Despite ongoing debate in the

JIALI FANG is a lecturer in the School of Economics and Finance at Massey University in Auckland, New Zealand. j-fang@outlook.com BEN JACOBSEN is a professor at TIAS Business School in the Netherlands. b.jacobsen@tias.edu YAFENG QIN is a senior lecturer in the School of Economics and Finance at Massey University in Auckland, New Zealand. y.qin@massey.ac.nz Popularity versus Profitability: Evidence from Bollinger Bands JIALI FANG, BEN JACOBSEN, AND YAFENG QIN Despite ongoing debate in the academic literature on its profitability, technical analysis remains popular. Some of the most widely used techniques involve Bollinger Bands, which were introduced by John Bollinger in 1983 on the Financial News Network (which eventually became CNBC), where he was chief market analyst. 1 Since then, Bollinger Bands have gradually gained popularity among investors. In 2001, Bollinger published his book, Bollinger on Bollinger Bands, on this indicator. In four years time, the English version of the book garnered seven editions, and the book has to date been translated into 12 languages. Recent survey results suggest that Bollinger Bands have become a technical analyst favorite (see, for instance, Ciana [2011] and Abbey and Doukas [2012]). Did this increasing popularity affect the potential profits of Bollinger Bands based trading strategies? Bollinger Bands are an interesting natural experiment to verify whether and how the popularity of trading strategies affects their profitability. First, unlike other popular technical analysis strategies, this trading strategy was not known before 1983. Second, Bollinger Bands are easy to construct and implement because they use only information derived from historical prices. Third, we have a reasonable indication of their increasing popularity over time and large enough data samples to measure profits in different time periods. Fourth, Bollinger Bands originated in the U.S. market, and Bollinger on Bollinger Bands was first published there. So if profits are arbitraged away, we would expect the impact to show up in the United States. Fifth, this might explain why the profitability of Bollinger Bands in other studies that rely on different sample periods and countries is mixed. 2 And last but not least, given their popularity among investors, it is interesting to see how the profitability of Bollinger Band strategies have developed over time. Our results indicate that potentially profitable trading strategies self-destruct with increasing popularity. Bollinger Bands generate significant outperformance in all 14 major international market indexes in our study when measured over the full sample period. Before the introduction of Bollinger bands in 1983, the profitability was strong with high average returns in all countries. However, in the next subsample from 1983 to 2001, when Bollinger s book was published, the profitability of Bollinger Bands decreased by around 50% on average in all markets. In the United States, there is no longer outperformance. After the book s publication, the profitability of Bollinger Bands further shrank with an average decline of 156% for all countries. Although it is often assumed that trading will make the profits of anomalies disappear, few studies have tried to see whether and when this happens. Our results suggest that 152 POPULARITY VERSUS PROFITABILITY: EVIDENCE FROM BOLLINGER BANDS SUMMER 2017

E XHIBIT 1 Popularity of the Bollinger Bands from 1993 2013 investor trading can indeed destroy such profitability over time. While our evidence suggests that trading is the most likely underlying cause of the disappearing profitability of Bollinger Bands, we cannot, of course, fully eliminate the possibility of data snooping or any other statistical biases. DATA AND METHODOLOGY Bollinger Bands generally include three parameters with the following default settings (Bollinger [2001], p. 23): a middle band formed from 20-day moving averages of the underlying prices, an upper band that is two standard deviations above the middle band, and a lower band that is two standard deviations below the middle band. A buy (sell) signal is generated when the underlying price closes outside the upper (lower) band. 3 As noted in the introduction, Bollinger Bands have become increasingly popular. Exhibit 1, which reports the number of news articles on Bollinger Bands in Factiva, provides a good indication. Our study includes 14 major stock market indexes from 13 countries: Australia, France, Germany, Hong Kong, Italy, Japan, Korea, New Zealand, Singapore, Spain, Switzerland, the United Kingdom, and the United States. For each country, we use the best known market index; and for the United States, we use both the Dow Jones Industrial Average (DJIA) and the S&P 500 Index. To avoid data snooping, we include all countries that have at least 10 years of daily stock market data available before 1983 and we use the longest available daily data series from Global Financial Data. The DJIA has the longest sample, starting in 1885, with Spain having the shortest sample, starting in 1971. Following Brock, Lakonishok, and LeBaron [1992], we run the following OLS regression for each country to study the predictive ability of Bollinger Bands for the full sample and three subsamples: before 1983, from 1983 to 2001, and after 2002: R t D t 1 +εt (1) where R t represents the daily log returns of a market index, D t 1 is a dummy variable that equals one (zero) when a buy (sell) signal is generated, and ε t represents the residual term. We test two null hypotheses. Under Hypothesis 1, the first null hypothesis, if Bollinger Bands do not produce useful trading signals, the buy and sell signals should not generate statistically different returns. Therefore, β should not be statistically different from zero (that is, R buy = 0). Hypothesis 2 studies the buy and sell signals separately. We test whether average buy/sell returns are significantly different from the same period market returns. If Bollinger Bands do not produce useful trading signals, the conditional buy (sell) returns should not be statistically different from the market returns (that is, R buy/sell = R m ). 4 MAIN RESULTS Exhibit 2 shows our results for the full sample in the top panel, followed by the results for the three subsample periods in the panels below. We first report the market returns, R m, the average spread between conditional buy SUMMER 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT 153

