atticus, please post a chart. God knows you're better at it than I am. (seriously, if I do it, I'll show price instead of yield, and the scale will be wrong).
Atticus, yes indeed price of bonds and interest rates share an inverse relationship, and the data that I'm looking at show that clearly. But that price/interest rate relationship does not affect contango/backwardization: when interest rates go up, prices go down - but the futures contracts are still in backwardization (sorry, I know wrong term here). And when interest rates fall, prices go up - but the futures contract are still in backwardization. The only time I see t-bill futures go into contango is when the short term interest rates are higher than the longer term interest rates. I'm trying to understand why the t-bill futures trade this way???
The futures don't pay a yield, so they're discounted to spot to account for the zero-coupon (i.e. spot EDs). As the curve inverts, the futures will trade at a sequential premium ("contango") on duration due to the -convexity of the curve, provided there are no kinks. The relationship between the futures and yield curve will resemble a volatility cone; +convexity on futures while -convexity on yield, with the slope relating to the swap.
This cme tutorial explains it pretty well: http://www.cmegroup.com/trading/interest-rates/files/Understanding_US_Treasury_Futures.pdf Specifically page 28 and it is very close to what nazzdack mentioned. Here's the overview: "In a normal upwardly sloping yield curve environment where long-term rates exceed short-term rates, there is a positive result to buying and carrying a bond on a leveraged basis. In other words, financing costs (represented by short-term rates) are less than the payouts on the security (represented by long-term rates). As such, âpositive carryâ prevails and bond futures can be expected to trade at successively lower and lower levels in deferred months." The same is true but opposite when the yield curve inverts.. cost of carry becomes negative and the futures contracts go into contango.
Actually, per the tutorial I posted above, you don't erode "all" of your interest earned, just the "long term" portion. Here's what the tutorial says about it... "Consider the implications of a hedge, specifically, by selling futures against a long-term bond, one commits (at least temporarily) to the delivery of the security in the short-term. In other words, one effectively turns a long-term investment into a short-term investment. Accordingly, one cannot expect to earn a long-term rate of return but rather a short-term rate of return." In today's very low interest rate environment, your returns on a such a hedge would indeed be very small, but not zero.