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Trading the Equity Curves


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Procedia Economics and Finance 32 ( 2015 ) 50 – 55

2212-5671 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of Asociatia Grupul Roman de Cercetari in Finante Corporatiste doi: 10.1016/S2212-5671(15)01363-5


Emerging Markets Qu

Trading th

Pavel Kisela


*, Tom

aTechnical University of Košice, Fa bMatej Bel University, Faculty of E


Nowadays, financial markets are no longer only for “big Each of them uses their own strategy and therefore there which gives us very important inside of how good or bad gained from the one specific trading strategy and find ou factor, sharp ratio etc.) by applying some most used performance by trading the equity curve itself? The used and the rules are applied on various currency pairs. In the managed equity curves of this trading strategy.

© 2015 Authors. Published by Elsevier B.V. This is an open acce (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Emerging M

Keywords:Equity curve analysis, trading strategies, divergences,

1. Introduction

Each participant of the financial markets uses so ideas. Many of these trading systems are based on

* Corresponding author. Tel.: +421-55-602-3263;

E-mail address: pavel.kisela@tuke.sk

eries in Finance and Business

he equity curves

máš Virdzek


, Viliam Vajda


aculty of Ecomonics, Košice 040 01, Slovakia Economics, Banskj Bystrica 974 01, Slovakia

g players”. Also small investors and traders have strong presence. are countless strategies. Each trading strategy has an equity curve, d this strategy is. Aim of this paper is to look at the equity curve ut, if it is possible to improve it (improve the final return, recovery technical indicators on it. In other words, will we gain better strategy is built on the well known idea of trading the divergences e results there is comparison of raw equity curves (unmanaged) and

ess article under the CC BY-NC-ND license

Markets Queries in Finance and Business local organization FOREX

ome investment strategy or trading system based on various n mechanical rules. These systems experience good periods

© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).


with profits and periods with more losses. And therefore each trader wants to identify profitable periods and holds on them as long as possible; on the other hand he wants to find the points, where the strategy may stop working. Functioning of the trading system can best be assessed just by looking at thes hape of the curve Equity (EC) or by looking at the statistical metrics of these trading systems. Mark Douglas (1990) is saying that if traders were to chart their equity, these charts would look very much like the typical bar charts and charts like these also can have the same predictive value as in the markets. That’s why traders strive to find the way to predict the possible changes in their systems.

The area of the risk management, which tries to solve this problem, is called “Equity curve analysis”. (Vladimir Stepnov, 2002)The most common way of analyzing is to use moving average (MA). Octavio Riano(2012) in his work presents this approach. He analyses one EC with using various MAs and presents results with improved final return and flattened curve. In his work is used just one EC and from this cannot be clear, if this approach work, or does not. Therefore in this paper extended research on this topic will be presented.

Every economic sector is in presents times interconnected with ICT(Gavurová, B., Šoltés, B. &Balloni, A. J ,2014), including Financial sector. In current development of trading system the developers still use TA indicators (Billingsley and Chance, 1996; Taylor, Mark P.; a and Allen, Helen, 1992) and these trading systems are being traded not only by traders, but also by computers. As Cheol-Ho Park and Scott H. Irwin, 2007 mention in their paper, there is wide discrepancy about profitability of these TA indicators. Especially between traders and academics. The usage of the indicators is to apply them to the price of the financial instrument. Other approach presented in this paper is to apply these indicators to the values of the EC, likewise mentioned above with MAs.

From all above one hypothesis is considered: TA indicators can improve EC and statistical metrics of the trading systems.

