A topic that seems to keep resurfacing is the EG vs EU-GU debate. Earlier in the thread I mentioned my opinion and stated that I would follow up with a chart comparison to put this debate to bed. Far from being definitive, this post is simply a pictorial description of EG vs EU-GU for future reference.
Some say EG = EU-EG. Some say EG is not equal to EU-GU. I will leave the editorializing to others and simply provide two pictures that show how they appear on the chart, then describe how they are similar and how they are different. The chart is EG 1 hour in green with an overlaid DodgerBlue EU-GU plot fixed at the starting point of the chart. The data shown is 7/28/2010 - 9/7/2010. The dates were selected because it shows the point on the chart where the green and DodgerBlue are identical. I kept the scaling identical on the two charts to show exactly the difference.
The first chart shows EG with overlaid EU*1.0-GU*1.0 on the same scale. This is what you would get if you compare EG to EU-GU side by side.
The second chart shows EG with overlaid EU*0.6-GU*0.6.
While the EG - (EU-GU)0.6 overlay is not a perfect match to EG, it bears a striking resemblance. But there are minute differences in chart formation that may be difficult to pick up on these smaller forum pictures. Not every peak on EG is mirrored exactly by peaks in (EU-GU).6, however it is worth noting that the chart formations are very close. It is expected that the charts would be similar because EG = EU/GU. However as any mathematician will say, dividing and subtracting are not the same thing. When you subtract EU-GU the USD portions don't cancel out completely, leaving slight differences in chart formation. I'll let the reader decide if those slight differences in chart formation are important or not.
The thing that is most notable about the first chart is the volatility of EU-GU compared to EG. [B]The volatility of EU-GU is much greater[/b] as shown in the scaling shift in the first chart than the underlying EG volatility. What are the implications of the difference in EG vs EU-GU volatility? I'll leave that for others to say.
How big was the difference in volatility shown the first picture? The range of EU-GU shown was about 400 pips. The range of EG shown was 273 pips. This makes EU-GU in this period 46.5% more volatile than EG.
It is worth noting as a post script that even the EG vs EU*0.6 - GU*.06 shows some significant and extended divergence at some points during the chart (not shown). The 0.6 beta is not a perfect weight over the entire data series. Using different weights will either increase or decrease the volatility difference between EG and EU-GU.