Letters - October 2007

October 2007 Letters To The Editor
or return to October 2007 Contents
The editors of S&C invite readers to submit their opinions and information on subjects relating to technical analysis and this magazine. This column is our means of communication with our readers. Is there something you would like to know more (or less) about? Tell us about it. Without a source of new ideas and subjects coming from our readers, this magazine would not exist.
Address your correspondence to: Editor, STOCKS & COMMODITIES, 4757 California Ave. SW, Seattle, WA 98116-4499, or E-mail to editor@traders.com. All letters become the property of Technical Analysis, Inc. Letter-writers must include their full name and address for verification. Letters may be edited for length or clarity. The opinions expressed in this column do not necessarily represent those of the magazine. -Editor

BETWEEN PRICE AND VOLUME
Editor,
I would like to thank Buff Dormeier for his well- written and insightful article, "Between Price And Volume" (July 2007). I have two questions for the author regarding the volume-price ratio (VPR) and normalization:
1) If the purpose of the VPR is to "accentuate the VPC+/- relative to the short-term price-volume relationship," it seems that the formula (VPR = VWMA/SMA) should be flipped (VPR = SMA/VWMA) when the closing price is below the SMA and the VWMA. As it was presented, the VPR would accentuate the VPC when the VWMA closely follows (more than the SMA) rising prices, but would actually decrease the VPC if the VWMA closely follows falling prices.
2) However, if the price is in between the VWMA (volume-weighted moving average) and the SMA (simple moving average), the VPR almost seems superfluous (which is the right direction, up or down?). I liked CMSFX's solution of normalizing the VPCI (dividing it by the closing price), and was curious about the author's thoughts on transforming the VPR step into a normalization step. That would make the VPCI more universally comparable between stocks, as well as getting rid of the VPR directional problems.
François Bertrand
Buff Dormeier replies:
Thank you for your email and kind words.
Please note your question refers to the following statement in my article: "VPR accentuates the VPC+/- relative to the short-term price-volume relationship. The VPR is calculated by dividing the short-term VWMA by the short-term SMA. For example, assume the short-term time frame is 10 days, and the 10-day VWMA is 25, while the 10-day SMA is 20. The VPR would equal 25/20, or 1.25."
1) That is correct: Not only does the VPR accentuate volume flows in rising short-term trends, but it may reduce or attenuate the Vpci in falling markets. This is by design, so that the VPR strengthens the VPCI in upmarkets with strong volume or in down markets with low volume. However, the VPR will also de-emphasize the VPCI when prices move down with high volume and when price moves up with low volume. Please see Figure 2 on page 24 of the July 2007 issue for further explanation of this relationship.
2) It could seem that the VPR is almost superfluous when price is in between the VWMA and the SMA, but this is not necessarily so. Remember, VPR is more than just price change. We are evaluating volume's influence on price trend. You may still have influences from volume changes even when they are not accompanied by price changes.
As for your comment about normalizing the VPCI (that is, dividing it by the closing price), it's a good point to bring up that you can modify the VPCI indicator to whatever way best suits your investment process. However, since VPCI already uses the division of average prices in its computation, in my work I do not see a need to normalize the VPCI to current prices.

VOLUME PRICE CONFIRMATION INDICATOR (VPCI)
Editor,
I am a subscriber of your fine magazine. In your July 2007 issue, author Buff Dormeier presents the VPCI ("Between Price And Volume"). I'm a user of MetaStock, so in the last pages of the article I found the formula of the VPCI for MetaStock. However, for the correct use of this indicator, the VPCI must be smoothed by a volume-weighted moving average (VWMA), according to Mr. Dormeier. So my question is: What would be the formula for a 28-day VWMA?
Victor Rendon
The volume-weighted moving average is available in the public domain. It is the standard moving average weighted by daily volume. A 28-day VWMA would be calculated by multiplying the closing price by the volume of days 1 through 28 and then taking the average of those values (dividing the total by 28).--Editor

