Available Online at http://www.recentscientific.com International Journal of CODEN: IJRSFP (USA) Recent Scientific

International Journal of Recent Scientific Research Research Vol. 11, Issue, 01(B), pp. 36805-36812, January, 2020 ISSN: 0976-3031 DOI: 10.24327/IJRSR Research Article

AVERAGE TRUE RANGE: HIGH AS A SUCCESS FACTOR FOR TRADING

Dr.Ulrich R. Deinwallner

PhD Management and Finance, Walden University, USA

DOI: http://dx.doi.org/10.24327/ijrsr.2020.1101.4999

ARTICLE INFO ABSTRACT

Article History: High volatility can be an indication to achieve excess returns with an investment strategy, according to the Efficient Market Hypothesis (EMH), since the underlying markets might exhibit less Received 6th October, 2019 th efficiency. In connection to this it was relevant to understand, if trading with low or high Average Received in revised form 15 True Range (ATR) values can improve the return results of a (MA) trading November, 2019 strategy. The purpose of this quantitative research was to compare different MA strategies in Accepted 12th December, 2019 th different U.S. markets and to find an optimal ATR setting, to determine if excess returns can Published online 28 January, 2020 be achieved. The research question (RQ) was: what ATR setting can improve the return results of a MA trading strategy for U.S stock market indices? The following computations occurred: (a) simple Key Words: moving average; (b) ATR; and (c) t-Tests. I find in this study that a ATR(5) with high values Average True Range, Volatility Trading, (threshold = 25.92) is the most profitable setting to improve a Simple MA (SMA) trading strategy Moving Average, Efficient Market for the S&P500 index with (i.e., rSMA (20)_High_ATR (5)_S&P500 = 21.84 % per month), hypothesis, Portfolio Management. although the Russel 2000 provided the most trading opportunities, with (n = 967-1,099 trading days) during the time period 1999-2018. An ATR with high settings can improve the profitability when applying a SMA trading strategy for an investment. For investors who are interested in considering

a volatility measure for their trading, this study can introduce empirical results.

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INTRODUCTION the current price candle falls (Yamanaka, 2002). The ATR is an average value and can also be seen as a moving average The Average True Range (ATR) was developed by Welles (MA), since generally 14 True Range values are selected and Wilder, J. in 1970 and measures the price volatility of for divided by 14 time units (Hays, 2019; Yamanaka, 2002). In example a security (Hays, 2019, Yamanaka, 2002). A praxis the ATR is commonly used as an indicator, to determine connection was seen between the price range of a high and a a price for a stop-loss order or to determine market turnaround low price of a security for a given time period and the points through a sudden increase of the ATR (see Vervoort, underlying volatility (Yamanaka, 2002). The ATR was named 2009). Essentially, the computation of the ATR represents an True Range, since the price that occurred during the previous average value of the True Range and is commonly used in time units closing was included, instead of only considering the praxis as an indicator. stock current price range (Yamanaka, 2002). The advantage was that after-hour announcements that impacted the market Volatility Trading price at its opening, were also accounted in the next day’s price Zhang, Shu, and Brenner (2010) stated that volatility was range (Yamanaka, 2002). This means that through such after- recognized as relevant for investing by academics and hour announcements, the price range would increase and this practitioners after the crash 1987. In the late 1980’s empirical higher occurring volatility is included in the true range and theoretic studies were published to the issue of volatility. (Yamanaka, 2002). The ATR can therefore be seen as a The reason was that hedging potential occurred for volatility measure of price volatility. changes, which was the basis of the discussion. Brenner and

For the computation of the true range, three scenarios are Galai (1989) introduced to hedging potential and volatility possible: (a) the current high and current low of the current changes a first reference volatility index in their study to cope price candle is considered if the previous price candle is with stochastic volatility of derivatives. In 1993 the Chicago smaller than the current price candle (price candle = high, low, Board Option Exchange (CBOE) introduced a volatility index opening, closing price); (b) current high and last close of the (VIX) that was based on the price movements of index options price candles are considered if the current price candle rises; (c) of the S&P 100 (Corrado & Miller, 2005). This means that the current low and last close of the price candles are considered if

*Corresponding author: Dr.Ulrich R. Deinwallner PhD Management and Finance, Walden University, USA Dr.Ulrich R. Deinwallner., Average True Range: High Volatility as A Success Factor for Trading

