THE ACCURACY OF SIMPLE TRADING RULES IN STOCK MARKETS

Transcription

1 THE ACCURACY OF SIMPLE TRADING RULES IN STOCK MARKETS Audrius Dzikevicius 1, Svetlaa Sarada 2, Aleksadra Kravciook 3 1 Vilius Gedimias Techical Uiversity, Lithuaia, audrius@piigusrautas.lt 2 Vilius Gedimias Techical Uiversity, Lithuaia, svetlaa.sarada@gmail.com 3 Vilius Gedimias Techical Uiversity, Lithuaia, alexadra.kravciook@gmail.com Abstract Pervious researches o the S&P 500 Idex usig the most widely used method of techical aalysis Movig Averages are more or less appellative. Most of research results were obtaied testig MA behaviour i weak-form efficiecy markets, tryig to fid relatioship betwee historical ad future prices, to survey ormal ad abormal returs. This paper compares Stadard ad Poor s 500 (S&P 500) Idex (US) to the 6 aother idexes: NASDAQ Idex (US), Nikkei 225 Idex (Japa), CAC 40 Idex (Frace), FTSE 100 Idex (UK), SCEC Idex (Shaghai), RTS Idex (Russia) with the respect that the Techical Aalysis methods ca be less effective tha it was thought util owadays. For daily observatios of S&P 500 ad other tested Idexes, test results imply that Movig Average method is iadequate to predict the directio of prices movemet. The method provides slightly differet forecastig results tha the real prices are. The results let make prerequisite for differet legths Movig Averages sustaiig differet systematic errors methods ad the results accuracy ca be characterized by deviatio. Keywords: Techical Aalysis, Movig Average, Stock Price, MA Legth, Forecast Accuracy, Systematic Error. Itroductio The fiace crisis of 2009 was the result of people belief that the owership value rises ad ever decreases. Traders ad ivestors use differet methods tryig to predict future stock prices ad expect high returs. Techical aalysis always posed a iterestig questio for the Movig Average method efficiecy. Techical aalysts argue that prices gradually adjust to ew iformatio. The movig average method (MA) is oe of the most used methods of techical aalysis. This method ivolves a compariso of the market prices or idex with the log MA. Most of MA research results were obtaied testig MA behaviour i weak-form efficiecy markets, tryig to fid relatioship betwee historical ad future prices, to survey ormal ad abormal returs. So the mai poit of this paper is to determie whether MA method is proper to predict stock prices i differet stock markets, examie methods for tred forecast accuracy evaluatio ad assess relatioship betwee MA legth ad error types (Mea Square Error, Mea Forecast Error ad Mea Absolute Percetage Error). The first stage research has to accept or refuse such hypothesis as whether Movig Average method is appropriate to forecast stock prices ad to fid out the forecastig accuracy; which MA (short or log) provide more correct forecast results; whether MA behaviour is the same i differet stock markets. I the secod phase of varyig degrees of accuracy (with a margi of error from 1 to 15 %) it ca be see how differet legths of Movig Average guess the price. The purpose of third phase is to evaluate errors. All boosted hypothesis ca be refused while testig stock markets. The orgaizatio of this paper is as follows. Sectio I provides a brief review of the relevat iformatio. Sectio II describes the research data. Sectio III presets methodology ad the Movig Average method. Sectio IV discusses the empirical results of this study. The last sectio cotais a brief summary ad coclusios. Literature review The movig average (MA) method is oe of the most widely used methods of techical aalysis. It icludes differet versios ad levels of sophisticatio. The MA method is easy to use ad apply i ivestmet decisio-makig or empirical tests (BeZio et al., 2003.) Edwards ad Magee (1992), Myers (1989), Prig (1993) describe techical aalysis as a techique which uses the patters of the price history of a fiacial istrumet i order to provide idicatios o the future behaviour of prices. Techical aalysis cosists of differet methods with a commo set of basic priciples ad is the mai alterative to fudametal aalysis which strives to assess the true value of fiacial istrumets. Sigificat retur from techical aalysis, eve i cojuctio with valuatio methods, treds to argue agaist the efficiet market hypothesis. Cosequetly, there is a close lik betwee validity of techical aalysis ad the iefficiecy of the market (Cagialp & Baleovic, 2003). Techical aalysis history starts with the belief that the historical price iformatio does ot reflect ew prices (Elliger, 1955, republished i 1971; Lo, Mamaysky ad Wag, 2000). I cotrast BeZio et al. 910