FIXED-FRACTIONAL POSITION SIZING
Editor,
I have been reading S&C for more than 10 years and enjoy it very much. I have some comments and thoughts regarding Christian Smart's August 2007 article, "Fixing The Flaws In Fixed-Fractional Position Sizing." I am an ex-electrical engineer and not a mathematician, but I think my comments are reasonable.
1) Figure 1 on page 33 compares "system expectation" (SE) to "fixed-fractional expectation" (FFE), showing that the SE average return (0.4%) has a far greater equity return over 5,000 trades than does the FFE return of 0.3573%, which is mathematically correct. What I suggest is that the 0.4% SE return, although correctly calculated (as explained in the text), it should not be used as an exponential (geometric) return that then acts on a compound basis. As a simple example: If two trades have a gain of 10% each, the compound gain is 21% and the average return is then 10.5%. It would not be correct to then calculate an SE-type gain of 1.105 * 1.105 = 1.221 (22.1%) and then state that the FFE gain lags behind the SE gain. At the top of page 33, the author states, "With fixed-fractional position sizing, the system does not achieve this expectation in the long run, but an amount less then than the system expectancy." I therefore assert that the SE return is not meaningful in anything other than a mathematical sense and should not be used on a compound basis (there is no "gap").
2) To make up for this "gap," the author recommends an "expected fixed-fractional" (EFF) approach, for which, if I understand his definition, the starting equity ($100,000) is adjusted upward each trade to "close" the gap. For his system expectation example of 0.20 and a fixed-fraction of 2%, the exponential adjustment would be 1.0004 compounding per trade. This would mean after N=1 an addition to equity of only $40, for N=2500 it would be $2,720, and for N=4,999 it would be $7,383. This last amount (of new equity money) strikes me as kind of silly when the total equity is now on the order of $617 million.
Let's suppose that we do want the higher results of the EFF approach. Why not simply increase the 2% bet up to what I calculated as the same ending equity by using a bet of 2.28% in lieu of 2.0? I calculated the bet for the maximum possible equity at 10%, so the 2.28% is well under that and would not have the maximum drawdown (MDD) associated with that more risky approach (although it would be higher than the 2% case).
3) Speaking about MDD, I believe that any given run of 5,000 trades would yield one MDD and of course a number of lesser drawdowns. Since the basis of the author's data is based on a "fair coin toss" bias of 40%, then the first run of 5,000 trades would yield precisely the equity that the author states, and a second such run would also replicate the first (assuming that bias stays exactly at 40%), but since the "path" to the final equity is bound to be different for each run, then each run would have its own (and different) MDD. This brings me to the question: Did the author run a large number of runs to establish the maximum MDD?
4) To get a feeling for this MDD problem, I ran various bet amounts (2/1 win/loss, bias =40%) five times each, and got the following results:
Bet=1% equity = $0.0128M    Mdd = -16.7%
    to -18.6%
Bet=2% equity = $55.6M    Mdd = -35.8%
    to -39.4%
Bet=3% equity = 484,515M     Mdd = -41.7%
    to -50.5%
Bet=4% equity = $45,836,357M     Mdd = -61.2%
    to -69.8%
Bet=10% equity = 1.23*E14M     Mdd = -66.5%
    to -73.4%
    (maximum
    growth bet)
Bet=20% equity = 0     Mdd = -100%
    (Gambler's ruin)
This table illustrates that the MDD does vary from run to run. More important, it shows the well-known tradeoff between return and risk (as measured by MDD). From my point of view, I could perhaps tolerate an MDD =-20%, but I would consider unacceptable MDDs on the order of -40% or greater. Thus, in the above example, betting the order of 1% would be acceptable, whereas 2% and higher would not be.
5) The author clearly points out the tradeoff of return vs. MDD, but I am wondering why he did not reference Avinash Agrawal's recent article, "Drawdown," appearing in Working Money (Working-Money.com, 9/27/2006). Agrawal's Figure 2 shows the equity results vs. risk per trade (bias = 50%, two-to-one win/loss) and in Figure 2 the resulting MDD vs. that same parameter. In addition, Kelly (1956) and Thorpe (1962) have contributed much to this issue and they were not referenced.
Norman J. Brown
Christian Smart replies:
1) Contrary to Mr. Brown's assertion, the 0.4% system expectancy used in the example in my article is indeed relevant to compounding. For a system with a 100% win percentage and 0.4% expectancy, traditional fixed-fractional position sizing returns a compounded 0.4% per trade.
As an example, starting with a $100,000 account, the equity after the first trade is $100,400 (=$100,000 *1.004), and after the second, it's $100,801.60 (=$100,400*1.004), and so on. When the win percentage is less than 100%, a gap appears between system expectancy and traditional fixed-fractional compounded returns. This is due to the uncertain equity stream resulting from smaller bets during losing streaks and larger bets during winning streaks. As a result, a trader is making the biggest bets at equity curve peaks and the smallest bets at equity troughs, contrary to common sense. What I show in my article is that it is possible to close this gap and increase returns in a systematic fashion by placing bets not on actual returns but on expected returns. This results in higher bets at equity troughs and lower bets at equity peaks.
2) Mr. Brown has made several mistakes in his second comment. The compounding factor he uses, 1.0004, has one too many zeroes. The compounding factor for my example is 1.004. Also, in expected fixed-fractional position sizing, the compounding factor is multiplied by the beginning equity to obtain the expected equity, not multiplied and then added, as in Mr. Brown's example. For N=2,500, the expected equity is $100,000*(1.004)^2,500 = $2.1 billion. I believe Mr. Brown's calculation for N=2,500 is 100,000*(1.0004)^2,500* 0.01 = $2,720. The extra 1% multiplied at the end also seems to be an error, since the calculation in Mr. Brown's comment is related to expected equity, not position size.
Mr. Brown correctly points out that it is possible to increase returns for fixed-fractional position sizing by increasing the amount of actual equity risked, but the point of my article is to show that returns can be increased by sizing positions using expected returns instead of actual returns. As I show in the article, this is quite different from simply increasing the amount risked of actual equity per trade. For a given percentage risk, betting on expected equity means that sometimes a trader risks less than with traditional fixed-fractional, and sometimes more. In addition, increasing the amount of actual equity risked per trade always means an increase in maximum drawdown. As I show in my article, expected fixed-fractional position sizing can result in increased risk-adjusted returns, demonstrating that expected fixed-fractional is not simply a higher-leveraged version of traditional fixed-fractional position sizing (as Mr. Brown seems to assert), but something altogether different.
3) and 4) I calculated the drawdowns from one single Monte Carlo simulation of 5,000 trials. I did this for the sake of simplicity. As Mr. Brown shows from his own simulations, different simulations of 5,000 trials yield different maximum drawdowns. This is due to the fact that the money management simulations do not converge after 5,000 trials. To obtain a more accurate approximation of maximum drawdowns, one can either perform additional 5,000 trial simulations, the results of which Mr. Brown has provided, or perform a larger number of trials, such as 50,000. I avoided the complexity of two-dimensional simulations in order to focus on my main point and I limited my simulations to 5,000 trials because the numbers obtained after compounding returns for 50,000 simulated trades are astronomically large and thus do not easily lend themselves to numerical examples. The variation in Monte Carlo simulation runs is worthy of an article on its own, and this topic has been the subject of previously published articles in financial literature, such as Michele Gambera's 2002 article in Business Economics.
5) I actually submitted my article to S&C in February 2006, long before the publication of Mr. Agrawal's article. The intent of my article is not to provide an exhaustive overview of the history of fixed-fractional position-sizing, but rather to introduce a new concept in money management. I believe that fixed-fractional position-sizing is so basic and well-known that references to Kelly and Thorp are not necessary, especially since my article is not a history of money management, but rather a concise introduction of a new and original idea. However, Mr. Brown makes a good suggestion and perhaps I should have cited one or two seminal papers in the field or the recent book on the subject, Fortune's Formula.

