade, and never increase or decrease the size of your positions: you always trade one lot. Fixed position sizing is ideal for backtesting, because it lets you see the raw performance of a trading method -- but it should generally not be used on a live account.

By far the most widely used and recommended MM approach is applying a Fixed Fraction (for example, 2%) to your account equity, and never risking more than this amount on a trade. Some people base it on the stop loss, others on the average historical performance of a trading method. Either way it amounts to basically the same thing.

This is much better than using a fixed position size, for the simple reason that as your account grows, so do your position sizes, which creates exponential growth. A trading method that makes 10% profit per year trading fixed lots might make 50% or 100% profit per year using fixed fraction MM. While this is a hypothetical example, it illustrates the power and importance of proper money management.

On the surface, fixed fraction MM seems like an ideal solution, but it has a fundamental flaw, which many people overlook. It is not a fatal flaw, and some people may not even consider it to be a problem (these people likely have large trading accounts already), but a flaw none the less. Let's take an example to illustrate this.

Joe has a trading account with $10,000 in it, and decides he will size his positions based on a fixed 2% fraction of his equity.

At the outset, Joe is risking $200 (2% of $10,000) per trade. Those $200 trades need to make $10,000 in profits before Joe will risk $400 per trade. At that point, the $400 trades need to make another $10,000 in profits before Joe will risk $600 per trade, and so on. The $600 trades need to create $10,000 in profits before $800 is risked, etc.

So at the outset, $200 worth of risk needs to create $10,000 in profits (over a sequence of trades), but once the account has grown to $40,000, each $200 risked only needs to create $2,500 in profits before the position size is increased to the next level. In other words, Joe's money has to work 4 times harder when he has $10k, compared to when he has $40k, to reach the next step or level of position size.

Ryan Jones calls this "unequal achievement" and identifies it as the central flaw of all fixed fractional MM formulas.

The premise behind Fixed Ratio MM is that the steps or levels of a money management sequence should be equally easy to achieve, regardless of your account balance at any moment in time.

Fixed fraction MM ensures a constant % risk as your account grows, but imposes unequal achievement: your money has to work harder when your account is small, compared to when your account is large.

Fixed ratio MM uses a variable % risk to ensure a constant ratio between position size and the rate at which position sizes increase: your risk is higher when your account is small than it is when your account is large.

I will leave it as an exercise to the reader to determine which approach is best for them, I am not here to prove one is better than the other; they are simply different.

Would you risk 100% of $500 to make $100,000? Would you still be comfortable risking 100% of $100,000, or would you want to preserve some of that capital? This is what Fixed Ratio MM does.

You risk more when you have less, because equity growth is more important than capital preservation (since you have almost nothing to lose). You risk less when you have more, because capital preservation is more important than equity growth (since you can live off your returns).

If you agree with this logic, then Fixed Ratio MM may be for you. However, the formula presented by Ryan Jones is somewhat inflexible, and not suited to forex where fractional lot sizes (mini and micro) are available.

Subscribed because I have a question about post #3, but I'll wait until you complete your initial series of posts. Good stuff!

alas.. something to look forward too..

Great post! I am eager to hear more..

Let's look at another example to uncover an interesting feature of fixed ratio that could cause problems if you just use the original formula blindly.

We'll look at two hypothetical accounts:

Account A
Starting Balance: $1,000
Starting Lots: 0.1
Delta: $500

Account B
Starting Balance: $10,000
Starting Lots: 1.0
Delta: $5,000

If you just glance at this, you might think the two are equivalent. In one we are increasing from one lot to two when each lot generates $5000 in profit; in the other we are increasing from one mini lot (0.1 standard lots) to two when each mini lot generates $500 in profit.

However since the delta is ten times bigger on account B, the two accounts will have vastly different performance:

Balance -|- Position A -|- Position B
$1,000 -|- 0.1 -|- 0
$2,500 -|- 0.3 -|- 0
$7,500 -|- 0.5 -|- 0
$10,000 -|- 0.6 -|- 1.0
$15,000 -|- 0.8 -|- 2.0
$25,000 -|- 1.0 -|- 3.0

Notice how on account B, if you drop to less than $7,500, you can no longer trade, and on account A, once you reach $10,000 you are already in "capital preservation" mode (your position sizes will increase very slowly compared to your balance).

