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The
use of 260 or 365 for computing annualised volatility supposes that the stock
follow a gaussian random walk, that is daily returns are scaling like
time power 0.5 (t^1/2). In fact, the statistical laws followed by stocks are
quite more complicated and the ones proposed by scientists (Levy stable laws,
GARCH models, fractal brownian motion,...) are very difficult to use (most of
them do not have analytical solutions). The problem of the gaussian random walk
is that it undervalues the risk and that is a major problem for option
valuation.
This
is to say that using 260 or 365 days to estimate volatility is not a major
issue. Imagine a stock scaling with a t^0.7 scaling law instead of 0.5, the
error on the estimation of the volatility is quite dramatic!
Just
stick to one of it, 260 or 365, to be able to compare stocks, keeping in
mind that the underlying model is not very accurate.
<FONT face=Verdana color=#800000
size=2>
<FONT face=Verdana color=#800000
size=2>Waz
<FONT face=Tahoma
size=2>-----Original Message-----From: Anthony Faragasso
[mailto:ajf1111@xxxx]Sent: lundi 29 avril 2002
04:24To: amibroker@xxxxxxxxxxxxxxxSubject: Re:
[amibroker] Measure a stocks' volatility with AB
?Richard,Since I also deal alot with Options,
Here is my reason for usingsqrt(365).Should you use 365 ( the
number of calendar days ) or 256 ( the numberof trading days), I believe
there is no absolutely correct answer. I use365 mainly for consistency.
One of the key functions in an option'sprice is time ( t). The time
component is expressed in terms offractions of a year and is universally
thought of as Sqrt(calendardays/365) as opposed to Sqrt(trading days /
256).This 365 day calendar effect can be best demonstrated by looking
at theprice behavior of an option from Friday afternoon to Monday morning.
Allother things being equal, the option's price will drop more from
Fridayafternoon to Monday morning than it would from Thursday afternoon
toFriday Morning. That's because you have about 2 3/4 days of time
decayof 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, Iuse 365, the number of calendar days. If you use 256, the
options pricedecline would be smooth every trading day, no matter howmany
calendardays transpired between trading periods.There is an even
more troubling problem when you use the number oftrading days, and that
has to do with an assets expected rate-of-returnand risk over the course
of a year. The formula for volatility is theannualized daily standard
deviation. Recall that you calculatevolatility by multiplying the standard
deviation figure by the squareroot of the number of periods in a year. If
you use 256( now) becausethat is the number of trading days in a year,
that means you'll have touse some other number when the number of trading
days per year ismodified. That means adding trading days would
increase volatility,eliminating trading days would decrease volatility.
Trouble is, changingthe available trading periods has already happened
several times, andthe real world results refute this notion.Prior
to 1952 the stock market traded on Saturdays. That meant thatthere were
more than 300 trading days per year, instead of the current256. When the
NYSE made the change in 1952, did market risk shrink ? No.Did market
returns shrink? No. Would diminished returns even be alogical expectation?
No. Because volatility is a measure of risk andreward, however, that is
what should have happened based on a reductionin the number of available
trading days. Not only are those conclusionsillogical, 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 dayspreviously would require that you use a larger
number now for certainassets ( like stock index futures traded on Globex).
If you used avolatility calculation model that used trading days in its
calculation,you'd need to increase the number of trading days to the
appropriateamount. With the standard deviation component constant,
volatilitywould have to increase due to the increased number of trading
periods.Some might argue that volatility would remain constant, even
with theincreasing and decreasing trading periods. If that is true and you
usetrading days to annualize volatility, increasing the number of
tradingdays would imply a smaller daily standard deviation figure. But
doesincreasing your sample size ( which you are effectively doing
byincreasing the number of trading days) imply a reduction in the
standarddeviation? Of course not.It doesn't even make intuitive
sense, and is not supported by empiricaldata. Taken a step further,
assuming that volatility remains constantwhile increasing the number of
available trading days means thatinvestors' reactions to news and events
should result in smaller pricemoves. For example, lets say that a stock
goes from $10 to $12. Asmaller standard deviation of the price change
means that the pricechange must be smaller. So the constant volatility
premise means thatinvestors are currently valuing the stock at an
artificially high priceof 12 instead of correctly valuing it at a lower
price, simply becausethe markets are currently closed on weekends.
That is wrong. The stockis priced at 12 because the information aboutthe
stock that iscurrently available warrants a price of 12. Saying that
volatiltiy wouldremain constant when the number of trading days changes
implies that themarket is currently irrational and inefficient due tothe
absence ofweekend trading.Since I believe neither 256 nor 365is
perfect , and because I wish tobe consistent with the way options behave
in the real world ( that is toemulate the time deterioration over the
weekend) I use 365 days in myoption models and my volatility calculations.
:-]]Best wishesAnthonyRichard 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 toopen
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 thisis
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! Groupsis
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.Your use of Yahoo! Groups is subject to the <A
href="">Yahoo! Terms of Service.
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