and sell returns, R buy, and the t-statistics for our test that R buy is not different from zero. In the next three columns, we report the number of buy signals generated and the average buy returns with the t-statistics from testing our second hypothesis. We perform the same test for the sell signals and put the results in the last three columns. In the full sample, R buy is significantly positive and higher than the 14 index returns. The average R buy is 0.294% across the 14 indexes, compared to an average market return of 0.026%. The results from the first subsample before 1983 indicate strong predictive power for Bollinger Bands. The average R buy across the 14 market indexes (0.454%) is much higher than the average market return (0.021%). Bollinger Bands start losing their predictive power after 1983, as they no longer produce significant positive R buy in Japan or in either index for the United E XHI B IT 2 Results on Bollinger Bands (20, 2) Breakout Method States from 1983 to 2001 (middle panel). This is the time period when Bollinger Bands are introduced, but the book Bollinger on Bollinger Bands has not yet been published. For other markets, the strategy still remains profitable. The predictive power of Bollinger Bands drops more dramatically after 2001, when Bollinger on Bollinger Bands is published. R buy remains only significantly positive in Italy and New Zealand. Moreover, R buy becomes even significantly negative for the French index and for the S&P 500. During the last subsample period, the average R buy drops to 0.002% or almost zero. The buy or sell signals might still work well separately (Hypothesis 2). Exhibit 2 shows that, generally, Bollinger Bands generate more buy signals than sell signals, which is consistent with the overall uptrend of the stock markets. Moreover, the buy (sell) signals produce positive (negative) returns that are significantly (continued) 154 POPULARITY VERSUS PROFITABILITY: EVIDENCE FROM BOLLINGER BANDS SUMMER 2017

E XHI B IT 2(continued) Results on Bollinger Bands (20, 2) Breakout Method higher (lower) than the market returns in 14 (12) markets in the full sample and in the first subsample. This result indicates that using either buy signals or sell signals alone generates superior returns before 1983. However, as for the combined signals, since 1983, using buy signals or sell signals shows only a decreased profitability. ROLLING WINDOW REGRESSIONS To check the stability of our results, we conduct rolling window regressions using the same regression used for Hypothesis 1. The windows are 10 years long and roll ahead one month each time. Exhibit 3 plots the average R buy over time. The plots uncover a gradually decreasing profitability in most of the sample markets. Note that in Exhibit 2, although the Bollinger Bands have generated positive returns in New Zealand since 2002, the profitability also shows a significant downward trend. Italy seems to be the exception, as Bollinger Bands provide useful predictions throughout. When does the predictive power of Bollinger Bands go down? Before 1983, Bollinger Bands provided reasonably stable predictability in all 14 indexes. For the DJIA, which started in 1885, with the exception of a short period during the 1930s, Bollinger Bands consistently deliver positive returns. After the Bollinger Bands go public in 1983, their predictability on the DJIA drops significantly, and it also begins dropping on the S&P 500 after the late 1980s. We then observe gradual worsening of the predictability results in Australia, Germany, France, Hong Kong, Spain, and the United Kingdom. In contrast, predictability in Italy, Korea, Japan, New Zealand, Singapore, and Switzerland remains relatively stable until 2001. Since 2002, however, the predictability of Bollinger Bands has decreased in nearly all markets. Moreover, since 2002, point estimates have often become negative (although not significantly so), SUMMER 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT 155

