Estimating Long-Bond Drawdowns from Historical AAA Yields
Summary
The document describes how to approximate historical monthly returns for long bonds when only a yield series is available. At each month end, the method assumes purchase of a hypothetical 30-year bond priced at par, with its coupon set equal to that month’s AAA yield. At the next month end, it reprices the remaining bond using the new yield and standard bond pricing, includes accrued interest, and repeats the process by rolling into a new 30-year bond. The resulting return series can then be used to calculate drawdowns.
This is an illustrative reconstruction, not a precise history of investor returns. Yield data alone cannot determine realized bond returns without assumptions about the bonds held. The estimate is sensitive to the assumed maturity and duration; actual investors generally held portfolios with shorter average duration than the hypothetical 30-year bond. More accurate drawdowns require a properly constructed total return index based on real cash bonds.
Key ideas
- Yield observations alone are insufficient to calculate historical bond returns without assumptions about the bonds held.
- A hypothetical rolling bond can be repriced monthly using the prior coupon and the new market yield.
- Monthly returns should account for both price changes and accrued interest.
- Drawdowns calculated from this approach are qualitative estimates rather than precise investor outcomes.
- A total return index built from real bonds can provide a more representative history.
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# How to compute bond drawdowns? # How to compute bond drawdowns? I came across a very interesting article which shows a picture with the drawdowns bondholders would have faced by investing in Fixed Income since 1919. The data is based on the Moody's seasoned AAA yield https://fred.stlouisfed.org/series/AAA . I do not understand how they computed the drawdowns. I thought it was the inverse formula of duration, but there is no duration information. Could you help? Many thanks. ## Answer by Helin (score 0, accepted) https://quant.stackexchange.com/a/40890 The first step is to calculate historical returns of AAA bonds. Bond yields alone are insufficient, so we inevitably have to make some assumptions. Based on the magnitude of the drawdowns reported in the paper, I calculated monthly returns using the following assumptions: - At the end of each month, we purchase a bond whose yield and coupon rate are equal to the AAA yield at the time. We further assume that the bond matures in 30 years. Since the yield and coupon rates are the same, the purchase price is simply 100. - At the end of the next month, we sell the bond, whose yield has changed to the new AAA yield at the time. The selling price can be computed easily using the standard price-yield formula (let coupon rate = previous month-end AAA yield, maturity = 29 years 11 months, and yield = current month-end AAA yield). - Given the starting price and ending price, it's simple algebra to calculate the return of the bond over the month. (Don't forget about the interest that has been accrued over the month!) - We can repeat this for each month from 1920 through today (i.e., at the end of each month, we sell the old 29-year 11-month bond and buy a new 30-year bond). Steps 2–3 above can also be approximated using the method outlined in this post. These returns allow us to compute the drawdowns: These are crude estimates, but allow you to get a good qualitative read into historical long bond performance. To calculate more precise drawdowns, you'll need properly constructed total return indices – instead of using hypothetical bonds, these indices buy and sell real cash bonds. I should also mention that the actual drawdown experienced by fixed income investors can vary greatly. Because the average duration of the bond market has not been even remotely close to 30 years (as assumed by the paper), losses incurred by an average investor was not as bad as depicted by the paper. The picture below shows the drawdown of all Treasury notes and bonds over time (weighted by amount outstanding):
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.