d Ifta Journal 13

13

A Professional Journal Published by The International Federation of Technical Analysts

Inside this Issue

6 The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX

13 Psychological Barriers in Asian Equity Markets

20 Regime-Switching Trading Bands Using A Historical Simulation Approach

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EDITORIAL

Rolf Wetzer, Ph.D. (SAMT)Editor, and Chair of the Editorial [email protected]

Aurlia Gerber (SAMT)[email protected]

Ralf Bckel, CFA (VTAD) [email protected]

Michael Samerski [email protected]

Mark Brownlow, CFTe (ATAA) [email protected] Editor

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IFTA Journal is published yearly by The International Association of Technical Analysts. 9707 Key West Avenue, Suite 100,

Rockville, MD 20850 USA. 2012 The International Federation of Technical Analysts. All rights reserved. No part of this

publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying for

public or private use, or by any information storage or retrieval system, without prior permission of the publisher.

Letter From the Editor By Rolf Wetzer, Ph.D............................................................................................................................5

Articles

The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX By Mohamed El Saiid, CFTe, MFTA.................................................................................................... 6

Psychological Barriers in Asian Equity Markets By Shawn Lim, CFTe, MSTA, and Bryan Lim....................................................................................13

MFTA.Papers

Regime-Switching Trading Bands Using A Historical Simulation Approach By Ka Ying Timothy Fong, CFTe, MFTA............................................................................................ 20

Using a Volatility Adjusted Stop Loss (VASL) to Enhance Trading Returns By Edward Rowson, CFTe, MFTA...................................................................................................... 28

Momentum Indicators: An Empirical Analysis of the Concept of Divergences By Stephan Belser, CFTe, MFTA.........................................................................................................35

Wagner.Award.Paper

Momentum Success Factors By Gary Antonacci.................................................................................................................................45

Educational

Heikin-Ashi: A Better Technique to Trends in Noisy Markets By Dan Valcu, CFTe............................................................................................................................54

Book.Review

Mastering Market Timing, Using the Works of L.M. Lowry and R.D. Wyckoff to Identify Key Market Turning Points By Richard A. Dickson and Tracy L. Knudsen Reviewed by Regina Meani, CFTe....................................................................................................60

Author Profiles..................................................................................................................................61

IFTA Board of Directors.................................................................................................................. 62

About cover photo: Abstract WavesPhoto by piccerella

IFTA JOURNAL 2013 EDITION

IFTA.ORG PAGE 3

IFTA2013 26TH ANNUAL CONFERENCE

Check the website for updates: www.ifta.org

San Francisco

IFTA2013 26TH ANNUAL CONFERENCE

Dear IFTA Colleagues and Friends:

In all our writings and teaching on technical analysis, we never forget to quote our mantra history repeats itself. If we go back 100 years and look at the Dow Jones Industrial Index, it seems that this is a good assumption. In 1912, the first quarter started with an upsurge. In Spring, the market went sideways, spiced with good volatility. In Summer, the market rose to a new high. Does this sound familiar?

The International Federation of Technical Analysts (IFTA) Journal is traditionally international, both in its contributions

and techniques described. This year, the Journal has four separate sections. In the first section, two articles were submitted by IFTA colleagues from the

Egyptian Society of Technical Analysts (ESTA) and the Society of Technical Analysts (STA). ESTAs contribution covers volatility bands based on the VIX Index. STA offers information on a strict testing procedure for psychological barriers in Asian stock markets; as our 2012 Annual Conference will be in Singapore, this article might offer additional insight into some of the Conference topics.

In the second section, there are three papers from our Master of Financial Technical Analysis (MFTA) program. One of the authors, Stephan Belser, MFTA, was awarded the John Brooks Memorial Award for 2011. Congratulations!

This year, aside from our own MFTA material, we are happy to publish a paper from another organisation. With the permission of the National Association of Active Investment Managers (NAAIM), we have included a paper by Gary Antonacci, winner of the NAAIM Wagner Award 2012. We hope that you find this paper informative.

We conclude with contributions from two of IFTAs current Board members. Dan Valcu, CFTe, IFTAs Membership Director and Vice President of Europe, has written an article on a Japanese charting technique. IFTAs former Journal Editor and Director, Regina Meani, CFTe, contributed a book review.

Again, like IFTA itself, the Journal is truly international. I would like to thank the authors for their contributions. And, not only do Journal articles come from all over the globe, our editors do too. I would like to thank Aurlia Gerber, Ralf Bckel, Michael Samerski and Mark Brownlow for their help in editing this Journal. Last but not least, I would like to thank Linda Bernetich and Jon Benjamin for the layout and their effort in putting the Journal together.

We are now in the fifth year of a financial crisis. In 1912, the year ended with a drawdown. Hopefully, as good market technicians, we should be prepared this time.

Letter From the Editor By Rolf Wetzer, Ph.D.

In all our writings and teaching on technical analysis, we never forget to quote our mantra history repeats itself.


IFTA.ORG PAGE 5

1. AbstractThis paper proposes a new method for extending the

statistical and visual capability of the Chicago Board Options Exchange (CBOE) market volatility index (VIX) over the S&P 500 (SPX). The paper subsequently provides several visual examples of the proposed method and discusses its implications and uses over the chart from a technical standpoint. Finally, the paper discusses implementing the same methodology on other implied volatility-based indices over their corresponding/underlying equity market indices. The methodology proposed in this paper will be referred to hence forth as the Implied Volatility Projection Range or IVPR.

2. Introduction

2.1.The.VIX.definitionThe Chicago Board Options Exchange (CBOE) market

volatility index (VIX) is a forward-looking index of the expected return volatility of the S&P 500 index (SPX) over the next 30 days. This forward-looking feature is implied from the at-the-money SPX option prices. As such, the VIX measures the volatility that investors expect to see, rather than what has been recently realized.1

The VIX estimates the expected volatility by averaging the weighted prices of the SPX puts and calls over a wide range of strike prices.2 In that respect and as opposed to equity market indices which are comprised of stocks, the VIX index is comprised of options, where each option price is intended to reflect the markets expectation of future volatility.3

The VIX was initially developed by Prof. Robert E. Whaley in 1993 and is a registered trademark of the CBOE. Since then, several modifications were introduced in its calculations.4

2.2.The.VIX.implications.(indications).over.the.SPXIn his writings, Whaley discussed that while volatility implies

unexpected market moves regardless of direction, the VIX is dubbed as the investor fear gauge. He justified this to be on the back of the current domination of the SPX option market by the hedgers. Hedgers demand on puts tends to increase when there is a concern for a potential decline in the stock market. Once that concern manifests, the VIX values tend to increase. Whaley coined this feature as portfolio insurance. As such, the VIX indicator tends to reflect the price of portfolio insurance.5

Attempting to prove his argument, Whaleys tests established the following:6

Small SPX daily changes result in negligible VIX changes. Volatility tends to follow a mean-reverting process. There is an inverse, yet asymmetric relationship between the

SPX and the VIX movements. According to Whaley, the latter feature is brought about by portfolio insurance.

To support Whaleys argument, we have performed a series of linear correlation tests between the SPX and the VIX over 5,520 daily closing values (from January 1990 to December 2011). The first correlation test performed was conditional exclusively on positive SPX returns. The second test was conditional only on negative SPX returns. The third to seventh tests were conditional on achieving returns greater than +/-0.50%, +/-1.00%, +/-2.00%, +/-3.00% and +/-4.00% in the SPX. The outcomes of these tests were then compared to a final non-conditional correlation test between the SPX and the VIX and the results are shown in table 1.

Table 1: Non-conditional vs. conditional correlation results between the SPX and the VIX

Correlation.test. Correlation..Coefficient.(R)

Non-conditional.correlation -0.70

Conditional.Correlation.Tests

Positive SPX returns correl. -0.46

Negative SPX returns correl. -0.60

Greater than +/-0.5% SPX returns correl. -0.76

Greater than +/-1% SPX returns correl. -0.79




From the results presented above we can make the following deductions:

A negative correlation does exist between the SPX and the VIX regardless of the correlation conditions. The negative correlation appears stronger at (R) conditional to negative SPX returns (-0.6) than at (R) conditional to positive SPX returns (-0.46). This reflects the asymmetry of movements of both indices as a result of portfolio insurance. Negative correlation increases or becomes more significant as the SPX returns become more volatile. In other words, the VIX values become more significant as the SPX daily returns surge and/or plunge.

2.3.How.the.VIX.is.currently.being.usedThe VIX generally exhibits two strong characteristics. One

being a consistent negative correlation with the SPX, while the

The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX By Mohamed El Saiid, CFTe, MFTA


PAGE 6 IFTA.ORG

other is the strong tendency for the VIX to revert to its long term mean, thus reflecting the absence of deterministic growth in volatility (unlike stocks).7 According to these two features, the common interpretations of the VIX values (as a standalone index) include the following:

Abnormally high VIX readings imply a potential bottom, or the occurrence of a counter-trend rally in the SPX. The opposite is true at relatively low VIX readings. On the other hand, an up trending VIX implies a potentially sustainable downtrend in the SPX and vice versa.

