Treasury Bond Dirty Price: Accrued Interest and Forward Compounding

Summary

The document asks how to calculate the settlement-date dirty price of a semiannual US Treasury bond. It gives a bond with stated par, coupon, yield, coupon dates, maturity, and settlement date. The author first values the remaining cash flows as of the previous coupon date, then adds accrued interest calculated using an ACT/ACT fraction. That approach produces a lower figure than the forward-compounded price quoted in the question.

The proposed adjustment is to compound the coupon-date present value forward to settlement using the yield over the elapsed fraction of the coupon period. The question is why simply adding accrued interest does not work and whether the coupon-date present value is a clean price. The excerpt presents the proposed calculation but no explanatory answer, independent verification, or discussion of pricing conventions. Its figures therefore illustrate the issue raised, rather than establish a general rule for every bond day-count or settlement convention.

Key ideas

• The document distinguishes a present value calculated at the prior coupon date from a price at settlement.
• It compares adding accrued interest with compounding the prior-date value forward at the yield.
• The example uses semiannual coupons and an ACT/ACT accrued-interest fraction.
• No answer verifies the quoted dirty-price calculation or explains its assumptions and convention limits.

Tags

# Dirty price of US T bill


# Dirty price of US T bill












I need to calculate the dirty price of a US T bond given the below details:

Assume the coupons on a U.S. Treasury bond are paid on January 1st and July 1st. The bond has a par of $1,000 and pays a semiannual coupon of 4.0% with a yield of 6.0%. The bond has a settlement date on April 4th, 2011. The bond matures on January 1st, 2016 such that there are ten (10) remaining semi-annual coupon payments. What is the dirty price (a.k.a., full price) of the bond?

My initial thought was to calculate the PV of the bond and add accrued interest/

I've been told this is incorrect and I need to compound the present value forward at the yield for for the 93 days between the last coupon Jan 1 and the settlement date April 4.

```
$914.6980*(1.03)^(93/181) = $928.696 is the full (dirty) price as of settlement date
```

My question: Why can't I just add accrued interest the the PV as of Jan 1 ? Is the PV as of Jan 1 not the "clean" price ?

This is what I tried

```
Use calculator to get PV:

Number of periods = 10
Yield = 6/2
Payment = 20
Future Vale = 1000
Resulting in a PV of $914.698

And then calculate the accrued interest from April 4 to July 1 using the ACT/ACT day     count such that:
AI = $20*(93/181)=$10.276

Resulting in the dirty price 914.698 + 10.276= 924.974
```

Thanks in advance.

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