Anna Cieslak and Pavol Povala—authors of the paper “Expected Returns in Treasury Bonds,” which was published in the September 2015 issue of The Review of Financial Studies—examined the time variation in the risk premium that investors require for holding Treasury bonds.

While most of the authors’ analysis relies on data starting in 1971 (when data for bond maturities 10 years and longer became available), they also reproduced their main conclusions over the longer sample period from 1952 through 2011 (using maturities of one through five years).

**Methodology**

Cieslak and Povala decomposed the nominal yield curve into the risk premium component and the expectations hypothesis (EH) term, which is the average expected short-term interest rate that investors expect to prevail during the life of a bond.

Specifically, they decomposed Treasury yields into inflation expectations and maturity-specific interest-rate cycles, defined as variation in yields unrelated to expected inflation. The economic basis for this division is the premise that the short-term nominal interest rate is (to a very good approximation) the sum of expected inflation and the real short rate. Thus, Cieslak and Povala have three variables with a direct link to economic quantities: expected inflation, the real rate and the risk premium.

They state: “The short-maturity cycle captures the dynamics of the *real* short rate at the business cycle frequency. Jointly with expected inflation, it comprises the expectations hypothesis (EH) term in the yield curve.”

**Findings**

By controlling for the EH term, the authors were able to extract a measure of the Treasury risk premium from the yield. Their cycle factor is a proxy for the time-varying risk premium in Treasurys. They found that the cycle factor:

- Is uncorrelated with short-rate expectations
- Predicts returns on Treasury bonds across the entire maturity spectrum
- Is the least persistent source of variation in the yield curve, implying that the risk premia in Treasury bonds vary at a frequency greater than the business cycle
- Is able to predict bond excess returns

Cieslak and Povala also found that a simple, real-time measure of trend inflation (a discounted moving average of past core inflation that reflects the reality that people update their inflation expectations sluggishly over time) forecasts future inflation well, especially at horizons of longer than one year. Below are the important findings that follow:

- Trend inflation accounts for roughly 85 percent of unconditional variance of yields, determining their overall level. Its explanatory power is stronger at long maturities.
- The one-period cycle (real factor) captures more than 60 percent of the movements in the yield curve slope (the difference between the long- and the short-term interest rate).
- While the cycle factor constitutes the smallest portion of yields’ variance, its contribution increases with the maturity, consistent with the intuition that long-maturity yields are most exposed to fluctuations in the risk premium.
- The three variables explain more than 99 percent of yield-curve variation across maturities.
- The evidence is consistent, with the mean-reversion of the short rate going toward slowly moving trend inflation rather than a constant mean.

**Conclusions**

Cieslak and Povala concluded that the short-maturity cycle co-varies with measures of the ex-ante real rate. At longer maturities, the cycles embed both short rate expectations and the risk premium, and their predictive power for bond returns increases with maturity.

Using this observation, the authors constructed a return forecasting factor, called the cycle factor, which forecasts bond excess returns across the entire maturity spectrum. The bottom line is that when the measured risk premium is high, expected returns are high.

*Larry Swedroe is the director of research for* The BAM Alliance*, a community of more than 140 independent registered investment advisors throughout the country.*