if the interest rate is expected to rise, buy or sell the t bill futures ?
i believe - Rates rise - you want to shorten duration of your bond portfolio - so sell futures…
A futures position is equivalent to a position in the underlying (well . . . almost equivalent).
If rates are expected to rise, the value of T-bills will fall. You’d sell the T-bills, so you’d sell (i.e., take the short position in) T-bill futures.
If rates are expected to fall, the value of T-bills will rise. You’d buy the T-bills, so you’d buy (i.e., take the long position in) T-bill futures.
Sell,Of course.
As S2000magician aptly wrote “A futures position is equivalent to a position in the underlying (well … almost equivalent).”
You should also be conversant with why sell futures,to reduce the exposure to rising interest rates-why not sell the T bills outright in the first place…
Be very careful here. The t-bill future is a promise to deliver a 15-25yr bond in exchange for cash. So all sorts of things can be happening if you have a duration matched portfolio. Chances are they formulate the portfolio so it behaves in the opposite manner to what is intuitive.
I believe that you’re mistaken.
T-bills have original maturities of one year or less.
You may be thinking of T-_ bond _ futures.
Yes i mis-complified it 
ok how about this.
you have a obligation in 30yrs for $1mio. rates curve is flat at 5%
you create a duration matched portfolio buying $2m 15yr bonds, borrowing $1m in short term instruments.
rates are expected to rise in a parallel shift by 100bps… what do you do to imunise the portfolio from the (after the??)expected shift?
a) sell $1m t-bill futures
b) buy 100k t-bill futures
rates increase, so the duration of the bonds lengthen a litte. correct response is to buy the futures and sell 100k of 15yr bonds.
…something like that… correct numbers are an exercise for the reader. key thing is the bonds have coupons, assume 5%. my brain is potato soup already