VIX is a volatility measure of the U.S. stock markets to allow information (Fama, 1970). This means that efficient are responding to volatility change. traded at a fair price level (Fama, 1970). When looking at efficient markets, these stock markets often appear to be In regard of what drives the return volatility, the subsequent irrational and hard to predict for investors. Investors can only factors can be mentioned. Gulen and Mayhew (2000) reported achieve higher profits from efficient stock markets, by that volatility is lower during time periods when U.S. stock accepting for their investments a higher risk. Therefore, index futures face high open interest. Gulen and Mayhew saw efficient markets seem to be perfectly allocated markets, where a connection between high volatility during periods when all information are reflected in the stock prices. future was high. Clark (1973), Gallo and Pacini (2000), Andersen (1996) confirmed the connection between Further distinctions were made to the EMH in the scholarly volatility and volume, while Clark postulated the “mixture of literature by other scholars. Farma (1970) investigated a model distribution hypothesis” that posits a correlation between return to EMH and found three market efficiency forms of: (a) weak; volatility and volume that is influenced by a latent event of (b) semi; and (c) strong. Oprean, Tănăsescu, and Brătian information flow. Andersen argued that volume and latent (2014) differentiated if stock markets follow an evolutionary events impact directly the return volatility and past return pattern or simply follow a random walk. Jiang (2017) shocks become insignificant. This means that volatility tends presented findings to the issue of time horizons to the to be low if there is a large demand for U.S. securities; discussion for the EMH, where for long time horizons stock however, the volume plays a significant role. If the volume of markets appeared to be efficient and for short time horizons the buying and selling securities increases [decreases] through stock markets appeared to be inefficient. Akbas et al. (2016) latent events, then the volatility is assumed to increase as well. confirmed that stock market efficiency can vary over time, and saw reasons in the availability of arbitrage capital. Where, Moving Average sufficient capital flow was seen as relevant to equalize Much has been written, in regard of gaining excess returns with arbitrage anomalies in the investigated stock markets (Akbas et the application of a commonly used method al., 2016). In conclusion, evidence was found in the of defining MA rules in the stock markets. In the scholarly researcher’s studies for a random walk price movement and for literature, publications occurred to the issue of MA trading the efficiency of stock markets. However, the efficiency varied strategies by for example Allen and Taylor (1990) who in the stock markets, depending on the markets time periods presented findings for technical and fundamental analyses; that are considered; available arbitrage capital; and depending Brock, Lakonishok, and LeBaron (1992) who reported in on sufficient capital flow in the stock markets. stochastic properties of stock returns; Antoniou, Ergul, Holmes, The current situation for the study is that several studies have and Priestley (1997), Blume, Easley, and Hara (1994) who been published to the issue of volatility, which was impacted presented findings to volume and technical trading; Gencay by volume increase and latent events, and using an ATR as a (1998a) investigated optimization and Gencay (1998b) and volatility measure to either price stop-loss orders of an Kwon and Kish (2002) analyzed the predictability of technical investment or to predict market turnaround points (see trading rules; Ready (2002) presented findings to the Yamanaka, 2002; Vervoort, 2009). profitability of technical trading rules, and Wong, Manzur, and Chew (2003) contributed with similar research to Singapore The general problem of the study was that if, according to the stock markets. The application of MA trading rules was in a EMH, the investors have a higher change of beating the market similar way applied in the studies, where either a price during inefficient market phases, then high volatility could be crossover or a double crossover MA signal was considered. In an indication to improve the profitability of a trading strategy, Ren and Ren (2018) and Deinwallner (2019) findings, an for which little has been investigated yet in regard of the ATR. alternative approach of applying MA rules was introduced. An The specific problem of the study was to understand the impact ANDOR strategy was more profitable to trade in the currency of using an ATR for investment strategies in U.S. security markets, where for an entry signal the price needed to cross markets. Meaning, it has not yet been investigated sufficiently, over both a short and a long MA, while for an exit signal the if an investment strategy can be improved by considering a price needed to cross over either a short or a long MA high or a low ATR. The investigation of the ATR and (Deinwallner, 2019). For the short and long MA’s a SMA(5, investment strategies can be interesting for retail investors and 150) was recommend, which was obtained through an analysis portfolio managers, because the investors can overcome market in the currency markets (Deinwallner, 2019). Essentially, two efficiency issues by considering volatility in their investment main topics were discussed in the scholarly literature by decisions. The study can close a in the scholarly literature researchers: (a) the discussion of an edge for technical analysis for the issue of the ATR application. I provide a thorough and (b) the validated of the profitability of technical analysis in analysis and a conclusion at the end of this study. various security markets. The purpose of this quantitative, comparative study is to test Efficient Market Hypothesis (EMH) MA investment strategies while controlling for an ATR, where low and high ATR values (independent variable) can improve According to the EMH, it seems impossible for a stock market the analyzed security returns (dependent variable) for U.S. investor to beat an efficient stock market. Fama (1970) securities. mentioned that capital market imperfections or abnormal returns are immediately exploited by investors. Jiang (2017) Research Question questioned in his study how well can asset prices adjust to This study is guided by one research question (R), R1: What stock market information? Generally, one can find that ATR setting can improve the return results of a MA trading efficient stock prices incorporate all relevant market strategy for U.S stock market indices? 36806 | P a g e International Journal of Recent Scientific Research Vol. 11, Issue, 01(B), pp. 36805-36812, January, 2020

To answer the research question, five Hypotheses (H) are SMA (20) with a high optimal ATR setting in the DJIA stock relevant to investigate market outperforms the other strategies and tested indices.