2. Methodology

2.1. Trading strategy rules

As was said earlier, the input data for equity curve analyses are the data, which represent progress of gains and losses of specific trading strategy in time. The strategy can be built on for example the stock picking based on the valuation of the companies (Užík, M. – Šoltés, V., 2009).For the purpose of this research was used trading strategy based on divergences between the price and the indicator. This trading idea is used among a lot of traders in many possible ways.(Alexander Elder, 1993)The rules of this strategy were very simple, so the amounts of input data were sufficient to test the hypothesis (TomášVirdzek, 2014). Rules were:

• BUY market, if the close price of the previous candle/bar is lower than lowest price of the X period and at the same time the value of the indicator is higher than the lowest value of this indicator of the X period • SELL, if the price is higher than the Y period exponential moving average

• SHORT, if the close price of the previous candle/bar is higher than highest price of the X period and at the same time the value of the indicator is lower than the highest value of this indicator of the X period • COVER SHORT, if the price is lower than the Y period exponential moving average

Timeframe for this trading strategy was also chosen in order to get the high amount of input data. Therefore the 30 min timeframe on the period from cca year 2002 till 2014 was chosen (Exact period was variable with each currency pair. The exact period was not important, because the results between currency pairs were not compared against each other). The strategy was applied on 9 most traded currency pairs and their various combinations, where 95% of all speculative trading in FX is accounted. Furthermore one futures market representing stock market for comparison was chosen - e-miny S&P500 (ES). Calculations were made in


trading and analytic platform, Trade Station. Initial balance was set on 100 000 USD (Setting were default, results were not depended on it). On each currency pair was traded 1 lot and on ES was traded 1 contract.

2.2. Equity curve analysis

As everything mentioned above was applied, the input data of equity curves (EC) were gained. Each EC was represented of more than 800 samples. On each EC were then applied some most used technical indicators.

The indicators were picked up from bigger groups – trend indicators (MA5 and MA20) and momentum oscillators (RSI and ROC). They were chosen in order to give sufficient amount of signals. Many indicators are not suitable for this analysis, because of their calculation. Or their calculation is very similar, so the results would be duplicated.

Simple moving averages (MA) – classical usage of this indicator is based on the idea, that price of a financial instrument is some time moving in one or the other direction. Problem is when the price is moving sideways. MAs do not predict price direction, but rather define the current direction with a lag. If the price is above the MA, traders tend to buy the financial instrument and hold the trend and vice versa. This is possible to apply on EC in order to find periods, where the trading strategy is in a trend mode, with following rules (EC MA5, EC MA20):

• Strategy is ON, if the EC is above the MA (trades are taken in accordance to the trading rules) • Strategy is OFF, if the EC is below the MA (trades are not taken)

Or (EC MA5 L/S, EC MA20 L/S)

• Strategy is ON, if the EC is above the MA (trades are taken in accordance to the trading rules)

• Strategy is in SHORT mode, if the EC is below the MA (trades are taken in opposite direction to the trading rules)

The rules above were used in the research on all EC. MA was chosen with period 5 and 20. Periods was chosen randomly. Short moving averages are quick to change, but can change indicate change of the trend too soon, before it really happens. In contrast, a long moving average contains lots of past data that slows it down and can hold the trend longer. Therefore both types were used.

The results of the MA are described below together with results of the other indicators.

Relative strength index (RSI, 10 period) and Rate of change (ROC, 12 period) – these indicators measure momentum, speed and change of the price. Periods 10 and 12 are commonly used by traders, therefore were chosen for calculation. As the other indicators from this group, each has its own calculation and usage. However, most of them have central line. This central line was important in the research (RSI – 50, ROC – 0). Although, oscillators are mainly used because of their overbought and oversold zones for identifying changes in the trend, their central line (CL) provides trading signals as well. Especially trend continuing signals. Classical Used rules are following (EC RSI, EC ROC):

• Strategy is ON, if the values of indicator are above the CL (trades are taken in accordance to the trading rules)

• Strategy is OFF, if the values of indicator are above the CL (trades are not taken) Or (EC RSI L/S, EC ROC L/S)

• Strategy is ON, if the values of indicator are above the CL (trades are taken in accordance to the trading rules)

• Strategy is in SHORT mode, if the values of indicator are above the CL (trades are taken in opposite direction to the trading rules)


3. Results

From all of the possible rules applied on the EC, 8 various strategies was created and each strategy then generated EC. Results are possible to be seen in the Table 1. In the row “Raw EC” is original unmanaged EC of the trading strategy and other rows represent all EC generated from applied TA indicators and their rules. Table 1 shows one of the most important metric which investor/trader look at when he wants to evaluate the profitability of the trading system, “Return on investment” (ROI).

