Backcast Long-Term German Government Bond Returns with a Par-Bond Proxy

Summary

The document proposes ways to fill an early gap in monthly total returns for a German government bond maturity bucket of ten years and above. One approach constructs a proxy using a chosen long tenor, with twenty years offered as a practical example. It uses the available ten-year yield as a stand-in for the longer yield, explicitly assuming the spread is zero unless a different spread estimate is available.

At each month end, the method models a newly issued par bond with a coupon set to the assumed long yield and an initial price of par. At the next month end, it reprices the bond with its remaining maturity reduced by one month and the new yield, then calculates the monthly return. A simpler alternative is to regress the observed long-bucket returns on returns from other maturity buckets and use the fitted relationship to estimate earlier values. Both approaches depend on assumptions; the response offers no backtest or validation, and the yield-spread assumption may affect the proxy's accuracy.

Key ideas

• A long-maturity return proxy can be built by modeling a par bond at a chosen tenor.
• The proposed example uses ten-year yields as a proxy for twenty-year yields by assuming no maturity spread.
• Reprice the modeled bond monthly at the new yield and its shortened remaining maturity to estimate returns.
• Regression on other maturity buckets is offered as an alternative backcasting method.
• The document does not validate either method, and proxy accuracy depends on its assumptions.

Tags

# any ideas how to get missing returns for german governement bonds, maturity bucket 10+


# any ideas how to get missing returns for german governement bonds, maturity bucket 10+












I am looking for a way to extrapolate monthly government bond returns (total return index) that are not available on datastream for the bucket of 10+ (maturities of 10 years and above). For the 4 previous buckets I have monthly data from 1978 onwards, but for the 10+ bucket I only have from 1986 onwards. Does anyone have any idea how I can fill in this missing return data? The easiest solution is just to cut out the missing portion of the sample completely but I think it would be a shame to do so.

## Answer by Helin (score 1)

https://quant.stackexchange.com/a/29598

This is my preferred way of generating bond returns proxies:

- Decide on a tenor for the 10+ bucket. 20-years is a common choice, primarily because Ibbotson's US long-term bond returns reflect that maturity.

- Take the 10-year yield series

- Make some assumptions about 10y/20y spread. The simplest assumption is to assume 20-year yield = 10-year yield.

- At the end of each month, buy a par bond whose 1) coupon = 20-year yield, 2) maturity = 20 years, 3) price = 100

- At the end of the following month, reprice this par bond, now a 19-year 11-month bond, by assuming its yield to maturity = the new yield. This lets you calculate the monthly return.

- Buy a new par bond and repeat.

You can also just regress the 10+ return you have against the other buckets and use the coefficients to backcast...

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