position sizing Archives - Algorithmic and Mechanical Forex Strategies

Are You Picking Up Pennies in Front of a Steamroller?

January 15, 2014 by Andrew Selby Leave a Comment

Strategies that can demonstrate huge winning percentages through unbiased backtesting are extremely appealing. Imaging the streaks that you could run up if your system was winning on better than 80% of its trades!

Of course we all know that these types of strategies are almost always accompanied by the same tragic flaw: potential for catastrophic losses. That flaw makes these types of strategies great for video games and practice accounts, but not for trading our hard-earned capital. There is no reset button when you are trading real money.

Many high win percentage strategies are described as “picking up pennies in front of a steamroller” because of their potential for severe losses.

These types of strategies are often referred to as “picking up pennies in front of a steamroller,” which provides a vivid mental image of the potential pitfalls. In a recent post, Dan from Theta Trend thought it would be an interesting case study to see how one of these “steamroller” strategies would have fared over the course of 2013.

Dan’s Accelerated pTheta Strategy

The strategy that Dan tested was a version of his pTheta strategy. Here is how he describes it:

The penny system sells out of the money vertical spreads in the $SPX every week using 10 delta weekly options with 8 days to expiration. Every Thursday the system sells a vertical spread.

If the market is closed on a Thursday (Thanksgiving), the strategy sells the verticle spread on the next day. Dan explains that his strategy uses the Parabolic SAR indicator as a trend filter to determine the direction of his trade:

If price is trading above the daily pSAR, the system sells put spreads below the market and call spreads are sold if price is trading below.

This gives us the basic outline of a simple options strategy that makes one trade every single week with a very high winning percentage.

Backtesting Dan’s Strategy

Over the course of 2013, Dan’s Accelerated pTheta Strategy would have made a total of 52 trade. Of those trades, 44 would have been profitable and 8 would have been losers. That works out to a win rate of 84.62%. 33 of the trades were on the long side, and the remaining 19 were on the short side.

The average winning trade returned a profit of 0.425%. The average losing trade cost the account 1.701%.

Dan tested two different positions sizes for the strategy. His 5% Max Loss version traded 2 spread and his 10% Max Loss version traded 5 spreads. The 5% Max Loss version returned 10.19% for the year with a maximum drawdown of 15.68%. The 10% Max Loss version returned 25.48% for the year with a maximum drawdown of 35.41%.

The Equity Curves

The equity curves Dan provides do a great job of illustrating the steamroller point. Both versions of the strategy were cruising right along when they were suddenly smacked with severe losses in early April. Dan explains that there were actually two huge losses in a row that month.

In order to explain how severe those losses were, Dan provides the returns for the year if those two trades weren’t made. In that case, the 5% Max Loss version would have returned 20.81% for the year with a 5.82% maximm drawdown. The 10% Max Loss version would have returned 52.03% for the year with a 13.14% maximum drawdown. Those returns sound great, but they are just wishful thinking because those two big losses actually did happen.

Dan explains that the major flaw with strategies like this is that when things get bad, they do so in a hurry. It is also a concern that the very low point of the equity curve is exactly where most traders would give up on the strategy. If you started trading the 10% Max Loss version with $10,000 in January of 2013, after the two big losses in April you would be left with less than $8,000. Would you have the courage to keep trading?

Reducing Volatility By Optimizing Position Sizing

November 15, 2013 by Andrew Selby Leave a Comment

One of the easiest ways for traders to improve the profitability and reduce the volatility of their systems is to optimize their position sizing algorithm. There are many different ways to break down your system’s optimal position sizing, but one of the most popular is to use the Kelly Criterion.

The Kelly Criterion is most famous for the way that Edward Thorp successfully applied it in his quest to create a strategy that could consistently beat the game of blackjack. Thorp also used the Kelly Criterion in his work with roulette and his hedge fund trading. The Kelly Criterion has also been linked to other famous traders like Warren Buffet and Bill Gross.

Much like in blackjack, applying the Kelly Criterion to your trading system can drastically reduce volatility over the long run.

