The vast majority of traders obsess over the percent accuracy of their expert advisors. Intuition makes it seem like that the more often a trader wins, the greater the chances or turning a profit. Alas, such an approach ignores a critical variable.

The average win-loss ratio plays an equally vital role in determining the net outcome. I meet a lot of would be scalpers. High frequency trading is incredibly popular, but a lot of traders involved with it only do so because it puts easy points on the board. They don’t pursue a strategy because it has any positive expectation. In other words, they are gambling and not trading.

One of the reasons that I love trading so much, and why I generally dislike gambling, is that you are always in control of the potential payout and the payout ratio. When I play blackjack, I only control the risk and payout. I do not control the *ratio* of the payout at all. It’s always 1:1.

My decisions in blackjack can only realistically improve the odds to 50%. More than likely, my game play will lower the odds below that threshold. Making decisions repeatedly will overwhelmingly result in human error. It’s our nature.

When I open my forex account, each trade commences a new round in the game. The critical difference between trading and blackjack is that I control the **ratio** of the payout, plus I still control the risk and quantity of the payout. The net outcome can still move against me due to random chance. The key distinction is that the typical outcome should shift in my favor with an algorithmic trading system.

One of my favorite trading books is Van Tharp’s Trade Your Way To Financial Freedom. We’ll be talking about this one soon; it’s the next item on Jon Rackley’s reading list. One of my favorite aspects of the book is its emphasis on money management strategies and trade expectation.

The term money management connotes many things to many people. The more accurate phrase would be to describe it as a position sizing strategy. When entering a trade, you realistically need to know:

- What is expected loss as a percentage of the account?
- What is the expected gain as a percentage of the account?
- What is the percent accuracy of my trades?

Answering these questions accurately leads to the decision of how many lots, contracts or shares to trade. Controlling the size leads to controlling the outcomes. When you control the outcomes, you ideally earn a profit for your efforts.

## Fixed fractional money management

Notice that I said percentage of the account in the bulleted items and not the dollar value of the trade. Thinking in terms of dollars is easier on the mind. The problems is that it ignores the wonderful benefits of exponential growth.

Every financial advisor on earth warns you that compound interest, which is a form of exponential growth, is the strongest force working for you with investments or against you with debts. Applying the same concept to trading, you want to put the power of compound growth on your side.

The fixed fractional formula is an ugly way to telling you to use exponential growth in your trading strategy. Say, for example, that you elect to risk 1% of the trading account based on the distance to the stop loss. If you have a $10,000 trading account, that’s only $100 of risk. Say that the trade works out and that you made $100. The next trade should risk $101.

Try not to roll your eyes at that one. Risking an extra dollar seems trivial and nit picky. I assure you that it is not.

I’m really not sure how to explain how all those little differences add up, but they do. I wrote a money management calculator a few years back that calculated how fixed fractional money management affects returns. The little things really do add up. With a very slight probability of winning and 50:50 odds, the returns were overwhelmingly larger when using a fixed fractional approach instead of a fixed lot approach. You should increase the position size after winners and decrease the position size after losers.

## Percent accuracy is half important

If I paid you $1 for every win and you win 99% of the time, should you play my game?

You don’t have enough information to make a decision yet. You need to find out what happens when you lose.

If you lose $100 or more on the trade that only loses 1 time in 100, you should never play my game. You will lose if you play too often. And no, there is no such thing as just playing ten times and stopping. You have the same risk of losing on the first trade as you do on the 100th. It’s not safe to play at all.

The only way that you should decide to play the game is if the total payout is better than even. The total result of wins equals 99 trades * $1/trade = $99. The one loss must be less than $99 to give me the green light on playing.

If I lose $80 one time and make $99 on the remaining trials, then I will have an average win loss ratio of $99/$80 = 1.24. A system like this would be wildly in my favor.

A 60% winning accuracy is a lot more likely to happen in the trading world. Let’s say that I make $100 on every winning trade. My total winning value is 60 trades (out of 100) * $100/trade = $6,000. The maximum average loss that this system could tolerate is:

The maximum average loss that we can tolerate is $6,000 / 40 trades = $150. I should consider trading this system if the average loss comes in at $149 or less. The smaller the average loss, the greater the net outcome.

## Kelly formula for Forex Trading

One problem we face with money management strategies is choosing the percentage of the account to risk. The difference between risking 1% or risking 2% of the account equity is simply one of proportion. One of the options either provides a risk-reward profile suitable to the trader or it doesn’t. The larger the appetite for risk and reward, the bigger the number involved.

The Kelly formula removes the proportionality for the question and takes a different approach: how do I make the absolute largest sum of money over time using my trading statistics. The goal is to make the maximum amount of money without getting margin called.

