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Construction and evaluation of trading systems: Warsaw index futures.

Abstract

This paper presents and compares 15 trading systems constructed for the Warsaw Stock Exchange futures contracts. These trading systems are constructed applying technical analysis and artificial neural networks (ANN). The efficiency of constructed trading systems is measured by the profit, which could be gained on the analyzed market when an investor uses various methods of buy and sell signals generating. Investigation is conducted for daily observations of stock index WIG20 futures from December 1, 1999 to November 28, 2003. The conclusion is that the combination of the technical analysis and artificial intelligence in order to gain profit from trading on the Polish futures market can bring much better investment results than trade in the traditional way. (JEL G10, C45)

Introduction

The stock exchange market in Poland was created from scratch after the political system transformation. The Warsaw Stock Exchange (WSE) started operation in 1991 with five companies listed. The Polish derivatives market came into existence recently, as the first futures were launched in 1998. The law frames for short sale trading of stock was just set in 2003. Before that it was impossible to make short sales on the Warsaw Stock Exchange. This, of course, did not refer to financial futures, which have been present on the WSE since 1998.

Investors apply different strategies either to maximize profit (or rate of return) or to minimize risk of loss (or probability of loss). These strategies are constructed using a great variety of quantitative methods. The question is to what extent can these methods be applied to financial markets to gain profit? To answer this question, it is necessary to test different trading systems using actual data. The future contracts are chosen to analyze the possibility of making profits not only when the prices increase but also when they decrease.

The exact forecast of prices on the stock exchange would allow earning without any risk and losses. However, most of the available prices forecasting methods, such as econometric models or artificial neural networks, give the outcomes that are of a mostly inaccurate. Therefore, relying on the indication of such forecasts is still very risky and can increase losses. Hence, the concept of reducing the inaccuracy of forecasts by filtering them, in a sense, through investment strategies, in particular by the technical analysis, are indicators that the trading systems are based on.

Thus, the aim of the paper is to answer the question of whether including the ANN forecasts of stock market prices to trading systems makes them more efficient and whether this kind of combination is more profitable than investing based only on the forecast indications.

Materials and Methods

In the research, technical analysis and neural nets are used to construct trading systems. Numerous authors recommend both methods. Technical analysis is widely described in literature by Murphy [1999] and Schwager [1997]. Neural network applications for financial markets have been discussed by Azoff [1994], Bosarge [1993, pp. 371-402], Chen [1994, pp. 1199-202], Dutta and Shekhar [1993, pp. 257-73], Gately [1995], Goonatilake and Treleaven [1995], Hawley et al. [1993, pp. 27-46), Hoptroff [1993, pp. 59-66], Hsieg [1993, pp. 12-5], Lowe [1994, pp. 3623-28], Refenes [1995], and Witkowska [2002].

Technical analysis comes from the assumption that stock price is set by the intersection of supply and demand, and an investor can make money by frequently buying and selling stocks. A technical analyst does not look at income statements, balance sheets, company policies, or anything fundamental about the company. The technician looks at the actual history of trading and price in a security or index. This is usually done in the form of a chart. The security can be a stock, future, index, or a sector. It is flexible enough to work on anything that is traded in the financial markets.

The technical analyst believes that the market price reflects all known information about the individual security. It includes all public and insider information. The market price reflects all the different investor opinions regarding that security. Securities move in trends, and these trends continue until something happens to change the trend.

Technical analysis indicators are used to determine the trend of a market, the strength of the market, and the direction of the market. Some technical analysis indicators can be quantified in the form of an equation or algorithm. Others can show up as patterns (e.g., head and shoulders, trend lines, support, and resistance levels). At some point, the technical analyst will receive a signal. This signal is the result of one technical analysis indicator or a combination of two or more indicators. The signal indicates to the technical analyst a course of action whether to buy, sell, or hold.

Artificial neural networks are information transforming systems which structure and function are motivated by the cognitive progress and organizational structure of neuro-biological systems. The basic components of the networks are highly interconnected processing elements called neurons, which work independently in parallel. Synaptic connections (weights) are used to carry messages from one neuron to another. Thus, neural nets are non-linear models which parameters (weights) are estimated during so-called training procedures. There are two main methods of ANN training: supervised and unsupervised. In the research, the authors apply the back propagation algorithm (supervised learning) to generate prices that are employed in the trading system.

