How do I calculate the statistical measure known as omega?

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Con Keating and William Shadwick at Duke University wrote a paper, An
Introduction to Omega, in which they describe Omega. It would be great if
Excel added it to its statistical functions. In the meantime, does anyone
know how to write the formula in excel?
 
You need to provide more information. I cannot find anything in Current
Index to Statistics by anyone named Shadwick nor can I find anything by a
Keating that also has "Omega" in the title or keywords. A search of the Duke
online phonebook also failed to find a Shadwick, and none of the three
Keatings seemed likely to be called "Con".

Jerry
 
Thanks. This paper and others on Omega can be found at
http://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/

Scroll down to Keating, and you can see some of his papers on Omega. The
Omega Function seems most useful. Continue to scroll down for two other pdf
files listed under Omega.

Keating_An_introducti+ 07-Jan-2004 14:00 190K
Keating_Asset_optimiz+ 07-Jan-2004 14:06 468K
Keating_The_omega_fun+ 07-Jan-2004 14:08 568K
 
I see why I could not find anything. The authors are at a center in London,
not at Duke University. The references suggest that this work has not yet
been published in refereed journals, and the document is labeled "Not for
Circulation".

For the Normal distribution, omega can be calculated as

=((mu-r)*2*NORMSDIST(-(r-mu)/sigma)*SQRT(Pi)*EXP((r^2+mu^2)/sigma^2/2)+SQRT(2)*EXP(1/sigma^2*r*mu)*sigma)
/((r-mu)*2*NORMSDIST((r-mu)/sigma)*SQRT(Pi)*EXP((r^2+mu^2)/sigma^2/2)+SQRT(2)*EXP(1/sigma^2*r*mu)*sigma)

For other distributions, I suspect that numerical integration would be
required, and I doubt that Microsoft will be interested until both of the
following occur:
- Use of this characteristic of a probability distribution becomes widespread
- Microsoft has implemented better algorithms to calculate the probability
distributions that they have.

Jerry
 
Thanks. Omega is gaining popularity in the alternative asset management
world where returns are not normally distributed. To confirm, the formula
below only works on normally distributed returns? I'm also wondering where
in the formula I put in the cell ranges that contain the data?
 
The paper you cited only defines omega in terms of integrals of theoretical
cdf's (cumulative distribution functions). Their example with financial data
is incompletely described. It is not clear whether they are
1. assuming some (unspecified) parent distribution whose parameters they
are estimating from the data
2. extending their formula #3 to involve sums of empirical distribution
functions
3. something else entirely, such as using an Edgeworth expansion to
approximate the cdf with cumulants estimated from the data

The formula I provided is specifically for the normal distribution. At the
time that they wrote their paper, Cascon et al stated that "The question of
the omega-characterization of the normal distribution is a natural one, to
which we do not as yet have a satisfactory answer. If that is still true,
where should I publish the closed form formula that I derived?

Jerry
 
H Jerry,

The data we would use would be a series of monthly or daily returns.
Usually I receive these on an excel spreadsheet. For example, the dates in
column A and the corresponding returns in column B. The question is how do I
put this data in to the Omega formula you wrote.

Thanks.
 
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