E XHIBIT 3 10-year Rolling Window Regressions again first for the United States around 1997 and then for the other market indexes. DECLINE IN PROFITABILITY Our subsample analysis above indicates apparent declines in Bollinger bands profitability over time. Can we link this more explicitly to the different subsamples? We follow McLean and Pontiff [2016] and run the following regression: RBB sds + β pdp +ε t (2) where R BB represents the daily returns of a Bollinger Bands based trading strategy, 5 D s is a dummy variable that equals one (zero) when the trading day is (is not) within the period 1983 2001, D P is a dummy variable that equals one (zero) when the trading day is (is not) within the period 2002 2014, and ε t represents the residual term. Because Bollinger Bands show strong profitability before 1983, we call it the in-sample period; and we refer to the period 1983 2001 as the post-sample (but before publication) period and 2002 2014 as the post-publication period. These match the key dates denoted by D s and D p, respectively. Therefore, if the introduction in 1983 and the publication in 2001 reduce the profitability, β s and β p should be significantly negative and their magnitudes should capture the sizes of the declines. We use an F-test to test the difference between D s and D p. This sheds further light on two issues. First, because we have seen that profitability decreases during 156 POPULARITY VERSUS PROFITABILITY: EVIDENCE FROM BOLLINGER BANDS SUMMER 2017

1983 2001 but disappears in most countries since 2002, we expect that the 2001 publication has a greater impact than the 1983 introduction that is, D p should be statistically smaller than D s. Second, if the out-of-sample decline in profitability is due to statistical biases but not the popularity of a trading strategy, we expect D s and D p to be statistically equal. Our results are in Exhibit 4. We first report the coefficient estimates with corresponding t-stats for D s and D p, respectively. In the next column, we report results of our F-test, testing the null hypothesis D s = D p. Next, we report the average daily returns of the Bollinger Bands based trading strategy R BB, followed by the percentage post-sample and post-publication declines in profitability calculated from D s /R BB and D p /R BB, respectively. Last, we report the differences between the post-sample and post-publication declines. The results add further strength to our previous findings. In seven markets, D s is significantly negative, indicating the significant drops in profitability since the 1983 introduction. The average decline is 56% across all markets, and the Japanese market experiences the greatest decline, 138%. Next, D p is significantly negative in all 14 markets except Italy, which suggests that the 2001 publication had an impact. The declines from this period are all significantly greater than those from the 1983 introduction, even for Italy; this means that even though the strategy still shows some profitability in Italy (as shown in Exhibit 2), its profitability is decreasing too. The average post-publication decline is 156%. The average difference in declines from the two periods of 100% highlights the additional impact the publication may have had. ECONOMIC SIGNIFICANCE AND OTHER ROBUSTNESS CHECKS To account for transaction costs and risk, we evaluate the economic significance of our results by including 1% for transaction costs and price slippage when switching between risk-free assets and the market. The results are in Exhibit 4. We first report the Sharpe ratios of the buy-and-hold strategy and of the Bollinger Band strategy. We then report the t-statistics testing the null hypothesis that the two Sharpe ratios are equal. 6 In addition, we calculate Jensen s α for the Bollinger Band strategy. 7 Our results remain similar. In the full sample, Bollinger Bands generate significantly higher Sharpe ratios than buy-and-hold strategies in five markets. Before 1983, Bollinger Bands generated higher Sharpe ratios in 10 markets; from 1983 to 2001, the number of markets dropped to two, and in the last subsample, from 2002 on, only in one market (Italy) do Bollinger Bands still beat the market. The results using Jensen s α are similar. We conduct several additional robustness checks (also available in the online appendix). For instance, we use different versions of Bollinger Bands, or GARCH (1,1), and robust regression models to estimate parameters. However, these variations do not affect our main results. Our results also remain the same if we consider economic significance without transaction costs or different holding periods after a trading signal is generated. When we construct a time variable that equals 1/100 in the first trading day and increases by 1/100 in each consecutive day in our sample, and we regress the time variable against returns of the Bollinger Bands based strategy for each country, the estimates are all significantly negative, confirming the significant downward profitability over time. Last, one may wonder if the declining profitability may indicate a contrarian investment opportunity. Although returns of the Bollinger Bands based strategies have turned negative gradually since 1983 in different countries, these negative returns are generally not statistically different from zero as shown in Exhibit 2. If we further take transaction costs into account, it seems difficult to make profits by using contrarian strategies. This is in line with our argument that returns of a profitable trading strategy will gradually converge to zero. CONCLUSION We uncover a gradual downward profitability in the use of Bollinger Bands for trading purposes in international stock markets, which is associated with the growing popularity of the strategy. Although using Bollinger Bands indeed generated superior returns before 1983, returns disappeared or turned negative once they became known. Since 2002, the year Bollinger s book was published, Bollinger Bands have largely lost their predictive ability in major stock markets. Although we cannot directly link profitability to actual trading on Bollinger Bands, our results suggest that the impact of investor overuse, rather than sample selection bias, causes this loss in the profitability. SUMMER 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT 157