Andrew Butler wrote a post for his blog, Butler’s Math, that does a nice job of why you might want to consider implementing the Kelly Criterion in your trading system. He begins by making a few modifications to the Kelly Criterion:

With a few modifications, this basic framework can also be applied to securities selection.
Let us define $V(f)$ as
$V(f)=V_0(1+r+f(x-r))$ where $V_0$ is our initial capital, $r$ is the risk free rate, and $x$ is our expected return on a given portfolio of securities. Thorp shows that for large number of “bets”, $n$ , the growth function for such a model is defined as
$g(f)=r+f(x-r)-0.5*s^2f^2$ .
Again, through simple calculus, the optimal $f$ occurs when $f=f^*=\frac{(x-r)}{s^2}$ .

Butler generated simulated data for a portfolio of 100 different stocks and ran 100 different simulations using the following three position sizing strategies:

Kelly Criterion for optimal growth: $f=f^*$

Full betting Strategy: $f=1$ .

Fractional Kelly Criterion: $f=0.5*f^*$ .

The results show that betting the full Kelly Criterion just barely outperformed the full betting strategy, but the Kelly Criterion has less overall volatility. The Fractional Kelly approach had inferior results, but an even greater reduction in volatility.

Butler made the following additional comments about his results:

Both the Kelly Criterion strategy and the Full Betting strategy provide comparable final capital at the end of the simulation.

The Kelly Criterion strategy in fact provides an additional 0.32% net growth.

Additionally, the volatility of the Kelly Criterion Portfolio is significantly less than that of the Full Betting strategy. This in theory could reduce irrational financial decision making as a more stable growth is observed.

The Fractional Kelly strategy is the least volatile but also provides the least potential for growth.

As you can see, implementing the Kelly Criterion is not going to suddenly turn a poor system into a profitable one. However, the primary goal of any trader is to avoid the erosion of capital, and using the Kelly Criterion to reduce volatility can do just that.

Using Volatility Based Position Sizing To Improve Performance

June 20, 2013 by Andrew Selby 1 Comment

Dr. Van Tharp is famous for saying that a system based on coin flips can be traded profitably with good position sizing and risk control.

While position sizing and risk control won’t turn a poor system into a good one, they can improve a system that does have an edge. Adjusting the size of your trading to the current volatility of the market can have a dramatic impact on both total return and maximum drawdown.

Good position sizing can make a dramatic impact on performance… even with a modest strategy

While there are multiple ways to implement volatility based position sizing, all of them are capable of outperforming a fix percentage position sizing strategy.

Volatility-Based Position Sizing

I came across an article from QUSMA this weekend that compared three volatility-based position sizing methods. The article set up a system that would trade the SPY based on a simple set of rules. It then compared the results of three volatility-based approaches to investing 100% of capital in each trade.

The goal was to compare the results of the different position sizing models against each other. The overall return of the system was not important because the numbers are only of value relative to each other. When compared to the fixed percent position size method, the number that the volatility-based approaches posted was very impressive.

The Results

Each of the volatility-based position sizing methods was able to outperform the 100% position size model in total return as well as maximum drawdown. The backtesting period started in January of 1993 and ended in mid-2012. The system was a long-only strategy that used four technical indicators with no stops or targets.

During that time, investing 100% of capital in each trade signal produced by the system would have returned a total of 204.24%. The three volatility based approaches returned 226.04%, 231.39%, and 232.25% trading the exact same system during that time period.

The 100% capital approach experienced a maximum drawdown of 19.52% while the volatility-based strategies had drawdowns of 18.6%, 18.31%, and 18.13%. As you can see, all three volatility approaches achieved higher returns with less risk.

Different Fixed Position Sizes

I was initially curious as to how investing a different fixed percentage would affect the results. You could certainly reduce the maximum drawdown by dropping the position size to 50% of capital. Of course that would also dramatically reduce your overall return.

Therefore, we can achieve an improvement in maximum drawdown over the volatility-based systems at the cost of overall return. We cannot, however, achieve an improvement in overall returns of the 100% capital approach without increasing maximum drawdown as well. If we leveraged the account and traded 200%, we would dramatically increase our risk of ruin.

