Quote from let it run:
I'm amazed at the lack of understanding here. I don't think you need to necessarily know these things inside out in order to trade instruments but if you want to understand how/why they move, it would be handy if you thought about these angles before you start playing.
The answer is people are prepared to pay a little more for the futures contract because they don't incur the cost of carry attached to buying the bond outright, now i.e. spot price. Higher price = lower yield.
Imagine the opportunity cost of paying full price for these bonds now as opposed to locking in a price now (by paying the margin on the futures contract), safe in the knowledge that you could earn interest on the money/invest it somewhere else until you have to settle the difference on the delivery which could be up to 3 months from now. This also explains why spot/futures prices converge when that particular contract closes in on expiry.
Hi. I concede I was rather confused when I tried to quote future bonds at that time.
Now things are much clearer.
And what explains most of the difference is not what you said, but the real maturities of futures.
For instance, the 30Y futures is related to the delivery of a bond which is from 16.5Y to 30Y, that is to say that most of the time, when bond rates (YTM, not coupons) are below the 6% level, the bond with the nearest maturity is the one that would be the Cheapest To Deliver (CTD).
Therefore the 30Y futures relates currently to the 16.5Y bond, which is of course very different from the
pricing of the 30Y bond !
What about the other thing which is very important ?
The conversion factor !
Quote from scriabinop23:
30 yr spot (bloomberg):
30-Year 4.750 02/15/2037 96-03+ / 5.00 0-00 / .000 05/25
30 yr futures (the entire strip Jun07 - Jun08): 109 9/32
Cost of carry is not what explains this price discrepancy. Furthermore, futures and spot do not converge, at least numerically (like indices do) since futures refer to bonds similarly priced assuming a fixed 6% coupon, whereas spot coupons vary.
Otherwise you'd see steadily increasing prices across the futures curve, just as most other commodity and indices show. But futures are priced locked to a 6 percent coupon. Look at ZB - all the futures are priced -practically- identically.
Still, simple math doesn't give me useable results. Haven't read the CBOT summary of bond pricing lately, but I know accrual, and conversion factor are two key items here.
I believe conversion factor is derived by 6/current coupon.
6/4.75 = 1.26
1.26 x 96 = 121.26 (instead of 109.xx)
If anyone else wants to get me from 96 -> 109 9/32 by showing the calcs, please do. Perhaps my conversion factor is too high and/or something else is at work I'm missing.
I do not have enough time to explain how you can calculate the conversion factor, but the easiest way is to pick it up from the cbot website, as the calculation is more complex than 6 / 4.75...
Please do not hesitate to take the most recent CF there :
http://www.cbot.com/cbot/pub/cont_detail/0,3206,980+20356,00.html
Then multiply the CF of the CTD bond by its security price, and you would find "nearly" the future price.
At last, there remains some discrepancies, especially the différence between the repo rate and the YTM rates of the CTD bond (before the delivery day...), and the valuation of the "option" that you pay when you short futures (to ask for delivery or not...)