Clarifications about the "quotations" of Treasury Bills and Treasury Bonds

Question

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?

Answer 1

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 But because traders like it opaque they do not quote the cash price but instead some 'quoted price' that is calculated from the cash price.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.