H01: if a SMA(50) simple price cross over trading strategy is Summary applied to the S&P500 stock index returns while controlling for In this study, I investigate if considering a volatility measure a ATR(14), then the average monthly returns of a SMA(50) for an investment strategy can improve the profitability for an trading strategy with high ATR(14) values is not the most SMA trading strategy. In specific, I compare the returns of a profitable combination to trade in this comparison. SMA price crossover trading strategy, when selecting high H11: if a SMA(50) simple price cross over trading strategy is ATR values. In the empirical findings section, I first determine applied to the S&P500 stock index returns while controlling for if considering high ATR(14) values for a SMA trading strategy a ATR(14), then the average monthly returns of a SMA(50) has an impact on the profitability. Second, I investigate if trading strategy with high ATR(14) values is the most shorter time horizons exhibit lower market efficiency and profitable combination to trade in this comparison. therefore higher return results. Third, I test for the optimal ATR(n) to maximize the profitability of a SMA trading H 2: if short and long time horizons are compared for a 0 strategy. Fourth, a comparison is conducted between different SMA(20) trading strategy while controlling for the ATR, then volatility measures, the ATR(n), STD(n), and VIX(n) to assess short time horizons with a high ATR(14) settings are not the if the ATR(n) is superior compared to the other volatility most profitable to trade in this comparison. measures applied to an SMA trading strategy. Fifth, different H12: if short and long time horizons are compared for a SMA(n) strategies are tested in different stock markets, to find SMA(20) trading strategy while controlling for the ATR, then the most profitable strategies and market settings and short time horizon with a high ATR(14) settings are the most combinations. I find that an ATR(10) with high values is the profitable to trade in this comparison. most profitable setting to improve the SMA(20) strategy in the S&P500 market with (r = 21.84 % per H 3: if different ATR threshold values of (6.08, 16, 25.92 SMA(20)_High_ATR(5)_S&P500 0 month), although the Russel 2000 provided the most trading ATR) are used to determine high phases and different ATR(n) opportunities with (n = 967-1,099 trading days) during the time number of average day values of (n = 5, 10, 14, 20, 25 days) period 1999-2018. The findings can improve the profitability are compared for a SMA(50) simple price cross-over trading when applying a SMA strategy for investors. For investors who strategy of S&P500 index returns, then the ATR(14) Threshold(25.92) are interested in considering a volatility measure for their S&P500 index returns are not the most profitable ATR setting trading, this study can present empirical results. to trade in this comparison. Data and Methodology H13: if different ATR threshold values of (6.08, 16, 25.92 ATR) are used to determine high phases and different ATR(n) In this study, I consider stock market indices data of the four number of average day values of (n = 5, 10, 14, 20, 25 days) most prominent U.S stock indices: (a) Dow Jones Industrial are compared for a SMA(50) simple price cross-over trading Average (DJIA), (b) National Association of Securities Dealers strategy of S&P500 index returns, then the ATR(14)Threshold(25.92) Automated Quotations (NASDAQ) Composite, (c) Russel S&P500 index returns are the most profitable ATR setting to 2000, (d) Standard and Poor’s (S&P) 500 for the time period of trade in this comparison. January, 1999 until December 31, 2018, which represents 20 years of daily return data. The selected time period is relevant H 4: if the returns of a high optimal ATR(n) applied to a 0 because it covers a digressive time period during the financial SMA(50) simple price cross-over strategy are compared to the crisis around 2008 and a progressive time period in the years returns of applying the VIX(n) or the after. The data is obtained from the source Yahoo!Finance (see (STD)(n) to the same SMA strategy as for the ATR, then the Ren & Ren, Deinwallner, 2019). For the computation of the optimal ATR is not more profitable for a SMA(50) trading ATR, I require opening, closing, high, and low prices which strategy in comparison. need to be considered for the data collection. I will consider H14: if the returns of a high optimal ATR(n) applied to a dividend adjusted end of day closing prices to assess the SMA(50) simple price cross-over strategy are compared to the profitability of each investment strategy in my analysis. returns of applying the VIX(n) or the STD(n) to the same SMA Since I am only testing strategies for U.S. stock indices, strategy as for the ATR, then the optimal ATR is more deviations could occur when projecting the findings to stocks, profitable for a SMA(50) trading strategy in comparison. securities and other different markets. Especially, small cap H05: if different number of days (20, 50, 100 days) for a SMA stocks could exhibit generally a higher volatility for which the trading strategy are compared with the application of an study’s results could deviate. Further, other countries could optimal ATR setting for high ATR values in different U.S. also exhibit a different volatility and efficiency in their security stock markets (S&P500, DJIA, Nasdaq, Russel 2000), then the market movements. Therefore, I limit the study’s findings to SMA(20) with a high optimal ATR setting in the DJIA stock the U.S. indices data. market does not outperform the other strategies and tested I am testing the ATR as a measure of volatility and I am indices. comparing the results in this study to U.S. volatility measures H15: if different number of days (20, 50, 100 days) for a SMA to answer the RQ. This means that other volatility measures, trading strategy are compared with the application of an than the ones tested in this study or applied in other markets or optimal ATR setting for high ATR values in different U.S. applied to other securities, could also exhibit relevant results. stock markets (S&P500, DJIA, Nasdaq, Russel 2000), then the Further, I make the assumption in this study that from the 36807 | P a g e Dr.Ulrich R. Deinwallner., Average True Range: High Volatility as A Success Factor for Trading application of simple MA trading strategies, generalizations Where, X is the return,  is the STD, and n is the number of can be made for other investment strategies regarding the cases. application of the ATR. These assumptions might need to be Research Design further investigated and corroborated by other researchers. Essentially, the findings in this paper are relevant for other In regard of the research design, the task is to answer the researches to better understand the application of the ATR as research question R1, by testing SMA trading strategies and an indicator, to improve the performance of an SMA investigating the performance under the consideration of investment strategy. different ATR settings in comparison. To answer the RQ, it will be relevant to test five hypotheses as subsequently METHODOLOGY described.