Data

The trading systems are constructed for the index futures. The underlying instrument of this contract is the stock index WIG20, which calculates for 20 companies of the highest capitalization and volume on the Warsaw Stock Exchange. At this moment, the Warsaw Stock Exchange has index futures, currency futures, and individual stock futures, but WIG20 futures allow a trader to be present in the market during increasing trends, as well as decreasing trends. Investigation is conducted for daily observations from December 1, 1999 to November 28, 2003. Tests include the following series of WIG20 futures: FW20H0, FW20M0, FW20U0, FW20Z0, FW20H1, FW20M1, FW20U1, FW20Z1, FW20H2, FW20M2, FW20U2, FW20Z2, FW20H3, FW20M3, FW20U3, FW20Z3. All the series are joined into the continuous, spread-adjusted futures as it is described by Schwager [1997, pp. 245-6, 664-9].

In addition, observations of DAX, DJIA, NIKKEI and exchange rates of EURO/PLN (PLN-Polish zloty), and USD/PLN are employed.

Construction of Trading System

In order to analyze the impact of the forecast application on efficiency of the technical trading rules, the same investing systems will be tested out in three different ways. The first one includes the perfect forecast, i.e. the next session close prices (it is assumed that future prices are known by the investor). The second way covers the analysis of the next session prices predicted by artificial neural networks. The third one refers to the analysis of prices in the past, not their forecasts. All three solutions will deal with the same methods of trading decision making that are based on the technical analysis indicators, such as moving averages, Bollinger bands, oscillators, or breakouts. The following is a description of each.

1) Channel breakout -- buy signal: long position for the next day open if the predicted next day close price is higher than the maximal price from the last five days; sell signal: short position for the next day open if the predicted next day close price is smaller than the minimal price from the last five days; out of the market signal: if the predicted next day close price does not fulfill any of these conditions.

2) Bollinger bands -- buy signal: long position for the next day open, if the predicted next day close price is higher than the upper Bollinger band line; sell signal: short position for the next day open if the predicted next day close price is smaller than the lower Bollinger band line; out of the market signal: if the predicted next day close price does not fulfill any of these conditions.

UL = MA(n) + k * [square root of ([[n.summation over (i=1)] ([C.sub.i] - MA(n))[.sup.2]]/n)],

LL = MA(n) - k * [square root of ([[n.summation over (i=1)] ([C.sub.i] - MA(n))[.sup.2]]/n)] (1)

where UL is the upper Bollinger band line, LL is the lower Bollinger band line, MA(n) is the moving average from the last n sessions, C is the close price, and k is the parameter that describes the distance between the upper line and lower line from the moving average.

3) Momentum oscillator -- buy signal: long position for the next day open if the predicted next day close price is higher than the close price before five days (momentum oscillator is above zero); sell signal: short position for the next day open if the predicted next day close price is smaller than the close price before five days (momentum oscillator is below zero); out of the market signal: signal does not occur.

M = C - [C.sub.n] (2)

where C is the next day close price and [C.sub.n] is the close price before n days.

4) Moving averages -- buy signal: long position for the next day open, if MA3 crosses up MA15 (both moving averages include the predicted next day close price); sell signal: short position for the next day open if MA3 crosses down MA15; out of the market signal: signal does not occur.

MA(n) = [[n.summation over (i=1)] [C.sub.i]]/n (3)

Additionally, to compare the results, an investment without trading rules is also tested. The buy signal occurs when the predicted next day close price is higher than the present-day close price. The sell signal occurs when the predicted next day close price is lower than the present-day close price.

To summarize, one may say that there are five methods of buy-sell signals generating (moving average, Bollinger band, oscillator, breakout, and "no system method"), and three types of input information: perfect forecasts, i.e. actual future close prices, forecasts of close prices estimated applying neural nets, and past close prices. A combination of five methods and three types of input information will make 15 trading systems, which are the subject of the next part of the paper.

Calculation of Forecasts

From the investor's point of view, the longer forecast horizon the better. However, the research shows that prediction error usually increases with the lengthening of the forecast horizon. Therefore, in the investigation, one session ahead of forecasts is applied.

There are many methods of obtaining a security or derivative price forecasts. The most popular are: econometric models, deterministic chaos models, models based on stochastic process theory such as ARIMA and (G)ARCH models, as well as artificial neural networks and related methods. Examples of applying these methods to stock price prediction are discussed by Beinsen and Kuhrer [1999], Kohara et al. [1996, pp. 142-8], Papla and Jajuga [1998, pp. 5-16], Refenes et al. [1994, pp. 375-88], White [1993, pp. 315-48], and Witkowska [2002].

