From the December 2013 issue of Futures Magazine • Subscribe!

Using fractals in forex

Setting up the trade

Here are the basic facts of our trade scenario:

  • Book balance $10,000
  • Position size €10,000
  • Instrument: Spot €. No transactions fees are paid when trading spot forex.
  • Backtested data: Spot four-hour data (Jan. 1, 2007 to June 30, 2013). Data provided from 
  • Trading periods: Execute only on four-hour candlestick window. Testing on data with 1 a.m., 5 a.m., 9 a.m., 1 p.m., 5 p.m. and 9 p.m. candlestick windows. The importance of the timing of the four-hour candlestick is stressed. Monthly U.S. economic information is released at 8:30 a.m. and 10 a.m. It is important to note that the model transaction will occur after/before possible periods of market stress (like on the release of the monthly employment data).
  • Book leverage: Approximately 1.30
  • Trend indicator: Exponential moving averages (EMA). Fast EMA: 10-period (10 periods of four-hour blocks of data). Slow EMA: 20. This pair was backtested as optimal for this currency and this time interval.
  • Transaction times: At the open of each four-hour candlestick. No other transactions are allowed
  • Transaction limit: 40 pips per €10,000 position; each pip is worth $1
  • Transaction stop: 20 pips

We have examined a set of trades that are low risk, provide consistent low returns with a leverage of less than 1.5 and can be automated, which ensures low human capital fees. We consider this group of trades the “annuity” trade of the portfolio, or the first step of a return pyramid for a speculative portfolio. In terms of a baseball metaphor, this model is the first base of firm profit and not a home-run trade.

As the model operates in the short-term, we use technical indicators, particularly EMAs, to indicate the possibility of a trend. This is our only attempt to create some logic out of the noise that is produced at the short end of the market. It has been shown that short-term investors rely heavily on technical indicators.

Think of the greed and fear patterns (the positive and negative price movements) of the four-hour candlestick chart as a country’s coastline. Determining the length of a country’s coastline is not as simple as it appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the Richardson effect (Mandelbrot, 1983). In fact, the answer depends on the length of the ruler you use for the measurements. A shorter ruler measures more of the sinuosity of bays and inlets than a larger one, so the estimated length continues to increase as the ruler length decreases.

Traders do not know the optimal “ruler” to use to catch the maximum amount of profit for each “inlet” of price movement (trend). Our ruler is the limit order and our inlets are the trends of the four-hour market as depicted by the 10- and 20-period EMAs. Each inlet has two legs: The long trend (10 EMA > 20 EMA) and the short trend (20 EMA > 10 EMA). Because the optimal limit order is not known and the frequency and magnitude of each inlet are not consistent, we aim for profitability by taking a small bite out of each leg of each market wave. 

The optimal EMA period lengths, limit orders and stop order amounts for the trading model were determined through backtesting using data from 2007 to June 2013 (four-hour data from Regarding limit orders and stop orders, we looked for a combination that supplied consistent profits with low risk  levels. Our backtesting return analysis for this model is found in “Cumulative results” (below). All returns are produced using CFA-recommended methodology: Geometrically linked returns.

Regarding the use of leverage in this model, the mean hedge fund industry leverage is approximately 2.13 with a standard deviation of 0.616. Hence, we sought to construct a model that targeted this industry average.

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