Figure 1 visually depicts both features of the VIX; the tendency to revert in an oscillatory-type motion despite experiencing trending phases in the process, as well as the negative correlation with the SPX. This is evident by the VIX peaks and valleys that coincide with key SPX lows and highs, respectively. In this chart we have indicated relatively high and low VIX readings with reference to the 30% and 16% levels, respectively, based on visual inspection over the period presented. A common strategy among traders when using the VIX is to go long on equities when the VIX rebounds from key highs and sell (or short) equities when the VIX rebounds from key lows.

3. Statistical interpretation and inferences of the VIX values

3.1.Statistical.interpretationThe VIX calculation produces a probability-based

interpretation with respect to the estimated range of the SPX rates of returns over the next 30 days.8

Example: Assume that the SPX closed at 1,300.00 and the VIX closed at 25.00 today. Since the VIX values are annualized standard deviation values multiplied by 100, to transform the value back to represent the 30 days (or 1 month) sigma, we divide 25 by 100 and then divide the outcome by the square root of 12.9

In this example the result was 7.22%. According to the statistical Empirical Rule, this is interpreted as follows: there is a probability of 68.2% (approximately) that the expected range of the SPX returns over the next 30 days will lie within +/-7.22%, or within the range of (1,206.18 1,393.82).

3.2.Statistical.inferencesTesting the VIX interpretation according to the Empirical Rule

and using historical daily closing values for the VIX from January 1990 to December 2011, we present the outcomes in table 2.

Figure 1: Upper window: The SPX indexDaily valuesCandlestick chartNormal scale Lower window: The VIX indexDaily valuesCandlestick chartSemi-logarithmic scale

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Periods marked in red indicate key highs on the SPX which coincided with VIX lows as identifiedby the 16% level

Periods marked in blue indicate key lows on the SPX which coincided with VIX highs as identifiedby the 30% level


IFTA.ORG PAGE 7

Table 2: Statistical results

Standard Deviation

0.5 1 1.5 2 2.5 3

Inside VIX range

2,417 4,177 5,111 5,395 5,472 5,498

43.8% 75.7% 92.6% 97.7% 99.1% 99.6%

Outside VIX range

3,104 1,344 410 126 49 23

56.2% 24.3% 7.4% 2.3% 0.9% 0.4%

Outside lower VIX range

1,060 494 221 112 47 23

19.2% 8.9% 4.0% 2.0% 0.9% 0.4%

Outside upper VIX range

2,044 850 189 14 2 0

37.0% 15.4% 3.4% 0.3% 0.0% 0.0%

Total observed data

5,521 5,521 5,521 5,521 5,521 5,521

Empirical Rule 38.20% 68.20% 86.60% 95.40% 98.80% 99.80%

As observed from table 2, the VIX estimates managed to contain the SPX action quite well over the period (5,521 days) under study.

Accordingly, this paper proposes extending the statistical and visual capability of the VIX by representing the statistical interpretation of the VIX values over the SPX in the form of a projection range that moves dynamically as the SPX progresses forward in time.

4. Introducing the Implied Volatility Projection Range (IVPR)

In this section, we introduce the IVPR and convey the means to visually plot it over the SPX. With reference to the interpretation previously presented, we regress the results over time (shown in table 3) and plot the resulting SPX range(s) over the SPX values on the chart (visualized by figure 2).

Figure 2: Upper window: The SPX index vs. the IVPRDaily valuesCandlestick chartNormal scale. Lower window: The VIX indexDaily valuesCandlestick chartNormal scale

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Lower SPX VIX range shifted forward by 30-days

Figure 2 introduces the IVPR when visually plotted over the Table 3: Calculating the SPX projection range based on the VIX values

Date SPX.Close VIX.close VIX.adj.to.30.days.Volatility

Lower.IVPR

Upper.IVPR

05/25/2010 1,074.03 34.61 9.99%

05/26/2010 1,067.95 35.02 10.11%

05/27/2010 1,103.06 29.68 8.57%

05/28/2010 1,089.41 32.07 9.26%

06/01/2010 1,070.71 35.54 10.26%

06/02/2010 1,098.38 30.17 8.71%

06/03/2010 1,102.83 29.46 8.50%

06/04/2010 1,064.88 35.48 10.24%

06/07/2010 1,050.47 36.57 10.56%

06/08/2010 1,062.00 33.7 9.73%

06/09/2010 1,055.69 33.73 9.74%

06/10/2010 1,086.84 30.57 8.82% Results.are.plotted.30.days.forward.as.implied

06/11/2010 1,091.60 28.79 8.31%

06/14/2010 1,089.63 28.58 8.25%

06/15/2010 1,115.23 25.87 7.47%

06/16/2010 1,114.61 25.92 7.48%

06/17/2010 1,116.04 25.05 7.23%

06/18/2010 1,117.51 23.95 6.91%

06/21/2010 1,113.20 24.88 7.18%

06/22/2010 1,095.31 27.05 7.81%

06/23/2010 1,092.04 26.91 7.77%

06/24/2010 1,073.69 29.74 8.59%

06/25/2010 1,076.76 28.53 8.24%

06/28/2010 1,074.57 29 8.37%

06/29/2010 1,041.24 34.13 9.85%

06/30/2010 1,030.71 34.54 9.97%

07/01/2010 1,027.37 32.86 9.49%

07/02/2010 1,022.58 30.12 8.69%

07/06/2010 1,028.06 29.65 8.56%

07/07/2010 1,060.27 26.84 7.75%

07/08/2010 1,070.25 25.71 7.42% 966.72 1,181.34

07/09/2010 1,077.96 24.98 7.21% 959.99 1,175.91

07/12/2010 1,078.75 24.43 7.05% 1,008.55 1,197.57

07/13/2010 1,095.34 24.56 7.09% 988.55 1,190.27

07/14/2010 1,095.17 24.89 7.19% 960.86 1,180.56

07/15/2010 1,096.48 25.14 7.26% 1,002.72 1,194.04

07/16/2010 1,064.88 26.25 7.58% 1,009.04 1,196.62

07/19/2010 1,071.25 25.97 7.50% 955.81 1,173.95

07/20/2010 1,083.48 23.93 6.91% 939.57 1,161.37

07/21/2010 1,069.59 25.64 7.40% 958.68 1,165.32


PAGE 8 IFTA.ORG

Figure 3: The SPX index vs. the IVPRDaily valuesCandlestick chartNormal scale

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1000101010201030104010501060107010801090110011101120113011401150116011701180119012001210122012301240125012601270128012901300

Lower low failed to break below lower IVPR

Lower low outside lower IVPR

Subsequent rally

W-shape formation

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Subsequent decline

Higher high outside higher IVPR

Higher high failed to break above upper IVPR

M-shape formations



Subsequent decline


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Lower low outside lower IVPR

Subsequent rally

W-shape formation

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Subsequent decline



M-shape formations



Subsequent decline


IFTA.ORG PAGE 9

Figure 2 introduces the IVPR when visually plotted over the SPX (upper window) and depicts the VIX (lower window). As a result of the visualization process, the IVPR boundaries are plotted 30-days forward as implied by the VIX calculation. Accordingly, the VIX implies a probability of 68.2% (approximately) that the expected range of the SPX returns over the next 30 days will lie within terminus points of the IVPR.

5. Technical interpretations of the IVPRAdditional to the common uses/applications of the VIX

previously stated, we introduce further interpretations by using the IVPR.

5.1.During.the.SPX.trending.phasesDuring up-trending phases, volatility (the VIX) trends

down. Meanwhile the SPX trends close to the upper IVPR and occasionally trends above it for a relatively short period. As the SPX forms higher highs, the SPX exceeds the projected estimation of the upper IVPR. However, in specifically observed cases, failing to reach the upper IVPR during up-trends implies weakness in the trend and suggests a counter-trend correction. This can sometimes lead to a change in the overall SPX trend direction, especially if the VIX itself reverses direction. We recommend adopting the technique associated with the M-shape formations as a trading pattern that aims at highlighting such weaknesses. The M (& W) shape formations were proposed by Bollinger through his works on the Bollinger Bands (B-Bands) as two useful techniques to identify weaknesses in the underlying trends.10

Moreover during up-trends, the SPX rarely makes any attempts towards the lower IVPR. In fact, all the SPX attempts towards the lower IVPR during a structurally-maintained uptrend and excluding trend reversal events are considered key lows in that up-trend. These dips are regarded as buying opportunities in the market.

