«Key to Trading Profits – Matching the Probability Distribution of A Contract with An Appropriate Mechanical Trading Strategy Gary Tan Business ...»
International Journal of Economics and Finance Vol. 2, No. 2; May 2010
Key to Trading Profits – Matching the Probability Distribution
of A Contract with An Appropriate Mechanical Trading Strategy
Business School, University of Adelaide
10 Pulteney Street, SA 5005, Australia
Tel: 61-(0)8-8303 7215 E-mail: firstname.lastname@example.org
Most research on technical trading strategies had centred only on testing the efficacy of common trading rules applied to various contracts. Other research on the implications of moments of distribution tends to concentrate on asset or portfolio valuation perspective as opposed to trading rules.
Given the controversy surrounding the usefulness of mechanical trading strategies per se, this paper seeks to match the distribution of a contract with an appropriate trading rule to determine the profitability or lack thereof of such an approach.
We tested this approach using Light Sweet Crude Oil futures for the period 1994 – 2008. On the whole, our results strongly support the approach employed. We also tested the results against the weak form EMH and found that there may be some non randomness in prices that one can exploit with the use of mechanical trading methods.
Keywords: Mechanical Trading Strategies, Technical Trading Rules, Futures Trading, Oil Futures
1. Introduction Technical analysis is commonly perceived to involve the prediction of future asset price movements from an analysis of past movements, employing either qualitative methods (such as chart pattern recognition) or quantitative techniques (such as moving averages), or a combination of both.
Whether one takes a qualitative or a quantitative approach, the techniques available are many and varied, and that complicates a systematic assessment of the usefulness of technical analysis. It comes as no wonder then, that empirical tests of specific trading rules and their attendant signals are often less than satisfactory tests of the efficiency of technical analysis in general, since traders typically employ not one but a range of technical indicators. Additionally, many traders also apply considerable market intuition to complement the insight gained from technical analysis, so there will always be an element of subjectivity with its application.
Since the publication of Fama & Blume (1966) most academics have considered the usefulness of technical analysis in forecasting to be probably close to nil. For many others, the continued and widespread use of these techniques Taylor & Allen (1992); Yin-Wong Cheung & Menzie D. Chinn (2001) is even puzzling since technical analysis shuns economic fundamentals and relies only on information on past price movements.
Historical information, according to the weak form market efficiency, should already be embedded in the current asset price, thus its use is unprofitable.
Burton G. Malkiel (1996), suggested that “technical strategies are usually amusing, often comforting, but of no real value”. Malkiel’s dismissal of technical analysis is glaringly at odds with the fact that technical analysis is widely used by market professionals.
On the other hand, Sweeney (1986, 1988) presents results consistent with some usefulness to technical rules.
More recent studies have included Taylor (1992), LeBaron (1994), and Levich & Thomas (1993). The latter two employed bootstrap techniques to further emphasise the magnitude of the forecastability. Other related evidence includes that of Taylor & Allen (1992) which shows the extent to which traders continue to use technical analysis. Brock et al (1992) showed using a bootstrap methodology that the rules did at least generate statistically significant forecastability.
It is not difficult to understand why technical analysis did not or could not sustain academic interest as long as the available evidence was not of a more systematic nature. The scepticism with which academic economists initially viewed (and to some extent continue to view) technical analysis can be largely attributed to the intellectual standing of the efficient markets hypothesis (EMH), which, in its “weak form” Fama (1970), International Journal of Economics and Finance www.ccsenet.org/ijef maintains that all historical information should already be embodied in asset prices, making it impossible to earn excess returns on forecasts based on historical price movements.
If technical analysis reflects rational thinking that leads to profitable trading rules, how is it that market processes do not arbitrage these profit opportunities away? It is offered that in well functioning markets one would expect that profit opportunities will be exploited up to an extent where agents feel appropriately compensated for their risk. To take open positions is inherently risky, whether the decision is based on fundamental or technical considerations.
Or perhaps technical analysis is an indication of irrational behaviour, as can only be concluded if one follows the traditional understanding of the EMH and regards markets as at least weakly efficient; Fama (1970). However, to interpret technical analysis as an indication of irrational or even not-fully rational behaviour goes against the grain that virtually all market professionals rely on technical trading rules, albeit to varying degrees. Surely market professionals cannot all be exhibiting suboptimal behaviour, much less irrationality, even if temporarily.
Such is the paradox, so is it any wonder then, that evidence relating to the profitability of technical analysis tends to be inconclusive? Not at all, for if technical analysis was never profitable, its widespread use would be hard to fathom; if, on the other hand, technical analysis was always profitable, it would perhaps imply that the market is inefficient to a degree that many academics would not find credible.
Clearly, technical analysis remains an intrinsic part of the market. For market practitioners, the challenge is to constantly refine technical trading strategies as potentially important tools in the search for excess returns. For academic researchers, technical analysis must be understood and integrated into economic reasoning at both the macroeconomic and the micro structural levels.
This paper hopes to contribute to the existing literature by matching the distribution of a contract with an appropriate trading rule, thus integrating the characteristics of a contract with the capability of a trading strategy.
In this regard, knowing that a contract’s distribution is negatively skewed, for instance, one can expect a higher probability of making many small wins and a low probability of risking a larger loss. Thus by choosing the appropriate contract to trade vis-à-vis one’s risk profile, one is already ahead of the game in terms of staking the odds of winning trades in one’s favour even before selecting a trading strategy. As different trading strategies cater to different characteristics of price movements, back testing with different trading rules can uncover a trading rule that best exploit the characteristics of the intended contract, thus achieving a competitive edge.