2 (2003) observed that prices gradually adjust to ew iformatio. Cooter (1961) tested 45 NYSE stocks usig weekly data for estimatig movig average ad foud that the variace of the tradig rules approximately 30% less tha that of the buy-ad-hold (B&H) strategy. Lo ad MacKaily (1988, 1999) demostrated for a weekly U.S. Stock idexes that historical prices may be used to forecast future returs to some degree. Seasoal effects i iteratioal developed equity markets were discovered by Cadsby ad Rater (1992) while Agrawal ad Tadom (1994) ad Agrawal ad Rivoli (1989) idetify seasoality i emergig markets. Brock et al. (1992) reviewed the literature ad cocluded that most of simple tradig rules have foud o statistical validity. They test the hypothesis of the movig average tradig rule that cosists of a buy sigal whe the price moves above a particular movig average ad a sell sigal whe the price crosses below the average. Usig the data set of the Dow Joes average for several decades, they foud almost o et gai for usig either the buy or the sell sigal. Scietifically testig all three day reversal patters discussed i Morris (1992), o a 265,000 day data set of daily ope, close, high, low for each of the S&P 500 stocks for a five year period, they foud sigificat predictive power. However, a recet study by Blume et al. (1994) explores techical aalysis as a compoet of agets learig process. They focused oly o the iformatio role of volume ad coclude that sequeces of volume ad price ca be iformative ad argue that traders who use iformatio cotaied i the market statistics attai a competitive advatage. Hudso, Dempsey ad Keasey (1996) employ 60 years of daily returs from the Fiacial Times 30 Idex o the Lodo Iteratioal Stock Exchage. They coclude that log-term B&H strategies exclude the possibility of abormal returs. Ito (1999) used the same tradig techical system as Brock et al. (1992) testig 6 atioal equity markets. The obtaied results suggested that the profit fairly compesates the risk of tradig rules. Taylor (2000) reviewed 6 idexes usig daily data. The techical tradig system he has selected was short ad log movig averages. He realized that differeces of mea returs betwee buy ad sell positios were maily positive. Coutts & Cheug (2000) coclude that all tested tradig rules geerate buy or sell sigals which mea returs are sigificatly higher or lower tha ucoditioal mea returs. Skouras (2001) aalyzed Dow Joes idustrial Average stock market ad foud that time-varyig estimated rules outperformed various fixed movig average rules employed by Brock et al. (1992) as well as the B&H strategy. Whe the market is bullish or bearish, techical tradig rules perform better or worse tha tradig strategies based o some time-series models. Authors who have tested tradig rules o developed markets outside the US geerally also fid that the profits geerated do ot offset trasactio costs (Marshall et al. 2009). Cagialp, G., Baleovich, D. (2003) state that to techical aalysts the failures are ot surprisig. Data descriptio The techical sample tradig rules ca be calculated at differet data frequecies (Table 1). Table 1. Idex time period data ad summary statistics for stock market idexes Period Statistics From To Total (years) N St.dev. Kurt. Skew. S&P NASDAQ Nikkei CAC FTSE SCEC RTS I this research we use daily data ad our sample icludes stock market close prices of 7 idexes: US - S&P 500 ad NASDAQ; Europe - FTSE 100, CAC 40, RTS; Asia - Nikkei 225 ad Shaghai Composite. The idexes were tested i atioal currecy. Iformatio o local daily prices was foud o the stock market s respective web sites. We source data for differet periods, because we have tested all idexes sice they had bee appeared util the 22 d of May, 2009 because these idicate the first daily data which is available. Japa market is most risky ad this propositio is based o stadard deviatio while US markets S&P 500 ad NASDAQ are the least risky respectively ad The daily data of 911

