There is a large spread between 1M and 3M ED futures, roughly 20 bps. For example, from Bloomberg, on Jun 29, 2009.The quote for 3M ED futures Sep contract is 99.36 (0.664%). The quotes for 1M ED futures Sep, Oct and Nov contracts are 99.5875 (0.4125%), 99.5225 (0.4775%) and 99.465(0.535%).Since the convexity adjust is small (less than 1bp), so we can ignore it. When we compound the 3 1M rates of 0.4125%,0.4775% and 0.535% , it does not give 3M rate of 0.664%. In fact, it is 20 bps lower. Is the spread between 1M and 3M ED futures that big? or am I missing something?

There have been many threads here discussing the term basis issues, in their various guises. It all comes down to the fact that you can't obtain a 3M LIBOR rate from three 1M LIBOR rates, as they have different liquidity characteristics.Quite apart from that, I wouldn't really place much faith in prices of 1M eurodollar futures. Even if they trade, they're extremely illiquid, from what I can see.

are these 20bps linked to the 3s1s Dollar basis swap ?

yes there is a large spread, since the respective contracts settle to the libor fixings, they are subject t liquidity constraints (availability for financing) With a 3 month libor borrowing, an institution can lock in financing over the next quarter end, whereas by rolling 1m, you are subject getting a new rate each month (fine so far). However, there is the possibility that there might be a situation where you might not be able to roll your borrowing at some point in the future, and it is this liquidity option that are paying for in the 3m fixing.

Rickynu,thank you very much for your answer.Yes, when we roll 1 month ED futures, there are liquidity and credit issues. At first sign, 20bps seems too large.

For a rough guide, all you have to do is look at the spread between the spot 1M and spot 3M USD LIBOR fixings. That differential is arnd 23.5bps, of which roughly 2 - 3 is due to pure base rate change expectation/risk premium. The remaining 20bps is due to the 3s1s basis.