It doesn’t matter what fixed percentage is used to determine position size, the volatility-based approaches will outperform it.

The Best Performing Approach

The Realized Volatility position sizing approach outperformed each of the other two methods in both, total return and maximum drawdown. The author explains that the realized volatility is the realized standard deviation of returns over the last ten days multiplied by the square root of 252 to annualize the number.

In order to calculate the position size, you divide your target standard deviation by the realized volatility. This will give you the optimal percentage of capital for the trade. (The author was targeting a standard deviation of 11.5%, but used 17% to “overshoot” because the system was not always in the market.)

The underperforming volatility-based approaches were based on the GARCH model and the VIX. While all three of these models outperformed a fixed percentage position sizing method, I have to wonder if they are more complicated than they need to be.

I am a big fan of simple strategies. As a general rule, if I can’t explain or demonstrate a system to my mother, it’s probably too complicated. I would love to see how an ATR position sizing approach would have compared to these more complex systems. It would work on the same principle as these three methods, but is much simpler to explain.

Adjusting Position Sizing for Volatility

April 28, 2013 by Andrew Selby Leave a Comment

Most losing traders spend too much time on entry and exit points. Before you going looking for the next holy grail, let’s focus first on stopping the bleeding.

The bleeding is the trader’s poor assessment of risk. Have you lost more than 2% on a trade before? If so, I’m talking to you. You need to focus on developing an appropriate position size for your trades.

Maximum Tolerable Risk

There are two types of risk associated with trading: capacity for risk and tolerance for risk. Capacity for risk is the total amount that a trader can lose before wiping out his account. Basically, it’s the amount of money in your account.

Tolerance for risk defines how much a trader can stomach losing and still sleep at night. When determining the maximum risk we are willing to take for a given trade, I factor in both of these types of risk.

Even if the trade is an immediate loser, we will still be a long way from our capacity for risk or tolerance for risk limits. A trader’s primary goal should be to survive to trade another day. Keep this in mind when developing trading systems.

In order to calculate the maximum tolerable risk for a given position, you must first decide how much of your equity that you are willing to risk on a single trade. I have seen this number range anywhere from 0.25% to 2.5%, but 1% seems to be the most common recommendation. The key here is to go with a number that will keep your trading above your capacity for risk and tolerance for risk even during losing streaks. It is always better to lean towards the conservative side.

The maximum risk for a single trade is calculated by multiplying the percentage you are willing to risk by your trading capital.

Position Sizing Formula

The goal with this formula is to smooth out the volatility between different securities so that each position you take will have the same impact on your overall portfolio. To do this, we must adjust for the historic volatility of each position.

Accounting for volatility makes each position have the same influence, good or bad, on the results. This adjustment can level the playing field by making lower volatility securities more appealing and higher volatility securities less dangerous.

In order to determine the an appropriate position size accounting for volatility, divide the our maximum tolerable risk by a multiple of the Average True Range (ATR). For the examples in this post, I will use a multiple of 2, which will allow the position to move double its average daily move without going past the maximum tolerable loss. This multiple can be adjusted up or down depending on your own personal appetite for risk.

Max Risk / (X * ATR) = Position Size

Traders can adjust the risk number or ATR multiple to achieve any desired amount of risk, but should always backtest and lean towards the conservative side. Remember, the goal is to live to trade tomorrow. It is also important to set an initial stop loss, which can also be done using ATR.

Position Sizing Example

Assume that we have a $10,000 portfolio and that we are willing to risk 1% of that portfolio on any given trade.

A position sizing example using Microsoft (MSFT)

In this chart, MSFT has a recent closing price of 31.79 and an ATR of 0.704. Take the $100 we are willing to of risk and divide it by 2 ATRs to calculate our position size.

$100 / (2 * .704) = 71.023

Since we are not able to trade partial shares of MSFT, we will round down in order to stay conservative. This means we can purchase 71 shares of MSFT for a total commitment of $2257.09.

KORS has a different ATR and price. The position size is different from MSFT.