The base lot size and the delta both have a large part to play in how the MM will perform as your account grows. However the original fixed ratio formula isn't very flexible in this regard, it always scales your position based on one "unit" (and whether that is a standard, mini or micro lot will make a world of difference).

Another thing that we have to deal with in forex is that 1 lot is not the same as another. If you have an account in USD, 1 lot of GBPJPY is quite a bit different than 1 lot of AUDCHF.

So from now on, I will generally not speak about position size in terms of lots, but in terms of true leverage.

If you have a $10,000 account, and your position has a value of $10,000 (0.1 lots of a USD based pair), you are using 1:1 leverage.

On the same account, if your position has a value of $100,000 USD, you are using 10:1 leverage.

Sizing our positions based on leverage accomplishes two things, it decouples the MM formula from a particular currency, and it lets you set your "base position size" to anything you want, giving you more control over your MM (compared to using "1 lot" as the base position size as in the examples in the previous post).

There are a few more points that haven't been covered yet, but I'm going to close it here for now and let them come up in discussion.

I am attaching a spreadsheet I use for my MM. Here are some instructions on how to use it.

There are two worksheets, one for the generalized fixed ratio formula, which calculates your base leverage given your account balance, and another to adjust this base leverage based on the expectation of each of your trading strategies.

The main formula has four parameters:

Account Equity: this is how much money you have in your account right now.
Offset: can be used to emulate traditional fixed ratio, but I normally set it to 0.
Target Balance: this is basically the fixed ratio "delta", your MM will increment in steps of this amount (actually, the delta is target balance minus offset).
Target Leverage: the base leverage you wish to use at your target balance. When your equity is lower than your target balance, leverage will be higher; when your equity is higher than your target balance, leverage will gradually be reduced. Note that your leverage will be double this amount when your equity reaches zero (offset).

*Note if you trade EUR or GBP pairs, you will also want to make sure that the EUR and GBP values are current. You may find you need to add other currencies here, e.g. AUD, NZD or CHF, depending on what pairs you trade.

The following values will be calculated based on the four variables:

Shifted Power: this is basically your progress towards your target balance, you don't need to use this value directly as everything else is calculated for you.
Base Leverage: this is your base leverage, which will be adjusted based on the expectancy of each trading strategy (see next worksheet).
Base Lots, EUR Lots, GBP Lots: Base leverage converted to standard lots.

I highly recommend that you also use the second worksheet, especially if you trade multiple strategies.

The second worksheet will adjust the Base Leverage according to the mathematical expectancy of each trading strategy. For each strategy, enter your average win, average loss and win %. The spreadsheet will calculate the true leverage, and position size in lots.

Please note that I only just added "offset" back into the mix, and that errors will result if your equity is less than the offset. I always set the offset to 0, because this makes more sense to me. I added the offset back in in case anyone wants to use this to calculate Ryan Jones style fixed ratio.

Please be aware that I am a musician not a mathematician!

The calculations are correct to the best of my knowledge and this is what I use to size the position of my live trades.

There is a good chance that this formula could be improved upon, and I am happy to receive suggestions.

If you have an idea how to fix the Offset errors, let me know (as mentioned, I don't use it, so may not bother trying to fix it).

So now the thread is open for discussion, criticism, comments, etc...

Bless.

I updated the spreadsheet, fixed two of the calculations to eliminate errors when:

- equity equals offset (used to result in a divide by zero error)
- equity is less than offset (base lots used to be calculated incorrectly)

There are still errors when your equity falls too far below the offset, however I don't think there is a way around this, as it is present in the original fixed ratio formula (see above example with Account B falling too far below $10,000, position size becomes 0).

This is part of the reason I started this thread, to force me to think everything through more thoroughly, and make improvements

I still recommend setting offset to 0, however if you choose to set it to a different amount things will now work as expected.

Hmm - thanks for the spreadsheet, which could be useful.

I could tell a story or two about Ryan Jones - I met him once in a McDonalds in Florida (truly !) ...

OK, here's my question about post #3, where you conclude that there's a problem with fixed fraction.

The part in bold isn't true; Joe is just adding some whacky inflexible rule to his MM. Why?