In the research, the forecasts of prices are estimated using the most popular artificial neural network type, Multilayer Perceptron (MLP), which is trained applying back-propagation algorithm. To apply neural nets, the output and input variables must be selected. Variables are denoted due to the following system: C is the close price, O is the open price, H is the maximal price, L is the minimal price, D is the absolute increase, V is the volume, and numbers in brackets denote delays. For instance, C(0) denotes close price from the last session in the observation period, C(-1) is the close price lagged by one, etc.

The output variable is defined as the difference between the next session close price C(1) and the latest session close price C(0).

D(1) = C(1) - C(0) (4)

The set of input variables consists of three subsets: variables related to the WIG20 futures, the technical analysis indicators, and the external factors (Table 1).

The forecast horizon is divided into 12 separate sub-periods that are each about three or four months long. Every sub-period is a testing set for its own neural network. Due to this operation, training sets for consecutive networks could be enlarged.

The output variable generated by ANN is the difference between the last session close price and the next session close price [Equation (4)]. However, the next day close price is the value that will be applied in further empirical tests. The research shows that forecasts with output variables that are defined as the increases characterize smaller prediction errors compared to the forecast with output variables that are directly defined as the level of phenomena (i.e., price itself). The output data are transformed into the price forecast [^.C](1), which is the next session close price.

[^.C](1) = C(0) + [^.D](1). (5)

Forecast generated by ANN can be evaluated in terms of average errors calculated for:

[E.sub.i] = [^.C.sub.i](1) - [C.sub.i](0). (6)

The forecast errors of the future close prices are: MAPE = 1.39% and RASE = 1.85%. The direction of changes is predicted correctly in 59.2% of cases.

Empirical Results

To evaluate the efficiency of chosen trading rules, the authors compare the results obtained from three types of input data that are introduced to the trading systems. The assumption is made that a hypothetical trader invests with only one future contract. Empirical results are presented in the tables that contain the transaction efficiency parameters.

In Table 2, there are results obtained for all buy-sell signals generating methods applying perfect forecasts as input data. This allows one to recognize the potential of chosen trading strategies.

According to the results presented in Table 2, in the case of the hypothetical situation in which a trader knows exactly what will happen during the next session (i.e., he or she has the perfect forecast of the close price value), the most profitable method of investing would be the one without a trading system. More than 130,000 zl per one future contract could be earned from December 1999 to November 2003. This is the maximum profit that could be obtained from one future contract during this time on the market.

It is worth mentioning that buy-sell signals, generated by all investigated technical analysis indicators shown in Table 2, let the investor gain the profit. When applying these methods, 60-87% profitable transactions are obtained. When applying Bollinger bands, the smallest maximum net loss in one transaction and the highest proportion of average net profit to average net loss are obtained. The highest maximum net profit in one trade and average net profit are gained using moving average.

In Table 3, the authors present results obtained for trading systems with one session ahead of the price forecasts as input data. In contrast to the previous situation, the present solution is possible. If the forecasts are close enough to the real values, then the data misplacement effect should remain. In this case, the strategy "without system" is no longer the most efficient one. The highest net profit could be gained with the momentum method and it is 22,170 zl. All the trading systems remain profitable.

To verify how the forecast application in trading system influences the investment outcomes, the buy sell signal generating rules are tested out in the traditional way, i.e., on the historical data. Obtained results are presented in Table 4. The biggest profit could be gained again from the momentum strategy and it is 10,230 zl. However, this amount of money is only 46% of the profit obtained in the same strategy but with ANN forecast implementation, so the income is much smaller when there is no available forecast. If an investor relied only on past prices and on the strategy without system, the loss would have reached the level of 30,000 zl.

Conclusions

The research result shows that the trading systems tested out on the data in advance, with the perfect forecast, had much better investment results than the ones tested out in the traditional way (Table 5). Due to the misplacement data application, the systems that are not profitable actually turn out to be income producing. This is proven in the third stage of the research. Changing the perfect forecast into the forecast obtained from ANN results in maintaining the effect of the data misplacement, and the trading rules kept making profits. Compared to the results obtained from the strategies tested on historical data (the traditional way), the implementation of the ANN forecasts also caused the improvement of the other factors that are useful by evaluation of trading systems, i.e., percentage of profitable transactions and average profit--average loss ratio.