In regard of the methodology, I will consider the computation First, I will test the assumption that trading can be more of the ATR. The Equation of the ATR for the computations in profitable for an investment strategy under high volatility the subsequent parts is: market phases, with the test of H1. The assumption for H1 is TR  MAX [(H  L), Abs(H  C ), Abs(L  C )] that in volatile market conditions, the market efficiency can P P vary and traders can face larger market movements, which [1] could lead to more profitable investment conditions (see Fama, n  1  1970). I will compare the results for S&P500 stock index data ATR   TRi [2] for a SMA (50) simple price cross-over strategy, while  n  i1 controlling for an ATR (14). I expect the SMA (50) trading strategy to outperform during market phase with high ATR(14) Where, C is the closing price (P), H is the highest price, L is values. the lowest price, TRi is a particular true range i = 1, …, k; k = the number of true range values; and n = the time period Second, I will test the effect of three different time horizons employed (see Hays, 2019). This means that three events can (day, week, and month) for S&P500 stock index data, for a occur, when computing the ATR: SMA (20) simple price cross-over strategy, while controlling for an ATR(14) with the test of H2. I will test the assumption that during longer time horizons the markets are more efficient compared to shorter time horizons (see Jiang, 2017). I expect short time horizons to outperform during market phases with high ATR (14) values.

Third, I will test with H3 for the effect of different ATR variations considering different low and high ATR vales and considering different ATR (n) number of days. I plan to determine through this test an optimal ATR setting with the highest profit expectation for a SMA trading strategy. Essentially, I will test an SMA (50) trading strategy while Figure 1 True range of the greatest distance between the security returns. Where (a) is today’s high and today’s low; (b) is yesterday’s close and today’s high; and (c) is varying the ATR settings for the S&P 500 index data.

