Futures prices on bonds arent directly reflecting of market interest rates.
The futures contract
price takes [the fact the seller can deliver a package of bonds with different maturity dates] into account so prices have less to do with current rates, and more to do with what existing bonds in the market are cheapest to deliver to the buyer.
The directionality of the price movement works in that a rise in the quote price means the value of the 6% note has become more expensive and the yield
has gone down. With a quote price of 100000 (6% interest) as a baseline, if the price is below 100000 then the interest rate must be above 6% and if the price is above 100000 then the interest rate must be below 6%.
Treasury bonds tend to have a negative correlation to the equity market. So, if the equity market becomes very fearful (risk off
), Treasury bonds will tend to rally ie the quote price will rise which means the yield is falling because the bonds are in such demand that buyers are prepared to receive a lower yield.
See also: https://www.cmegroup.com/education/f...ry-futures.pdf