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if volatility is calculated in the way that is conventional for
the "statistical" volatility used in McMillan's and Natenberg's
books on options, then volatility is the annualized standard
deviation of of the log of the daily returns. I don't have
the EL code for this, but it might look something like this
(I have tried verifying this code, if you get it working, please
post your solution to the group):
{ function statvol - statistical volatility }
inputs: P(numericseries), N(numericsimple);
vars: logr(0);
logr = log(P/P[1]);
if currentbar > N the begin
{ we can't compute statvol until we have enough data }
statvol = StdDev(logr, N) * SquareRoot(260.0) * 100.0;
end else begin
statvol = 20.0; { some number }
end;
(I wasn't too sure about the need to check for currentbar above,
or whether specify the input price, P, as a series or not. Any
suggestions on a better way to write this function in EL?)
Given the annual volatility, 25% in your example, the anticipated
range (1 std. dev.) with an approximate prob. of 70% of the price
finishing in that range, is given as:
one_std_dev_as_pct = exp(annual_vol_as_pct * sqrt(N / 260)) - 1.0
for v = 25%, and N = 20, the anticipated 1 std. dev. range is:
exp(0.25 * sqrt(N / 260)) - 1.0 => 0.07
thus, at this 25% vol. level, there's a 70% chance the price will
be in the range of the current price +/- 7%. Two standard deviations
give a 95% confidence, and that would come out to +/- 14%, or
between 17.2 and 22.8 for a stock trading at 20.
If your measure of volatility doesn't use the log function, but
just a straight annualized std. dev., this calculation should work:
one_std_dev_as_pct = annual_vol_as_pct * sqrt(N / 260)
(above, N, is measured in trading days, and 260 is an approx. for
the number of trading days in a year.)
> Subject: Re: Volatility & Predicting Future Range
> Cab Vinton wrote:
> > Given an asset's present volatility, it should be a
> > fairly simple matter to predict the future range of
> > that asset N days into the future.
>
> Sure. Look in your indicator tool box for Bollinger or Standard
> deviation formulas. These indicators predict statistical range
> based on exactly what you are talking about. :)
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| Gary Funck, Intrepid Technology, gary@xxxxxxxxxxxx, (650) 964-8135
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