Table 1. Return on investment in percentage


EC MA5 L/S EC MA20 L/S EC RSI EC RSI L/S EC ROC EC ROC L/S USDCHF -9.33% -21.36% -18.38% -34.43% -29.61% -17.15% -26.05% -9.81% -11.25% AUDNZD 41.74% 27.79% 27.42% 13.38% 13.92% 35.20% 28.73% 4.73% -32.40% AUDUSD -12.49% -17.14% -17.22% -21.40% -21.00% -21.68% -30.29% -11.52% -9.78% EURGBP 14.41% 1.53% 3.52% -10.90% -7.34% 8.67% 2.57% -3.90% -22.00% EURUSD -9.27% -20.83% -22.48% -32.86% -34.36% -31.29% -52.84% -4.19% 1.71% GBPUSD -11.93% -6.82% -9.30% -3.68% -6.80% -13.15% -16.98% -10.38% -11.01% USDJPY -20.35% -21.44% -20.98% -24.18% -24.58% -7.96% 1.15% -3.14% 11.01% EURJPY -38.39% -33.28% -34.28% -27.03% -27.69% -38.35% -37.47% -19.80% -0.35% USDCAD 7.24% -8.54% -6.56% -25.20% -23.02% -0.53% -10.10% -2.89% -14.74% ES 79.76% 49.56% 48.65% 20.55% 19.41% 47.15% 15.29% 19.21% -40.63%

# Better than Raw EC 2 2 2 2 2 2 5 5

As can be seen, better results using TA indicators were reached only in few cases (22 from 80). And furthermore, it was only in cases, where the final return of raw EC was negative. In situation, where return of raw EC was positive, the TA indicators weren’t able to enhance the ROI in any case. Looking up at the indicators separately, the best results can be seen using ROC indicator, in both variation of strategy (5 from 10).

However, ROI is not the only important metric. Trader needs to know, how much risk should expect. For this purpose is used, for example, metric “Drawdown” (Magdon-Ismail, M.; Atiya, A; Pratap, A; Abu-Mostafam, Y., 2003), largest relative (expressed in percentage points) drop of the account balance, showed in the Table 2.

Table 2 Relative drawdown


EC MA5 L/S EC MA20 L/S EC RSI EC RSI L/S EC ROC EC ROC L/S USDCHF 22.00% 26.73% 25.35% 38.77% 34.85% 23.55% 32.47% 15.30% 22.35% AUDNZD 2.87% 3.57% 3.57% 7.50% 7.50% 2.62% 4.52% 1.57% 32.56% AUDUSD 29.20% 23.58% 23.58% 33.91% 33.91% 28.52% 34.52% 21.64% 26.12% EURGBP 15.55% 12.28% 12.18% 19.37% 17.21% 16.85% 25.94% 11.96% 32.61% EURUSD 23.66% 25.46% 25.46% 35.33% 35.03% 39.14% 59.38% 10.52% 17.84% GBPUSD 50.67% 31.53% 31.53% 22.71% 22.71% 30.86% 25.87% 13.65% 35.60% USDJPY 25.46% 24.46% 24.25% 27.60% 27.60% 11.76% 11.37% 5.63% 9.83% EURJPY 45.93% 39.49% 39.49% 50.53% 50.53% 41.60% 52.37% 24.21% 32.22% USDCAD 17.51% 16.91% 14.10% 29.33% 26.38% 9.98% 16.35% 7.48% 21.35% ES 5.75% 7.20% 7.20% 11.88% 11.88% 5.08% 13.00% 3.84% 41.34%

# Better than Raw EC 6 6 1 1 7 3 10 5

This metric achieved better results (39 from 80), but still it’s even less than 50%. If ROC indicator is taken separately again, it reached better results in more cases. EC ROC had better results in all 10 cases.