3 idicated periods provide a sufficiet umber of daily observatios to allow for the formatio review ad ivestigatio of the techical sample tradig rules. Methodology The Techical Aalysis is characterized by a large umber of rules ad idicators committed to idetify ad explai the regularity of historical prices dyamics. Such type of the relatioship ca be used to forecast future prices treds. The time for trasactios ad best prices ca be also set usig forecastig methods i Techical Aalysis. This paper is focused o the oe of Techical Aalysis idicators - simple movig average (SMA) rule ad the possibility to use this method for prices ad their treds forecastig was tested. The methodology disassociates from particular buy-ad-sell strategies ad specific rules applicatios. The research was coducted i three mais stages. The first stage was to determie whether it is appropriate to use Movig Average method for the market price tred forecast. The secod stage of this research was to appoit how differet legth Movig Averages ca predict the future prices with a margi of error of 1 to 15%. The third stage was to estimate bias. A1. For the hypotheses validatio or refutatio the first stage of the research was resolved ito 3 levels. I order to determie whether it is appropriate to use the MA idicator for the prices tred forecast S&P 500 (US Stock market) Idex was tested. Movig averages idicators were calculated usig S&P 500 Idex close prices: where Y t t= 1 Yt t MA = =1 (1) is the sum of the prices for the time period. As well it was valuated whether the real prices treds match the forecasts of prices treds ad the percetage of predictio was justified. A2. I order to determie whether some Movig Average legths usage for the prices tred predictio is superior to other, MA idicator was tested 499 times testig differet MA legth: = 2, 3, 4, 5,..., 500. A3. I order to appoit whether i differet stock markets research results differ A1 ad A2 researches were made additioally i 6 stock markets usig 6 idexes daily close prices data (see Table 3). B. The secod stage was to determie what the average value of prices forecast reliability is estimatig a differet precisio level. S&P 500 Idex was tested for this purpose calculatig the separate legths of Movig Average (2-500) ad the percetage of all forecasted series level with the bias of 1, 2, 5, 10 ad 15%. C. The third stage of the research helped to determie the bias of Movig Average method usage. Mea Square Error (MSE). Forasmuch ay error is beig raised with the square, so this way highlights the sigificat error values. This feature is quite sigificat because forecastig methods with approximatios of bias are frequetly more suitable tha the method which gives ot oly egligible errors but sigificat. ( Ft Yt ) MSE = (2) Mea Forecast Error (MFE). Very ofte it is very importat to estimate whether the forecast method has a systematic error id est the preset forecast value is always major (or mior) tha time series value. I this case the mea forecast error is beig used. If the systematic bias does ot exist the MFE value will be equal zero. If the forecast value is sigally egative the forecast method overestimates tred series. If the systematic bias is sigally positive the forecast method geerates major values the time series. MFE = ( F t Yt ) (3) The Mea Absolute Percetage Error (MAPE) is useful whe assessig the forecast error a importat factor is the estimated value. MAPE estimates the size of bias comparig with time series values. This fact is very importat whe the times series value is quite large. Ft Yt MAPE = 1 (4) Yt This stage of the research assessed the relatioship amog MA legths ad metioed bias types. All 499 Movig averages were tested usig 7 Idexes daily data idetifyig the relatioship

