Brothers, revisited

I mentioned them thar brothers: stocks (actually ETFs) that moved in opposite directions, each day. There's a gaggle of 'em, here: http://www.hbpetfs.com/pub/en/Etfs.aspx. They got Bull & matching Bear ETFs, ending in U and D (for Up and Down, I reckon). One might think that Bull and Bear ETFs would behave like mirror images. For example, them that's tied to the Gold Index Well, close but no cigar ... but they do get a cigar each day: HGU was UP 4.8% yesterday and HGD was DOWN 4.6%. Good, eh? However, it's quite possible that both the Bull & Bear ETFs have negative (or positive) annual returns (as opposed to opposite daily returns). For example, these guys (tied to crude oil futures) both ended up with a negative annual return: Yet, on a daily basis they look like ... uh, twins, eh? (Or is it brothers? What's a good name for these guys?) Is it the accumulation of tiny differences over a year? Surprisingly, the answer is NO! If they are closely tied to some underlying Index or Future, they can both lose over just 2 days. For example, suppose the "underlying" goes UP 10% on Monday and DOWN 9.1% on Tuesday. The net result is (1.10)*(.909) = 1.00, so the underlying Index is back where it started. Yet the two cousins (what are we calling them?) both lose over these 2 days. The Bull has returns of 20% and -18.2%. (Them's 2x the underlying Index returns, eh?) The Bear has returns of -20% and +18.2% (That's -2x the underlying Index, eh?) Check it out: they both end up with a negative 2-day return. (About -2% and -5%.) Now that deserves a Mamma mia! These Gemini ETFs (what are we calling them?) are fascinating and I really need to find a way to make a $killing.