2B TOPS AND BOTTOMS
Editor,
Regarding "Breakouts, Pullbacks, And Gaming The 2B" by David Penn (April 2007), I have looked all over for a definition of 2B tops/bottoms in my technical analysis books and online. Is it just a double bottom and double top? Is it important to have rounded saucer-like formations too? I love Penn's articles and use both TradeStation and VectorVest to trade.
I usually reread all of his articles because I get the most out of them. I would just like to be certain about his 2Bs.
Mac McNaughton
Technical Writer David Penn replies:
Thank you for the kind words.
The 2B is a technique I first heard described by Victor Sperandeo in his books, Methods Of A Wall Street Master and Principles Of Professional Speculation.
I have written a great deal about the 2B. They are a surprisingly common pattern. In a sense, you are right in that they reflect a sort of double bottom or double top. But the 2B is very scalable -- on the shortest time frame, a 2B can occur in as little as three sessions.
It may be easiest to think of the 2B in the context of a test of top or bottom, rather than as a chart pattern, per se. If the market fails the test, then it is likely a 2B is taking place.
I'd also like to add that momentum oscillators (TRIX, stochastics, RSI, MACDH) can be of great assistance in both confirming and timing 2Bs.
We just had a 2B bottom in the S&P 500 during its most recent correction. I wrote about that pattern in an article that was posted to Traders.com Advantage on July 6, 2007 ("A 2B Test Of Bottom In The S&P 500").