yesterday’s close and today’s low (see Hays, 2019) Fourth, I will test with H4 how different volatility measures In this study, I will measure the effect which an ATR has on perform in comparison to the ATR. I plan to compare the the profitability of a MA trading strategy. For the computation return results of the VIX and of the average standard deviation of the MA, I will compute a simple moving average (SMA) (STD (n)) with n equal to the number of days of the optimal with the equation: ATR (n). Through the test of H4, the results of a SMA trading strategy with high ATR values will be set into relation P  P  ...  P M M 1 M (n1) [3] compared to other volatility measures. SMA  n Fifth, I will test the impact of the optimal ATR (n) high values in comparison to different SMA(n) trading strategies and Where, PM = the price of the asset M; and n = the number of different U.S. stock markets, by testing H5. I assume that days considered for the closing prices (Nedeltcheva, 2015). because stocks with the highest earning expectations, which are From the computation of the SMA, I can test a simple price represented in the DJIA, and because small number of days for cross over strategy of the SMA with 20, 50, and 100 time units. the SMA (n) perform better than large number of days SMA I obtain an entry signal if the price crosses the SMA from (n) (see Deinwallner, 2019). This means that the returns of a below to above, and I will obtain a sell signal vice versa. SMA (20) in the DJIA stock market will outperform the other tested SMA trading strategies and stock markets, when The significance is computed with a t-test through the applying an optimal ATR(n) with high values. following equation: In regard of the threats to external validity, the findings for the X  X t  1 2 [4] U.S. stock market indices might not be able to be generalized 1 1 for U.S. stocks and for other stock markets with a different   market efficiency and volatility structure. The threats of n1 n2 internal validity could be that the selected time period might not be sufficient to make implications for future market 36808 | P a g e International Journal of Recent Scientific Research Vol. 11, Issue, 01(B), pp. 36805-36812, January, 2020 developments and the results for applying the optimal ATR (n) extended the computations for weekly and monthly data. I and variations. The data used could be wrong in some cases or computed the SMA (20) instead of an SMA(50) for the analysis could deviate from other data sources. Further, the measure of of H2. A smaller number of days (weeks or months) for a the ATR (n) might not be able to fully capture the present SMA were relevant to choose, because for weekly and monthly volatility of an underlying security. At this point it is to stress data a smaller number of weeks or months for the MA are that because retail investors tend to lose capital in the financial required to obtain valid trading results. Where, Zoicaş-Ienciu markets, this study is for educational reasons, does not (2014) recommended a MA range of [10, 100] as a relevant represent investment advice, and investors should conduct their time period for a long-term investment dimension of a MA, own research before investing their capital (see Abbey & while Glabadanidis (2015) recommended 24 months for Doukas, 2012). SMA’s, to obtain valid trading results. In my analysis, I tested four dispositions for the SMA trading strategy with and without Empirical Findings the application of the ATR. The average deviation was for Analysis and Discussion of H1 week data (ATR(14)week = 37 index points) and was for month data (ATR(14) = 74 index points). I computed all return For the analysis of H1, I computed a SMA(50), and I month data to monthly returns for an optimal comparison. determined the Buy and Sell signals/phases according to the data of the S&P500 index returns (i.e., if the S&P500 price From Table 2, I can find that trading the SMA (20) strategy, crossed the SMA(50) from below to above, then a “Buy” signal with “Buy” signals, was most profitable for the (SMA occurred). Then, I determined in what cases of the True (20)Buy_High_ATR(14)_Day = 9.84% per month). In comparison, the Range: “a, b, or c” (as described in Figure 1 in the method daily data exhibited the highest monthly returns, which section) occurred for the S&P500 index data (i.e., for case “a” confirms that shorter time horizon are more profitable to trade = lower highs and higher lows of the previous day compared to than long time horizons. Also, the deviation of the STD was the next day). From this, I could compute the true range for higher for short time horizons (STDSMA(20)_Buy_High_ATR(14)_Day = each day of data. Then, I computed the 14 day average value 29.38% per month) compared to longer time horizons for the True Range, to obtain the ATR (14). From the ATR (STDSMA(20)_Buy_High_ATR(14)_Month = 3.51% per month). This data, I computed the average deviation of the ATR (14) = 16 finding could be an indication which can support Jiang (2017) average points. This means that the S&P500 index data findings that long time horizons in stock markets appeared to deviated on average by 16 index points per day during 1999- be more efficient compared to short time horizons, where the 2018 for an ATR of 14 days. stock markets appeared to be semi-efficient according to the EMH. I could reject the Null Hypothesis 2 at a 1% alpha level In Table 1, I conducted a comparison for six possible occurring according to the results for SMA(20) return events (with “Sell” signals excluded). I could find that the Buy_High_ATR(14)_Day compared to SMA(20) return with a t-test average daily returns cumulated to monthly returns, with 20.9 Buy_High_ATR(14)_week with t(219) = 9.2014, p < .001. And, for the results of for days assumed for one month and with the equation (((1+r daily SMA(20) return compared to ^20.9)-1) = r ), exhibited the highest value, if the SMA(50) Buy_High_ATR(14)_Day monthly SMA(20) return with a t-test with t(92) = “Buy” phases and high ATR(14) > 16 average values were Buy_High_ATR(14)_month 22.7847, p < .001. considered with (rSMA(50)BUY_High ATR(14) > 16 = 7,15% per month). I can confirm that a higher volatility in a stock market can lead Table 2 Comparison of short and long time horizons for a to abnormal excess returns, when following an SMA(50) SMA (20) trading strategy, while controlling for the ATR(14) investment strategy in the U.S. stock markets. The findings of S&P500 day, week, month data during 1999-2018 can corroborate the results of Fama (1970) in regard of the Day Week Month