The formula to use is **K = W – (1-W)/R** where:

K = percentage of capital to be put into a single trade.

W = Historical winning percentage of a trading system.

R = Historical Average Win/Loss ratio.

The approach is most suitable for those trading small accounts, perhaps those with only a few thousand dollars, that they want to grow with maximum aggression. Losing a few dollars is thoroughly unpleasant (been there, done that!), but it’s not financially devastating, either.

It’s important to keep in mind that the Kelly formula attempts to push the trading system to its absolute maximum without busting. Knowing how close it is to the edge of busting, it’s critically important that you understate the good assumptions and overstate the bad ones. Drop the expected percent accuracy by several percentage points to accommodate the chance of error. Lower the win:loss ratio for the same reason.

The easiest way to reduce error and the chance of acting too aggressively is to make sure that you calculated the EA’s percent accuracy and its win loss ratio on a large enough sample size. I would consider 100 trades as the absolute bare minimum. 300-400 is sufficient. 1,000+ trades makes for an adequate sample for most expert advisors and trading robots.

Of course, you can always take the easier approach and simply cut the Kelly formula’s risk suggestion in half. It adds a bit of scientific flair to the strategy, while minding the fact that we are human. Watching an account drop near zero will break the heart of even the most battle tested trader. It’s impossible to stop caring about drawdown, which the Kelly formula totally ignores.

Rimantas Petrauskas says

Very useful information for every Forex trader and programmer.

Shaun Overton says

I’m glad you enjoyed it.

quentin says

What are your thoughts on adding more positions as they go in your favor while risking the original 1% on the trade?

Shaun Overton says

That’s my current research interest. I really like the idea of working a core position in and out of the market over hard entry and exit signals. But.. I haven’t done the analysis yet, so I’m not sure whether it’s a good idea for an algo. The best traders that I work with all use that approach, so there’s obviously merit in the idea.

Michal Sourek says

Hi Shaun, hi all OSR fans!

Yes, yes, yes.

The true créme-a-la-créme of any Trading Strategy is the appropriate Money Management.

If interested in more details,

kindly ref. below to a Dynamic Money Management approach visualisations, because it is fair to say at the very begining that there is both a (_huge_) reward and also a (_FATAL_) risk, that both have to be kept under (best an online, adaptive …) control to benefit from a well done dMM() in real-time.

In order to have some visual approximation into which orders of mangnitude a proper dMM() can boost one´s Trading Strategy, let me direct your kind attention to animations alike

[1]

An animation of a systematic boost introduced from a dMM()

>>> https://drive.google.com/file/d/0B8sqJKnR7ik_QzJUVE1CTS1jb3c/edit?usp=sharing

and

[2]

An animation of a professional trader performance with various boost levels available from using a dMM() approach

>>> https://drive.google.com/file/d/0B8sqJKnR7ik_bWh1dkpEbkhjcVk/edit?usp=sharing

More notes on this very subject could be found published on Linked In, so do not hesitate to go get it there.

>>> http://cz.linkedin.com/in/RiskIsFriend/

Hope these views help inspire further professional development in this exciting area.

Best regards

MS

Shaun Overton says

Hi Michal,

The animations are certainly interesting. Can you please explain in more detail what we’re looking at?

Michal Sourek says

Sure, Shaun

XYZ-coordinate spaces in both animations are different, whereas in both of them, the Z-axis is the profit factor over the reviewed TradingEPOCH.

So

factor

of

1.00 means both starting Equity and/or break-even state

0.99 means 1% loss

0.90 means 10% loss

2.00 means 100% gain on TradingEPOCH initial deposit

10.00 means 1,000% gain

Let me sketch and post a few notes about each of the views.

[1] Animation demonstrates 4D functional dependencies (aStateSPACE) for aTradingSTRATEGY

Z-axis shows resulting aProfitFACTOR(s) gained

X-axis range RRR-levels ( notice how low these are…(*)

Y-axis reads success/fail ratios of a generalised sequence of P/L Trades

and

the fourth dimension is listed in legend … a dMM() intensity factor [%]

(*: btw. RRR is a very simplified and very mis-leading factor in the state-of-art dMM() boosters )

One may notice a moving “coast-line” where even infinite equity gets sunk into trully limit-less ocean of losses

( 1.00 .. 0.00 >

[2] Animation depicts trader’s results ( manual trades )

Z-axis shows profitFACTOR achievable after each trade

X-axis ranges a dMM() intensity factor ( 0.00 .. 1.00 )

Y-axis sequences ordinal# of each trade ( start .. end )