How Treasury Bill and Bond Quoted Prices Relate to Cash Prices
Summary
This explanation distinguishes quoted prices from the amounts actually paid for Treasury bills and bonds. For Treasury bills, the quoted price is calculated from the cash price using a convention based on a nominal value of 100 and the bill’s remaining calendar days. It is therefore a price quotation, not itself a yield, although a ratio involving the quoted and cash prices can express a simple yield measure.
For Treasury bonds, the quoted clean price is obtained by subtracting accrued coupon interest from the dirty cash price. The quotation is not calculated by applying the Treasury bill formula and is not equivalent to yield. The discussion emphasizes that clean and quoted prices can be converted to cash prices, which represent the payment exchanged in a transaction. It offers conceptual clarification rather than numerical examples or a broader account of yield conventions.
Key ideas
- A Treasury bill’s quoted price is calculated from its cash price using a convention based on a nominal value and remaining days.
- The bill quotation is not itself a yield, though a ratio of quoted and cash prices can express a simple yield measure.
- A Treasury bond’s clean quoted price equals its dirty cash price minus accrued interest.
- Bond clean price and yield are distinct quantities, and the bill quotation formula does not determine bond prices.
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Full text
# Clarifications about the "quotations" of Treasury Bills and Treasury Bonds
# 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?
## Answer by Ami44 (score 1, accepted)
https://quant.stackexchange.com/a/34311
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.