The perfect forecasts application shows that the biggest profit is produced by the strategy without any system. Any result obtained from other strategies is not comparable. This leads to the conclusion that technical analysis indicators are not useful in the case of complete information about the state of the market or perfect forecast. However, the situation changes when the ANN forecast is applied instead of actual data. Bollinger bands, momentum, and moving averages turn out to be better than the strategy without a system. Only the channel breakout strategy has a worse outcome.

Testing all the strategies in the traditional way, which is the verification of the results obtained from both, perfect, and ANN forecasts implementation, revealed that, again, three of the systems based on technical analysis indicators are income producing, except for channel breakout.

Testing the strategy without system using the third method (i.e., in the traditional way, with historical data) is, in fact, the implementation of the naive forecasts. Since it is assumed that if the last session close price was higher than the close price from the session before, an investor would buy and, in the opposite case, he or she would sell. So the naive forecast consists on the assumption that the next session close price will differ plus or minus from the last session close in the same value than as the last day. This naive forecast application brings the worst results among all of the strategies and methods of testing. Using the ANN forecast in the strategy without system significantly improves its outcomes.

The results presented in the paper show that technical analysis indicators are highly effective when they operate on the data in advance, i.e. the data that could not be known in this particular moment in time, for example, when setting today's sell or buy signal, tomorrow's price is applied. In situations like this, it is likely to happen only in a process of trading strategy testing with historical data. The result of the data misplacement in the trading system is a significant improvement of investment outcomes. Naturally, this improvement is only revealed on paper, and the theoretical profit does not show the real one. However, the conducted research proves that the unusual efficiency of technical analysis indicators in tests can be, to some degree, maintained in the real investment process by including forecasts in the trading systems.

References

Azoff, E. M. Neural Network Time Series Forecasting of Financial Markets, 1st ed., Chichester: Wiley, 1994.

Beinsen, L.; Kuhrer, M. "Comparison of Exchange Rate Forecasts by Neural Networks and By Econometric Methods," paper presented on International Atlantic Economic Conference in Vienna, Austria, March 1999.

Bosarge, W. "Adaptive Processes to Exploit the Nonlinear Structure of Financial Markets," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 371-402.

Chen, C. H. "Neural Networks for Financial Market Prediction." Proceedings IEEE International Conference of Neural Networks, Orlando, USA, 1994, pp. 1199-202.

Dutta, S.; Shekhar, S. "Bond Rating: A Non-Conservative Application of Neural Networks," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 257-73.

Gately, E. Neural Networks for Financial Forecasting, New York: Wiley, 1995.

Goonatilake, S.; Treleaven, P. Intelligent Systems for Finance and Business, New York: Wiley, 1995.

Hawley, D. D.; Johnson, J. D.; Raina, D. "Artificial Neural Systems: A New Tool for Financial Decision-Making," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 27-46.

Hoptroff, R. G. "The Principles and Practice of Time Series Forecasting and Business Modelling Using Neural Nets," Neural Computing & Application, 1, 1993, pp. 59-66.

Hsieg, C. H. "Some Potential Applications of Artificial Neural Systems in Financial Management," Journal of Systems Management, April 1993, pp. 12-5.

Kohara, K.; Fakuhara, Y.; Nakamura, Y. "Selective Learning for Neural Network Forecasting of Stock Markets," Neural Computing & Applications, 4, 1996, pp. 142-8.

Lowe, D. "Novel Exploitation of Neural Network Methods in Financial Markets," Proceedings IEEE International Conference Neural Networks, Orlando, 1994, pp. 3623-8.

Murphy, J. J. Technical Analysis of the Financial Markets, New York: Prentice-Hall, 1999.

Papla, D.; Jajuga, K. "Chaos Theory in Financial Time Series Analysis--Some Theoretical Aspects and Empirical Results," Dynamic Econometric Models, 3, 1998, pp. 5-16.

Refenes, A. P. Neural Networks in the Capital Markets, Chichester: Wiley, 1995.

Refenes, A. N.; Zapranis, A.; Francis, G. "Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models," Neural Networks, 7, 2, 1994, pp. 375-88.

Schwager, J. D. Technical Analysis. Schwager on Futures, Chichester: Wiley, 1997.

