# 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.

## 1 Answer

This is my preferred way of generating bond returns proxies:

1. 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.
2. Take the 10-year yield series
3. Make some assumptions about 10y/20y spread. The simplest assumption is to assume 20-year yield = 10-year yield.
4. At the end of each month, buy a par bond whose 1) coupon = 20-year yield, 2) maturity = 20 years, 3) price = 100
5. 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.
6. 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...