In this chart, you can see that KORS has a recent closing price of 56.12 and an ATY of 2.03. Using the same formula, we will take our $100 risk amount and divide it by twice the ATR.

$100 / (2 * 2.03) = 24.63

We can purchase 24 shares of KORS for a total commitment of $1346.88.

Since KORS is the more volatile company, we will be purchasing much less of it. MSFT has a history of moving slower, so we can be more comfortable taking a larger position in it.

Keep in mind that this is simply an example using round numbers and that investing 22% of your portfolio in MSFT or 13% in KORS might be more exposure than you are willing to accept. In that case, you can adjust the maximum tolerable risk or ATR multiple to get to a position size that works best for you and your trading strategy.

Position Sizing for the Scalper EA

April 2, 2013 by Shaun Overton 10 Comments

Andrew posted a great comment on the Scalper EA noting how he increased profits dramatically with position sizing. You can think of the expert advisor as the orange and the potential profit as the juice. We want to squeeze out every last drop.

Squeeze more profit out of your expert advisor with position sizing rules

I always talk about winning percentage and the R multiple together. It doesn’t matter that if win 99% or 15% of the time. It matters how much you win compared to how much you lose. Winning frequently does not correspond to profitable trading.

Only when you know the percent accuracy and R multiple can you determine expectancy: do I expect to make a profit or not following this expert advisor?

The explanation reveals two assumptions:

I know the real accuracy of the system
I know the real R multiple

NinjaTrader backtest reports show the percent accuracy and the R Multiple (ratio of avg win to avg loss)

I don’t know either for a certain fact. The real accuracy and real R multiple may be above or below the numbers seen in backtesting.

It’s important that we consider how we developed these numbers. I found them after analyzing an entire year’s worth of chart data. There’s a real risk that they overestimate future performance.

The forward test for 2012 discounted that notion – the R multiple and percent accuracy numbers actually improved on the blind data. But, as most of you know, I’m extraordinarily risk averse.

I assume the worst case scenario in nearly everything that I do. If the worst case isn’t so bad and the average case is fantastic, that’s the only threshold that pushes me past my risk inhibition. It has to be a really amazing opportunity for me to pull the trigger.

A pessimist’s view on position sizing

The goal is not to maximize profits. It’s more complex than that. The real goal is to maximize profits with a view to how many losses you can stomach.

That number is pretty low for me. Use bigger numbers if you can tolerate more pain.

I operate with the same attitude when selecting my position sizing strategy. It’s important to make reasonable, yet pessimistic, assumptions when selecting your money management approach.

Step 1: Decrease the strategy’s accuracy by 5%

Strategies vary in their accuracy with the chart and instrument where it operates. I have not done an analysis, but my rule of thumb is that accuracy fluctuates ±5%. The worst percent accuracy seen is usually within 5% of the best percent accuracy seen.

The rule generally holds across multiple instruments and time frames. Once you get a feel for the accuracy, you take the observed accuracy and subtract 5%.

The scalping strategy profited 75.93% of the time after including trading costs. Removing 5% off of that number leaves a reasonable worst case assumption of 70.93% accuracy.

Step 2: Decrease the R multiple by 20%

The method used here depends on the expert advisor’s trading style. Range trading expert advisors usually come out with an R multiple (average win/average loss) within a consistently narrow band. Trending EAs exhibit wild fluctuations in the R multiple.

This should make sense to readers with several years of trading experience. Range trades earn profits on the majority of trades. No individual trade contributes dramatically to the final outcome.

Trend trades do exactly the opposite. A small handful of trades contribute enormously to the overall result. The traders faces the risk of overemphasizing how well volatility played to his in advantage in the past. If trends of similar magnitude fail to materialize, the trader’s estimate for the R multiple will be wildly off the mark.

Rules of thumb for adjusting R multiple assumptions:

Cut the observed R multiple for a ranging strategy by 20%
Cut the observed R multiple for a trending strategy by 33-50%

The scalper EA trades ranges and showed an R multiple of 0.53. Cutting that number by 20% reduces it to 0.424.

