Jeff Augen’s Price Change Behavior Model

Jeff Augen’s book “The Volatility Edge in Options Trading: New Technical Strategies for Investing in Unstable Markets” is one of my favorite books.

Jeff says in his book: “My goal was to develop an investment strategy based on the fundamental mathematical properties that describe financial markets. Properly executed, such a strategy should provide excellent returns in a variety of market conditions. It should also be persistent in the sense that it transcends short-term trends. A perfect strategy would embody risk-management mechanisms that allow an investor to precisely calculate the expected return and worst-case loss for a given set of trades.” That is exactly what I am trying to do recently.

In that book, Jeff introduced a new way to look price change behavior of a stock. He calculates the daily standard deviation of natural Logarithm of price change, and the price change for the stock is then expressed in terms of daily standard deviation. Below is such a plot for AAPL.

Please note that the standard deviation here is calculated from Natural Logarithm of price change. We know that the Historical Volatility(HV) is actually the standard deviation on annual basis of log of price change, so to find daily STD, all we have to do is that HV being divided the SQRT of trading days in a year (252):

Daily STD = (HV for that day)/sqrt(252)

Then we calculate the daily STD price change:

Daily STD price change for the Next day = (Daily STD)*ToDayPrice

Now we use the actual data as an example, on 02/11/2010, the Historical Volatility of AAPL is calculated as 0.3986 (I will put the script into my Financial Scripting with FreeMAT blog)

On 02/11/2010, the daily STD is 0.3986/sqrt(252) = 0.0251; thus the price change is

0.0251 * 198.670 = 4.9866 (198.670 is the close price on 02/11/2010). Note that this price change is going to be used for the NEXT day,

So the price change expressed in STD on the NEXT day (02/12/2010) is:

(200.38-198.67)/4.9866 = 0.3429   (Note 200.38 is the close price on 02/12/2010.)

So 0.3429 is the price change expressed in STD for 02/12/2010.

Our calculation of Historical Volatility is based on 20 days sliding window unless otherwise stated. It is important to note that each price change is measured against a window that ends just ahead of the change. That is, the change being measured does not influence the calculation.

Please also note that the calculation is NOT the same as the traditional Bollinger Bands, as the standard deviation in Bollinger Bands is calculated from price change alone, not the Natural Logarithm of price change. The Bollinger Bands STD usually are much larger than the STD we are talking about here.

The detailed numbers for AAPL are summarized in the table below:

Summary of Daily Moves over last 200 days (STD calculation based on 20 day sliding window); Generated on 02/12/2010

Type of Daily Move	# of Days	Percent of All Days	Avg Move	Dates of the Moves
UP over 2 STD	8	4	2.91	05/04/2009,05/26/2009,09/16/2009,10/20/2009,10/21/2009, 12/09/2009,12/24/2009,01/19/2010
UP between 1 to 2 STD	28	14	1.43
UP between 0 to 1 STD	78	39	0.42
DOWN between 0 to 1 STD	61	30.5	-0.42
DOWN between 1 to 2 STD	18	9	-1.33
DOWN over 2 STD	7	3.5	-2.45	05/12/2009,05/13/2009,08/17/2009,10/01/2009,10/30/2009,01/22/2010,01/28/2010
Total # of UP Moves	114	57	0.84
Total # of DOWN Moves	86	43	-0.77
Total	200	100	0.15
Note:

We can make the following observations based the plot and the table above:

·        In the majority of days, the price change stays within 1 STD. 139 (78+61) days stay within 1 STD, that’s 69.5% of 200 days. (The normal distribution theory tells us that we have 68.2% probability that it should stay within 1 STD, that’s very close)

·        AAPL experienced 15 (8+7) very large price spikes (over 2 STD) in the last 200 days.

·        When move up, it is in average of 0.84 STD; When move down, it is in average of 0.77 STD; Thus AAPL moves up more than goes down.

·        Over last 200 days, it is average move up 0.15 of each day’s STD.

I am a swing/positional trader. I don’t like a stock with a large numbers of big spikes (over 2 STD).

I am also interested in to study what “hint” is given if when a stock experienced an over 2 STD price change.

Does a big spike signal the beginning of a new trend?, or is there any reason to suspect a reversal after the spike?

Here are some plots for AAPL, make your own conclusions:

For the last 200 days, when APPL downed over 2 STD, it is a good buy signal.

When APPL up over 2 STD, some are strong indication of trend up, some are short-term top.

For SPY’s last 200 days:

SPY only experienced 2 up over 2 STD over last 200 days.

Instead of studying the single stock over last n days, we can also study the behavior of the whole market, for example, we can summarize the S&P 500 stocks’ behavior on 02/12/2010.

Summary of S&P 500 Stocks Daily Price Change Behavior Model on 02/12/2010

Type of Daily Move	# of Stocks	Percent of all stocks	Avg Move	Symbols of the Moves
UP over 2 STD	1	0.20	3.75	MFE
UP between 1 to 2 STD	9	1.80	1.44	A,ANF,AON,AZO,JDSU,MOT,ODP,VIA.B,WFMI
UP between 0 to 1 STD	192	38.40	0.30
DOWN between 0 to 1 STD	281	56.20	-0.36
DOWN between 1 to 2 STD	16	3.20	-1.34	AYE,CFN,CLX,CPB,CSC,CTL,DTV,DVA,ED,FLIR,JNPR,SCG,SYMC,UNH,UTX,WLP
DOWN over 2 STD	1	0.20	-2.15	ADBE
Total # of UP Moves	202	40.40	0.37
Total # of DOWN Moves	298	59.60	-0.42
Total	500	100	-0.10
Note: On 02/12/2010, 202 stocks moved up on average of 0.37 STD, 298 stocks moved down on average 0.42 STD. For all 500 stocks, it moved down on average 0.1 STD. One stock (MFE) experienced a over 2 STD spike, and one stock (ADBE) experienced a big spike down move.