The opposite holds true during down-trending phases. The VIX trends up, while the SPX trends close to/and occasionally exceeds the projected estimation of the lower IVPR, as it registers lower lows. In certain cases, failing to reach the lower IVPR during down-trends implies weakness in the trend and suggests a counter-trend correction. This can sometimes lead to a change in the overall SPX trend direction, especially if the VIX itself reverses direction. Similarly, we propose the trading technique associated with the Bollinger W-shape formations as an appropriate tactic to be used during such events. On the other hand, during down-trends, rare attempts for the SPX towards the upper IVPR are observed and are considered key highs/selling opportunities in the market.

Figure 3 shows the IVPR plotted over the SPX. Unlike the May/June low, the lower low created in July failed to move below the lower IVPR, implying that the market failed to exceed its prior 30-day volatility expectations and implied lesser volatility going forward. This was followed by a counter-trend rally that sustained till August. This trading pattern is comparable to a W-shaped B-Band pattern.

Figure 4 shows the IVPR plotted over the SPX. The chart suggests two cases of M-shaped B-Band formations and their subsequent countertrend declines.

5.2.During.the.SPX.trendless.phases.and.trend.reversals:

5.2.1.Trendless.phasesDuring trendless or sideways phases in the SPX, the buying

and selling power in the market are generally not sufficient to build-up or sustain a structured trend (up or down). It was observed that all price excursions from both IVPR boundaries were unsustainable.

We propose using both IVPR boundaries during such phases as overbought (OB) and oversold (OS) levels for the SPX. As such, reaching or breaking the upper boundary, followed by a pull-back inside, is regarded as a selling (trading) opportunity and vice versa for the lower IVPR. This tactic is similar to that used with moving average-based envelopes during sideways trends.11


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IVPR aids in identifying OB/OS conditionsduring SPX sideways or trendless phases

Figure 5 shows how the IVPR boundaries can be used to help identify OB and OS levels once a sideways phase has been identified over the SPX.

.5.2.2.Trend.reversalsA trend reversal phase may be viewed as a temporary

sideways or trendless condition in which an exchange in power between the buyers and sellers occur. This causes an existing trend structure (up-trend or down-trend) to reverse to the opposite trend structure.

We have observed that during structural trend reversals in the SPX, volatility of the SPX also tends to change in behavior. During reversals from down trends, the following occurs: The undergoing rise in volatility (up trending VIX) begins to reverse from high levels (above 30%) at the same time or prior to the actual reversal of the SPX. The SPX begins to fall short of moving below the lower IVPR boundary, orat leastmakes brief attempts at the lower IVPR when compared to previous lows in that same bear trend. The SPX performs successful attempts to reach the upper IVPR, signaling new strength in buying power.


PAGE 10 IFTA.ORG

The IVPR boundaries fail to mark lower lows indicating that volatility is receding. The trend reversal is confirmed when the SPX successfully moves and sustains outside the upper IVPR following an initial structural trend-reversal pattern.

Figure 6, shows the bottoming phase which occurred on the SPX following the 20002002 bear trend. Additional to the classic reversal structure which consisted of a higher low (in March 2003), followed by a higher high (in May/June), we have highlighted the behavior of the SPX with the IVPR. The last registered lower high of the SPX (November 2002) managed to breach above the IVPR on the near term frame. This was followed in March 2003 by a relatively brief breach below the IVPR and a higher SPX low was created during that same month. This higher SPX low was confirmed by a higher IVPR low. Finally, the higher SPX high which occurred later in May/June 2003 was associated with a breach of the upper boundary of the IVPR.

Figure 7 shows the topping phase which occurred on the SPX prior to the 20002002 bear trend. A lower high (in September 2000), followed by a lower low (in December 2000) constituted a trend reversal pattern. Confirming this reversal, the last registered SPX peak during this period (March 2000) was accompanied by a breach above the upper IVPR. The following (lower high), however, failed to move outside the upper IVPR (a confirmed weakness). This was followed by a lower low in December that succeeded to move below the lower IVPR to confirm the market reversal.

ConclusionWithout any doubt, the VIX is

an invaluable market indicator that provides essential market clues and expresses the SPX trend conditions from the volatility standpoint. In this paper, we have recognized the virtues of the VIX as a standalone index and proposed a new method that aims at extending the statistical and visual capability of the VIX, namely, the IVPR. The IVPR transforms the stationary/statistical


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A higher SPX high (reversal confirmation)accompanied by a breach of the upper IVPR

This SPX high was associated with a breach of the upper IVPR; an event unseen in this 2-year bear trend except during May 2001.

A higher SPX low


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Figure 8: The NASDAQ 100 index vs. the IVPRDaily valuesCandlestick chartNormal scale

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IFTA.ORG PAGE 11

interpretation of the VIX values into dynamic boundaries that project the SPX expectations in the future, derived from a statistical standpoint.

The IVPR is yet still not without limitations. Although the IVPR managed to contain the SPX data according to predetermined statistical probabilities, the SPX will often exceed the IVPR boundaries and sustain over the NT horizon. We attribute this to a TA-based premise stating that markets move in defined trend structures.12 In part, this is evident when the SPX values track one of the IVPR boundaries during a trending phase and not the other.

Nevertheless, the IVPR offers a more comprehensive statistical and visual capability when compared to the VIX index (on a standalone basis). This advantage is especially valuable when trying to understand the relationship between the VIX and the SPX, and ultimately aidsto some extentin forecasting the expected moves of the SPX in the future.

References[1, 2] Chicago Board Options Exchange

(CBOE), VIX White Paper, 2009. Pages: 1 and 4 respectively. [3, 4, 5, 6, 7] Whaley, Robert E.,

Understanding the VIX, The Journal of Portfolio Management, Spring 2009. Pages: 98, 99, 100 and 101 respectively.[8, 9] Rhoads, Russel, Trading VIX

Derivatives: Trading and Hedging Strategies Using VIX Futures, Options, and Exchange Traded Notes, Wiley, 2011. Page 23.10 Bollinger, John A., Bollinger on Bollinger

Bands, McGraw-Hill, 2001. Page 94.[11, 12] Murphy, John J., Technical

Analysis of the Financial Markets, New York Institute of Finance, 1999. Pages: 207 and 3 respectively.

Figure 9: The Russell 2000 index vs. the IVPRDaily valuesCandlestick chartNormal scale

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Figure 10: The SPX index vs. the IVPR @ 2 standard deviationsDaily valuesCandlestick chartNormal scale

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Software and dataData courtesy of Bloomberg and Reuters. Charting software courtesy of Equis

International MetaStock v.9.1.

BibliographyBollinger, John A., Bollinger on Bollinger Bands, McGraw-Hill, 2001. Chicago Board Options Exchange (CBOE), VIX White Paper, 2009.Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 2000.Mason, Robert D., Marchal, William G., Lind, Douglas A., Statistical Techniques in

Business & Economics, McGraw-Hill/Irwin, 2002.Murphy, John J., Technical Analysis of the Financial Markets, New York Institute of

Finance, 1999.Pring, Martin J., Technical Analysis Explained: The Successful Investors Guide to

Spotting Investment Trends and Turning Points, McGraw-Hill, 2002. Rhoads, Russell, Trading VIX Derivatives: Trading and Hedging Strategies Using

VIX Futures, Options, and Exchange Traded Notes, Wiley, 2011.Whaley, Robert E., Understanding the VIX, The Journal of Portfolio Management,

Spring 2009.


PAGE 12 IFTA.ORG

In this study, we investigate the presence of psychological barriers in the equity indexes of 10 Asian Markets over a 10-year period from 20012011. This investigation was conducted through the use of uniformity tests, barrier proximity tests and tests on the predictability of stock returns. We have found evidence for barriers at the 1000 level for 6 of these markets (JKSE, KLSE, N225, STI, KS11, TWII) and at the 100 level for 4 of these markets (AORD, JKSE, KLSE, STI). However, while there may be evidence of psychological barriers, there is little evidence for the predictability of stock returns induced by the presence of these psychological barriers.

IntroductionHang Seng Index: Investors hope for support at 19,000,

Nikkei rebounds after slipping below 8,500, KOSPI may test support at 1,900 points, and the list goes on. This is just a small snapshot of news headlines taken in May 2012, but the underlying theme is a distinctively familiar one. Regions of round numbers have often been regarded with special significance in the financial press, with the approach or penetration of these levels often taken by financial commentators to be of particular importance and is hence often used as a barometer of market sentiment.

However, while the evidence that people (or at least the press) view levels around round numbers as important is indisputable, is the added attention truly warranted? Empirical studies applied to US markets have found some evidence of psychological barriers (Donaldson and Kim 1993) while evidence for return predictability has been weak (Koedijk and Stork 1994). While there has been substantial empirical research on the presence of these effects in Western markets, there has been considerably less research focused on Asian markets and this study attempts to supplement this growing body of knowledge by testing for the presence of psychological barriers around round numbers in Asian Equity Indices. There are 3 ways that tests for psychological significance are often conducted; tests on the distribution of digits, tests on the frequency of digits, and the behaviour of returns around presupposed barriers. This study tests for barriers using these 3 categories of tests as applied to the 10 selected Asian Equity Indices.