Apply pessimistic assumptions to model money management

The adjusted numbers for the scalping strategy are 70.93% accuracy and an R multiple of 0.424. I can now take these numbers and start playing with the money management software.

The first thing that I did was to reduce the number of trades in the test to 100. That equates to roughly 1 year of trading, which is a meaningful period of time for this expert advisor.

Fixed fractional money management using 1% risk and the pessimistic assumptions puts the trader slightly ahead of breakeven after trading costs (a 1% profit). The worst case scenario shows an annual loss of 25%. Nobody wants a loss like that. But, it’s something that I can handle as a plausible worst case.

Final numbers

The pessimistic money management assumptions still show an average profit.

Increasing the percent number to 2% doubles the minimum and maximum outcomes. Tripling it to 3% triples the worst and best outcomes. You should select a number whose worst outcome strikes you as something personally acceptable to you.

I selected 1%. The worst case scenario is something that I can handle. The next step is to split the difference between the observed numbers and the pessimistic number for the percent accuracy and R multiple.

The numbers are 73.43% accuracy and 0.477 for the accuracy and R multiple. When I plug the numbers into the software, it spits out an average return of 8.9% with a maximum upside of 40.9% after 100 trades.

Moderate assumptions for position sizing show an average return of 8.9%.

Using fixed fractional money management squeezed more juice out of the orange. We brought the worst case scenario up to -25% and the best case scenario on moderate assumptions to over +40%. More importantly, the average return increases without affecting the best and worst cases.

What position sizing ideas do you have? Leave your thoughts in the comments section below.

Money Management for High Probability Systems

March 12, 2013 by Shaun Overton 8 Comments

I spent last weekend overviewing trading systems with my favorite money management software. Normally, when traders think of a great trading system, they expect fantastic results like 80% winners and every trade has to make $2 for every $1 that it loses.

The edge in real trading systems typically falls wildly short of that goal post. Rather than convince you with software, try running the numbers in your head.

Say that we do 100 trades with a $100 account balance. 80% of them win and make $2, which is $160 in profit. 20% of them lose $1, which is $20 in total losses. Now ask yourself, “Does it sound plausible to earn a 40% return after only 100 trades?”

The answer to the question probably correlates with your trading experience. If you answered yes, then I also have some oceanfront property to sell you in Arizona. Experience should make it clear that such numbers are fairy-tale optimistic.

Las Vegas makes billions of dollars every year with a total edge of 0.5%. You don’t need to hit grand slams to take money out of the markets. Little base hits will get you there, too.

What is high-probability

At the risk of moving the goal posts, I define high probability as anything above 50%. Many traders comes across the word “high probability” and start drooling over 80-90% winners.

Remember that winning percentage isn’t everything. If we play a game where you win 99% of the time but lose $200 when you lose, you’d quickly figure out to not play. The name of the game is to walk away with a profit over time. It doesn’t matter how you get there.

A high probability, one which exceeds 50%, offers the unique advantage that you can aggressively use money management to enhance returns. High probabilities also come with the unique property of offering long streaks of consecutive winners. Consecutive losing streaks are comparatively rare.

Money management in a real strategy

One of my clients trades a strategy with 60% winners. The ratio of the average winner to the average loser. That is, the average winner earns $1. The average loser loses $1.

Because it wins 60% of the time, that means it makes $60 for every $40 it loses, which is a profit factor of 1.5. Not bad.

A strategy with this property expects to earn a return of 40.9% after 200 trades if it risked 1% of the original account balance per trade.

The strategy using fixed dollar risk expects to make a 40.9% average return after 200 trades.

Making a minor change so that the strategy risks 1% of the current balance per trade makes a huge difference in the average return. It jumps nearly 10% to an average return of 50.7%.

Fixed fractional money management is the idea of keeping the risk proportional to the current balance. Using a $10,000 account as an example, a trade risking 1% of the balance risks $100. If the account balance increased to $11,000, each trade now risks $110. The dollar risk grows with time while the percentage risk remains unchanged – hence, it’s fixed fractional.