White, H. "Economic Prediction Using Neural Networks: The Case of IBN Daily Stock Returns," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 315-48.

Witkowska, D. Artificial Neural Networks and Statistical Methods. Selected Problems in Finance, Warsaw: C. H. Beck, 2002 (in Polish).

DOROTA WITKOWSKA* AND EDYTA MARCINKIEWICZ*

*Technical University of Lodz--Poland.
TABLE 1 Set of Input Variables

Description                     Formula/Symbol

A. Variables related to the
  WIG20 futures
Close prices of WIG20 futures   C(0), C(-1), C(-2), C(-4)
Natural logarithms of simple    ln[[C(0)]/[C(-1)]], ln[[C(-1)]/[C(-2)]],
  index numbers of prices       ln[[C(-2)]/[C(-3)]], ln[[C(-3)]/[C(-4)]]
Relative change (%) of close    [[C(0) - C(-1)]/[C(-1)]],
  prices                        [[C(-1) - C(-2)]/[C(-2)]],
                                [[C(0) - C(-4)]/[C(-4)]]
Differences between maximal     [D.sub.HL](0) = H(0) - L(0),
  and minimal prices, and       [D.sub.CO](0) = C(0) - O(0),
  between close and open        [D.sub.HL](-1) = H(-1) - L(-1),
  prices                        [D.sub.CO](-1) = C(-1) - O(-1),
                                [D.sub.HL](-2) = H(-2) - L(-2),
                                [D.sub.CO](-2) = C(-2) - O(-2)
Relative change (%) of volume   [[V(0) - V(-1)]/[V(-1)]]
Difference between values of    [C.sub.WIG20](0) - C(0)
  index WIG20 and index WIG20
  futures
Number of days to WIG20 future  --
  expiration date
B. Variables related to the
  technical analysis
  indicators
3-day Simple Moving Average     MA3
5-day Exponential Moving        EMA5
  Average
9-day Rate of Change            ROC9
  oscillator
William's oscillator            Wm%R
5-day Average True Range        ATR5
C. Variables related to the
  external factors
Close value of index WIG20      [C.sub.WIG20](0)
Relative change (%) of WIG20    [[C.sub.WIG20](0) - [C.sub.WIG20](-1)]
  close values                  /[[C.sub.WIG20](-1)]
Relative change (%) of WIG20    [[V.sub.WIG20](0) - [V.sub.WIG20](-1)]
  volume                        /[[V.sub.WIG20](-1)]
Relative change (%) of EURO/    [[C.sub.EURO](0) - [C.sub.EURO](-1)]
  PLN close prices on Polish    /[[C.sub.EURO](-1)]
  currency market
Relative change (%) of USD/PLN  [[C.sub.USD](0) - [C.sub.USD](-1)]
  close prices on Polish        /[[C.sub.USD](-1)]
  currency market
Relative change (%) of DAX      [[C.sub.DAX](0) - [C.sub.DAX](-1)]
  close values                  /[[C.sub.DAX](-1)]
Relative change (%) of DJIA     [[C.sub.DJIA](0) - [C.sub.DJIA](-1)]
  close values                  /[[C.sub.DJIA](-1)]
Relative change (%) of NIKKEI   [[C.sub.NIKKEI](0) - [C.sub.NIKKEI](-1)]
  close values                  /[[C.sub.NIKKEI](-1)]

TABLE 2 Reports on the Trading Systems with the Perfect Forecast

                        Channel      Bollinger
                        Breakout     Bands        Momentum

Commission [zl]             15           15           15
Number of                  238          112          191
  trades
Number of                  118           58           96
  buy signals
Number of                  120           54           95
  sell signals
Max. net profit           3980         4730         4000
  (in one trade) [zl]
Max. net loss            -1130         -540         -880
  (in one trade) [zl]
Average                    463.69       689.17       656.74
  net profit
  (per trade) [zl]
Average net loss          -205.31      -148.75      -168.23
  (per trade) [zl]
Ave. net profit/             2.2585       4.6331       3.9039
  Ave. net loss
Number of                  206           96          129
  profitable
  transactions
Number of loss              32           16           62
  transactions
% Profitable                86.55%       85.71%       67.54%
  transactions
Gross profit [zl]       96,090       67,140       80,020
Net profit [zl]         88,950       63,780       74,290
Commision                 7140         3360         5730
  paid [zl]