EMH that with higher volatility the markets efficiency might Strategy r STD n r STD n r STD N None SMA(20); vary. I could reject the Null Hypothesis 1 at a 1% alpha level 0.21 28.31 5,031 0.39 10.78 1,091 0.37 4.22 251 None ATR(14) according to the results of a t-test with t(3162) = 4.3699, p < SMA(20)Buy; None 5.58 20.10 3,037 2.39 7.34 735 1.04 3.17 191 .001, where the return (rSMA(50)Buy;HighATR(14) > 16 = 7.15%) was ATR(14) SMA(20)Buy; High 9.84 29.38 902 3.53 9.12 220 1.13 3.51 93 significantly higher compared to the return (rSMA(50)Buy;NoneATR(14) ATR(14) > M SMA(20)Buy; Low = 3.46%). 3.83 14.74 2,135 1.91 6.39 515 0.96 2.84 98 ATR(14) < M Table 1 Comparison of ATR(14) and SMA(50), displaying average Note. In the table, a comparison was conducted for a SMA(20) trading strategy, while monthly returns of the S&P500 index during 1999-2018 controlling for a ATR(14) and considering different time horizons. Where r is the monthly return in percent (%). M is the mean of the ATR and equaled for the S&500 Strategy r STD n index to ATR(14) =16 points. All return data were cumulated to monthly data and were None SMA(50); None ATR(14) 0.29 32.9 5,031 computed with 20.9 days and 4.3 weeks for a monthly data comparison. The return data represents the results for the S&P500 stock index. SMA(50)Buy; None ATR(14) 3.46 21.1 3,163 SMA(50)Buy; High ATR(14) > 16 7.05 31.2 778 SMA(50)Buy; Low ATR(14) < 16 2.13 17.1 2,385 Analysis and Discussion of H3 None SMA(50); High ATR(14) -0.01 51.9 1,878 None SMA(50); Low ATR(14) 0.63 19.5 3,153 For the analysis of H3, I considered the data of the S&P500 Note. In this table, high, low, and none ATR(14) settings were compared for a index, I computed the SMA (50), the ATR (n = 5, 10, 14, 20, SMA(50) trading strategy regarding “Buy” and none signals. Where r is the average monthly return in percent, STD is the standard deviation, and n is the 25 days), and determined the SMA(50) “Buy” phases and the number of trades that occurred. The average deviation of the S&P500 index ATR(n) high phases for three ATR thresholds of (ATR was ATR(14) =16 average deviation points.

threshold = 6.08, 16, 25.92 average ATR deviation) that

Analysis and Discussion of H2 deviated by 0.62% from the ATR mean of 16 points. This For the analysis of H2, I conducted the same computations as I means for example, if the ATR threshold value was equal to considered for H1 with S&P500 stock index data, and I only 6.08, then an ATR value of 7 would provide a “high” ATR 36809 | P a g e Dr.Ulrich R. Deinwallner., Average True Range: High Volatility as A Success Factor for Trading signal, where the threshold = 16 represents the average ATR of did not outperformed the second largest return value the S&P500 index. significantly of the STD(5) according to a t-test with t(186) =0.7266, p < .232 because of a large STD of (STD = From Table 3, I could find that high ATR threshold values led VIX(5) 68.21). to abnormal excess SMA (50) trading strategy returns with (rATR(5)_Threshold(25.92) = 22.81% monthly return). When Table 4 Comparison of the optimal ATR to the VIX and the STD, for computing the r/STD, which represented a coefficient (related S&P500 index data, for a SMA (50) trading strategy during 1999- 2018, displaying average monthly returns. to the Sharpe ratio) to determine the risk and return relation, the ATR (5) Threshold(25.92) was superior in its results compared to the Volatility Measures r STD r/STD n other strategies according to Table 3. However, the ATR (5) ATR(5)25.92 22.84 49.44 0.46 84 VIX(5)32.30 14.85 68.21 0.22 71 Threshold(25.92) led to n = 84 trading days, while the ATR(14) STD(5)1.59 11.47 52.61 0.22 187 Threshold(16) led to n = 778 trading days during the given time Note. In the table, a comparison was conducted between the ATR(n), period. A low Threshold (6.08) exhibited only high ATR (25) VIX(n), and STD(n). r is the monthly average returns in percent (%). r/STD phases and led to n = circa 3,163 trading days. This means that represented a coefficient for the return and risk relation. n is the number of an ATR (14) with an average threshold was most practicable to trading days. For the return results, only SMA(50) “Buy” phases were selected and only ATR, VIX, or STD high phases above the threshold were trade for an SMA (50) trading strategy, when considering the selected . risk and return relation and the number of trading days. I could not reject the Null Hypothesis 3 at a 1% alpha level since the Analysis and Discussion of H5

ATR(14)Threshold(25.92) did not exhibit the highest S&P500 For the analysis of H5, I investigated the performance of an returns in a comparison conducted in Table 3. However, I optimal, high ATR(5) for different SMA strategies and different could not find significant differences at a 1% alpha level U.S. stock markets. I computed the SMA(20, 50, and 100) for through a t-test with t(72) = 1.1431, p < .262, between the the S&P500 index, DJIA index, NASDAQ Composite index, monthly return results of a ATR (5)Threshold(25.92) versus Russel 2000 index in the analysis of H5. Then, I determined ATR(14)Threshold(25.92). the ATR(5) values and the thresholds (which were 62% higher Table 3 Comparison of different ATR (n) settings for S&P500 index than the ATR(5) mean; listed in Table 5) and I retrieved the data, for a SMA (50) strategy during 1999-2018, displaying average returns, STD, and n values for “Buy” phases and high ATR(5) monthly returns. phases of the SMA trading strategies and for all investigated

ATR 5 r/STD 10 r/STD 14 r/STD 20 r/STD 25 r/STD indices.

