Algorithmic and Mechanical Forex Strategies | OneStepRemoved

How to be 99.999% accurate when your system is only 49% accurate

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Virtu Financial, the high frequency trading firm whose initial public offering of stock was caught in the unexpected firestorm that was the book “Flash Boys” by Michael Lewis, is reviving the IPO plan they shelved last year amid controversy, is seeking $100 million.

Virtu Financial board

99.999 win percentage is an odd statistic

As a recent Securities and Exchange filing reveals, the company, operated by a litany of some of the exchange world’s top executives, boasts that out of 1,485 trading days it has only one losing day.  This is the key statistics that left those familiar with algorithmic trading scratching their heads.

On the surface this 99.999 win percentage is a rather unworldly performance statistic in the world of algorithmic trading.

Virtu Financial notional

Virtu Financial is not a trend follower

The most popular managed futures strategy, trend following, has an average win percentage near 55 percent. Trend following might not be the best algorithmic strategy to compare to Virtu, however, as the firm claims in its S-1 that their trading “is  designed to be non-directional, non-speculative and market neutral.” Micro-trend following and benefiting from market moves in one direction is a popular high frequency trading strategy, but based on their S-1 this is not the primary strategy.

This doesn’t explain the win percentage.

The highest win percentage of all managed futures strategies, near 75 percent, is short volatility, which is also the least popular strategy. While the strategy is known to win most of the time, the key statistic is to understand its small win size and large loss size. In managed futures the size of a trader’s wins can often be more important than how often they win. In the case of short volatility, while they win most of the time, when they lose they lose big – with an average loss size that is close to double that of a discretionary trading category, for example.

While risk in Virtu may exhibit strong downside volatility during crisis, much in the same way market crashes bankrupt many individual market makers in the golden days of the trading floor, comparing Virtu’s strategy to a short volatility strategy is inaccurate.

Perhaps the most applicable managed futures strategy to benchmark might be the relative value / spread arbitrage category. The spread-arb strategy has a high win percentage, near 60 percent, and it also has the best win size / loss size differential. The strategy works by buying one product and then selling a related product. The directional strategy works when a market environment of price relationship dislocation occurs.

While the fit isn’t perfect, nonetheless the most relevant managed futures strategy for which to compare Virtu is its direction-less, market neutral approach taken by certain spread-arb CTAs. The primary difference being Virtu doesn’t hold positions for directional profit. What they do, much like a short term trend follower, is take a position and then immediately lay off risk in a hedge. For instance, they may buy oil and then immediately hedge that position in another market and perhaps even using a derivatives product with different product specifications. In the olden days one could simply describe this as a “market making” strategy, but in the new school world of high frequency trading, separating two-sided liquidity providers from directional trend followers has oddly become more difficult.

99.999 percent daily win percentage overshadows 49 percent intra-day win percentage, highlighting the importance of win size

When comparing Virtu to known managed futures strategies, the 99.999 win percentage sticks out like a sore thumb – until you read the next punch line in the most recent S-1. That is when the firm reveals that its win percentage on an intra-day basis is 49 percent.

This puts the pieces of the puzzle together. The 99.999 percent win percentage needs to be considered in light of the 49 percent intra-day win percentage. This highlights the fact that Virtu, by logical default, is benefiting from size of win. Just like a trend follower, it isn’t always win percentage that matters most but size of win and controlling loss. This is likely the secret sauce inside Virtu’s success.

This article originally appeared on Virtual Walk and was authored by Mark Melin.

Martingale Forex

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Trading forex with a Martingale money management system will almost inevitably lead to blowing up an account. I’ve written about this inevitable outcomes repeatedly over the past six months. At the risk of beating a dead horse, I figured that visual proof would alleviate any lingering hopes once and for all.

Recall that Martingale systems aim to never lose money. Instead of accepting losses and moving on, a Martingale betting strategy doubles the previous bet. Whenever a win finally does occur, all losses up until that point are wiped out. The trade also gains the same amount of profit that the original trade hoped to capture.

The experiment assumes that the trader uses fixed fractional money management set at 1% of the account value. Recall from earlier experiments that a 1% risk value will almost never blow up an account after 200 trades. The percent accuracy for the trades remains at 50%, which is perfectly random. The random number file has been upgraded to include 10 million random numbers instead of the previous half a million.

The goal of the exercise is to focus on the risk of ruin rather than the profits accrued. As time goes on, the likelihood of ruin increases with the number of trades placed. A trade is each time a new transaction enters. It does not matter whether or not the last trade was a winner or a loser.

Fifty trades on most Martingale systems corresponds to anything from several days to several weeks. The level of aggression used in the trade level (i.e., the pip distance used to open a new trade) is what most strongly affects the amount of time required to reach fifty trades.