THE MACD HISTOGRAM
Editor,
I recently read the article by David Penn in the July 2007 S&C, "Charting Cramer: NYX, AAPL, And CSCO." Therein he discusses the P-p-P pattern in the MACD histogram. I could not locate the two December 2006 articles referenced at the conclusion ("Trading The MACD Histogram, parts I and II") since I am not a subscriber to Working-Money.com. Could you please advise if these two articles can be found and accessed elsewhere?
Enjoy all David Penn's articles.
JF Ward
Technical Writer David Penn replies:
Both articles were republished in our Traders.com tabloid (March/April 2007 issue). Copies of back issues may be available through our circulation department (circ@traders.com).
Thank you for the kind words -- and for reading STOCKS & COMMODITIES.

MOVING AVERAGE TRIOS
Editor,
I read David Penn's article "Moving Average Trios" in the August 2007 STOCKS & COMMODITIES. It got me excited about trading and I plan to use this method in my trading plan.
I have a few questions about getting started. I only have $5,000 to trade with. What markets would you suggest I begin with? Will moving average trios work in the forex market? What about charting?
Name withheld
Technical Writer David Penn replies:
Thank you for writing.
With that level of capital, a forex mini account might be a good way to get started. Forex markets -- particularly the more widely traded currency pairs -- often feature excellent trends compared to stocks. Mini accounts allow you to trade versions of these currency pairs in which one pip equals $1. This would give you the opportunity to "learn on the job" without having to worry as much about taking on a great deal of risk with a regular-sized forex account.
Another plus with forex trading is that you can try out your strategies with a free, 30-day demo account that most forex brokerages offer before you open a real account. A number of forex brokerages advertise in this magazine; I would suggest trying demo accounts with some of them to see if one might be a good fit. Don't feel pressured to open an account before you are ready to put real money on the line.
You asked about charting. Another nice aspect about forex is that most of the brokerages provide real-time charting that is sufficient for all but the most short term of traders.
Best of luck!

THREEBLACK CROW PATTERN
Editor,
I was going over some old material and would like to bring this to your attention. In a November 2002 S&C article by Giovanni Maiani, "How Reliable Are Candlesticks?" the author states, "From this standpoint, three black crows anticipates an up day 67.65% of the time, a down day 27.45%, and unchanged prices 4.90% of the time."
However, in the book Candlestick Trading, author Stephen W. Bigalow states that the threeblack crow pattern is a negative signal and not an up day, as stated in Maiani's article. Can you help me reconcile these statements?
Richard Pokornik
Venice, FL
Different people perform analytical studies on chart patterns in different ways and not everyone gets the same results or comes to the same conclusions. Maiani's results could have shown one thing whereas someone else's may have shown something else.
You may wish to take a look at Sharon Yamanaka's article "Counting Crows" in our September 2007 issue, with the introduction, "One man's sell is another man's buy signal. Which is best?" In the article, she discusses how two other analysts, Oliver Velez and Steve Nison, seem to interpret the threeblack crow pattern in opposite ways, and she attempts to reconcile the rules for interpreting the pattern by looking at market context.--Editor

DAYTRADING
Editor,
I am a new subscriber. Recently, I received your 2007 Bonus Issue and I noticed that there is no "Day Trading" category in the Readers' Choice Awards section.
I know you cannot give advice. However, I would like to know in which year's Bonus Issue that category was included. I am interested in daytrading indexes. I understand there are many courses and systems available to purchase. Where can I get more information about them? Is it really possible to make money day trading indexes nowadays?
In addition, which course is the best? Where can I go to get an honest opinion? I would be grateful for any guidance in this respect. I know about FuturesTruth.com, but that is about system results, not product reviews.
Anil Bharne
Sorry, we do not have a "Day Trading" category in our Bonus issue. You are correct that we are not an advisory service. But more so, you are the only one who can determine which course is best for you. You need to identify courses that teach strategies that are in line with who you are. We have an exhaustive list of Courses & Seminars in our Traders' Resource database at our website, www.Traders.com. I would recommend you start there and go to the websites of some of those companies to determine whether they might meet your needs.--Editor

Back to October 2007 Contents
Originally published in the October 2007 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2007, Technical Analysis, Inc.