25.92 22.84 0.46 18.41 0.42 15.07 0.35 13.78 0.30 13.85 0.33 16 7.16 0.21 7.00 0.21 7.05 0.23 6.18 0.20 6.22 0.21 Through a comparison of the results in Table 5, I could find 6.08 3.47 0.16 3.41 0.16 3.41 0.16 3.41 0.16 3.41 0.16 that the SMA(20) was the most profitable strategy to trade with Note. In this table, a comparison was conducted between different ATR(n) (rSMA(20) = 18.66% per month) for the S&P500 index with values and three different ATR threshold values. The first column of the (rSMA(20)_S&P500 = 22.84 % per month) and the best risk and table represents ATR threshold values, where the threshold 16 represented return relation of (r/STD = 0.47 coefficient). This means that the average ATR deviation of the S&P500 index. The first row of the table represented n = number of day settings for the computation of the ATR(n). smaller SMA number of day can produce higher returns than The returns are average monthly returns in percent (%) and only represent larger SMA number of day strategies. Also, the S&P500 could the selection of SMA(50) “Buy” phases and the selection of high phases of outperform the other investigated markets significantly. the ATR (i.e., only return data above the ATR threshold were considered). However, the most trading opportunities occurred for the Analysis and Discussion of H4 Russel 2000 in the comparison conducted in Table 5, with (n = 967 until 1,099 trading days). I could not reject the Null For the analysis of H4, I decided to proceed with the ATR (5) Hypothesis 5 at a 1% alpha level, since the returns of the as optimal number of day ATR setting and the average optimal, high ATR(5) for a SMA(20) trading strategy in the threshold value for high phases of 25.92. The ATR (5) setting DJIA stock market did not outperformed significantly the other was selected to analyze if this setting is superior compared to tested strategies and U.S. stock markets returns. the application of the STD (5) and the VIX (5) for a SMA (50) price crossover trading strategy. I computed the STD (5), by Table 5 Comparison of the optimal ATR to the DJIA, NASDAQ considering the STD of two days, I multiplied the value by 100, Composite, Russel 2000, S&P500 for different SMA(20, 50, and 100) then, I selected 5 of these STD values and divided them by 5. trading strategies during 1999-2018, displaying average monthly returns. The VIX (5) of the S&P500 index was similarly computed and S&P Russel was an average of 5 days (see parenthesis value). The mean of DJIA NASDAQ the STD (5) was (M = 0.99 STD) and the mean of the VIX(5) 500 2000 r r/STD R r/STD r r/STD r r/STD was (M = 19.94 VIX), however, I multiplied the mean by 62% SMA(20) 22.84 0.46 21.44 0.42 18.39 0.26 12.95 0.30 and added this value to the mean, to obtain the threshold SMA(50) 18.41 0.42 16.1 0.40 6.56 0.10 7.33 0.18 similarly performed for the optimal ATR(5) threshold. I SMA(100) 10.14 0.26 7.14 0.18 5.73 0.09 4.26 0.11 determined the “Buy” phases for the SMA (50) and selected the n 80-159 109-156 207-220 967-1,099 Average r r/STD high phases for the ATR (5), STD (5), and VIX (5). Finally, I SMA(20) 18.66 0.36 annualized the daily return data to monthly returns with 20.9 SMA(50) 12.10 0.27 days per month, see Table 4. SMA(100) 6.82 0.16

Note. In this table, a comparison was conducted between a SMA(20, 50, and 100) From Table 4, I can find that the ATR (5) with the threshold trading strategy, for four U.S. stock markets, while controlling for high optimal ATR. 25.92 seemed superior in comparison to the other two volatility All r results are in (%) per month. The optimal ATR was an ATR(5), with an threshold measures with (r = 22.84% per month). I could not reject (T) value was 62% higher than the ATR(5) mean of DJIAATR(5)_T = 224.09; ATR(5) NASDQATR(5)_T = 69.15; RusselATR(5)_T = 16.43; S&P500ATR(5)_T = 25.92 the Null Hypothesis 4 at a 1% alpha level, since the ATR(5) 36810 | P a g e International Journal of Recent Scientific Research Vol. 11, Issue, 01(B), pp. 36805-36812, January, 2020

CONCLUSION Akbas, F., Armstrong, W. J., Sorescu, S., & Subrahmanyam, A. (2016). Capital market efficiency and arbitrage In this study, five hypotheses were investigated to answer the efficacy. Journal of Financial and Quantitative Analysis, RQ: what ATR setting can improve the return results of a MA 51(02), 387-413. doi:10.1017/S0022109016000223 trading strategy for U.S stock market indices? Allen, H. & Taylor, M. P. (1990). Charts, noise and

