Volumeweighted Exponential Moving Average (VEMA)
and the Directional Movement Indicator

We collect Price and Volume data for some stock (or mutual fund), for the past N days, namely:
(P_{1}, V_{1}), (P_{2}, V_{2}),
(P_{3}, V_{3}), ...
(P_{N}, V_{N})
and compute, with this info:
Num(Now) = EMA of last N values of (Volume)*(Price)
and
Den(Now) = EMA of last N values of (Volume)
>That doesn't explain how to calculate them!
Patience. Tomorrow, once we've got the Price, P_{N+1}, and Volume, V_{N+1},
we calculate:
Magic Formula :
VEMA(Next) = Num(Next)/Den(Next)
where
Num(Next) = α Num(Now) +
(1  α) V_{N+1} P_{N+1}
and
Den(Next) = α Den(Now) +
(1  α) V_{N+1}

and "Num" and "Den" stand for Numerator and Denominator, respectively
and α = 1  2/(N + 1) so, for N = 14
(a 14day VEMA) we'd have α = 1  2/15 = 0.867
(See Technical Analysis stuff.)
To start this procedure (before we've got a bunch of Prices and Volumes) we just use
Num(Now) = (1  α) Volume x Price
and Den(Now) = (1  α) Volume
Thereafter, we use the Magic Formula.
>Example?
Okay, suppose the closing Price and Volume are $23.50 and 5,250.9, in thousands of shares traded.
Suppose, further, that we're working with a 14day moving average, so
α = 0.867. and
Num(Now) = (10.867) (5,250.9) (23.50) = 16,412
and
Den(Now) = (10.867) (5,250.9) = 698.37
so
VEMA(Now) = Num(Now)/Den(Now) = 16412/698.37 = $23.50 hence ...
>But that's just today's price!
I'm glad you noticed. However, we need to have a starting value for Num and Den.
Tomorrow, we suppose that our Price and Volume are $24.50 and 1,477.8 kiloshares, so now
we use Magic Formula :
Num(Next)
= α Num(Now) +
(1  α) V_{N+1} P_{N+1}
= 0.867(16412)+(10.867)(1477.8)(24.50) = 19044.6
and
Den(Next) = α Den(Now) +
(1  α) V_{N+1}
= 0.867(698.37)+(10.867)(1477.8) = 802.03
so
VEMA = 19044.6/802.03 = $23.74
>And so on ... and so on.
Right. As we continue, we generate a Volumeweighted Exponential Moving Average and ..
>Is that what you're after? A Volumeweighted ...?
Well ... uh ... not exactly. We're really after a Volumeweighted
Directional Movement Indicator (DMI).
>I've forgotten what that is.
Then go back and read the Technical Analysis stuff. However,
in a nutshell, we calculate a sequence of Bull Points
and Bear Points (depending upon the increases in
the daily highs compared to the decreases in daily lows) and we then compute the Exponential
Moving Averages (EMA) of these two sequences of Bull
and Bear points, calling these EMAs
DMI+ and DMI and we get excited
when DMI+ rises above DMI
because we then expect the stock to take off ... so we look at their difference:
ADX = (DMI+)  (DMI) so that ...
>I'm sorry I asked.
We want to consider the difference between the ordinary, gardenvariety DMI and
the Volumeweighted version, which we'll call VDI.
Consider the following charts, where we're doing the DMI thing ... ignoring the volume of trades:
Notice that the ADX dipped negative in midMay. Maybe that's the start of a decline. Maybe
we should sell. Maybe we should worry.
However, this dip follows a period of
low volume (see upper left chart). Had we included the Volume in our calculations ...
>You mean, use
VDI+ and VDI and VDX = (VDI+)  (VDI) instead of ...
Don't interrupt. If we include Volume ... we find the following:
... and now, if we own the stock, we're happy. The stock, we think, will quickly recover.
>But it could go the other way. I mean ...
Yes, it could go the other way. Including the Volume might make you very nervous.
For example, here's another stock.
Without using the Volume weighting (but just the standard
DMI), the ADX doesn't go negative in early May. However, if we include
the Volume,
the VDX goes negative ... for a week or so.
>So what's the moral of this story?
The moral? I guess we should think about buying (or selling) only when the VDX goes
positive (or negative) by a significant amount.
>What's significant?
Hmmm ... good question. I'd suggest using
VDX = 100 { (VDI+)(VDI)}
/{ (VDI+)+(VDI)}
then we'd get a "percentage" and we'd relax unless the VDX rose above, say, 30%
or fell below, say, 30%:
>So if I see the VDX drop to 15%, as in the above chart, I just go back to sleep.
Exactly.


