Clean Versus Dirty Prices in Bond Portfolio Duration

Summary

The discussion considers whether Macaulay duration for a portfolio of conventional bonds should use clean prices or dirty prices. The answer favors clean prices on theoretical grounds: accrued interest corresponds to a past accrual period, while interest rate exposure should reflect future cash flows. It also presents an alternative accounting view in which accrued interest sits in an overnight cash balance, making it relevant to the overnight rate pillar.

The response says the present value change for a one basis point rate move is nearly the same under either convention, because the overnight pillar has little sensitivity. However, dividing by portfolio present value changes the duration normalization: dirty price includes accrued coupon interest, which shifts the denominator. The document offers a concise conceptual argument rather than a full derivation, and notes that an update points to further discussion without providing it here.

Key ideas

• Clean prices isolate the value of future bond cash flows from accrued interest.
• Accrued interest can instead be treated as cash exposed to overnight rates.
• The two conventions produce nearly identical PV01 according to the response.
• The duration normalization differs because dirty price includes accrued coupon interest.

Tags

# Portfolio Duration . Dirty or Clean Price?


# Portfolio Duration . Dirty or Clean Price?












When I calculate the Macaulay Duration of my portofolio (vanilla bonds) Should i have to use clean or dirty price to price my portfolio? What is the logic to use one or the other?

Thanks a lot!

## Answer by Kermittfrog (score 1)

https://quant.stackexchange.com/a/59708

Update: Please follow the link in @Sharad's comment.

Original:

From a purely theoretical point of view, I would go with the clean price. My reasoning is, that only future cash flows can ultimately bear interest rate risk.

Nevertheless, you could argue that the accrued interest resides in some overnight cash account and that you want to disclose interest rate risk on the overnight pillar as well.

Numerically, the PV01 (PV impact of a 1BP shock in the rate) is nearly the same under both approaches (i.e. the overnight pillar has very little sensitivity) but the normalising factor $\frac{1}{PV}$ is of course off by $\tau c$, with $\tau$ the accrual period and $c$ the periodic coupon.

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.