Forex scalping: AUD/JPY under the microscope

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Written by Forex Automaton   
Thursday, 26 March 2009 10:08
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Forex scalping: AUD/JPY under the microscope
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I analyze the correlation structure of AUD/JPY on the time scales between 10 minutes and 10 seconds and see dramatic differences between the real market and the efficient market expectations on the one hand and among the time scales of the real market, on the other. High frequency data are particularly puzzling. Are we looking at the traces left by algo trading in large volumes? The study uses AUD/JPY time series of about 10,000 data points each, obtained from a popular provider (an ECN broker).

Naturally, from the efficiency point of view, traders chase quick execution, but from the strategy point of view, what matters is the time scale on which the trader analyzes the market and makes decisions. According to the efficient market hypothesis, markets have no prehistory dependence, therefore the size of the spread and cost of capital are the main factors making the difference between the time scales.

Indeed, even if the market is a random walk, with volatility (RMS of price return) growing with time scale as a square root, you do not want to trade on the time scale such that the volatility of price on that time scale is comparable to or less than the spread -- just surrendering your entire account to the broker will save you time, with the same effect on your budget. Tighter spreads make smaller time scales possible, but you still don't want to trade a random walk on any time scale, unless you seek legal gambling.

With real world being so different from the hypothetical world of efficient market theorists, there is a new dimension to the problem: once some measure of non-randomness is found, how does it change with time scale? Efficient market theory is of no help since according to it, all such measures are null, therefore there is no field for study.

How far is that from truth?

The forex "pulser"

Distribution of AUD/JPY logarithmic returns on 10 s scale Autocorrelation of AUD/JPY logarithmic returns on 10 s scale

Fig.1: Top: distribution of AUD/JPY logarithmic returns on 10 s scale. The distribution is discrete due to the discreteness of the price itself (coming in pips), more visible in this figure than on longer time scales. Bottom: autocorrelation of AUD/JPY logarithmic returns on 10 s scale shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of AUD/JPY in this same piece of time series. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series. The noise series are constructed to have the same distribution of returns, as evidenced by the top panel where the corresponding simulated distribution is also shown in red. The data cover the time from 03/15/2009 20:13:21 to 03/17/2009 08:44:31.

In principle time series may acquire structure as a result of market dynamics or imperfections of the dealing system. The structure seen in Fig.1, bottom panel, seems artificial. If this were an analog signal, one could suspect that a pulser signal got caught up via induction or some other way.

How tight a spread is needed to trade this "pulser"? Autocorrelations 101 for forex scalpers.

Needless to say, time series like this are highly predictable. Here is a little quantitative exercise to calculate how tight a spread is needed to capitalize on such a feature of the autocorrelation. The simplest way to do that would be to

  1. assume that the time series consists entirely of the pulser signal, that is to disregard the 0 lag correlation amplitude above, say, 0.015 × 10-6.
  2. assume ln(1+a) = a, discarding terms of the order a2 which is good for very small a.
Further, I simplify the time series itself:
simle time series
The corresponding series of returns becomes
returns time series
Figuring out the autocorrelation is easy: it's got to have the same period and its 0 lag value, the variance, is simply the average of square deviations between the time series at each point and the mean of the time series, which is a2.



Trading such a time series is profitable if the spread (difference between bid and ask prices) is below a, and if the execution time is instantaneous or at least much smaller than the period of the series. Therefore the rule of a thumb is -- if in the autocorrelation of logarithmic returns we see a regular feature of a certain magnitude, the spread (expressed is a fraction of price) must be below square root of that magnitude. Getting back to Fig.1, the feature of magnitude 0.015 to 0.02 (times 10-6) requires spread of 0.00012 to 0.00014 as a fraction of price; with the actual AUD/JPY exchange rate about 65, that translates into 0.008 to 0.009 -- most likely, just one pip. The actual spread on the retail market may be 0.03 or 0.04 (3 or 4 pips), obviously much higher.

The spread problem is not the only problem. After all, there are brokers who claim to have zero spread. In the best of all worlds, there is still a problem of synchronizing your trading to the "pulser" (whatever its origin and nature is). A real-time trading system with sufficiently high frequency of operation is needed to analyze the pattern. How stable is the pattern? Perhaps the amplitude gets higher at times? Perhaps the phase varies? Are we looking at a destructive interference of several time histories with varying phases, in the ten thousand point strong sample that made Fig.1? Perhaps each of those constituent series, while stable, is suitable for profitable trading? These are open questions at the moment. Whatever the answers, many forex brokers frown upon forex scalpers!

What could cause the effect?

At the moment I can only speculate about this. I can discuss three possibilities.

  • Hypothesis A: Greedy broker. It is conceivable that the broker itself intentionally makes the quote wander around the true quote by regularly adding and subtracting one pip. The rationale would be to shake traders out of their positions by causing more stop-losses than the natural market would require. The slight increase in trading activity would have a positive effect on the broker's revenue, but I seriously doubt that it's worth the trouble. And if the broker did that, they would have probably come up with a pattern which is not so easy to detect, and would not make the data publicly available.

  • Hypothesis B: Imperfect infrastructure. There is software behind forex price, and software tends to have bugs and features. Theoretically it is possible that these features show up as correlation features but I don't know enough about it to elaborate.

  • Hypothesis C: Algorithmic trading by large volume players. This is the most natural and the most likely scenario. Large players do practice algorithmic trading, one of the major problems being the sheer scale of the trading. Large institutions move money on the scale where their trading itself is able to move the market. Concealing their intentions and minimizing the effect of the trading on price is one of the top priorities. A conceivable solution is to distribute the volume thinly over time. There is no apparent reason to do that by placing trades in bursts, rather than continuously, other than it's a natural thing to do for a computer (computers simulate continuity by discreteness of high frequency, and the programmers may have decided that once per 30 seconds is frequent enough). There may be another large institution placing the opposite trades in the same manner at the same time. It's not difficult to see that the net result of such activities may produce an autocorrelation like Fig.1.


Another feature of the autocorrelation is the familiar "bipolar disorder", a tendency to form quickly alternating rises and falls, more pronounced than in a fully unpredictable time series of the same volatility, shows up as negative deeps surrounding the zero-time lag peak. This feature has been seen in LIBOR and forex, including data from different providers. For LIBOR and stock market data this has been seen on the day scale, for forex -- on the hour scale and as we now see, down to 10 s scale, although I would not be surprised to see it on the day scale for forex as well.

Distribution of AUD/JPY logarithmic returns on 1 min scale Autocorrelation of AUD/JPY logarithmic returns on 1 min scale

Fig.2: Top: distribution of AUD/JPY logarithmic returns on 1 min scale. Bottom: autocorrelation of AUD/JPY logarithmic returns on 1 min scale. Simulation results are shown in red in both panels.

Moving to the minute scale, the pulser effect is no longer visible, but the "bipolar disorder" is even stronger than in Fig.1, being the only significant feature.

Distribution of AUD/JPY logarithmic returns on 10 min scale Autocorrelation of AUD/JPY logarithmic returns on 10 min scale

Fig.3: Top: distribution of AUD/JPY logarithmic returns on 10 minute scale. Bottom: autocorrelation of AUD/JPY logarithmic returns on 10s scale. Simulation results are shown in red in both panels.

Finally, on the 10 minute scale, the "bipolar disorder" effect is gone, and even though the autocorrelation looks a bit suspiciously oscillatory, this is by no means the scale of the predictability seen in Fig.1.

In summary, forex time scaling studies looks like a promising field of activity as yet almost untapped by Forex Automaton.

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