# How bidders determine price for T-bills?

Let's take for example 4 week T-bill issued today, 3/1/2018 (https://www.treasurydirect.gov/instit/annceresult/press/preanre/2018/R_20180227_1.pdf).

Price of t-bill is determined on auction by competitive dealers and if's par value is \$100.

``````Question number one:
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Do bidder bid with price or with discount rate? Do they say, I offer \$99.88 for this t-bill, or they have to bid with discount rate?

``````Question number two:
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Where in this report I can find auctioned rate? It only states high rate, median rate and low rate, but all auctioned t-bills should be sold using unique price, right? As far as I know, The highest yield accepted is called the stop-out yield, and all t-bills should be sold using that rate, in this case 1.495%.

Note that I'm using yield and rate interchangeably, but when talking about t-bills we assume that we talk about bank discount yield?

Question number three:

If in question number two, it is true that auctioned yield is 1.495%, why am I not getting the same price as stated in the report?

Bank discount yield:

# Bdy = (F-P)/F*360/t

(100-99.883722)/100*360/30 = 1.395336% and not 1.495%

## 1 Answer

Do bidder bid with price or with discount rate?

T-bills are typically quoted by their equivalent interest rate, or yield, so the quote would be 1.495%. This makes quotes comparable regardless of their tenor, since a 1-day t-bill valued at \$99 has a much higher annualized yield than a 180-day t-bill at the same dollar price.

why am I not getting the same price as stated in the report?

Because you are using the wrong value for `t`. These are 28-day bills, not 30-day bills, so the formula should be

``````(100-99.883722)/100*360/28 = 1.495%
``````
• Thank you! Using what formula have you found equivalent interest rate? If (F-P)/P*365/28 than the result is 1.51%, or as named in the report (investment rate or the coupon equivalent). – Nikola Feb 28 '18 at 14:55
• I edited my first comment. I mean the quote of 1.45% that you mentioned, what's formula for that? – Nikola Feb 28 '18 at 15:03