4 Empirical results A. All three hypotheses boosted i the study begiig were refused ad the followig fidigs were made. A1. The usage of Simple Movig Average for the stock market prices tred forecastig is ot reasoable ad valid. The tred forecast accuracy level fluctuates from % i NASDAQ market to 52.53% i SSE market. No oe of the successful tred forecasted values averages exceeds % level. The predictio accuracy is ot sufficiet for the successful forecast of stock prices tred trasformatio (Table 2). Table 2. Tred Forecast Accuracy (%) CAC40 NASDAQ RTS NIKKEI 225 FTSE SCEC S&P 500 Mi value Max value Average value A2. This paper researched whether some Movig Average legths are superior to other assessig them usig forecast accuracy estimatio method. The study claims that superior Movig Average legths do ot exist because the stock prices tred forecast accuracy level of all Movig average legths is approximately the same. However it was oticed durig the research that MA legth has some ifluece o the tred forecast accuracy: the loger Movig Average provides the lower tred forecast accuracy level. But this tedecy may be valid oly i some separate markets. A3. These study fidigs were cofirmed i all tested markets so sigificat results margis were ot foud. B. The usage of the Movig Average method for stock market close prices forecast delivered slightly differet results. For example, the Fig. 1 shows S&P 500 Idex forecastig results usig Movig Average method. It represets the relatioship betwee the successful prices forecast umber with the error of 0, 1, 2, 5, 10 ad15 % ad Movig Average legth. Figure 1. The S&P 500 Idex forecasts The example illustrates that the usage of Movig Average method for price forecastig i absolute terms provides better results tha the usage of this method just for the stock prices tred forecast. The shorter Movig Average ca forecast more accurate price value. So the ivestors or researchers ca select desirable bias level. It should be oted that i separate markets Movig Average method provides differet results (Fig. 2). 913

5 Figure 2. The average percetage of predictio accuracy of the tred depedece of the legth of MA i differet markets I assessig, the average predictio accuracy values ca be assumed that sigificat predictio accuracy of the MA method is oly available with 10 or more percet of acceptable error level, ad oly i predictig the S&P 500 ad the Nikkei Idex ad SCEC Idex chages. I other markets, forecastig results are much worse, eve with a 15% margi of error. C. The evaluatio of the relatioship betwee Movig Average legth, MSE, MFE ad MAPE bias was made. C1. For specific time series separate Movig Average legths differ by forecast accuracy level. This demostrates MSE values. I particular markets this idicator provides lower or higher bias level. The average value of MSE i Nikkei 225 stock market is oly (Table 3). It meas that the differece betwee real ad forecasted prices is ot sigificat ad the lowest amog all tested Idexes. Cotrarily MSE of SCEC Idex forecasted values are characterized by large swigs from till Although the market is ot very risky (st. deviatio is ) comparig with other markets. The forecasted values are uvalued ad overvalued worst i this market. Wherewith the MA loger, ipso facto Mea Square Error value is higher. This tedecy domiates i all markets. So it meas that the loger Movig Average geerates more iaccurate value F t. Movig Average legth has ifluece o MSE values from 96,33% (CAC 40) till 99,90% (NASDAQ). Table 3. Statistical Error Estimates ad Successful Forecast Ratio CAC40 NASDAQ RTS NIKKEI 225 FTSE SCEC S&P 500 MSE % % % % % % % MFE % % % % % % % MAPE % % % % % % % Mea Square Error (MSE) evaluatio Mi Max Mea Forecast Error (MFE) evaluatio Mi Max Mea Absolute Percetage Error (MAPE) evaluatio Mi Max Successful Forecast Ratio Ratio 0,47 % 0,82 % 2,89 % 0,29 % 0,28 % 17,91 % 17,89 % 914