Psychological barriers refer to regions of support or resistance around round numbers, hence at the 11300, 11400, 11500, etc levels for barriers at the 100 level and at 12000, 13000, 14000, etc for barriers at the 1000 level. As there is no fundamental reason for these levels to be of particular importance, the presence of regions of support or resistance around these levels have been attributed to behavioural biases, hence the term psychological barriers. Some

explanations that have been offered for these round number effects include psychological preferences for round numbers (Ziemba et al 1986), coordination on limited price set (Harris 1991), convenience (Mitchell 2001), odd pricing (Schindler and Kirby 1997), bounded rationality and aspiration levels (Sonnemans 2006).

DataThis study uses closing prices for the following 10 Asian

Equity Indices for the 10-year period from 1 Jan 2001 to 31 Dec 2011 as obtained from Yahoo Finance. Table 1 provides a summary of the indices used and their range over the test period.

Table 1: Summary of the 10 Asian Equity Indices and their range from 1 Jan 01 to 31 Dec 11

Symbol Name Market. High Low

AORD All Ordinaries Australia 6853.6 2673.3

SSEC Shanghai Composite China 6092.06 1011.5

HSI Hang Seng Index Hong Kong 31638.22 8409.01

BSESN BSE 30 India 21004.96 2600.12

JKSE Jakarta Composite Indonesia 4193.44 337.48

KLSE KLSE Composite Malaysia 1594.74 553.34

N225 Nikkei 225 Japan 18261.98 7054.98

STI Straits Times Index Singapore 3875.77 1213.82

KS11KOSPI Composite Index

Korea 2228.96 468.76

TWII Taiwan Weighted Taiwan 9809.88 3446.26

M-ValuesIn order to test for the presence of psychological barriers,

it is first necessary to introduce the concept of M-values as is often used in empirical tests for barriers.

M-values are two digit numbers, ranging from 00 to 99 and represent a point, with 00 representing the region around a round number. We use 2 sets of M-values for each index, M 1000 for M-values to test the presence of barriers at the 1000 level and M 100 for M-values to test the presence of barriers at the 100 level. These are defined as follows:

mod 100.

( ) mod 100.

Where Pt is the integer part of Pt. For example, if prices are 24998.02 and 54738.12, M 100 are 98 and 38 respectively.

mod 100.

( ) mod 100.

Psychological Barriers in Asian Equity Markets By Shawn Lim, CFTe, MSTA, and Bryan Lim


IFTA.ORG PAGE 13

For example, if prices are 24998.02 and 54738.12, M 1000 are 99 and 73 respectively.

When examining barriers at the 100 level, we would expect to see the index closing less frequently at the xx00.xx level if the barriers existed, and for the 1000 level we would expect to see the index closing less frequently at the x00x.xx level. This is what the respective M-values represent and is the rationale for using them in the tests specified throughout the rest of this paper.

Frequency.Distribution

The following charts show the distribution of the M-values for the 10 markets:


PAGE 14 IFTA.ORG

Presence of Psychological Barriers

Uniformity.TestTo investigate the presence of psychological barriers, we

conduct tests for positional and transgressional effects at the M 1000 and M 100 levels by carrying out a chi-square test using 3 different set ups and the resulting test statistics are reported in Table 2 and Table 4. We regard the thousand and hundred levels as potential psychological barriers and hence test the M-values at the corresponding levels.

If there are no particular areas with any significance, we would then expect the M-values to follow a uniform distribution, i.e. there would be no particular reason for an index to close at, for example, 11900 (M 1000 = 90, M 100 = 00) more frequently than 11870 (M 1000 = 87, M 100 = 70) over the 10 year period investigated and hence we would expect to see the index closing at approximately an equal number of times at the 99 M-value as at the 45 M-value and so forth. If there


IFTA.ORG PAGE 15

are regions of resistance or support close to round numbers, however, we would then expect to see less M-values close to the 00 region and for the distribution of all the M-values to not follow a uniform distribution. Hence, the first test (Absolute Test) tests the distribution of all the M-values against a uniform distribution with the hypothesis h0: the 100 M-values follow a uniform distribution against h1: the 100 M-Values do not follow a uniform distribution. The Chi-Squared Test static for each index is computed as follows:

If there are no particular areas with any significance, we would then expect the M-values to follow a uniform distribution, i.e. there would be no particular reason for an index to close at, for example, 11900 ( = 90, = 00) more frequently than 11870 ( = 87, = 70) over the 10 year period investigated and hence we would expect to see the index closing at approximately an equal number of times at the 99 M-value as at the 45 M-value and so forth. If there are regions of resistance or support close to round numbers, however, we would then expect to see less M-values close to the 00 region and for the distribution of all the M-values to not follow a uniform distribution. Hence, the first test (Absolute Test) tests the distribution of all the M-values against a uniform distribution with the hypothesis : the 100 M-values follow a uniform distribution against : the 100 M-Values do not follow a uniform distribution. The Chi-Squared Test static for each index is computed as follows:

( )

Where stands for the number of observations in each category i (i=0..99 for Absolute Test, i=1..10 for Barrier

Test and i=1,2 for Remainder Test) and stands for the number of observations expected (

( )).

The number of degrees of freedom for each test is computed as df = n-1.

Where Oi stands for the number of observations in each category i (i = 099 for Absolute Test, i=110 for Barrier Test and i = 1,2 for Remainder Test) and Ei stands for the number

of observations expected

If there are no particular areas with any significance, we would then expect the M-values to follow a uniform distribution, i.e. there would be no particular reason for an index to close at, for example, 11900 ( = 90, = 00) more frequently than 11870 ( = 87, = 70) over the 10 year period investigated and hence we would expect to see the index closing at approximately an equal number of times at the 99 M-value as at the 45 M-value and so forth. If there are regions of resistance or support close to round numbers, however, we would then expect to see less M-values close to the 00 region and for the distribution of all the M-values to not follow a uniform distribution. Hence, the first test (Absolute Test) tests the distribution of all the M-values against a uniform distribution with the hypothesis : the 100 M-values follow a uniform distribution against : the 100 M-Values do not follow a uniform distribution. The Chi-Squared Test static for each index is computed as follows:

( )

Where stands for the number of observations in each category i (i=0..99 for Absolute Test, i=1..10 for Barrier

Test and i=1,2 for Remainder Test) and stands for the number of observations expected (

( )).

The number of degrees of freedom for each test is computed as df = n-1. . The number of

degrees of freedom for each test is computed as df = n-1.The second test (Barrier Test) follows the methodology

adopted by Koedijk and Stork (1993) and splits the M-values into 10 disjunct categories of equal size, i.e. 06-15, 16-25,, 96-05. We register the number of times the index closes with an M-Value in these categories and perform a chi-square test with 10 categories in the manner described above. This test for uniformity is similar to the Absolute Test but widens the range of the potential areas of significance and is consistent with the conventional wisdom of areas of support and resistance being price bands and not absolute price levels.

While the first and second tests pick up whether the distribution of M-values follows a uniform distribution, they say little about the location of these deviations and whether they are indeed around regions of round numbers, as per the purpose of the investigation. For example, if the index closes much less frequently in the 40-50 M-value region but is uniformly distributed over the remaining values, the null hypothesis would be rejected in the first two tests but this would not be the effect we are trying to test for. Hence, a third test (Remainder Test) is introduced that attempts to separate this effect by splitting the M-values into 2 categories (96-05, 06-95) and a chi-squared-goodness-of-fit test with the expected number in each category based on the expected number if it followed a uniform distribution has also been conducted and the results reported below. The barrier tests and remainder tests have also been conducted for a wider 20 point band (90-09,etc) but the results were qualitatively similar to the tests for the 10 point band and hence have been omitted in the presentation below.

