# Clarifications about the “quotations” of Treasury Bills and Treasury Bonds

Good morning. I would like to ask you some clarifications about the "quotations" of Treasury Bills and Treasury Bonds.

Quoting "J.C. Hull":

In general, the relationship between the cash price and quoted price of a Treasury bill in the United States is $$P=\frac{360}{n}(100-Y)$$ where P is the quoted price, Y is the cash price, and n is the remaining life of the Treasury bill measured in calendar days.

So the quotation in this case is equivalent to the yield?

The quoted price of Treasury bond, which traders refer to as the clean price, is not the same as the cash price paid by the purchaser of the bond, which is referred to by traders as the dirty price. In general:

Cash price = Quoted price + Accrued interest since last coupon date

But, in this case, how is the "Quoted price" determined? Is it equivalent to bond yield, applying the same formula?

Treasury Bills: $P$ is not the yield because it's calculated with a nominal of 100. $100 \cdot P/Y$ is something like the simple yield of the bill.

Treasury Bond: You calculate the quoted price from the cash price not the other way around:

Quoted price = Cash price - Accrued

The quoted price for bonds has nothing to do with the yield as you can easily see if you look at some clean prices.

In both cases is the relevant price the cash price. That is the amount of money that will actually change hands. But because traders like it opaque they do not quote the cash price but instead some 'quoted price' that is calculated from the cash price. But one can be converted into the other.

• Thanks for the answer! About Treasury Bills: P is the quoted price? Also I didn't understand how the quoted price for Treasury Bond is determined. For example, if I have the interest rate, coupon value, expiration period, and facial value, can I determine the quoted price? – Mike9 May 20 '17 at 13:49
• Yes P is the quoted price. I'm not sure what your question is. Re Bonds: Say you are a bond trader and you have a bond to sell. First you think about how much money you want to get for your bond. That is then your cash price. Then you calculate the current accrued and deduct from your cash price and voila you have the price to quote. – Ami44 May 20 '17 at 14:08
• You can not use the following formula for Treasury Bond: $$P=\frac{360}{n}(100-Y)$$ because for Treasury Bond, unlike Treasury Bills, we must consider the payment of coupons and the expiration period that lasts several years. But at this point because I can not calculate the price quoted as $$P=100- \left(100 - \sum_{i=1}^{n} \frac{coupons}{r^i}\right)$$? – Mike9 May 20 '17 at 14:18
• Im not sure what you are asking. What is this citation from and what is the context? The last sentence seems to be hacked of in the middle. – Ami44 May 20 '17 at 16:24
• the quoted price does not necessarily have a interpretation as yield or something similiar. Treasury bonds are quoted by their clean price. Its just market convention. – Ami44 May 20 '17 at 17:29