6 C2. Tryig to determie whether the selected forecast method Sample Movig Average has a systematic bias the Mea Forecastig Error was evaluated. Iasmuch the MSE value of Nikkei 225 Idex forecast is ad is earby 0, ad the the systematic bias does ot exist. There are some egative average values of MSE i tested markets: CAC ( ), FTSE ( ) which idicate that i Frech ad UK stock markets the forecasted stock prices values are beig overvalued. It comes to a coclusio that i all markets except Nikkei 225 high systematic errors exist tryig to predict the stock prices usig Movig average method. This method is liked to provide overvalued forecasted prices. The loger Movig average iflueces MFE lower value. This regularity is valid for all markets except Nikkei 225.Movig method usage i Japaese stock market (Nikkei 225) provides the lowest values of MFE. Movig Average legth is a cosequece of % MFE values. F t forecast value is higher tha the real price Y t is o this day i Japaese markets ad coversely i all aother markets the forecasted value F t is lower tha the real price Y t. C3. Sice the time series values are quite high, the MAPE was assessed. This method highlights a part of systematic error comparig with the whole time series. The sigificat segmet 35.90% mealy exists i RTS stock market usig Movig Average method. The MAPE values i other markets swig amog 6.34% ad 16.78%. The loger average of MA iflueces the higher the average absolute relative error MAPE. This tred is cofirmed i all markets, oly the degree of precisio varies from 92.26% to 99.83%. C4. Tryig to determie the percetage ratio betwee successful forecast umber ad the sample it was proved that Sample Movig Average method stads oly predictig values of some particular markets ad this ratio is quite low. The successful forecast values umber with the error was the highest i Shaghai Composite stock market ad S&P 500 stock market. The higher successful forecast umber is the highest i S&P 500 market (17.89 %) ad SCEC market (17.91 %). I the other markets the ratio sigs betwee 0.29 % (Nikkei 225 Idex) ad 2.89 % (RTS Idex). I CAC 40, NASDAQ, Nikkei 225 ad FTSE 100 stock markets this ratio does ot reach eve 1 %. So the study results imply that Movig Average method ca geerate sigificat forecast value errors ad deviatios from real prices ad is ot successful i price movemet tred geeratio. Discussio ad coclusio This paper examies the Movig Average method usage i differet stock market ad its forecast accuracy. Previous research o S&P 500 did ot tested tred forecast accuracy. The Movig Average method is a type of Techical Aalysis. For market idexes it ivolves the compariso of short (1 day or idex by itself) ad log movig averages. The data i this research cosist of daily closig prices of 7 idexes: Stadard ad Poor s 500 (S&P 500) Idex (US) to the 6 aother idexes: NASDAQ Idex (US), Nikkei 225 Idex (Japa), CAC 40 Idex (Frace), FTSE 100 Idex (UK), SCEC Idex (Shaghai), RTS Idex (Russia). Trasactio costs ad ivestmet strategies are ot ivolved ito this study. Startig with tred forecast accuracy the fidigs of this paper suggest that MA method is ot useful tryig to predict the price movemet tred. There are o exceptioal MA legths which ca provide more accurate results more tha 49 % mealy. For specific time series separate Movig Average legths differ by forecast accuracy level. The forecast values are uvalued ad overvalued worst i SCEC market Wherewith the MA loger, ipso facto Mea Square Error value is higher. This tedecy domiates i all markets. The loger Movig average iflueces MFE lower value. This regularity is valid for all markets except Nikkei 225.Movig method usage i Japaese stock market (Nikkei 225) provides the lowest values of MFE. The loger average of MA iflueces the higher the average absolute relative error MAPE. The successful forecast values umber with the error was the highest i Shaghai Composite stock market ad S&P 500 stock market. The higher successful forecast umber is the highest i S&P 500 market (17.89 %) ad SCEC market (17.91 %). Accomplished research shows that MA method ca ot predict the price movemet treds. The method provides slightly differet forecastig results tha the real prices are. The results let make prerequisite for differet legths Movig averages sustaiig differet systematic errors methods ad the results accuracy ca be characterized by deviatio. So the study results imply that Movig Average method ca geerate sigificat forecast value errors ad deviatios from real prices ad is ot successful i price movemet tred geeratio. 915

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