Building a Bond Total Return Index from Clean and Dirty Prices
Summary
The document explores how to estimate a custom total return bond index when only clean and dirty prices are available. It begins with a price-index formula using dirty prices, then notes that dirty prices fall around coupon payments as accrued interest is removed. That price drop can obscure coupon income, making a dirty-price series alone unsuitable for representing total return in the way the author expected. The example considers a fixed-rate bond with semiannual coupons and observable clean and dirty prices.
The proposed adjustment is to calculate accrued interest as dirty price minus clean price, then identify dates when accrued interest declines and treat the prior dirty price as matching the current clean price. This is presented as a workaround for recognizing coupon events without coupon-date data. The author says the bonds under study are from lower-rated countries, but provides no detailed validation, index results, or robustness analysis. The method therefore remains a tentative data-handling suggestion, and its reliability may depend on pricing frequency and other changes in accrued interest.
Key ideas
- Dirty prices include accrued interest, which can drop when a coupon is paid.
- A price index based on dirty prices may fail to represent coupon income as intended.
- Accrued interest can be estimated as dirty price minus clean price.
- A decline in estimated accrued interest can be used to infer a coupon event, though the approach is not validated in detail.
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Full text
# Total Return Bond Index calculation using only Clean and Dirty prices
# Total Return Bond Index calculation using only Clean and Dirty prices
I have been looking at ways to construct a custom Total Return Bond Index given only the Clean and Dirty Prices. First I constructed the following, thinking that Price Index formula would capture coupon payments if I use Dirty Prices:
The Price Index formula is: $$ PI_t = PI_{t-1} \times \frac{{\sum} {P_{i, t} \times N_{i, t-1}}}{{\sum} {P_{i, t-1} \times N_{i, t-1}}} $$
There is no big difference between Price Index and Total Return Index. I expected that Total Return Index should be higher than Price Index as it collects the coupons of the bonds in the index. Then I figured that post coupon payment Dirty Prices go down significantly and thus the accrued interest is being swept away.
I tried to examine the following case:
- 1) A 6% fixed rate coupon bond with semi-annual payments;
- 2) Face Value is 1000;
- 3) Both Clean and Dirty prices are observable;
Some details:
- The bond starts to trade at 1000;
- Post coupon payment `dirty price(t-1) = clean price(t)`; `dirty price(t) = clean price(t) + AI(t)`;
So, there is a difference between the Total Return and Clean Price Return and I am assuming that I should include this while building my Total Return Index. I cannot think of a approach how to properly do this.
I have also looked at the difference between the Dirty Price and Clean Price and I can extract the accrued interest from there.
Any ideas how to solve this? I cannot use coupon payment dates as I have no info about them.
## Answer by AK88 (score 0, accepted)
https://quant.stackexchange.com/a/34302
I think I finally got it. First I simply subtracted Clean Prices from Dirty Prices to get Accrued Interest. Then for each date where $ \mathrm{AccruedInterest}_{t} < \mathrm{AccruedInterest}_{t-1} $ I did $ \mathrm{DirtyPrice}_{t-1} = \mathrm{CleanPrice}_{t} $. The result is:
Bear in mind that I am looking at "BB-" rated countries' bonds here. I am still open if there are any comments/suggestions.
Here is the weekly average Yield of these bonds: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.