$Fixed fractional money management$

A fixed fractional money management approach increases the average profit to 50%.

A unique money management idea

Remember how I mentioned that high probability systems are prone to streaks of winners and losers? Check out what happens if you increase the risk after each winning trade by 10%.

The median outcome gets pulled up enormously. The average isn’t jumping to 63% because of a handful of massive returns. Instead, almost every series in the test experiences a huge increase in performance.

The average balance after 200 trades jumps yet another 12% for a 63% return. The only disadvantage is that the worst case scenario dropped from a 6.8% loss to a 10.3% loss.

Position sizing for consecutive winning trades

Increasing the risk by 10% from the previous trade increases the average return to 63% and the median return to 58%.

Applying the rule so that consecutive winners only increase their risk when the balance is greater than the starting balance makes the worst case scenario slightly less bad. It comes at the price of a slightly lower average and median return.

Consecutive winning trades applied only to a profitable balance

Applying the consecutive winning trades rule only slightly helps the worst case scenario. It comes at the expense of a lower average and median return.

Conclusion

You’d be a fool to stick with fixed risk if your system offers offers high probability winners without huge losing trades. Simple steps like fixed fractional money management can substantially increase profits. Applying a trick like increasing the risk by 10% after each consecutive winner offers another huge performance boost.

The average outcome started at a healthy 41%, which is already stellar. Applying the simple techniques outlined here increased the average performance after 200 trades to a 63% return. That’s some world class trading.

Profit solely through money management

July 12, 2012 by Shaun Overton 7 Comments

Most traders view the idea of profit protection as a concept that applies to an individual trade. Whenever a trade floats a large profit, they protect the unrealized profit by moving the stop loss closer to the market.

I like to view trading more as a collection of outcomes rather than the result of any particular transaction. This article looks out how to protect realized profits after they accrue in the account rather than protecting the unrealized profit from one trade.

The money management project started off by asking the question, “is it possible to make money with a perfectly random strategy solely using money management.” The strategy is not quite to the point where it will work in the real world. Nonetheless, this new method shows substantial progress toward that goal.

I operate on the assumption that a random strategy is one with 50% profitability and an R multiple of 1.0; we earn a dollar for every dollar we risk. The net outcome over hundreds of trials should average out to the starting balance. My earlier videos and blog on money management modeling verifies that this is indeed the case.

Random outcomes tend to fluctuate above and below the average value. At any given time, half of all possible outcomes should be above average. The opposite holds true for outcomes below the average. The idea here is to get away from standard notions of money management like fixed fractional money management. The risk amount should follow not only the account balance, but also factor in the degree of profit accrued.

The fluctuations above the starting balance are totally random. If a trader is lucky enough to obtain a profitable, realized balance, then it makes sense to decrease the risk. Obviously, decreasing the risk limits the potential profits.

Consider an example. We start with a $100,000 account balance risking 1% of the original balance. Note that all future trades base the risk on the original balance and not the accrued profit and loss.

When a random winner rolls in, it brings the account balance to $101,000. The odds of winning on the next flip are still 50-50. Rather than risking giving it all back, I found that you increase your chances of a final, meaningful profit if you decrease the original risk as profits accrue.

Reducing the original risk by 1% for every $1,000 of profit changes the dollar risk from $1,000 to $990. This may not seem like very much. That’s because it is not. The goal is to suck tiny little advantages as they come. A loss occurs half of the time in this situation. When it does, the account balance still shows a $10 realized profit.

If the second trade (we are now at $101,000) is a winner, the account balance increases to $101,990. A loser following the win drops it down to $100,010. The process is slow, but we’re also making money without a trading strategy. We’re just betting.

Importantly, a change to the risk amount as a balance loses money completely destroys the money management strategy. It is critical that the risk amount not vary in any way whatsoever.

Real examples of how the median return increases with trades placed

The median outcome after 200 trades is 0.6%

The median outcome after 500 trades is 1.5%

The result after 1,000 trades is a 2.4% return

The result after 10,000 trades is a 19.7% return

Forex Money Management

January 5, 2012 by Shaun Overton 7 Comments

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.