2. Data and Summary Statistics
2.1 Data This study uses daily exchange series from Nymex as provided by Telequote Networks. The series represent the daily data for the Light Sweet Crude Oil futures extending almost 15 years and 3,714 observations. We first determine the distribution of daily lognormal returns for the in-sample period from 01 January, 1994 through to 31 December, 1998 and 1,254 observations. Based on the said distribution an appropriate trading strategy was adopted to trade subject commodity for the out-of-sample period from 01 January, 1999 through to 31 October, 2008 yielding 1,596 trades out of 2,460 observations. We also test the distribution of the out-of-sample period to determine the continuity of the distribution established for the in-sample period.
2.2 Summary Statistics
The daily return series is generated as follows:
Rt = ln (Pt/Pt-1) (1) where ln is the natural logarithm operator, Rt is the return for period t, P is the closing price for period t and t is the time measured in days.
The descriptive statistics and results of the normality test for the daily returns are presented in Table 1.
The skewness coefficient, being the third moment about the mean/cube of the standard deviation is -0.0118 for
in-sample period and -0.2615 for out-of-sample period, and is measured as follows:
(2) where N is the number of observations, is the mean of the series and is an estimator for the standard deviation.
The distribution of the daily lognormal returns appeared to be slightly negatively skewed for the in-sample period, a characteristic that extended to the out-of-sample period. This suggested that wins are small and likely, and losses can be large but are far and few. In other words, there is the occasional large loss at the expense of promising consistent winnings. Negative skewness, although commonly viewed as risky, is not without its own appeal to traders as the occasional large downside can be more than mitigated by the frequent and smaller upside with appropriate trading strategies that deliver robust win/loss ratios. A trading strategy that has a high percentage of wins would generate significant profits in the long run when compounded by a robust win/loss ratio.
The kurtosis coefficient, being the fourth moment about the mean/square of the second moment is 5.6983 for
in-sample period and 6.2375 for out-of-sample period, and is calculated as follows:
(3) where N is the number of observations, is the mean of the series and is an estimator for the standard deviation.
This indicates that the in-sample distribution is also more peaked than normal, a characteristic that is also carried forth into the out-of-sample period, a condition otherwise known as leptokurtic. This suggests a not so significant deviation from its mean, which implies less volatility in future returns and lower probability of extreme price movements. This implies lower risks and therefore more stable returns, thus mitigating sharp drawdown risks as is feared with a significant negatively skewed distribution.
The Jarque-Bera (JB) test of normality was employed to further test the normality as it is an asymptotic or large-sample test that is appropriate given the large number of observations in this study. For a normally distributed variable, S = 0 and K = 3, hence the Jarque-Bera (JB) test serve to test the joint hypothesis that S = 0 and K = 3 and thus the null hypothesis that the series is normally distributed.
(4) where N is the sample size, S is the skewness coefficient and K is the kurtosis coefficient.
The JB statistic as computed is 380.4543 with a p-value of 0 for in-sample period and 1,102.3620 for out-of-sample period with a p value of 0. As to be expected from our calculation of skewness and kurtosis in the foregoing, the value of the statistic is far from zero and the p value zero. Thus, one can reject the null hypothesis of normal distribution. This only lend more credence to the significance of focusing on the third and fourth moment of distribution.
Insert Table 1: Summary Statistics In Table 2 the autocorrelation coefficients at various lags are very high for both in-sample and out-of-sample periods, starting at 0.9980 and 0.9990 at the first lag and only declined to 0.9880 and 0.9940 at the 5th lag respectively. Autocorrelations up to 5 lags for both periods are also individually statistically significant from zero since they are all outside the 95% confidence bounds.
We also tested the statistical significance of the autocorrelation coefficients by using the Ljung-Box (LB)
statistic. The LB statistic is defined as:
(5) where T is the sample size and is the j-th autocorrelation.
The LB statistic tests the joint hypothesis that all the pk up to certain lag lengths are simultaneously equal to zero.
From Table 2 the value of the LB statistic up to 5 lags is 6,205 for in-sample and 12,235 for out-of-sample.
There is also zero probability of obtaining such a LB value under the null hypothesis that the sum of 5 squared estimated autocorrelation coefficients is zero. Accordingly, one can conclude significant time dependence in the return series due perhaps to some form of market inefficiency. This suggests that trends and reversal tendencies are present and can be detected. As a result, patterns in short term price changes can be exploited for significant profits by the intelligent use of mechanical trading methods.
Insert Table 2: Autocorrelation International Journal of Economics and Finance www.ccsenet.org/ijef
3. Mechanical Trading Model Having established that the distribution of the contract in question is negatively skewed and leptokurtic, we next determine an appropriate trading strategy to employ. Many strategies exist to trade a negatively skewed market, with statistical arbitrage and convergence trading among the more common or popular methods.
This model seeks to initiate a trade when the current price breaks above the previous high or below the previous low. So if one is trading on the basis of daily time frames as is envisaged in this paper, one would be comparing the current price with the previous day high and previous day low.
This can be expressed as follow:
Buy if: Pt ≥ max (Pt-1) + 1 tick (6) Sell if: Pt ≤ min (Pt-1) – 1 tick (7) where Pt the price at time t and 1 tick refers to the minimum price fluctuation of the contract.
Once a trade is entered, say to buy one contract, in accordance with the rule specified in the foregoing, hold until an opposite signal is given by the market (again in accordance with the rules above) to sell. When that occurs, sell two contracts – one to square the earlier position and the other to simultaneously enter a new short position.
The process is then repeated every time the rule is triggered.
Insert Table 3: Examples of Trade Selection As a result net position is always one contract, long or short, at any one time. This also means no adding to positions when consecutive long signals or consecutive short signals are given by the model.