Barrier.Proximity.TestOne major limitation of the uniformity tests is the lack of

information on directionality, in that while it may present evidence for a non-uniform distribution due to unexpected deviations in our region of interest, it fails to show if that is because the index closes more frequently in those regions (price clustering) or because the index closes less frequently (evidence of barriers). This information is picked up in our second test, the barrier proximity test, as described by Donaldson and Kim (1993). We employ a variant of the methodology that yields more interpretable information in line

with that adopted by Koedijk and Stork (1994).We test by means of a OLS regression test whether

the distribution of M-values is linked to the presence of psychological barriers. A vector P(M) with length 100 is created, which registers the relative frequency of each M-value occurring along with 3 dummy variables, D1, D2 and D3 and which equal 1 if the M-value of the index at closing is in one of the following ranges: 98, 99, 00, 01, 02 for D1; 93, , 97 or 3, , 7 for D2; 85, , 92 or 8, , 15 for D3. We then regress the P(M) vector against these 3 variables:

We test by means of a OLS regression test whether the distribution of M-values is linked to the presence of psychological barriers. A vector P(M) with length 100 is created, which registers the relative frequency of each M-value occurring along with 3 dummy variables, , and which equal 1 if the M-value of the index at closing is in one of the following ranges: 98, 99, 00, 01, 02 for ; 93, , 97 or 3, , 7 for ; 85, , 92 or 8, , 15 for . We then regress the P(M) vector against these 3 variables:

( )

If there are no psychological barriers and the M-values follow a uniform distribution, what we would expect is an intercept of C = 1 and , and 1, 2 and 3 = 0. If the values are significant and not equal to zero, what this implies is that the relative frequency of M-values at the respective levels is greater (lower) than 1 if the values are positive (negative). For example, if C = 1 and 1 = 0.2 and 1 is statistically significant, what this suggests is that the relative frequency of occurrence of a M-value if it is in the 98, 99, 0, 1, 2 region is 1 0.2 = 0.8, i.e. significantly less than we would expect if the M-values are uniformly distributed and supportive of the presence of psychological barriers at round numbers. The results of this regression are shown in Table 3 and Table 5 below.

Positional EffectsIn this section we investigate if the indices close more or less

frequently around round numbers by performing the uniformity tests and barrier proximity tests on the M-values of the closing prices across the 10 years from 1 Jan 2001 to 30 Dec 2011.

Uniformity.TestsFrom the uniformity tests, we see strong evidence against

a uniform distribution of M-values at the level for 8 out of 10 of the indices in the absolute test (AORD, SSEC, BSESN, JKSE, KLSE, STI, KS11, TWII), with the results confirmed in the barrier tests and in 5 out of 8 of these indices in the remainder tests (SSEC, JKSE, KLSE, STI, KS11). For the AORD, BSESN and TWII indices that show evidence for non-uniformity in the absolute and barrier but not remainder test, this could be indicative of non-uniformity in this distribution of M-values, not due to significantly less (or more) values in the region of interest, but outside the round number region. For the 100 level we find some evidence against uniformity in the barrier tests for 2 out of 10 of the indices (N225, STI).

Barrier.Proximity.TestsFrom the regression, we see evidence of psychological

barriers at the 1000 level in 6 out of 10 of the indices (SSEC, JKSE, KLSE, N225, STI, KS11) consistent with the results from the uniformity test, as well as evidence of barriers at the 100 level in the 3 out of 10 of the indices (JKSE, KLSE, TWII). We also find evidence of clustering around the 93-97, 3-7 levels as indicated by the positive and significant 2 values in the AORD and TWII M 1000 regressions, which could be an explanation for the results they exhibited in the remainder tests.


PAGE 16 IFTA.ORG

Table 2: Chi-squared test statistics from the uniformity tests on closing prices

Index Absolute.Tests Barrier.Tests Remainder.TestsM 1000 M 100 M 1000 M 100 M 1000 M 100

AORD 263.0792 90.95103 128.1602 13.46813 1.490377 0.006762SSEC 190.039 100.3166 74.8177 14.86272 12.42461 2.481287HSI 105.3825 115.4372 14.63206 6.12204 0.292451 0.972475

BSESN 140.3906 67.92364 27.82085 2.997063 0.375918 0.127916JKSE 921.707 86.17156 631.0271 6.863106 32.06673 0.529898KLSE 1204.126 121.0935 675.8046 12.65403 101.7024 1.281192N225 102.7389 100.0682 9.578635 18.88131 3.85905 0.079789STI 233.121 116.7521 113.2472 18.25046 20.70616 2.916069KS11 717.5943 82.83391 490.082 11.41339 38.64807 0.842507TWII 144.1781 96.86387 62.41943 6.841795 2.596026 1.444853Results significant at the 95% confidence level are in yellow

Table 3: Regression parameters for the barrier proximity tests on closing prices

Index c Pc 1 P1 2 P2 3 P3AORD

M 1000 0.99 0.00 0.04 0.79 0.25 0.01 -0.13 0.12M 100 1.01 0.00 -0.06 0.50 0.01 0.85 -0.08 0.11

SSECM 1000 1.05 0.00 -0.29 0.01 -0.25 0.00 -0.07 0.34M 100 0.98 0.00 0.00 0.98 0.13 0.04 0.04 0.46

HSIM 1000 0.98 0.00 0.07 0.42 0.05 0.47 0.10 0.06M 100 1.00 0.00 0.16 0.08 -0.13 0.06 0.02 0.75

BSESNM 1000 1.00 0.00 0.05 0.67 0.10 0.21 -0.06 0.38M 100 1.00 0.00 0.09 0.20 -0.02 0.68 -0.01 0.82

JKSEM 1000 1.16 0.00 -0.58 0.02 -0.46 0.01 -0.50 0.00M 100 1.02 0.00 -0.15 0.07 -0.01 0.85 -0.09 0.07

KLSEM 1000 0.97 0.00 -0.63 0.03 -0.20 0.35 0.49 0.01M 100 1.01 0.00 -0.19 0.06 0.04 0.58 -0.03 0.64

N225M 1000 1.03 0.00 -0.26 0.00 -0.09 0.17 -0.04 0.47M 100 1.02 0.00 0.02 0.82 -0.10 0.12 -0.05 0.32

STIM 1000 1.06 0.00 -0.35 0.01 -0.31 0.00 -0.08 0.27M 100 1.01 0.00 -0.09 0.33 0.04 0.53 -0.08 0.16

KS11M 1000 1.05 0.00 -0.30 0.20 -0.43 0.01 0.04 0.76M 100 1.01 0.00 -0.03 0.79 0.05 0.38 -0.06 0.19

TWIIM 1000 0.98 0.00 0.04 0.69 0.15 0.06 0.02 0.75M 100 1.01 0.00 0.03 0.72 -0.13 0.05 -0.01 0.81

Results significant at the 90% confidence level are in yellow. PA represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0

Table 4: Chi-squared test statistics for the uniformity tests on M-value transgressions

Index Absolute Tests Barrier Tests Remainder TestsM 1000 M 100 M 1000 M 100 M 1000 M 100

AORD 248.0737 100.1657 105.9686 88.91875 10.85873 31.79044SSEC 97.82411 31.10837 59.21055 17.73228 0.529747 0.046776HSI 51.86512 35.74191 36.30685 27.80382 6.650109 9.455114

BSESN 33.93022 37.25957 23.1322 32.05841 0.174333 6.604553JKSE 548.9661 86.78622 403.9064 62.89023 48.19487 10.54079KLSE 263.1542 220.4746 133.578 116.1296 69.24603 23.0023N225 90.12974 23.93532 71.15175 17.56112 7.453099 0.117918STI 328.871 127.7222 214.8117 94.26897 30.37677 6.990322KS11 756.551 36.22413 606.6621 7.233078 15.31477 1.150354TWII 396.3475 10.93114 355.3461 6.762931 0.329328 0.006915

Results significant at the 95% confidence level are in yellow

Transgressional EffectsIn this section we test for the

presence of psychological barriers by investigating if the regions around round numbers have been transgressed less frequently than other regions. For instance, if the index jumps from 1420 to 1532, the M 1000 values from 43 to 53 are transgressed and the M 100 values from 21 to 32 are transgressed. We conduct chi-squared tests for uniformity and perform the barrier proximity tests using the same specifications as above on the distribution of M-values that have been transgressed for each index and the results are presented in an identical format to Tables 2 and 3 in Tables 4 and 5.

Uniformity.TestFor the uniformity tests, we see

evidence against a uniform distribution of M-values in all the indices at the 1000 level and for 8 out of 10 indices at the 100 level (AORD, SSEC, HSI, BSESN, JKSE, KLSE, N225, STI) in the barrier tests. This is confirmed in 7 out of 10 indices at the 1000 level (AORD, HSI, JKSE, KLSE, N225, STI, KS11) in the remainder tests and in 6 out of 10 indices in the absolute tests (AORD, JKSE, KLSE, STI, KS11, TWII). At the 100 level, this is confirmed in 6 out of 8 indices in the remainder tests (AORD, HSI, BSESN, JKSE, KLSE, STI) and in 2 out of 8 indices in the absolute tests (KLSE, STI). The stark difference in the number of indices that demonstrate evidence against a uniform distribution in the absolute test compared to in the barrier and in the remainder tests particularly at the 100 level suggests that for some of these indices the individual M-values may be approximately uniformly distributed, but when grouped into categories around the barrier levels there is evidence against a uniform distribution, which can be seen as evidence for the presence of psychological barriers in the region around round numbers but not at the exact round number level, consistent with the conventional wisdom of support and resistance existing as regions around a level instead of at a single fixed level.