If Joe makes a profit of only 0.5% on his account, he can immediately increase his per trade risk.

He starts with $10,000, and let's say he achieves a profit of $50. He now has $10,050. If he wants to risk 2% of this amount, he simply needs to risk $201 on each trade instead of $200. This is the beauty of continuous (or virtually continuous) compounding.

Why wait to make $10,000 in profits before increasing risk when you could do it with a simple $50 profit?

I simplified the example for sake of illustration. I could have taken it down to each 0.1 lot increment or even each 0.01 lot increment, however the dynamics will remain the same. It would still be the same if you could trade in 0.000000001 lot increments, or what have you.

For example to go from 1.00 lots to 1.01 lots, your $200 of risk needs to generate $100; to go from 1.01 to 1.02, each $200 that you risk needs to generate $99.01; from 1.02 to 1.03, it is $98.04, and so on.

The basic feature of fixed fractional MM is that your risk remains constant regardless of account balance, and position size is increased more and more rapidly as your account grows. The flip side of this is your money has to "work harder" when your balance is low, as the example above is intended to illustrate.

With fixed ratio, position size is increased at a constant rate, but you have more risk when your account balance is low, and scale back the risk as your equity grows, which helps preserve your capital.

Does this answer your question?

Ahh, I think I see where the confusion is. You're moving position size up while keeping dollars risked constant. In your example you've gone from 1.00 lots to 1.03 lots, but you've kept your amount at risk at $200 each time.

My understanding of fixed fraction is that the amount at risk increases in direct proportion to the position size. So in your example above, a fixed fraction trader would actually be risking $200 for 1.00 lots, $202 for 1.01 lots, $204 for 1.02 lots, and $206 for 1.03 lots. Not $200 each time. So there is no issue of your money having to "work harder" at one level as opposed to another Everything is directly proportional between any two levels, no matter how far apart.

Not exactly; I said "each" $200 of risk needs to produce $100, $99, $98 in profits. Obviously when you are trading 1.02 lots (in our example) your actual risk is $204. Those $204 need to produce $100 in profits, so by extension "each" $200 needs to produce (200 / 204 * 100) or $98.04.

A better way to look at it might be "how hard does each dollar that I put on the line have to work before I will increase my position size." In our example, your dollars have to work twice as hard when your balance is $10k, compared to when it is $20k. Here we are measuring "work" in terms of how fast your position size is increasing.

Contrast this with a fixed ratio example with starting balance of $10k and delta of $5k:

$10k - trade 1 lot
$15k - trade 2 lots
$25k - trade 3 lots
$40k - trade 4 lots

To go from 1 to 2 lots, you need $5000 profits (each dollar risked needs to generate $25) -- to go from 2 to 3 lots you need $10000 profit (each dollar risked needs to generate $25) -- to go from 3 to 4 lots you need $15000 profit (each dollar needs to generate $25).

Continuing the above example let's look at how we would increase our position sizes using fixed fraction MM

$10k - trade 1 lot
$20k - trade 2 lots
$30k - trade 3 lots
$40k - trade 4 lots

To get to $20k, each dollar risked needs to generate $50; to get to $30k, each dollar risked needs to generate $25; to get to $40k, each dollar needs to generate $16.67. (I am going back to the simplified example of whole lots, I hope we can agree it would be the same if we were discussing fractional lots.)

Also notice what happens once you pass $40k, for both FF and FR. With fixed ratio, although it was more risky to get to this level, after this level your risk is less than with fixed fraction. In other words you would experience more rapid growth up to this level, and then slower growth and less risk (preserving capital) after this level.

Whether you think this is a good idea or not, is a matter of personal taste... But I hope we can at least agree on the basic qualities of these two MM strategies.

Forgive me if I am misunderstanding your post, but the above is not a Fixed Ratio progression, which with a delta of $5k would be :

$10k - 1 lot
$15k - 2 lots
$20k - 3 lots
$25k - 4 lots
$30k - 5 lots
$35k - 6 lots
$40k - 7 lots

In other words, whilst Fixed Ratio is good for aggressively expanding your account, provided your system maintains its positive expectancy, it can decline equally fast in a severe drawdown, as Ryan found out rather publicly back in in the 2000 or 2001 Robbins Futures Trading Championship.