Through H1, I could find that if high ATR values are selected fundamentals in the foreign exchange market. Economic and a SMA(50) trading strategy is applied to the S&P 500 Journal, 100(400), 49–59. doi:10.2307/2234183 index return data, then high ATR values for a SMA(50) trading Andersen, T. G. (1996). Return volatility and trading volume: strategy can outperformed none or low ATR values An information flow interpretation of stochastic volatility. The Journal of Finance, 51(1), 169-204. significantly, with (rSMA(50)_High_ATR(14) = 7.15% per month). Through H2, I could find that if different time horizons are doi:10.1111/j.1540-6261.1996.tb05206.x applied for a SMA(20) trading strategy with a high ATR(14) Antoniou, A., Ergul, N., Holmes, P., & Priestley, R. (1997). setting, then shorter time horizons are more profitable Technical analysis, trading volume and market compared to longer time horizons with (i.e., efficiency: Evidence from an emerging market. Applied Financial Economics,7(4), 361–365.doi: rSMA(20)_High_ATR(14)_Daily = 9.84 % per Month versus 10.1080/096031097333475 rSMA(20)_High_ATR(14)_Monthly = 1.13% per month). Through H3, I could find that an optimal ATR, for the investigated SMA Blume, L., Easley, D., & O’hara, M. (1994). Market statistics trading strategies in the S&P500 market, was the ATR(5) with and technical analysis: The role of volume. Journal of Finance, 49(1), 153–181. doi:10.1111/j.1540- (rSMA(50)_High_ATR(5) = 22.81% per month). Through H4, I could find that an optimal ATR(5) with high values seemed more 6261.1994.tb04424.x profitable to combine with a SMA(50), compared to the Brenner, M.,& Galai, D. (1989). New financial instruments application of high values for a STD(5) or the VIX(5) (but not for hedging changes in volatility. Financial Analyst significantly more profitable than the VIX(5) caused through a Journal, 45(4), 61-65. doi:10.2469/faj.v45.n4.61 large volatility) . Through H5, I could find that a SMA with a Brock, W., Lakonishok, J., & LeBaron, B. (1992). Simple smaller number of day setting, like the SMA(20), is more technical trading rules and the stochastic properties of profitable to trade than a larger number of day SMA, like the stock returns. Journal of Finance, 47(5), 1731–1764. SMA(100) (However, there is a threshold downwards for a doi:10.1111/j.1540-6261.1992.tb04681.x smaller number of day setting for a SMA trading strategy, also Clark, P. K. (1973). A subordinated stochastic process model see Deinwallner, 2019). For this study, the optimal market to with finite variance for speculative prices. invest in comparison to the DJIA, NASDAQ Composite, Econometrica: journal of the Econometric Society, 135- Russel 2000 was the S&P500, with return results of 155. doi:10.2307/1913889 Corrado, C. J., &Miller, Jr, T. W.(2005). The forecast quality (rSMA(20)_High_ATR(5) = 22.84 % per month and r/STD of CBOE implied volatility indexes. Journal of Futures SMA(20)_High_ATR(5) = 0.46, which lead to n = 159 trading days during 1999-2018). In regard of the trading opportunities, the Markets 25(4), 339-373. doi:10.1002/fut.20148 Russel 2000 exhibited (n = 967-1,099 trading days), which Deinwallner, U. R. (2019). Moving average: How do the represented 52 -55 trading days per year. These findings can ANDOR and ANDAND strategy perform in currency answer the RQ in this study. markets. International Research Journal of Applied Finance, 10(11), 299-314. Retrieved from This study investigates and introduces a volatility driven https://nebula.wsimg.com/32633e21ef617f878da1f6e9d1 investment strategy. According to Zhang, Shu, and Brenner’s 75e98a?AccessKeyId=A83663472B839ECDD54B&dis (2010) results, I also find that volatility can be most relevant position=0&alloworigin=1 and profitable for investors to consider. The assumptions for a Fama, E. F. (1970). Efficient capital markets: A review of volatility driven investment trading strategy were influenced by theory and empirical work. The Journal Finance, 25(2), the EMH. This means that capital market imperfections or 383-417. doi:10.1111/j.1540-6261.1970.tb00518.x abnormal returns can be exploited more easily by investors Gallo, G. M., & Pacini, B. (2000). The effects of trading during high volatility market phases, which can be explained activity on market volatility. The European Journal of through semi- efficient market conditions during high volatile Finance, 6(2), 163- markets (see Fama, 1970). In regard of positive social change, 175.doi:10.1080/13518470050020824 the investors can improve the application of trading an MA Gencay, R. (1998a). Optimization of technical trading strategy, by following only “Buy” signals during high ATR strategies and profitability in security markets. values meaning high volatility market phases. The application Economics Letters,59(2), 249–254. doi:10.1016/S0165- of high ATR market phases can improve the MA trading 1765(98)00051-2 strategy performance for a portfolio manager. Further research Gencay, R. (1998b). The predictability of security returns to the issue of considering an ATR could be conducted for with simple technical trading rules. Journal of Empirical different markets, securities, and different volatility measures. Finance,5(4), 347–59. doi:10.1016/S0927-

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How to cite this article:

Dr.Ulrich R. Deinwallner. 2020, Average True Range: High Volatility as A Success Factor for Trading. Int J Recent Sci Res. 11(01), pp. 36805-36812. DOI: http://dx.doi.org/10.24327/ijrsr.2020.1101.4999

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