IFTA.ORG PAGE 17

Table 5: Regression parameters for the barrier proximity tests on M-value transgressions

Index c Pc 1 P1 2 P2 3 P3AORD

M 1000 1.00 0.00 0.13 0.08 0.16 0.00 -0.12 0.01M 100 1.02 0.00 -0.08 0.00 -0.08 0.00 -0.05 0.00

SSECM 1000 1.00 0.00 -0.02 0.70 -0.04 0.26 0.03 0.36M 100 1.00 0.00 0.01 0.60 -0.01 0.47 0.01 0.28

HSIM 1000 0.99 0.00 0.05 0.00 0.03 0.00 0.02 0.00M 100 0.99 0.00 0.04 0.00 0.03 0.00 0.02 0.00

BSESNM 1000 1.00 0.00 0.01 0.44 0.00 0.87 0.01 0.21M 100 0.99 0.00 0.04 0.00 0.03 0.00 0.02 0.00

JKSEM 1000 1.14 0.00 -0.53 0.00 -0.37 0.00 -0.46 0.00M 100 1.02 0.00 -0.04 0.01 -0.08 0.00 -0.05 0.00

KLSEM 1000 1.04 0.00 -0.68 0.00 -0.44 0.00 0.27 0.00M 100 1.01 0.00 -0.06 0.26 -0.14 0.00 0.05 0.14

N225

M 1000 1.02 0.00 -0.10 0.10 -0.04 0.00 -0.08 0.00

M 100 1.00 0.00 0.00 0.74 -0.01 0.06 0.00 0.56

STIM 1000 1.05 0.00 -0.30 0.01 -0.27 0.00 -0.05 0.39M 100 1.02 0.00 -0.03 0.13 -0.07 0.00 -0.06 0.00

KS11M 1000 1.00 0.00 -0.14 0.49 -0.20 0.20 0.16 0.19M 100 1.01 0.00 -0.02 0.24 -0.02 0.04 -0.02 0.04

TWIIM 1000 1.01 0.00 -0.01 0.85 -0.01 0.81 -0.07 0.09M 100 1.00 0.00 0.00 0.67 0.00 0.38 0.00 0.95

Results significant at the 90% confidence level are in yellow. PA represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0

Table 6: Regression parameters for the test on return predictability

Index c

AORDM 1000 0.000023 0.92 -0.000348 0.70 -0.000272 0.66 0.000874 0.14 -0.022171 0.24M 100 0.000048 0.84 -0.021365 0.26 0.000869 0.45 0.001191 0.07 -0.000713 0.21

SSECM 1000 0.000191 0.62 -0.000634 0.71 -0.001853 0.13 0.000021 0.98 0.004302 0.82M 100 0.000110 0.78 -0.000380 0.84 -0.000816 0.44 0.000090 0.92 0.003468 0.86

HSIM 1000 -0.000161 0.67 0.000781 0.58 0.001611 0.12 0.000206 0.81 -0.025871 0.18M 100 0.000189 0.61 -0.002124 0.23 0.001279 0.25 -0.000929 0.28 -0.026532 0.16

BSESNM 1000 0.000634 0.10 -0.000085 0.95 -0.000510 0.62 -0.000786 0.38 0.078057 0.00M 100 0.000195 0.60 -0.004174 0.02 0.001333 0.22 0.001692 0.05 0.076570 0.00

JKSEM 1000 0.000759 0.02 0.001957 0.27 -0.000756 0.52 -0.000205 0.83 0.117766 0.00M 100 0.000689 0.05 0.000338 0.86 0.000841 0.39 -0.000277 0.74 0.116878 0.00

KLSEM 1000 0.000078 0.77 0.000792 0.64 0.002787 0.00 0.000166 0.75 -0.132408 0.00M 100 0.000539 0.04 -0.002514 0.07 -0.000857 0.24 -0.000231 0.71 -0.134908 0.00

N225M 1000 -0.000143 0.70 0.000264 0.87 0.000102 0.93 -0.000392 0.65 -0.03418 0.08M 100 -0.000512 0.16 0.001925 0.28 -0.000608 0.58 0.002081 0.02 -0.034389 0.07

STIM 1000 0.000147 0.61 0.000045 0.97 0.000885 0.34 -0.000606 0.37 0.010741 0.57M 100 0.000203 0.48 -0.000377 0.82 -0.001220 0.13 0.000367 0.60 0.010346 0.59

KS11M 1000 0.000749 0.05 -0.000864 0.61 -0.000260 0.85 -0.001428 0.09 0.022893 0.23M 100 0.000496 0.19 -0.005436 0.00 0.001097 0.30 0.000016 0.99 0.023296 0.22

TWIIM 1000 0.000279 0.42 0.000370 0.78 -0.002336 0.01 0.000563 0.48 0.059239 0.00M 100 0.000097 0.77 0.000732 0.64 0.001230 0.23 -0.000666 0.40 0.060986 0.00

Results significant at the 90% confidence level are in yellow. represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0

Barrier.Proximity.TestFor the barrier proximity tests, we

see evidence supporting the presence of psychological barriers in 5 out of 10 of the indices at the 1000 level (JKSE, KLSE, N225, STI, TWII) and evidence of price clustering around round numbers in 2 out of 10 of the indices at the 1000 level (AORD, HSI) with the remaining indices with intercepts that are not statistically significant, suggesting the absence of psychological barriers. At the 100 level, we see evidence supporting the presence of psychological barriers in 6 out of the 10 indices (AORD, JKSE, KLSE, STI, KS11, N225 (with weak evidence)) and evidence supporting price clustering in 2 out of 10 indices (HSI, BSESN) with the remaining indices with intercepts that are not statistically significant.

Return PredictabilityHaving examined the presence of psycho-

logical barriers, we proceed to investigate if these levels can be used to predict stock returns. We employ the methodology of Koedijk and Stork (1994) and test the follow-ing specification over the sample:

Having examined the presence of psychological barriers, we proceed to investigate if these levels can be used to predict stock returns. We employ the methodology of Koedijk and Stork (1994) and test the following specification over the sample:

( )

( )

( )

Where

( )

Having examined the presence of psychological barriers, we proceed to investigate if these levels can be used to predict stock returns. We employ the methodology of Koedijk and Stork (1994) and test the following specification over the sample:

( )

( )

( )

Where

( )

And where rt stands for the stock return, st for the index at time t, Dt(1) stands for the value of the first dummy variable at time t, Dt(2) stands for the value of the second dummy variable at time and t and Dt(3) stands for the value of the third dummy variable at time t. The dummy variables are specified in the same way as the regression that was run for the barrier proximity test.

From the regression, we find little evidence to support return

Where


PAGE 18 IFTA.ORG

predictability for most of the indices with most of the parameter estimates for the dummies of the psychological barriers not statistically significant. Only in the BSESN at the 100 level, KLSE at the 1000 and 100 level, the KS11 at the 100 level and the TWII at the 1000 level is there some evidence of the predictability of stock returns induced by the presence of psychological barriers.

DiscussionTable 7 summarizes the results from all the tests with a final

conclusion on whether there is sufficient evidence for positional effects, transgressional effects and psychological barriers. When there were conflicts in the results within each section, they were resolved in the following manner: If there was evidence of a non-uniform distribution but no evidence of barriers in the regression test, it was concluded that there was no evidence for that section. If there was evidence of barriers in the regression test but no evidence of non-uniformity in all the 3 tests, it was concluded that there was no evidence for the section. If there was evidence of barriers in the regression test and evidence of non-uniformity in only one of the 3 tests, if that non-uniformity test was the barrier test, then it was concluded that there was no evidence for the section; but if the non-uniformity test was the remainder test then it was concluded that there was evidence for the section.

For conflicting results between the section for transgressional effects and positional effects, they were resolved in the following manner: If there was evidence of transgressional effects but not positional effects, it was concluded that there was evidence of psychological barriers. If there was evidence of positional effects but not trangressional effects it was concluded that there was no evidence of psychological barriers.

This is because the data set for the testing of transgressional

effects is larger and hence the evidence would have to be stronger for there to be evidence of barriers. In addition, the test for transgressional effects specifically looks at movements from one day to the next and hence would capture the presence of barriers in a more compelling manner than the test for positional effects.

ConclusionIn this study, we have examined the presence of

psychological barriers in the equity indexes of 10 Asian Markets over a 10 year period from 2001-2011. We have found evidence for barriers at the 1000 level for 6 of these markets (JKSE, KLSE, N225, STI, KS11, TWII) and at the 100 level for 4 of these markets (AORD, JKSE, KLSE, STI). However, while there may be evidence of psychological barriers, there is little evidence for the predictability of stock returns induced by the presence of these psychological barriers.

