Treasury Bills and Bonds: Quoted Prices, Cash Prices, and Value

Summary

The document distinguishes Treasury bill discount quotations from Treasury bond clean and dirty prices. Its main correction is that bills do not pay coupons: they are issued below face value and redeem at face value, so the relevant quotation in the presented bill relationship is a quoted yield rather than a quoted price. A lower bill purchase price implies a higher effective return, all else equal.

For coupon-bearing Treasury bonds, the stated distinction is sound: the cash, or dirty, price includes accrued interest, while the quoted, or clean, price excludes it. The question also asks how a bond’s value based on a zero curve or yield relates to quoted and cash prices, but the response does not address that valuation comparison. The document offers a terminology correction and a basic pricing distinction, without detailing yield conventions or bond valuation calculations.

Key ideas

• Treasury bills have no coupon and are typically sold below face value.
• A bill quotation in the described relationship should be a quoted yield rather than a quoted price.
• A lower bill purchase price corresponds to a higher effective return, all else equal.
• A Treasury bond’s dirty cash price equals its clean quoted price plus accrued interest.
• The document does not explain how model-based bond value compares with market prices.

Tags

# Treasury Bill and Treasury Bond : Quoted Price VS Cash Price VS Value of Bond


# Treasury Bill and Treasury Bond : Quoted Price VS Cash Price VS Value of Bond












I have confused by three concepts and following is my understanding:

`Quoted Price` and `Cash price` are totally different things in the `Treasury Bill` and `Treasury Bond`?

In the `Treasury Bill,` they are the two alternative ways to state the amount of coupon over face value 100 and we have the relation $$\dfrac{n}{360}\times\text{Quoted Price} = 100 - \text{Cash price}.$$

But in the `Treasury Bond,` they describe the current price of bond with the relation: $$\text{Cash price = Quoted price + Accrued interest since last coupon date}.$$ $$\text{Cash price = Dirty price}$$ $$\text{Quoted price = Clean price}$$

The `Value of Bond` is calculated by the zero curve or the yield of the bond, when the coupon structure is known. The `Value of Bond` have the relation with `Quoted Price` and `Cash price` in `Treasury Bond`(>,< or =), but has nothing related in `Treasury Bill.`

I am not sure whether above understanding is correct.

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/36067

Bills do not have a coupon. They are sold at a discount to 100, but you get your 100 back at maturity. The equation should read 'Quoted Yield' not 'Quoted Price'. Yield is the effective return on your investment. The lower the cash price, the higher the return.

The equations for bonds are correct.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.