Investing - Theory, News & General • Great Expectations? Anticipated and realised bond returns with rising yields

There have been a number of threads about bonds on these boards recently, at least some prompted by recent increases in yields and a concern that a ‘bond bear market’ is underway. I was curious to see just how much difference there was between what might be expected for bond returns and the subsequent realised returns when yields were rising. The results of that curiosity for a long maturity bond fund are presented in this post.

The period from 1942 to 1982 saw US treasury yields rise by about 13 percentage points from 2.0% to over 15%. This is illustrated in the upper panel of the following figure where the weighted yield for an index of all treasuries (regardless of tax status) with maturities over 10 years is plotted (i.e., a long maturity index) as a function of time. In the lower panel, the weighted maturity and weighted modified duration are shown. Yield, maturity, and duration, all weighted by amounts in issue, are derived from the monthly prices and amounts in issue of individual treasuries (see my paper at https://papers.ssrn.com/sol3/papers.cfm ... id=5422914 for more details).



From the above graphs, a number of points can be made:
1) As already mentioned, the yield rose from just over 2% to a peak of over 15% during this period. However, this increase occurred over two distinct intervals, a fairly steady rise from 2% to 8% between 1942 until just before 1980 followed by a much steeper rise over the next two years (with a fall towards the end of the period shown).
2) The weighted maturity was variable and dependent on the bonds in issue with new issues (or restructuring of existing issues) and bonds leaving the index by falling below the lower limit of maturity (i.e., 10 years) both having a significant effect particularly earlier in the period when fewer bonds existed. For example, the steady climb in maturity from 17 years to 25 years in the early 1960s was a result of a number of exchanges (i.e., where a shorter treasury could be swapped for a longer one, e.g., the 3.5% bond maturing in November 1998 went from $2.3b outstanding when issued in October 1960 to $4.4b by the end of 1962), while the linear decline from the mid-1960s to 1970 occurred because no new long treasuries were issued at all. The sudden drop and subsequent fluctuations in weighted maturity in the mid-1950s was caused when the price of a number of callable bonds rose above par (which meant that maturity was then calculated to earliest callable date – hence the fall in weighted maturity) and subsequently fell below par again (maturity was then calculated to the date of maturity).
3) Since yields were positive, the weighted modified duration always fell below the weighted maturity with the difference between them increasing as yields increased towards the end of the period.

The following graph shows the annualised nominal return that was expected and then realised over a subsequent period either equal to the maturity or duration (labelled as realised(mat) and realised(dur), respectively). The expected (or anticipated) return has been defined as the return of a single bond with a semi-annual coupon equal to the weighted yield and assuming a flat yield curve constant in time, i.e., r=(1+y/2)2, where r and y are the fractional return and yield, respectively.



During this period of, generally, rising yields the realised return (whether measured over either the period of maturity or duration) was highly variable, but usually fell below the expected return, on occasions by a significant amount (e.g., around 1958, the realised annualised return over the duration period was 3 percentage points below that expected).

A different view of the same data can be found in the following figure where the realised returns are plotted as a function of expected return (over the duration and maturity periods in the left and right hand panels, respectively).



From the graphs, three points can be made.
1) The realised return was reasonably well correlated with the expected return, i.e., a larger expected return tended to result in a larger realised return
2) As already noted, the realised return tended to be lower than that expected, although the difference was variable. For example, in the left hand panel three groups can be identified, two clusters with realised returns about 0.5 percentage point lower than anticipated at expected returns of between 2% to 3% and centred on 4% and a third, more extended, group found across the whole range of expected returns (i.e., from 2% to 7%) where the realised return was essentially linearly related to, but lower by 1 percentage point or more than, the expected return.
3) There was considerable scatter of realised returns even within each group.

For this long maturity bond index one conclusion that can be drawn is that using the initial yield to predict the likely future return was not particularly effective, except in the broad sense that buying this bond fund at higher yields was likely to have a better outcome than buying it with a lower yield.

One question that arises is then, what happened if an index with a shorter maturity is used instead? That will be the subject of the next post.

cheers
StillGoing

Statistics: Posted by StillGoing — Sun Sep 27, 2026 1:36 am