E XHIBIT 4 Decline of Profitability and Economic Significance Tests 158 POPULARITY VERSUS PROFITABILITY: EVIDENCE FROM BOLLINGER BANDS SUMMER 2017

ENDNOTES 1 See http://www.prweb.com/releases/2008/04/ prweb814374.htm and http://www.bollingerbands.com/ services/bb/rules.php. 2 Papers that study the profitability of Bollinger Bands include Leung and Chong [2003], Lento, Gradojevic, and Wright [2007], Balsara, Chen, and Zheng [2009], Lento and Gradojevic [2011], and Mühlhofer [2017]. 3 Here we use the most elegant direct application of Bollinger Bands (Bollinger [2001], p. 127), but our results are robust if we use variations. The additional results are in the online appendix. 4 We use White [1980] standard errors to correct for heteroskedasticity and a conservative 10% significance level. 5 We go long on Bollinger Bands buy signals and short on their sell signals and we invest in short-term deposits when there is no signal. The risk-free rates are described in the online appendix. 6 The significance test on the Sharpe ratios is performed according to the methodology proposed by Lo [2002] and de Roon et al. [2012]. 7 We run the following regression to calculate Jensen s alpha: r BB r f = α + β (r m r f ) + ε t, where r BB represents the returns from using Bollinger Bands, r f represents the risk-free rates, and r m represents the market returns. REFERENCES Abbey, B.S., and J.A. Doukas. Is Technical Analysis Profitable for Individual Currency Traders? The Journal of Portfolio Management, Vol. 39, No. 1 (2012), pp. 142-150. Balsara, N., J. Chen, and L. Zheng. Profiting from a Contrarian Application of Technical Trading Rules in the US Stock Market. Journal of Asset Management, Vol. 10, No. 2 (2009), pp. 97-123. Bollinger, J. Bollinger on Bollinger Bands. New York, NY: McGraw-Hill, 2001. Brock, W., J. Lakonishok, and B. LeBaron. Simple Technical Trading Rules and the Stochastic Properties of Stock Returns. The Journal of Finance, Vol. 47, No. 5 (1992), pp. 1731-1764. Ciana, P. New Frontiers in Technical Analysis: Effective Tools and Strategies for Trading and Investing. New York, NY: Bloomberg, 2011. de Roon, F., E. Eiling, B. Gerard, and P. Hillion. Currency Risk Hedging: No Free Lunch. Working paper, Tilburg University, 2012. Lento, C., and N. Gradojevic. The Profitability of Technical Trading Rules: A Combined Signal Approach. Journal of Applied Business Research, Vol. 23, No. 1 (2011), pp. 13-28. Lento, C., N. Gradojevic, and C.S. Wright. Investment Information Content in Bollinger Bands? Applied Financial Economics Letters, Vol. 3, No. 4 (2007), pp. 263-267. Leung, J.M.J., and T.T.L. Chong. An Empirical Comparison of Moving Average Envelopes and Bollinger Bands. Applied Economics Letters, Vol. 10, No. 6 (2003), pp. 339-341. Lo, A.W. The Statistics of Sharpe Ratios. Financial Analyst Journal, Vol. 58, No. 4 (2002), pp. 36-52. McLean, R.D., and J. Pontiff. Does Academic Research Destroy Stock Return Predictability? The Journal of Finance, Vol. 71, No. 1 (2016), pp. 5-32. Mühlhofer, T. They Would if They Could: Assessing the Bindingness of the Property Holding Constraint for REITs. Real Estate Economics, March 2017. DOI: 10.1111/1540-6229.12141. White, H. A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test of Heteroskedasticity. Econometrica, Vol. 48, No. 4 (1980), pp. 817-838. To order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or 212-224-3675. SUMMER 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT 159