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I have had a few responses about the fbm bands and I will try to address
some of them:
"Ron, are you saying that these bands increase in width monotonically
with (the square root of) time?
That would say that volatility ALWAYS increases. But surely that can't
be true. I don't have enough historical data to test it, but I would bet
there have been plenty of volatility contractions."
"Would you mind explaining how you take the square root of time."
" HAVE YOU RUN THIS CALCULATION ON FUTURES MARKETS ?
DOES THIS THEORY HOLD FOR STOCK INDICIES AND THE OEX ONLY OR DOES THE
BANDS
INCREASE AS A FUNCTION OF TIME IN FUTURES MARKETS "
For a very detailed discussion of "Chaos and Fractals in Financial
markets" go to this site and work your way down to the section on
economic commentary. There are six articles on Chaos and Fractals in
Financial Markets.
http://www.aci.net/kalliste/homepage.html#ifm
I have attached part of this explaining the idea of the "square root of
time"
Gary made a very good argument about volatility "not" being able to
always increase. I think that the idea of the drift of daily changes in
stock prices does increase cumulatively over time. If you measure
volatility over a predetermined moving time period (20 days, 6 mos,
1year) you will get the common type of reversion that we see when we
measure volatility this way. The bands I constructed measure the drift
of the range expansion (volatility) cumulatively over time. The trick is
to pick the starting point. I use a significant low. Part of the idea in
using this analysis is that you would not want to trade something unless
its range is expanding over time (high growth). Unless you are
specifically looking for something that only trades in a range (no
expansion of volatility, no growth) So I think the idea of volatility
contraction (which does happen) is more a function of your time frame. A
more short term trader would use a different low then I used in my
example. So I believe this is why over a longer period of time you see a
greater expansion of range in markets, because the cumulative effect of
the daily changes.(volatility) This is also why I believe you can get an
index (whose majority of components are making new lows) to be able to
make new highs.
I have used this on futures markets and it seems to work as well as on
equities. Otherwise it wouldn't be "Fractal"
The formula is based on a regression calculation Pf=a+b*(x+1) . I don't
know what file size limitations RT has for attachments so I will try to
send a copy of the excel spreadsheet in a separate post.
hope this helps
any comments or criticisms appreciated (it helps improve the analysis)
Ron McEwan
Attachment Converted: "c:\eudora\attach\squaretime.doc"
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