There's a spreadsheet you can play with. You can choose ADX or the Volumeweighted
VDX. It looks like this:
Just RIGHTclick on the picture to download the .ZIP'd spreadsheet.
In the meantime, here's a few VDXs (as opposed to ADXs) to ponder:
And, for a change of pace (because there ain't no Volume figures for this Index),
the ADX for the Nasdaq, below:
>But what about the big drop in the NAZ, last year?
Okay, here's a picture for that:
>So, it looks like ADX anticipated the drop ...sorta ... if we get excited about a 30% drop.
Do you believe in this technical analysis stuff?
>Well ... uh ... not really.



>For example, would this ADX stuff have kept you out of the
Nasdaq, for all of the year 2000?
Good question ... let's see. Suppose we have $1,000 invested in the Nasdaq, in January,
2000 and we watch the ADX.
When it drops below 30% we sell everything, put the money under a pillow and wait. When the
ADX goes above 30% we buy back in ... and stay in until it drops below 30% again.
>Looks like you made 12.9% for the year while the NAZ dropped ... what? Over 40%.
Yes, but notice that I sold in March and held the cash until the end of May.
I also bought back in, sometime near the end of August, and got out later when the
ADX dropped from +30% to 30% in about a week or so ... and I lost money!
>So, do you believe in this technical analysis stuff?
Well ... uh ... not really.

 So, guess what stock we should worry about, now, on May 27, 2001?
>How many guesses do I get?
Just one.
>Pfizer? Are you sure?
Ask me again in a week or three.

... here's a more recent Pfizer:
>Aha! So your prediction is lousy!
Ya win some. Ya lose some.


>But is VDX, the volumeweighted stuff, really better than ADX??
Uh ... let's try it on some stock that's been around for a while, like maybe ...
>How about General Electric. It's been around since the DOW had only a dozen stocks and I'd say that ...
Okay, here's what we'll do:
 At the end of each week we note the Open, High, Low and Closing prices for that week.
 Using the average of these four prices, (Open+High+Low+Close)/4, we calculate the 4week VDX.
 If the VDX rises above +30% we buy the stock at next week's Opening price.
 If the VDX drops below 30% we sell the stock at next week's Opening price and stick the money into money market, at 2% per year.
On the right, the final result (from Jan/85 to Jun/01)


Below, some closeups, where the wee dots indicate switches between the stock and Money Market:
>So what was the annualized gain for the ...?
For GE, the annualized gain from Jan/85 to Jun/01 was 20.0% and for VDX it was 23.1%.
>What about ADX? What if you just ignored the volume?
For ADX the annualized gain was about 22.9%.
>Big deal!
Aah ... but if you had $100K invested for those years, it'd make a difference of over $100,000
in your final portfolio  if you used VDX instead of ADX  from about $2.9M to $3.0M and
that's significant, eh? And if we just did a buyandhold with the GE stock, we'd have about $2M
by June/01.
>That 4week averaging. Is that the best number? And that 30% figure  what about ...?
The 30% is up to you. I call it the tranquility parameter.
You want tranquility? Choose +/ 100%, relax, do nothing. You need the adrenaline rush?
Choose +/ 5%.
>Aha! So you looked at the historical data and picked the parameters, like 4week and 30%, so as to make VDX look good!
Well ... uh, one must use historical data for each stock in order to gauge the appropriate
parameters for that particular stock. I mean, not all stocks behave in the same way.
Some are more volatile. Some are ...
>Mumbo Jumbo. Besides, you ignore the cost of trading and
what about longer time spans and ...?
>And if you ignored the volume and just used ADX?
The annualized gain would have been ... uh ... 17.0%, but I must say that it makes more sense to
include the volume. After all, share prices associated with a higher volume surely are
more important than the share price when just a few shares trade. There are usually more people
involved. Volumeweighted prices give us an estimate of the average price paid for a stock.
Using the price, alone, is like saying the size of a car  ignoring the weight
of the car  that just its size alone will determine how much force is required to move the
car. It's like saying that ...
>zzzZZZZ
for part II.
For gyrfalcon and other Nortel and XIUwatchers:
See Part II
NOTE: There's a simple spreadsheet available. You just type in the Stock Symbol, click
a button (while you're connected to the Net!) and it downloads the pertinent data and
plots the VDX (thanx to Ron M!). The spreadsheet looks like
this.
To download the spreadsheet,
RIGHTclick HERE
and "Save Target" or "Save Link".
