# Forward

The price of a 90-day forward contract on a 90-day Treasury bill will be: A) above the current price of a 90-day T-bill. B) either above or below the current price of a 180-day T-bill. C) above the current price of a 180-day T-bill. D) equal to the current price of a 180-day T-bill.

C?

Can you further explain.

Remember that T-bills are priced like discount instruments. All else equal the further from expiration, the lower the price. Thus, a 180-day T-bill might sell for 96 but a 90 day T-bill would sell for 98 or similar. a 90-day forward contract on a 90-day T-bill ought to have a price that looks like a 90-day T-bill price which right away ought to led you to C. If it was below the price of a 180 day T-bill, I would go long forward contract, short the 180, put the proceeds into 90-day T-bills. In 90 days I would use proceeds of expiring T-bills to exercise forward contract and make a guaranteed profit. E.g. 180-day T-bill @ 96 90-day T-bill @ 98 Forward @ 95 and check it out (I’m too lazy).

not 100% sure, but also think it’s C by eliminating other answers A) if the current price of t-bill is 98 that means i will get 100 in 90 days, forward selling above this price, 99, gives me right to buy t-bill in 90 days at 99 and get my 100 in 90 days after that (180 days total) i would rather get 100 earlier ( in 90 days not 180) so A is out, plus is only choice mentioning 90 day t-bill so it’s gotta be wrong. if 90 day forward for 90 day t-bill again is selling for 98 that means that in 90 days i can buy it for 98 and then receive 100 in another 90 days if 180 t-bill is selling for 98 too, why would I buy it if i can enter in forward and keep my 98 for 90 days and earn interest and then buy t-bill which will get me the same 100 in the end. Therefore, 180 tbill has to sell lower to compensate for the first 90 days. I hope i’m right and this helps.

D? To ensure no-abritrage… 90 day forward to purchase a 90 day tbill. your lookin at the 90 day discounted price of a 90 day tbill.

You probably get it by now ditchdigger, but I think the reason why it can’t be D is the following: The 90 day forward on the 90 day TBill means I can hold on to my money today and invest it for 90 days (say in another 90 TBill or something higher like commercial paper which should have higher rates than Tbills). After 90 days pass, I will take that money now and use it to fulfill my contractual obligation to buy the Tbill. 90 days after that (180 days total from today), I will receive the face value of the TBill. Now, because I don’t have to give up money now but later, and in the mean time earn interest, it would be unfair or an arbitrage opportunity if the price is the same as a 180 day Tbill (which requires that I invest in it today). The key is that in the first 90 days, I can put that money into any instrument I want, which might give me higher interest than what a 180-day TBill will. To make up for this freedom, the price of the 90 day forward on the 90 day Tbill has to be higher. Please correct me if I am wrong. Thanks guys!