|
PureBytes Links
Trading Reference Links
|
Richard,
Since I also deal alot with Options, Here is my reason for using
sqrt(365).
Should you use 365 ( the number of calendar days ) or 256 ( the number
of trading days), I believe there is no absolutely correct answer. I use
365 mainly for consistency. One of the key functions in an option's
price is time ( t). The time component is expressed in terms of
fractions of a year and is universally thought of as Sqrt(calendar
days/365) as opposed to Sqrt(trading days / 256).
This 365 day calendar effect can be best demonstrated by looking at the
price behavior of an option from Friday afternoon to Monday morning. All
other things being equal, the option's price will drop more from Friday
afternoon to Monday morning than it would from Thursday afternoon to
Friday Morning. That's because you have about 2 3/4 days of time decay
of the weekend instead of the usual 3/4 day of decay during the week.
Just to be consistent with the way options behave in the real world, I
use 365, the number of calendar days. If you use 256, the options price
decline would be smooth every trading day, no matter how many calendar
days transpired between trading periods.
There is an even more troubling problem when you use the number of
trading days, and that has to do with an assets expected rate-of-return
and risk over the course of a year. The formula for volatility is the
annualized daily standard deviation. Recall that you calculate
volatility by multiplying the standard deviation figure by the square
root of the number of periods in a year. If you use 256( now) because
that is the number of trading days in a year, that means you'll have to
use some other number when the number of trading days per year is
modified. That means adding trading days would increase volatility,
eliminating trading days would decrease volatility. Trouble is, changing
the available trading periods has already happened several times, and
the real world results refute this notion.
Prior to 1952 the stock market traded on Saturdays. That meant that
there were more than 300 trading days per year, instead of the current
256. When the NYSE made the change in 1952, did market risk shrink ? No.
Did market returns shrink? No. Would diminished returns even be a
logical expectation? No. Because volatility is a measure of risk and
reward, however, that is what should have happened based on a reduction
in the number of available trading days. Not only are those conclusions
illogical, they're not supported by actual events.
Another example is the proliferation of overseas and 24-hour trading.
Based on the increasing number of trading periods, using 256 days
previously would require that you use a larger number now for certain
assets ( like stock index futures traded on Globex). If you used a
volatility calculation model that used trading days in its calculation,
you'd need to increase the number of trading days to the appropriate
amount. With the standard deviation component constant, volatility
would have to increase due to the increased number of trading periods.
Some might argue that volatility would remain constant, even with the
increasing and decreasing trading periods. If that is true and you use
trading days to annualize volatility, increasing the number of trading
days would imply a smaller daily standard deviation figure. But does
increasing your sample size ( which you are effectively doing by
increasing the number of trading days) imply a reduction in the standard
deviation? Of course not.
It doesn't even make intuitive sense, and is not supported by empirical
data. Taken a step further, assuming that volatility remains constant
while increasing the number of available trading days means that
investors' reactions to news and events should result in smaller price
moves. For example, lets say that a stock goes from $10 to $12. A
smaller standard deviation of the price change means that the price
change must be smaller. So the constant volatility premise means that
investors are currently valuing the stock at an artificially high price
of 12 instead of correctly valuing it at a lower price, simply because
the markets are currently closed on weekends. That is wrong. The stock
is priced at 12 because the information about the stock that is
currently available warrants a price of 12. Saying that volatiltiy would
remain constant when the number of trading days changes implies that the
market is currently irrational and inefficient due to the absence of
weekend trading.
Since I believe neither 256 nor 365 is perfect , and because I wish to
be consistent with the way options behave in the real world ( that is to
emulate the time deterioration over the weekend) I use 365 days in my
option models and my volatility calculations. :-]]
Best wishes
Anthony
Richard Alford wrote:
> Anthony, I suspect you should use sqrt(260), the common number of
> bars/year, instead of sqrt(365). The result will agree with published
> results, for instance on McMillan's site. I took the liberty of
> attaching the indicator I use if you have the nerve to open it with
> all the virus running around.
> Cheers, Richard ----- Original Message -----
>
> From: Anthony Faragasso
> To: amibroker@xxxxxxxxxxxxxxx
> Sent: Sunday, April 28, 2002 6:49 PM
> Subject: Re: [amibroker] Measure a stocks' volatility with
> AB ?
> Hello, Derek,
>
> I don't know if this is what your are looking for, but this
> is what I
> use for volatility:
>
> pds=20;//Set your time period
> Graph0 = StDev(log(C/Ref(C,-1)),pds)*sqrt(365)*100;
>
> Anthony
>
>
>
> dereklebrun wrote:
>
> > Hi is there any technical analysis way to measure a
> stock's price
> > volatility in AB ?
> > If yes, how ?
> >
> > Thanks,
> > Derek
> >
> >
> > Your use of Yahoo! Groups is subject to the Yahoo! Terms
> of Service.
>
>
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of
> Service.
>
>
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
|