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2005-06-30 http://toronto.tasug.com johncw_97@yahoo.com 1

Volume’s Value episode II

Continuation of April 26th 2005 meeting

• Revisit abnormal trading days• Look at a few normalization indicators• Relationship between price and volume

Martin J. Pring[1] summarized the following:

1. Volume is measured in trends, and the trends are always interpreted in relations to the recent past.

2. It is normal for volume to expand with rising prices and contract with declining ones. Anything to the contrary is abnormal and warns of an impending trend reversal.

Martin J. Pring[1] summarized the following (cont):

• During bullish trends, it is normal for volume to lead the price.

• Selling climaxes clear the air. They do not necessarily signal the final low for the move but are almost always followed by a rally.

• Record volume coming off an important low usually signals a strong rally

Martin J. Pring[1] summarized the following (cont):

1. A parabolic expansion in price and volume represents an exhaustion move, which is typically followed by a sharp decline.

Pring[2] has expanded material on volume.

Singal[3] (in chapter 4) concluded

• “In general, there is no evidence of tradable price regularities following large price events. If large price changes are accompanied by other traits of information, such as high volume and public dissemination of news, the patterns become stronger. … The annualized return after transactions costs can be estimated at 36% annually for positive price changes and 15% for negative price changes. This strategy works even in bear markets!”

Average Return on Day of Large Change for stocks > $10

• Singal[3] states also that the average return on day of large change in 1990 to 1992 in increasing relative return on day 0, was 7.13% and 0.08% from day 1 to day 20. For average decline on day 0 of -7.13% there was an return of -0.48% by day 20.

Brian R. Bell[4] states:

Normalizing an indicator allows you to do several things.

2. Allows historical analysis to become easier since the values of the indicator are more consistent over long periods.

3. Cross-market analysis becomes possible, since the values of the indicator are more consistent across different instruments.

Brian R. Bell[4] states:

1. Analysis over several time frames becomes easier, since the values of the indicator can be made consistent.

2. Effects from sudden changes in volatility can be removed.

Some normalization techniques

Bell[4] gave example of a 4/8 moving average price oscillator normalized to the 1st 4 methods techniques listed below:

2. Average price3. Standard deviation of price4. Average true range of price5. Range of the oscillator itself6. Using log function – as seen (aka Jeff) in

TASUG meetings. See also Mandelbrot [5] chapter 4 “Images of the Abnormal” for price examples.

Examples of what is abnormal volume?

• One of the criteria Bollhorn[6] uses to check for “Abnormal Activity to Predict New Upwards Trends” is to compare the volume today, relative to the 20 day volume average.

• Swing[7] produced a scan based on Pritamani et al[8]*. Criteria is as follows:

2. Liquidity of 100,000 traded/day on average.

3. Twice the average volume.4. Positive short-term momentum.5. Exceptionally strong intra-day trend.* Note that reference [3] and most likely [8] are based on information in reference [9].

// Translation of Swing[7] scan using in Amibroker[10] afl // liquidity: 100,000 shares traded per Day, on average.MAv = MA(V,20);// require the High Volume, as in Pritamani AND Singal[8].// Specifically, twice the average Volume.Filter_v = MAv>100000 && V>MAv*2;// Require positive short-term momentum.// Use the directional indicators and the 1-day change as proxy for this.Filter_d = PDI(14)>MDI(14) && (C/Ref(C,-1)-1) > 0.05;// Finally, we require an exceptionally strong intra-Day trend,// as calculated by how much of the intra-Day volatility translated// into upwards movement.Filter_t = (Close-Open)/(High-Low) > 0.75;// Exploration scan using criteria aboveFilter = Filter_v && Filter_d && Filter_t;

• Some one had mentioned that one should look at 3 times the average volume …

• Bajo[11] computed the normalized abnormal volume (NAV) with Number of Trading Days (NTD=66) using:

• Bajo[11] computed the normalized abnormal volume (NAV) with NTD=66.It is just a normalized standard deviationtechnique. It is written in Amibroker afl as:

nav = (V - MA(V,66))/StDev(V,66);

In statistics, this formula is known as

“Z-score”.

Using volume standard deviation method as in Bajo[11]

• Using standard deviation(SD), we know that 95.5% of the change in volume should be within 2SD and 99.7% within 3SD.

• Bajo[11] used the levels of over 2.33SD and 3.1SD for indicating abnormal volume.

• Since there are about 250/251 trading days in the North American markets, using 20 (NTD=60) or 21 (NTD=63) trading days per month may be appropriate. References [3,6,7,8,9] uses 20 days per month in SD or average calculation.

Normalization Consideration?

• When normalizing, one may consider not using the current price or volume in the calculation. For moving average normalization, instead of 2*MA(V,20), one can use twice the previous average volume. i.e. 2*ref(MA(V,20),-1).

• Period used.• Advantages/Disadvantages?

Example Charts using AmiBroker[10]

• Next set of slides are example charts of some normalization methods with different periods.

