Help: T-bill future pricing

Dear all: I’m confused in Deriatives-- T-bill pricing, can someone pliz expain intuition to understand the logic behind, and why it difficult to price Eurodollar futures (LOS 61.g).

Tbill Pricing For some wierd historical reason and to make our life miserable, T-Bill is quoted differently from its price - meaning its quote is not its price. It is quoted at annualized discount. So adjust accordingly. So if quoted at 4% annulaized discount, the price is really (1-.04*90/360) i.e .99 So you pay .99 and get 1 when it expires. The yield ® for 90 days is (1-.99)/.99 . Futures pricing Remember two things. Firstly, good old formula Future price, F= S*(1+r)**T. where r = risk free rate and T is expiration Time of future. Secondly, note (usual tripping point), there are two expiration days here 1) expiration of future and 2)expiration of underlying. The T above is expiration of future. the underlying is typically a 90 day instrument but it could be any h day T-bill. Step 1 Get S To get future price of n days on a 90 day underlying from you will need a T-bills greater than n days i.e n+90 days. If the future is for a h day (instead of 90 day) instrument then the you need T-bill expiring in n+h days. Anyway once you have this, use above Tbill pricing formula to get the spot price. So from CFAI text 140 day bill trading at 4.6% discount is 1 - .046*140/360=.9821 Step 2 Get (1+r)**T; r is the risk free rate. So the (1+r)**T can also be looked at the yield on a T-bill for n days. So get the yield on a second T Bill expiring in n days. This corresponds to expiration days of t-bill Future. Assuming 50 day tbill is at 5% discount , price is 1-.05*50/360 =.9931. So (1+r)**T is equal to 100/.9931. Step 3 Future Price = Step 1* Step 2. Note you have computed future price for a future expiring in 50 days for 140-50 i.e 90 day underlying T-bill. Valuation Actual futures values are not so painful as forwards as they are exchange traded and marked to market dialy - so one does not have to worry about value. Their value at end of each day is 0. Eurodollars They are priced like as T-bills future. This is not to confuse traders who were used to the T-Bill quotes. But that is not how Eurodollars time deposits are executed in practice. The interest is a add on yield . So a $1 Eurodollar time deposit is not priced at less than 1. It is priced at $1 and after n day you you get (1+r*90/360). A T-bill would be priced at (1-r*90/360) and executed thus in practice too. So the (1+r)**T in eurodollar Future does not match yield in practice. Hence the problem.

Thank u so much thadim! wonderful expaination.

Thadium, Thanks for the explanation. You said that 1. - “They are priced like as T-bills future” 2. -"The interest is a add on yield . So a $1 Eurodollar time deposit is not priced at less than 1. " I am little confused : if they are priced like T-Bill futures, then how is it not priced at less than 1? Could you pl. elaborate it with an e.g.?

For the Eurodollar future --> there are two aspects. 1. Traders still see them with prices quoted like they would see a T-Bill future. So the (1-L*N/360) terminology. This is purely so as not to confuse the traders. 2. But in the real market place - they are worked with and priced as -> (1+L*N/360). so there is a mismatch between what you see and what you get. Hence you cannot exactly find the yield on a Eurodollar future. Nonetheless, they are useful to be able to hedge against your other investments (used as a derivative security). Hope I am right in my understanding, and hth.

Thanks cpk.

Sorry to bump an old thread! I’m studying the Stalla materials and went to CFAI texts for reference but noticed that the entire section on pricing T-Bill futures are optional. I did a quick search(hence found this thread) and noticed no mention of this. I didn’t see T-Bill pricing on the LOS as well. Is it really optional or optional in a sense were you should have learned it in L1? CFA V6 text page 92.