How to Worry about Duration

Understanding How Rate Rises Will Impact Bonds

By: Greg Obenshain

Interest rates have moved sharply upward over the past year. The below chart shows interest rates by maturity for the US swap curve and how they have shifted.

Figure 1: Interest Rate Curves on December 31, 2020, vs December 31, 2021

Source: Bloomberg.

Rising rates translated to negative returns across the interest rate curve, with bond returns at longer maturities suffering more.

Figure 2: Hypothetical Zero-Coupon Bond Returns in 2021

Source: Bloomberg. Hypothetical zero-coupon bond returns calculated from swap rate curves.

In an environment where the Fed is predicted to hike rates and inflation concerns are high, there is an understandable desire to avoid duration risk in bonds, specifically the risk that rising rates will hurt bond prices. But unless you are willing to put 100% of your investments in volatile assets that might do well in inflation and rising rates, like gold, maybe some stocks, and perhaps other commodities, fixed income is likely to be part of your portfolio. Sure, inflation is not good for bonds, but it is worse for cash, and, as we argued in Cash and Equivalents, bonds are best thought of as cash equivalents. Remember, unlike stocks and commodities, bonds have contractual returns. Whatever the price movements, you will earn the promised return if they pay off and will earn coupons along the way.

But lauding the benefits of fixed income is certainly not the zeitgeist of the moment. So if we are going to worry about duration risk, how can we at least do it well?

The starting point is to realize that bonds are expected to have positive returns each year if the rate curve does not change (we are ignoring credit risk in this discussion). Rates must rise by enough to offset the positive expected return. A great place to start is to quantify how much rates need to rise to deliver a negative return. We’ll use the US swap curve and zero-coupon bond prices derived from it to answer this precisely.

Below, we show how much rates would have to rise to cause zero-coupon bonds to have negative returns at different maturities. It turns out that last year’s pain has dramatically improved the outlook for the short end of the bond curve. For a two-year bond to have a negative return, one-year rates now need to rise by over 1.0% instead of just under 20 basis points at the end of 2020 (the one-year rate determines the price of the two-year zero-coupon bond as it becomes a one-year bond at year end).

Figure 3: Required Rate Jump for a Negative One-Year Return, End of 2020 vs End of 2021

Source: Bloomberg, Verdad analysis.

Why such a big jump? Because not only did the two-year coupon rise from 0.13% to 0.58%, but the yield curve also got dramatically steeper. The rate jump from one to two years went from 0.03% at the end of 2020 to 0.33% at the end of 2021.

Now it’s tempting to look at this and think, wow, it’s hard to lose money on the short end, so I should just stay short. But that is not the way it works. You want to take duration risk (and higher coupons) up to the point that there are diminishing returns to doing so. You should move out the curve just to the point you think there is enough cushion to protect you from a negative return. It is easiest to do this in table form. Read down the table below and accept risk at the point where you think rates could potentially go higher than what is priced.

Figure 4: Indifference Table – Move Down Until You Disagree

Source: Bloomberg, Verdad analysis. Data as of January 18, 2022.

If you are looking at a 10-year duration and thinking that a 19bps “cushion” seems insane, remember that we’ve built this analysis from the perspective of an investor worried about avoiding drawdowns. An investor less worried about drawdowns will choose higher durations and yields, as will an investor using Treasurys for countercyclical protection, an approach we explored more deeply in Do Treasurys Still Work? and our countercyclical investing research.

How have these breakeven rate changes, or rate hurdles, changed over time? And do they correlate to returns? Below we show the hurdle rate and the subsequent one-year return using the four-year bond as an example.

Figure 5: Rate Hurdle and Forward Return for a Four-Year Bond

Source: Bloomberg, Verdad analysis.

Lower hurdle rates (solid line) are associated with lower forward returns (dotted line). But the figure also tells another story. As rates have fallen, there are more instances of negative returns.

The most recent negative returns came when the hurdle rate for negative returns was very low. It is higher now. If you are going to worry about rates, at least worry correctly. Use the current coupons and steepness of the yield curve to understand at least intuitively how much rates must rise to deliver a negative return. And don’t lose sight of the fact that bonds have contractual returns. One-year drawdowns do not mean permanent losses.