Placing 50 trades shows what most traders know. The returns look fairly nice at that point. A return of 20% on the account shows a 40% probability of occurring. The risk of wiping out the account looks meek at 8.5%.

Increasing the number of trades to 200, which corresponds to several weeks or months, the odds of outright failure skyrocket to 35%. The lucky traders that have not yet blown up show returns ranging from 20% all the way to 300%. The total risk is more apparent, although many traders fall victim to the lure of quick, large returns.  If it all looks too easy at this point in time, that’s because it is.

Going out to 1,000 trades, which I roughly ballpark as the amount of trades an average expert advisor might complete in 9 months to a year, is where the inevitable result is obvious. The odds of reaching a zero balance reach 95%.  A tiny handful of traders are floating huge returns. As the number of trades increases from 1,000 to 2,000 to 10,000, the tiny fraction of accounts left eventually dwindles down to zero.

Money Management Modeling

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We recently developed software to model the affects of random chance on money management. Although computers are capable of generating pseudo-random numbers, the pseudo-random process introduces bias into the random distribution.

We opted to source our random numbers from random.org. The web site generates purely random streams of bits taken from atmospheric noise. We then use binary mathematics to change those bits into numbers ranging from 1-10,000.  Say, for example, that we want to model a trading system with a winning percentage of 50%.  Whenever a number comes out between 1-5,000, we consider that a winner. Anything above 5,000 marks a loser.

Changing the winning percentage to 65% works the same way. Any number less than 6,500 represents a winning trade. Numbers above 6,500 signal a loss. The modeling quality is accurate to the thousandth decimal place.  That type of accuracy is way more accurate than the “known” accuracy of your trading system, which can only be known within a few whole percentage points.

Most traders fall into the trap of thinking about their trades as individual outcomes. The more appropriate way to view returns is as the sum of all individual outcomes. Losing on any given trade does not matter. It only matters whether the sum of all your winners is greater than all of the losers.

It gets more complicated, unfortunately. A system with 50% wins and a 1:1 payout will almost never come out at exactly breakeven. The mathematical expectation is that we expect to see a degree of drift in the returns solely due to random chance. I suggest reading more in the random trade outcomes and dollar profits section to get a better understanding of drift.

Lastly, we must define a sampling period for evaluating the final result. I arbitrarily set the default value to 200. That means that the software tells us the range of outcomes after 200 total trades. That may take more than a year for some traders. Daytraders may reach that benchmark in several weeks of trading.  The question that we are answering is “what is my account balance likely to be after placing 200 trades?”

Coin Toss Trading Experiment

The first experiment is to analyze how dollar returns vary with a coin toss game and the most basic money management method. A starting balance of $100,000 is used with a risk of 1%. The risk will not change as in the fixed fractional method. Instead, we will leave the lots fixed in order to strictly understand random chance. Wins always earn $1,000. Losses always lose $1,000. The odds of a coin toss are 50% wins with 50% losses and a 1:1 reward risk ratio.

The average trade comes out to $99,868.36, almost exactly $100,000. It’s what we expect for a 50-50 game with a 1:1 reward risk ratio. What I find interesting is the standard deviation of $14,377 and how it changes. I don’t want to cover scary math topics. The layman’s explanation is that the standard deviation is the “normal” range from the average that you might expect. The $100,000 balance, in most cases, would either lose $14,000 or make $14,000.

Everything beyond those standard deviation boundaries represent the less likely wild scenarios. The minimum outcome comes out to $58,o00, a massive 42% loss. This had a 0.54% chance of occurring. The maximum outcome shows as $158,000, a monster 58% return. This had an even smaller chance of occurring, only 0.1% (1 in every 1,000 trials).

Changing the account risk dramatically affects the standard deviation. 1% strikes most traders as sane and reasonable. Yet, there is a small chance of losing half the account to drawdown strictly because of terrible luck. Decreasing the overall risk by a fourth to 0.25%  drops the standard deviation by exactly one fourth.  The worst case scenario shrinks to a highly tolerable $11,500 drawdown (11.5%). Most traders would find a number between 10%-20% reasonable. The consequence of the reduced risk is that the best case scenario drops correspondingly down to a 14.5% gain.

Stretching the risk out to 2%, a normal industry practice, turns out to be risking accounting suicide with the coin toss game.  The worst case scenario drops the final account balance down to $8,000, a staggering 92% loss.

The goal is to help you define risk from a gut feeling matter into something more tangible and calculated. Too many traders enter the market day dreaming about profits. Risk enters the picture, but too few traders actually understand the relationship between risk and reward.  Hopefully, the picture of best, worst and average scenarios is starting to become more clear for you.