Moment and Omega Rankings of Index ETFs

I've taken some of the most commonly referenced indexes and calculated a general comparison of their respective tracking ETFs' behavior over the past 1,600 sessions. All numbers are calculated on daily adjusted log-returns.

Once these first four moments and the Omega measure are calculated, I rank them as optimally desired - increasing mean, decreasing standard deviation, increasing skewness, decreasing kurtosis, and increasing Omega ratio. Finally, the indexes are sorted by their average rank as shown in the last column.

• DIA: DIAMONDS Dow 30
• IJH: iShares S&P MidCap 400 Index Fund
• IJR: iShares S&P SmallCap 600 Index Fund
• IWB: iShares Russell 1000
• IWM: iShares Russell 2000
• IWV: iShares Russell 3000
• SPY: SPDR S&P 500

click to enlarge

The results are somewhat surprising and likely due to the equal-weighting of rankings. Other than the Dow 30 Diamonds, the iShares ETFs seem to take the cake as a whole, with the S&P 600, S&P 400, and Russell 3000 taking the top three spots.

Comments

[Susan:]

Since Omega already takes into account all the moments of the distribution, what is the rationale behind the double accounting?

Also, during bear markets, when the means are negative, skewness cannot possibly be a positive thing, right?

2007 Sep 25 11:46 AM

[Michael Bom...:]

Hello Susan, the double accounting is for two reasons - firstly, to confirm the ranking of the first four moments, and secondly, as you mention, to include the higher order moments.

Also, if you'd like an example of a distribution with negative mean and positive skewness, take December 31, 2001 to March 15th, 2003, and you should get just such a distribution. For reference, I calculate a log-return mean of -0.0011 and skewness of 0.4057. Make sure you're not using excess moments either.

2007 Sep 25 01:26 PM

[Daniel Moser:]

I have just recently discovered the concept of omega as a portfolio measure and I have a question for you...

How do you incorporate correlation measurements into portfolio construction using Omega as your maxmizing function during the construction process? I think I understand the objective behind seperating gains from losses for the purposes of capture various moments of the distribution but it seems like this process, on face, loses the ability to construct portfolios that utilize inverse correlations in the market place. Thanks for your help.

2008 Oct 16 10:12 AM