To compare trading systems with the highest possible profit with the lowest possible risk, traders use, for example, metric “Recovery factor”. It’s calculated as net profit divided by the maximum drawdown and


measures the ability of a trading system to recover from losses. In this metric all indicators failed. Just 13 times from 80 they beat the raw EC.

Another metrics, which measure both profit and the risk are “Sharp ratio” and “Sortino ratio”. Sharp ratio measures ratio between the received return and the experienced risk. Sortino ratio measures ratio between received return and the experienced downside risk. However these metrics could not be used to compare the raw EC against the TA indicators because of the negative return in some cases. In positive returns, when values of the ratio are higher (higher return – higher value of the ratio, lower volatility – higher value of the ratio), then the trading system is considered to be better. In negative returns, the higher value does not have to mean that trading system is better. It could be caused by higher return (lower loss), but also it could be caused by higher risk (because in calculation the value is in denominator). And the higher risk is not positive metric. And because the metrics would be biased, they could not be used.

From the point of view of the individual TA indicators, the worst results achieved moving averages. All variations of the rules were better than raw EC only in less than 30% of cases. The best results were gotten by rate of change indicator, almost 50%. The Table 3 shows the average success rate in the 8 important metrics, which were taken into consideration (ROI, RRR, Percent profitable, Profit factor, Relative DD, Recovery factor, Expected payoff and Standard deviation).

Table 3Summary of TA indicators, average success rate

EC MA5 EC MA20 EC MA5 L/S EC MA20 L/S EC RSI EC RSI L/S EC ROC EC ROC L/S Summary 23.75% 20.00% 28.75% 25.00% 35.00% 30.00% 36.25% 46.25% 4. Conclusion

The research showed no positive effect on raw equity curve with using TA indicators. In some cases the results were better, some metrics reached better values than values of raw EC, but it was mainly on EC, whose final return was negative. That is not satisfying at least from one reason. Traders tend to choose from trading systems, which in back test had positive final return. Profitable traders do not use losing trading system, so the idea, that using some TA indicators will lower their losses is unacceptable. They want to improve the EC of their profitable trading system and in none of the cases of this research was this achieved.

Therefore, with the selected settings and rules of the TA indicators, trading the equity curve presented in this paper is not more profitable than classical usage of trading system without managing its equity curve. Is possible, that some other; optimized settings of the used TA indicators could gain higher profit and better results. But with optimization is connected one big problem. With optimized rules even a small change in the market condition can result in “deactivation” of the trading system.


Paper was supported by the scientific grant agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic under the contract no. VEGA 1/0795/13.



Billingsley, R.S. and Chance, D.M., Benefits and limitations of diversification among commodity trading advisors (1996).Journal of Portfolio Management 23: 65–80.

Cheol-Ho Park; Scott H. Irwin, What do we know about the profitability of technical analysis (2007) Journal of Economic Surveys, Vol. 21, No 4, pp. 786-826

Douglas, M., The disciplined trader: developing winning attitudes (1990) New York Institute of Finance, New York, p 153 – 154. ISBN 0-13-215757-8

Elder, A. Trading for a Living: Psychology, Trading Tactics, Money Management. New York: J. Wiley, 1993. ISBN 978-0-471-59224-2 Gavurová, B., Šoltés, B. &Balloni, A. J. (2014).Ekonomickývýznamvyužívaniainformaþno-komunikaþnýchtechnológií v systémezdravotníctva. In: Ekonomic kýþasopis. 62 (1), 83-104. ISSN 0013-3035


Magdon-Ismail, M.; Atiya, A; Pratap, A; Abu-Mostafam, Y., The maximum drawdown of the Brownian motion (2003) Computational Intelligence for Financial Engineering, 2003. Proceedings. 2003 IEEE International Conference on , vol., no., pp.243,247, 20-23 March 2003

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