ReferencesAggarwal, R., & Lucey, B. M. (2007). Psychological barriers in gold

prices? Review of Financial Economics, 217-230Chen, M. H., & Tai, V. W. (2011). Psychological barriers and prices

behaviour of taifex futures. 2011 International Conference of Taiwan Finance AssociationDonaldson, R. G., & Kim, H. Y. (1993). Price barriers in the dow jones industrial

average. Journal of Financial and Quantitative Analysis, 28(3), 313-330.Dorfleitner, G., & Klein, C. (2009). Psychological barriers in European

stock markets: Where are they? Global Finance Journal, 268-285.Harris, L. (1991). Stock price clustering and discreteness. Review of

Financial Studies 4, 389-415.Johnson, E., Johnson, N. B., & Shanthkumar, D. (2008). Round numbers

and security returns. Koedijk, K. G., & Stork, P. A. (1994). Should we care? Psychological

barriers in stock markets. Economics Letters , 427-432.Schindler, R.M. and Kirby, P.N. (1997). Patterns of rightmost digits

used in advertised prices: implications for nine-ending effects. Journal of Consumer Research 24, 192-201.Ley, E. & Varian, H.R. (1994). Are there psychological barriers in the

Dow-Jones index? Applied Financial Economics, 4, 217-224.Mitchell, J. (2001) Clustering and Psychological Barriers: The Importance

of Numbers. The Journal of Futures Markets, 21, 395428.Sonnemans, J. (2006). Price clustering and natural resistance points in

the dutch stock market: a natural experiment. European Economic Review, 1937-1950.Ziemba, W.T., Brumelle, S.L., Gautier, A. and Schwartz, S. L. (1986). Dr. Zs

6/49 lotto guidebook. Vancouver, Canada: Dr. Z Investments.

Table 7: Summary of results for the various tests


IFTA.ORG PAGE 19

AbstractBollinger Bands have been one of the greatest tools

developed for technical analysis. In statistical terms, Bollinger Bands involve the construction of a 95% confidence interval around the moving average of a stocks price and they capture the mean plus and minus two standard deviations. Having said that, Bollinger Bands are subject to a number of limitations including the assumption that prices are normally distributed and ambiguity in terms of generating explicit trading decisions when prices move in trends. The key objective of this research paper is to develop the next-generation trading bands that not only use empirical price distributions without making a normality assumption but also include the use of autocorrelation to determine whether prices are moving in a trending or oscillating regime so that a better buy or sell decision can be made. The regime-switching trading bands using historical simulation will be applied to different test cases and the performance of these next-generation trading bands will be summarized in this paper.

1. IntroductionBuying low and selling high is one of the most fundamental

strategies in trading. Trading bands are intuitive and easy-to-use tools that can help traders in determining entry and exit points for their investments. The most popular and well-known trading bands are the Bollinger Bands, and Section 2 provides a fulsome review of Bollinger Bands and other trading bands that currently exist.

Bollinger Bands were developed by John Bollinger in the 1980s. Given the relatively limited computing power and technology during that period of time, it would be logical to develop a tool that is easy to calculate. One of the implicit assumptions made in the use and interpretation of Bollinger Bands is the normality of the distribution of stock prices. Interestingly, there is a great deal of empirical evidence that suggests that asset prices, such as equity prices, are better characterized by skewed and fat-tailed distributions rather than normal distributions. Therefore, it would be useful if we could develop trading bands that could capture the empirical behavior without making any simplifying assumptions about the shape of the distribution.

No single technical analysis tool is perfect and it is logical to complement an existing tool (i.e. Bollinger Bands in this case) with other metrics that could potentially fine-tune trading signals. The Directional Movement Indicator (DMI) developed by Welles Wilder is an interesting trading tool as it not only has an indicator component but also a metric called Average Directional Index (ADX) that determines whether or not prices move in trends, which in turn will determine whether the

DMI indicator itself should be used for generating a reliable trading signal. The DMI tool offers us two key lessons to consider in developing a new technical analysis tool. The first key lesson learned is that a comprehensive technical analysis tool or trading system should have two key components. One component acts as a filter to help the trader determine whether or not the tool or indicator itself should be used. The other component, of course, is the main indicator itself. The second key lesson learned is the importance of assessing whether the price is trending or oscillating in technical analysis.

This paper will describe the development of the next-generation trading bands that not only capture the skewed and fat-tailed nature of stock price distributions but also use a statistical filter to determine whether the price is in the trending or oscillating regime, in the short, term so that traders can make better buy or sell decisions.

2. Review of the Use of Bollinger Bands and Other Trading Bands

Bollinger Bands (BB) are one of the useful decision-making tools developed in technical analysis. They are typically calculated as the 20-day simple moving average of closing prices plus and minus two standard deviations over that 20-day period. The lower bound forms a support while the upper bound forms a resistance. It is important to highlight the linkage between Bollinger Bands and the concept of confidence intervals in statistics. In statistical terms, Bollinger Bands are basically 95% confidence interval around the moving average and they capture the mean plus and minus two standard deviations as long as the distribution is normally distributed. A buy signal is generated when prices are trending down and hit the lower band. Similarly, a sell signal is generated when prices are trending up and hit the upper band.

One of the implicit assumptions used in the interpretation and application of Bollinger Bands is normality and a significant amount of empirical evidence suggesting that security prices such as stock prices are not normally distributed. Instead, they show skewed and fat-tailed distribution exhibiting various degrees of skewness and kurtosis. Therefore, symmetrical bands around the moving average such as Bollinger Bands may not capture the skewness and kurtosis of the price movements adequately.

Bollinger Bands also make another implicit assumption that stock prices tend to be mean-reverting as a buy signal is generated when the price hits the lower band, while a sell signal is generated when the price hits the upper band. In other words, prices that go outside the bands are considered to be too extreme and therefore are expected to be pulled back to the

Regime-Switching Trading Bands Using A Historical Simulation Approach By Ka Ying Timothy Fong, CFTe, MFTA


PAGE 20 IFTA.ORG

moving average. A commonly identified limitation of Bollinger Bands is the lack of an appropriate signal when prices move in trends and in turn track along either the upper or lower band. Therefore, a statistical indicator or metric that could measure whether the prices are oscillating or reverting would be very useful for improving the accuracy of trading signals generated by these bands.

Other trading bands that are typically covered in standard technical analysis textbooks are Moving Average Envelopes (ENV), Keltners Channel (KC) and Donchian Channel (DC).

Moving Average Envelopes can be obtained by adding or subtracting a pre-determined fixed percentage, e.g. 5% to a simple or exponential moving average. An obvious advantage of ENV is its computational simplicity. However, the selection of the fixed percentage is perhaps too arbitrary, and there is no intuitive statistical interpretation of the pre-defined percentage and the resulting envelope.

Keltners Channel is made up of two bands plotted around an Exponential Moving Average (EMA) of typical prices. For the upper band, the Average True Range (ATR) is calculated over 10 days, doubled and added to a 20-day EMA. A similar procedure can be used to calculate the lower band. There are two key differences between Bollinger Bands and Keltners Channel. Firstly, Bollinger Bands use closing prices in the calculation while Keltners Channel uses typical prices in the calculation. Secondly, Bollinger Bands use standard deviation to measure dispersion but Keltners Channel uses ATR to measure variability. One should also observe that Keltners Channel has attempted to measure dispersion or variability by using ATR (which could capture gaps in the price series) rather than standard deviation, but it does not have a mechanism to tell under what conditions the channels themselves should be used.

Lastly, Donchian Channel (DC) is an indicator developed by Richard Donchian. It is formed by taking the highest high and the lowest low over the last n days. If the stock price is above its highest high for the last n days, then a buy signal is generated. On the other hand, if the stock price is below its lowest low for the last n days, then a sell signal is generated. The key difference between Donchian Channel and the other three trading bands (i.e. BB, ENV and KC) is that trading signals generated by Donchian Channel are based on breakout of the channels while trading signals from other trading bands are based on mean-reversion away from the channels.

One could see why Bollinger Bands are superior among these four trading bands as Bollinger Bands give rise to some

intuitive interpretation in the context of normal distribution. If the underlying prices follow a normal distribution, the 68-95-99 empirical rule could be used to interpret the results, i.e. 68% of the price data is within one standard deviation from the mean, 95% of the price data is within two standard deviations from the mean, etc. Therefore, prices going outside the bands are considered abnormal and are expected to revert to the mean. Table 1 below shows a summary of key features of the four commonly used and well-documented trading bands as well as the proposed regime-switching trading bands (or Fongs Bands, to keep it simple).

A key observation from the review of four commonly used and well-documented trading bands described is that none of them can be considered as a comprehensive trading system (which is previously defined as a tool that has two key components). Therefore, this paper will introduce the following three specific new dimensions into our regime-switching trading bands: 1) historical simulation approach to generate the trading bands so that the empirical price distribution can be captured, 2) an autocorrelation filter to make the bands a trading system by indicating whether the price is trending or oscillating, and 3) a swing confirmation filter to deal with the situation where prices have a higher tendency to increase momentum rather than reverting to the mean.

