Period Amplitude of Difference Between SPY, IWM Returns

Includes: IWM, SPY
by: Michael Bommarito

If you keep up with my scattered musings on the relationship between large and small caps, you'll know that I believe that the difference in returns tends to indicate the state of the important underlying market volatility level and risk premium.

I've begun analyzing this relationship in more detail, and so here's a preview of what's to come. The following is what's called a period amplitude distribution, and represents which frequencies are most "prevalent" in a signal. Understanding why certain frequencies are prevalent in a signal is often the first step in determining what variables truly drive the output, and often serve as valuable tools in determining reasonable "time-to-hold" values for automated trading systems.

This distribution was calculated on the difference time series of S&P 500 tracker(NYSEARCA:SPY) and the Russell 2000 tracker (NYSEARCA:IWM) from May 26th, 2000 to June 6th, 2007. For each date, the signal value is the log-return of SPY minus the log-return of IWM. I then calculated the DFT of the signal and this is the resulting distribution. Note that this figure does not display the detrended DFT.


I will try to keep my methods in this analysis relatively simple for the sake of communication and hope to be able to present the results in a digestible form. Keep an eye out this weekend.