Normalization summary

1. Volume Standard deviationVsd = (V – ref(ma(V,period),n))/ref(stdev(V,period), -n);

2. Volume Moving AverageVma = V/ref(ma(V,period),-n);

3. Volume with RangeVhr = 100*(V - LLV(V,period))/(HHV(V,period)-LLV(V,period));

For starters, try using value period from 20 to 60 and n should be at least 1. On page 507 of Kaufman[12], he uses n=5 for formula (2) above.

• Misc– Bollhorn[6] examples AAPL, MSFT…– Normalized price …– Scans …– Other normalized indicators– …

Statistically analyzing volume

• One method of visualizing data distribution is by plotting all the data in something like a scatter plot.

• By using methods like in Goodman[13], one may be able to help answer question like “Is an increase in the activity of a stock a meanful indication of the direction of the price?”

• Following two slides are scatter like plots. The second one is zoom in view of the first.

• One can tabulate the data in groups and display the result as a spreadsheet.

Note to make things simple, when you see the range like n-m, the values are greater than n and up to m. i.e. 0-2 means greater than 0 and including 2.

USvolumeTest_61_F20030101T20041231_0sv_P20_V1.csv

54917686381256876>15

5463462079646523050910-15

87511038194972302178765545-10

37577972950027612500140683-5

15941142933018572007147952-3

21041146535321342477269810-2|Price change| %

>53.1-52.33-3.12-2.331-20.5-10-0.5

Normalized volume (xSD)

• As a map

• As a bar chart

• As a colour bar chart

Filename/chart meaning

Note that the data file names end in V#.dat. When # is0 then the volume of at least 100000.1 then there is also a bullish candle requirement of (C-O)/(H-L)>0.752 then it uses the basic requirement of Swing[7] – see slide 13.

The first day is day 0. So if we were to buy, we use the next day (i.e. 2nd day) close0sv denotes standard deviation volume vs absolute price change on that day

1mv denotes moving average volume vs absolute price change on that day2pr denotes price range vs price change3di denotes standard deviation volume vs price change range4fp20d denotes price range vs future price change (20th day close over 2nd day close)5fq20d denotes price range vs maximum future price change in 20 days over 2nd day close6fr denotes price change vs the close of n day over the 2nd day close

Filename/chart example

The file nameUSvolumeTest_61_F20030101T20041231_0sv_P20_V1.dat

denotes that • the watchlist is called USvolumeTest• the watchlist number is 61• analysis is from 2003-01-01 to 2004-12-31• (0sv) standard deviation volume vs absolute price change chart• P20 – using a 20 period in the normalized volume• V1 – with additional bullish candle requirement of

(C-O)/(H-L)>0.75

US sample example

Sample of 1814 US stocks.• Minimum volume of 100000• Period of 2003-01-01 to 2004-12-31.

Following slides are colour charts of the results.

The outputs are produced by running Amibroker 3 times (i.e. V=0,1,2) on the watchlist USvolumeTest and then running Gnuplot[14] on the charts.

TSX sample

Using a sample of 725 TSX stocks and applying the following:

• Minimum volume of 100000• Period of 2003-01-01 to 2004-12-31.

Following slides are colour charts of the results.

Discussion

• …

References

1. Pring, Martin J., “Volume Basics”, Stocks and Commodities, July 2000, Volume 18, No. 7, pages 36-41.

2. Pring, Martin J., “Technical analysis explained”, McGraw-Hill 2002.

3. Singal, Vijay, “Beyond the random walk: a guide to stock market anomalies and low-risk investing”, Oxford University Press 2004, Chapter 4 “Short-Term Price Drift”, pages 56-77.

References

• Bell, Brian R., “Normalization”, Stocks and Commodities, October 2000, Volume 18, No. 10, pages 58-68.

• Mandelbrot, Benoit et al, “The (Mis)behavior of markets”, Basic Books 2004, pages 88-94.

• Bollhorn, Tyler, “Using Abnormal Activity to Predict New Upward Trends”, 2000. http://www.smallcapcenter.com/help/pdf/abnormal.pdf

References

• Swing, Larry, “Breakout Stocks”, May 12 2005. http://www.mrswing.com/artman/publish/article_1029.shtml

• Pritamani, Mahesh and Singal, Vijay, “Return Predictability Following Large Price Changes and Information Releases”, Journal of Banking and Finance, April 2001, Volume 25, No. 4.

• Pritamani, Mahesh, “Return Predictability Conditional on the Characteristics of Information Signals”, PhD Dissertation 1999. http://scholar.lib.vt.edu/theses/available/etd-042399-112528/

References

• AmiBroker 4.70, http://www.AmiBroker.com

• Bajo, Emanuele, “The Information Content of Abnormal Trading Volume”, May 24 2005 draft paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=313582

• Goodman, William M., “Statistically Analyzing Volume”, Stocks and Commodities, November 1996, Volume 14, No. 11, pages 465-470.

References

• Kaufman, Perry J., “New Trading Systems and Methods”, Wiley 4th Edition Feb 2005.

• Gnuplot data and function plotting routine. http://www.gnuplot.info

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