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Technical Analysis, Trading Strategies

Trading is Much More than Naive Statistics

If correlations meant anything significant as far as trading the markets then anyone who took a course in Statistics could become a rich man. Needless to say that trading the markets involves much more than math. Here I present trading system examples based on the widely purported correlation between the Euro and stocks. The results demonstrate that contrary to common misconceptions traders may experience huge losses when employing naive strategies that try to exploit purported correlations.

I have already shown in another post that the purported correlation between the Euro and stocks is just media hype. From 2006 to the middle of 2011, the 120-day rolling correlation between the two ETFs that track the Euro and the S&P 500, with tickers FXE and SPY, respectively, has ranged between -40% and 40%. Only after the middle half of 2011 the value of the correlation increased to about 70%, it peaked and it is now dropping, as shown on the chart below:

A naive strategy that attempts to exploit this correlation (often used by retail traders who do not do their homework before employing trading strategies) involves buying SPY at the close when FXE registers a gain on a daily basis, as follows:

Buy SPY at the close of today if Close of today of FXE > Close of yesterday of FXE
Sell SPY at the close of today if Close of today of FXE < Close of yesterday of FXE

This strategy holds a long SPY position for as long as FXE makes a higher close and reverses to a short position and stays short when FXE makes a lower close.

I backtested this strategy in Amibroker (Charts created with AmiBroker – advanced charting and technical analysis software. http://www.amibroker.com/”) in the period 12/12/05 – 01/09/2011. The settings were as follows:

Starting capital: $100,000
Commission paid: $7 flat per side
Fully invested (Number of shares = available equity/entry price, rounded)

The results were devastating:

Number of trades: 810
Long: 405 – Short: 405
Winners: 373 (46.05%)
Losers:    473 (53.95%)
Net profit: -$71,659.93
Max. Drawdown: 73.10%

It is even more interesting that since November 1, 2011, when the correlation rose above 40%, the results are even worse, with the win rate dropping to 33.33% and the net profit is -15.07%, just in that period. This is a screenshot of the backtest results in this case:

If the system is modified to consider a 2-day positive/negative close, the results for the whole testing period get a little better but still devastating:

Number of trades: 513
Long: 257 Short: 256
Winners: 243 (47.37%)
Losers:    270 (52.63%)
Net profit: -$26,271.60
Max. Drawdown: 67.42%

Things get even worse in relation if a 3-day positive/negative close is considered and remain bad for 4-day and 5-day periods.

Trade the inverted system?

I am not fond of inverted systems. Yet, the inversion of this system has produced a respectable gain in the period considered although the equity curve has been very volatile and the Sharpe ratio was only 0.32. The win rate was 52.47% and the net profit was 86.60% for the whole period, resulting in a compounded annual return of 5.32%.

Interestingly enough, in the period since November 1, 2011, when the correlation of FXE and SPY was rising, the inverted system produced a net profit of 15.74% with a Sharpe ratio of 3.21 and a win rate of 66.77%. The screenshot of the results is shown below:

It appears that the market was fading the correlation during said period.

The conclusion is that correlations cannot be exploited using naive methods. It takes much more sophisticated approaches to exploit such mathematical relationships that go beyond what someone learns in Statistics. Trading is certainly much more than Statistics.

Disclosure: no relevant positions.

Charting program: Amibroker (Charts created with AmiBroker – advanced charting and technical analysis software. http://www.amibroker.com/”)

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