Bond. Treasury Bond

The Federal Reserve publishes the yield-to-maturity of US Treasury bonds. However, the actual returns earned by investors are not publicly available. Nor are they readily and intuitively discerned from historical yields, since “a bond’s return equals its yield only if its yield stays constant and if all coupons (cash payments) are reinvested at that same yield” (Tuckman and Angel, 2013, p.95).

Recently, Laurens Swinkels of Erasmus University in the Netherlands estimated such a return series using publicly available data for US government bonds with 10-year maturity. The working paper accompanying the data is not yet available, but he has generously published his data in an Excel spreadsheet, including formulas for the return estimation process. You can find the data here.

One nice result of this data is that it enables the construction of a proxy for a bond price series, which can be thought of as representing a constant exposure to 10-year treasuries, and thus facilitate ex-post analysis of various timing models.

This idea of a constant exposure is much like an allocation to the ETF IEF or the ZN futures contract in that it is essentially a dynamic trading strategy to maintain a roughly constant time to maturity. However, IEF has only been around since 2002. ZN first traded back in 1982. Swinkels’ data set on the other hand goes back all the way to 1962, so offers the opportunity to explore bonds trading strategies over more than 65 years.

Background: what’s a treasury?

A treasury is a debt obligation issued by the US government to finance its spending. US Treasury securities are among the most liquid securities in the world and are perceived as one of the safest investments globally. In practical terms, this means that the demand for treasuries increases when something happens to scare investors. You can see this playing out for example in the recent price action of the TLT ETF, which holds long-duration treasuries:

Treasury bonds (also known as notes) entitle the holder to regular interest payments until maturity, at which time the principal, or the amount loaned in exchange for the bond, is returned. Treasury bills, on the other hand, have short maturities (one year or less) and only pay out at maturity.

The idea of “buying a single bond” is easy to understand. The coupons are just priced on a fixed rate and are never going to change. Say you buy a 10 year bond. It turns into a 9 year bond, then an 8 year, a 7 year, and eventually a 1 year, paying you a fixed amount at known intervals along the way. Then it matures and your principal is returned. Therefore, if you hold your bond to maturity you know exactly what yield you are going to get on the original capital you paid for it.

Maintaining an “exposure” to bonds is more nuanced. Conceptually, the value of the exposure’s cash flows changes based on current rate conditions and time to maturity of the actual securities held. And rate conditions can change differently at different points on the curve at the same time. This all gets quite complex – hence the value of Swinkels’ data set.

Returns to US treasury exposure since 1962

First, here’s the cumulative return from holding a constant exposure to bonds since 1962 (Column F from Swinkels’ data):

cumulative us treasury bond return

That’s a total return of about 4,400%.

Of course, one needs to take care interpreting this figure. This is the return you would have achieved if you could have maintained a constant time-to-maturity, re-invested all of your profits, and done so cost-free. So it’s not overly useful for estimating an investor’s actual returns, but it is useful for getting some insight into how US Treasuries, as an asset class, have performed over this time scale, particularly for comparison with other assets.

Returns to US treasury timing models

Before we get started exploring timing models, it bears stating that in this analysis, we’re not so much interested in actual returns, as there will necessarily be many assumptions baked into the analysis (like those mentioned above). But we are really interested in whether timing models can beat a benchmark under the same assumptions.

I’m not holding out a lot hope that we can do better than buy and hold, as bonds have done so well for so long. The reality of trying to time a bond exposure is that whenever you are “out” of bonds you are giving up exposure to the yield – that is, you forgo interest payments, which probably account for the majority of the total returns (although I haven’t verified this). In line with our Robot Wealth mantra to ‘trade humble’ I very much doubt the ability of any simple timing model to overcome this hurdle.

But you never know. In part 2 of this series, we’ll look at various factors in an attempt to outperform a buy and hold bond exposure. We’ll start by looking at the usual momentum and value factors, but if you have any ideas you’d like us to take a look at, let us know in the comments.

2 thoughts on “Bond. Treasury Bond”

  1. A very good post about Bonds. . I think the most common factors are momentum, value and volatility. Looking forward to part 2 with these factors.


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