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  • In July 2016, we argued that bond investors should be quick to celebrate the strong returns they had realized year-to-date.
  • The combination of a defined maturity and known coupon rate creates a gravitational pull for bond returns.
  • Using a global bond ETF universe, we develop a simple model to forecast future 1-year returns.
  • The model suggests that mean reversion is a strong forecaster of future returns. A combination of starting yield and prior excess returns provides an Rof 24.3%.
  • While bond investors may be frustrated today, mean reversion suggests that poor returns merely mean they have been pushing returns into the future, giving themselves something to look forward to.

On July 18th, 2016 we published a commentary titled Bond Returns: Don’t Be Jealous, Be WorriedAt the time of publishing, the iShares 7-10 Year U.S. Treasury ETF (“IEF”) was up 6.92% on the year, as the 10-year U.S. Treasury rate had fallen from 2.27% to 1.60%.

The entire point of the piece was that unlike stocks, bonds have a fairly well-defined value.  When you buy a bond with a given yield-to-maturity, barring the case of a default, you know what return you are going to receive.  Therefore, while the mark-to-market value of the bond may go up and down with changing interest rates, these fluctuations will have no impact on your ultimate realized return.

This is even true if we try to sell our bonds along the way.  Yes, we might be selling at a higher value than we bought, but we will be reinvesting that capital at a lower rate.1

With fixed income, today’s gains are just tomorrow’s returns realized early.  To quote the commentary,

IEF may be up 6.92% year-to-date, but the 10-year annualized expected return for 10-year USTs just fell by 67 basis points.  That may not sound like much, but the total return difference between a 2.27% annualized return and a 1.60% annualized return over a 10-year period is 796 basis points.  The paper gains we have today are simply the yield returns we won’t be receiving in the future.

From the date of writing, the 10-year U.S. Treasury rate has climbed to approximately 3.00%, a 140 basis point move.  Over this time period, IEF has realized a -2.71% annualized return.

We would love to pound our chests about this prescient timing, but ultimately it was just a case of math, some faster-than-expected mean reversion, and quite a bit of luck.

Two years later, we sit in a different place.  Year-to-date, IEF is down -2.42%.  The 10-year U.S. Treasury rate started the year at 2.46% and has climbed 54 basis points to nearly 3.00%.  The total return difference over a 10-year period between a 2.46% rate and a 3.00% rate is 688 basis points.

As the math shows us, losses today push returns forward.

For bonds, a combination of the stated coupons and the defined maturity creates a gravitational pull that almost always wins in the end.  Escape velocity from this pull is only really ever achieved in the case of default.  It is worth pointing out that for bond holders, there is no positive antithesis to default: borrowers don’t suddenly make surprise increases to coupons out of the goodness of their hearts.

Given that we believe mark-to-market gains and losses are really just the push- and pull-forward effects of future returns, a question worth asking is: can we use this relationship to forecast future returns?

Modeling Mean Reversion in Bond ETFs

To test this hypothesis, we are going to model returns in a universe of 29 fixed income ETFs.  The universe covers U.S. Treasuries of varying maturities, a spectrum of credit quality, asset-backed securities, and international exposures including emerging market debt.

Specifically, we will attempt to construct a linear model where we attempt to forecast future 12-month total returns by using a combination of prior returns and yield estimates.  Specifically, our variables will include current yield (“Y0”), the spread between realized 12-month returns and starting yield.  This spread is measured at the prior 12, 24, and 36-month points (labeled “S1,” “S2,” and “S3” respectively).

In effort to avoid overfitting our estimates, we employ two techniques. First, we combine the data from all the ETFs together.  While much of the data is overlapping in the time domain and shares common economic factors, the breadth of the universe helps the model from overfitting to a specific economic event.

Secondly, we will estimate our parameters use a cross-validated Lasso model, where we utilize the last 18 months of the data for testing and the remaining data for training.  To avoid information leakage, 12 months of data between the training and the testing set is embargoed.

A Simple Model for Forecasting Mean Reversion

After all this setup, the results are none too surprising.  The best fit parameters are:

Y0    1.431759
S1   -0.270067
S2   -0.033940
S3    0.164022

Our interpretation of these parameters is that future returns are a function of current yields (Y0) and the expectation that past spreads mean revert with a half-life of between 12- and 36- months (given that the S1 variable is negative and the S3 variable is positive).

The Rwithin the training set is 24.9% and the R2within the testing set is 24.3%, a strong indication that the model is robust.  This may seem like a rather low Rnumber, but it is worth acknowledging that this model forecasting 1-year returns, a notoriously volatile horizon.  Furthermore, this model does not incorporate any of the idiosyncratic information relevant to each bond sector.  By design, it is a hyper generic model.

Below we plot the forecasted versus realized 12-month returns over the testing period using this model.

While there is a reasonably large degree of variability, we generally see a strong fit. Mean reversion appears to be alive and well in the data of bond returns, as we would expect it to be. 


For an asset class with a known maturity date and defined cash flow, bonds can be frustratingly volatile for investors.  Perhaps counterintuitively, rising prices can actually be the harbinger of poor forward returns.  Consider that in 2016, falling interest rates caused bond prices to soar.  Since then, bonds have offered frustratingly flat, if not negative, returns.

We would argue, however, that the two facts are inextricably linked.  The higher return of 2016 simply “pulled forward” future returns, a price that was paid over the subsequent years.

This logic would suggest, then, that there might be some tactical opportunity for investors to adjust their bond allocations.  In this commentary, we build a very simple model to explore mean reversion across a large cross-section of global bond ETFs.  We find that a combination of current yield and prior realized returns in excess of yield is a reasonable predictor of future 1-year returns.

Of course, the fit is not perfect.  There is a large degree of variability.  To quote a recent Research Affiliates piece, “mean reversion is reliably unreliable.”2  After all, if it were easy and certain, everybody would do it and everybody would profit.

Yet when we consider that we are attempting to forecast a short horizon (12 months) and ignore further potentially meaningful information for each asset class (e.g. duration, yield-to-worst, et cetera), the strength of our results suggest that mean reversion is a powerful force at work in bond returns.

Investors frustrated by poor bond returns may very well have something positive to look forward to.

Information on Newfound’s income-focused strategies is available here.  Specific research and educational materials are available below:

  1. This assumes reinvestment in the same bond.  In practice, many constant maturity indices span multiple years, and there may be a roll yield that can be harvested. Nevertheless, the general premise holds as capital gains from changes in rates have little impact on long-term portfolio returns.
  2. Performance Measurement: How to Do It If We Must

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.