                        Moving       Without
                        Average      a System

Commission [zl]             15            15
Number of                   70           516
  trades
Number of                   35           258
  buy signals
Number of                   35           258
  sell signals
Max. net profit           4990          3570
  (in one trade) [zl]
Max. net loss            -1130         -1130
  (in one trade) [zl]
Average                   1079.52        397.21
  net profit
  (per trade) [zl]
Average net loss          -314.29       -143.97
  (per trade) [zl]
Ave. net profit/             3.4348        2.7590
  Ave. net loss
Number of                   42           391
  profitable
  transactions
Number of loss              28           126
  transactions
% Profitable                60.00%        75.78%
  transactions
Gross profit [zl]       38,640       152,660
Net profit [zl]         36,540       137,180
Commision                 2100        15,480
  paid [zl]

TABLE 3 Reports on the Trading Systems Tested Applying Forecasts

                           Channel    Bollinger
                           Breakout   Bands        Momentum

Commission [zl]              15           15           15
Number of trades            222          122          208
Number of buy signals       103           64          104
Number of sell signals      119           58          104
Max. net profit            1220         4371         3970
  (in one trade) [zl]
Max. net loss              -680        -1535        -1200
  (in one trade) [zl]
Average net                 302.47       766.30       651.61
  profit (per trade) [zl]
Average net                -212.87      -268.71      -285.29
  loss (per trade) [zl]
Ave. net profit/              1.4209       2.8518       2.2840
  Ave. net loss
Number of profitable         93           42           87
  transactions
Number of loss              129           80          121
  transactions
% profitable                 41.89%       34.43%       41.83%
  transactions
Gross profit [zl]          7570       14,348       28,410
Net profit [zl]             760       10,688       22,170
Commision paid [zl]        6810         3660         6240

                           Moving       Without
                           Average      a System

Commission [zl]                15           15
Number of trades               90          416
Number of buy signals          45          208
Number of sell signals         45          208
Max. net profit              4880         1820
  (in one trade) [zl]
Max. net loss               -3140        -2290
  (in one trade) [zl]
Average net                   957.14       356.42
  profit (per trade) [zl]
Average net                  -412.73      -273.27
  loss (per trade) [zl]
Ave. net profit/                2.3191       1.3043
  Ave. net loss
Number of profitable           35          190
  transactions
Number of loss                 55          226
  transactions
% profitable                   38.89%       45.67%
  transactions
Gross profit [zl]          13,500       17,790
Net profit [zl]            10,800         5960
Commision paid [zl]          2700       11,830

TABLE 4 Reports on the Trading Systems Tested Without Any Forecasts

                        Channel    Bollinger
                        Breakout   Bands      Momentum

Commission [zl]            15         15          15
Number of trades          238        112         191
Number of buy signals     118         58          96
Number of sell signals    120         54          95
Max. net
Max. net profit          1270       4110        3510
  (in one trade) [zl]
Max. net loss           -1130      -1380       -1750
  (in one trade) [zl]
Number of loss            142         77         121
  transactions
% of profitable            40.34%     31.25%      36.65%
  transactions
Gross profit [zl]        1740       4830      15,960
Net profit [zl]         -5400       1470      10,230
Commission paid [zl]     7140       3360        5730

                        Moving     Without
                        Average    a System

Commission [zl]            15           15
Number of trades           70          516
Number of buy signals      35          258
Number of sell signals     35          258
Max. net
Max. net profit          4440         1810
  (in one trade) [zl]
Max. net loss           -3390        -1920
  (in one trade) [zl]
Number of loss             46          339
  transactions
% of profitable            34.29%       34.30%
  transactions
Gross profit [zl]        7620      -14,800
Net profit [zl]          5520      -30,280
Commission paid [zl]     2100       15,480

TABLE 5 Comparison of Total Net Profits [zl] for All the Strategies

                      Channel   Bollinger            Moving   Without
                      Breakout  Bands      Momentum  Average  a System

Perfect forecasts--   88,950    63,780     74,290    36,540   137,180
  actual future data
ANN forecasts            760    10,688     22,170    10,800      5960
Historical data--      -5400      1470     10,230      5520   -30,280
  without forecasts
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Comment:Construction and evaluation of trading systems: Warsaw index futures.
Author:Witkowska, Dorota; Marcinkiewicz, Edyta
Publication:International Advances in Economic Research
Geographic Code:4EXPO
Date:Feb 1, 2005
Words:4686
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