3. The Significance of Historical Simulation, Autocorrelation and Swing Filter in Fine-Tuning the Decision-Making Process for the Use of Trading Bands

Historical simulation is a non-parametric approach that is often used in the context of Value-at-Risk calculation for trading books at banks. This approach makes no parametric assumptions about the price distribution and also involves the use of percentiles in measuring risk. One of the key assumptions in historical simulation is that past history will repeat itself in the future. This assumption is consistent with one of the three key principles or foundations of technical analysis that history will repeat itself (i). For risk measurement purposes, banks focus on the tail or the lower percentile of the return distribution. In the context of this research paper, the 5th percentile and the 95th percentile of the closing prices for the last 20 days will form the upper and lower bands, and the dispersion

Table 1


IFTA.ORG PAGE 21

of stock prices will be measured by the interpercentile range (i.e. the difference between the 5th percentile and the 95th percentile). We can also apply this concept to any percentile and for any historical look-up period. More importantly, depending on the skew and kurtosis of the price history, these bands that are generated by historical simulation capture the entire empirical distribution (including fat tails) and may be asymmetrical (unlike the Bollinger Bands).

The second key principle of technical analysis is the belief or observation that prices move in trends (i). An objective method of measuring whether prices are moving in trends or oscillating is very important in technical analysis. For example, Welles Wilders Average Directional Index (ADX) is a well-known indicator that measures the strength of the trend as part of the DMI trading system. Perhaps a more direct and intuitive way of measuring whether the price is trending or oscillating is to use the concept of autocorrelation. Autocorrelation is definitely a well-known concept for statisticians or econometricians in time series analysis. However, autocorrelation is somewhat underused in technical analysis. It is not a standard topic in technical analysis textbooks used for professional technical analysis designations, such as the CFTe program administrated by IFTA. Also, most technical indicators that are commonly available on popular websites such as Yahoo Finance or stockcharts.com do not take autocorrelation into consideration.

A brief overview of autocorrelation would be definitely helpful in illustrating its usefulness in the trading system proposed in this paper. Autocorrelation, also known as serial correlation, measures the correlation of the data points over time. The following is the sample autocorrelation formula:

Figure 1 Figure 2

where P is the closing price of a stock, h is the time lag, N is the number of observations and P is the average closing price over the respective period. In the context of measuring trends for daily prices over a short period of time, we are dealing with a time lag (h) of 1 specifically. It means that we are measuring whether an up-day is likely to be followed by another up-day and vice versa, where an up-day is defined as a day where the closing price is higher than the closing price on the previous day. The following two diagrams illustrate the key interpretation of autocorrelation in the context of technical analysis:

Figure 1 Figure 2

Figure 1 shows a situation where prices move in a perfect uptrend and the autocorrelation for this case is +1. On the other hand, Figure 2 shows a situation where prices are oscillating in such a way that a daily price change in one direction is followed by a daily price change of equal size in the opposite direction.

In this case, the sample autocorrelation will be -1. The sign of the sample autocorrelation tells the trader whether the prices move in trends or not. Positive autocorrelation implies that prices move in trends (i.e. trending regime) while negative autocorrelation implies that prices oscillate (i.e. oscillating regime). The magnitude of the sample autocorrelation gives an indication of the strength of a trend. In the context of identifying a change from a trending regime to an oscillating regime, if the autocorrelation changes from a positive sign to a negative sign, the direction of a price movement is more likely to reverse (more detailed explanation of the application of the bands can be found in Section 4) and therefore the use of historically simulated trading bands is more likely to identify optimal entry and exit points for a trade.

One of the problems encountered through the use of the Bollinger Bands is that the price can track along the bands when prices show exceptional momentum. In other words, the price could touch the upper or lower band multiple times over a short period of time, resulting in a false or premature buy or sell signal. In this case, even the autocorrelation filter might not help us resolve the problem completely when prices show extremely strong momentum. In this situation, a swing filter, first introduced by Arthur Merrill in his book, Filtered Waves, in 1977, will be useful in generating a correct buy or sell signal. The swing filter is basically a pre-determined percentage of price movement and is generally considered as a breakout trading tool. In other words, prices are assumed to continue on its trend until prices reverse more than the pre-defined threshold or trigger. In the situation where prices hit the trading band with positive autocorrelation, it means that the price is breaking out to levels observed in the extreme tails of the historical price distribution. The swing filter serves as a means to confirm the price reversal so that those extra miles from the trend can be captured more fully in the use of the trading bands. Detailed description of test cases is provided in Section 5.

4. The Methodology for Regime-Switching Trading Bands using a Historical Simulation Approach (Putting them all together) Transitions between a rising and falling trend are often

signaled by price patterns (ii). Many of these patterns involve the consolidation of prices manifested in the form of a zig-zag or whipsaw. These consolidation movements generally show negative autocorrelation, as shown in Section 3. The use of autocorrelation eliminates a cognitive recognition or assessment of these price patterns by the traders and it measures objectively whether the price is trending or oscillating, i.e. whether the price is going through the transition signaling a potential turn or reversal. In other words, the autocorrelation is positive when prices are trending and the autocorrelation is negative when prices are oscillating (i.e. giving a reversal signal). In the context of our regime-switching trading bands, if the autocorrelation is changing from positive to negative by crossing the zero line (when the price is hitting the lower band or upper band), it indicates that the price may be transitioning or consolidating and therefore it is more


PAGE 22 IFTA.ORG

likely for the historically simulated trading bands to give the traders the optimal entry/exit points right before the reversal of the price.

In the application of the regime-switching trading bands, when prices move in a downtrend towards or hit the lower band (for example), it will only trigger a buy signal when the price is in an oscillating regime (i.e. negative autocorrelation). Then, the swing filter rule of x% will be used to generate a buy signal, meaning that the prices need to revert to the upside for more than x% before a legitimate buy signal is generated. The

following diagram (Figure 3) illustrates how autocorrelation could facilitate the decision-making process for buying with trading bands (and the converse for selling is true as well):

A decision-tree generated from the regime-switching trading bands is outlined in Figure 4 below:

In terms of the parameters and other assumptions for the bands, we will use the 5th and the 95th percentiles over the last 20 days as our trading bands, with an autocorrelation filter, using the last 10 days of closing price data in the application of the regime-switching trading bands, using a historical

negative autocorrelation when prices oscillate or consolidate during a transition period use the lower band as entry point to buy

positive autocorrelation when prices move in a downward trend

If the price reverts to the upside for more than x%, it confirms that the price is breaking out from the consolidation pattern and a buy signal will be generated.

Lower Band

Stock Price

Price hits or gets close to the lower band.

If autocorr is positive (i.e. trending regime), then do nothing.


If autocorr is non-positive (i.e. oscillating regime), then buy only when the price reverts up by more than x%.

Price hits or gets close to the upper band.

If autocorr is non-positive (i.e. oscillating regime), then sell only when the price reverts down by more than x%.

Figure.3

Figure.4


IFTA.ORG PAGE 23

simulation approach. The detailed methodology of how the bands and the autocorrelation are calculated mathematically will be discussed below.

As mentioned in previous sections of this paper, the generation of the bands will involve the use of percentiles. The value of the Pth percentile of an ascending ordered price data series containing n data points with values such that v1 v2 vn is defined as vp . First of all, the rank for a given percentile P is calculated as follows:

Price hits or gets close to the lower band.



If autocorr is non-positive (i.e. oscillating regime), then buy only when the price reverts up by more than x%.

Price hits or gets close to the upper band.

If autocorr is non-positive (i.e. oscillating regime), then sell only when the price reverts down by more than x%.

where rank is further broken down into an integer component i and a decimal component d such that the sum of the two components is equal to the rank. Then the value of the P th percentile (VP )will be calculated as follows:

Given the above parameterization and methodology, the lower band (L) will be calculated as the 5th percentile and the upper band (U) will be calculated as the 95th percentile given the last 20 days of closing prices which are ranked in an ascending order such that p1 p2 p20. By using the above percentile concept, the lower band and the upper band on a given day will be calculated as follows:

Regarding the calculation of autocorrelation, only 10 out of 20 closing prices are used in order to make the autocorrelation value more sensitive to recent closing prices and preserve the principle of harmonicity developed by J.M. Hurst at the same time. Specifically, a time lag of 1 and the last 10 days of closing prices (i.e. R1, R2, , R10) will be used to calculate the daily autocorrelation value for the regime-switching trading bands where pt is the closing price on the tth day looking backwards. The following formula shows how the daily autocorrelation value (r1)is calculated:

where 9

9

1

=

=i

ipa and 9

9

11

=

+

=i

ipb

. It is important to note that a and b represent the respective averages over slightly different time periods i.e. {R1, R2, , R9} for the calculation of a vs. {R2, R3, , R10} for the calculation of b. The application of the regime-switching trading bands using empirical data and the associated results on their performance will be discussed further in the next section.

5. Application of Regime-Switching Trading Bands and Empirical Results

Data f

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