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Thanks Nand.....
Anthony
-------Original Message-------
From: amibroker@xxxxxxxxxxxxxxx
Date: Tuesday, April 29, 2003 12:56:16 AM
To: amibroker@xxxxxxxxxxxxxxx
Subject: [amibroker] Re: Coefficient of Variation
CV is one way. Yet another is z-ratio
zratio=(mean-sd)/sd
For comparing 2 stocks as Anthony did, the bigger the z-ratio, the
more volatile.
It has an advantage that the z-ratios have known probablities
under the Gaussian curve. One could translate these into
percentagea as well if it is easier to understand.
nand
--- In amibroker@xxxxxxxxxxxxxxx, "Fred" <fctonetti@xxxx> wrote:
> Anthony,
>
> As stated in most engineering texts the standard deviation
> calculation is a measure of reliability with respect to the mean ...
>
> So by using your calculation for CV this brings the two number
series
> into sync based on the fact that they have different means.
>
> This is why I personally like to do StdDev calcs based on the %
> Change of the individual series. This keeps them in their proper
> perspective to begin with, but the comparative results come out the
> same in the end.
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Anthony Faragasso"
<ajf1111@xxxx>
> wrote:
> >
> >
> > The Coefficient of Variation
> >
> >
> >
> > People who study the stock market use several different methods
to
> assess
> > any given stock's "volatility." One of these, the standard
> deviation!
> > If we were to record the closing price of a stock over several
> trading days,
> > we could compute the standard deviation of those numbers. The SD
> would be
> > equal to 0 if the stock's price never changed, it would be equal
to
> a small
> > number if the stock fluctuated just a little, and it would be
equal
> to a
> > large number of the stock's price jumped around wildly over the
> days we've
> > studied.
> > As proof that the SD is sometimes used as a measure of stock
> volatility,
> > consider these 2 statements pulled off some financially-oriented
> websites:
> > "Volatility: This describes the fluctuations in the price of a
> stock or
> > other type of security. If the price of a stock is capable of
large
> swings,
> > the stock has a high volatility."
> > "Volatility may be gauged by several measures, one of which
involves
> > calculating a security's standard deviation."
> > Now, it seems to me the coefficient of variation does a better
job
> of
> > assessing volatility than does the standard deviation. (As you
may
> recall,
> > the coefficient of variation is equal to the SD ( of a variable )
> divided by
> > the mean.
> > Let's say there are two investors (A and B) who each have $1,000
to
> invest.
> > Assume that Investor A buys 100 shares of a stock that's selling
> for $10 a
> > share, while Investor B buys 20 shares of a different stock
that's
> selling
> > for $50 a share.
> > Over 5 days, suppose the price of A's stock moves like this:
> Day1=$10,
> > Day2=$9, Day3=$13, Day4=$7, Day5=$11. Over this same period,
suppose
> > investor B's stock has this kind of fluctuation: Day1=$50,
Day2=$49,
> > Day3=$53, Day4=$47, Day5=$51.
> > As I hope you noticed, the two stocks under consideration
> fluctuated the
> > same absolute amount. In each case, the SD of the 5 prices is
equal
> to 2.
> > However, this measure of volatility misrepresents the
> investors' "ups and
> > downs" over the 5-day period we're considering. Investor A's
> holdings
> > fluctuated from $700 to $1,300 while Investor B's nestegg
> fluctuated between
> > $940 and $1,060.
> > If we calculate the coefficient of variation (CV) instead of the
> SD, look
> > what happens. For investor A, the CV = 2/10 = .20; for Investor
B,
> the CV =
> > 2/50 = .04. Comparing these CV indices, we see that Investor A's
> stock is 5
> > times as volatile as Investor B's stock. And doesn't that conform
> to the
> > fact that the overall value of Investor A's stock (with a range
> from $1,300
> > to $700) changes far more than does the total value of Investor
B's
> stock
> > (where the range extends only from $1,060 to $940).
> > I hope this little example shows how the coefficient of variation
> can be useful when trying to assess the degree of "spread" within a
> set of numbers. As illustrated by the performance of the two
> hypothetical stocks, the SD disregards the level of the mean when
it
> assess variability. The SD computes how variable the scores are
> around the mean, but the size of the mean is not taken into
> consideration. In contrast, the coefficient of variation looks at
the
> spread of scores (around the mean), adjusted for the size of the
mean.
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