Many recent articles discuss rising rates with a focus on how to weather them along with some predictions of when they will occur and how much they will rise. Duration is a common theme among the articles since it quantifies how much a particular bond is likely to lose when rates rise. We’ve written many blog posts in the past about duration (for instance: this and this), and earlier this year, we published a thought piece entitled Beyond Duration that covers some nuances of duration that may be forgotten when looking at portfolios or ETFs. One key issue when working with a portfolio of bonds is that even though the portfolio will have a single number as its weighted average duration, that value is only relevant if the yield curve shifts in parallel.

I recently read an article by Schwab entitled The Bond Investor’s Trilemma: Positioning for a Fed Rate Hike. The first dilemma the author covers is the issue of short-term interest rates rising more than longer-term rates with the conclusion that the sweet spot is in the intermediate (5-10 year) part of the yield curve. The article goes on to state that investors who are worried about price declines can add in some short-term bonds to mitigate the impact of rising rates.

With some assumptions, we can actually see how much a bond portfolio such as this would be affected under different rising rate scenarios. Let’s assume that you currently are playing the sweet spot of the yield curve by holding the iShares 7-10 Year Treasury Bond ETF (IEF) and are considering substituting in some of the iShares 1-3 Year Treasury Bond ETF (SHY) to lower the duration and attempt to reduce the impact of rising rates.

If rates rise, we can use the durations of the ETFs, $latex D$, to approximate the loss, $latex L$, of our new portfolio as:

$latex L = D_{SHY} \cdot x_{SHY} \cdot \Delta r_{SHY} +D_{IEF} \cdot (1-x_{SHY}) \cdot \Delta r_{IEF}$

where $latex \Delta r_{SHY}$$and$latex \Delta r_{IEF}$are the changes in short and long-term interest rates relevant to SHY and IEF, respectively, and$latex x_{SHY}$is the allocation given to SHY. If we did not add in any short-term bonds, the portfolio would lose$latex D_{IEF} \cdot \Delta r_{IEF}$. We can subtract this base case loss from our new loss after adding SHY and write the benefit,$latex B$, of adding SHY as:$latex B = x_{SHY} (D_{IEF} \cdot \Delta r_{IEF}-D_{SHY} \cdot \Delta r_{SHY})$We obviously want this benefit to be positive, which means that we need to have:$latex \frac{\Delta r_{SHY}}{\Delta r_{IEF}} < \frac{D_{IEF}}{D_{SHY}}$Notice that the amount allocated to SHY is absent in this equation. Whether or not adding SHY will benefit the portfolio depends only on the change in interest rates and the durations of the ETFs. The amount allocated to SHY only controls the magnitude of this impact. In our example, the duration of SHY is 1.82 years and that of IEF is 7.68 years, so we require that:$latex \frac{\Delta r_{SHY}}{\Delta r_{IEF}} < 4.2\$

to see any benefit from adding SHY into the portfolio. The chart below shows the minimum that long-term rates would have to rise for a given rise in short-term rates in this portfolio. Therefore, if you believe that the short term rates will rise by 2%, as long as you expect long-term rates to rise by more than 0.5%, you will see a benefit by adding SHY.

In this analysis, we assumed that we could treat the ETFs as individual bonds when they are really portfolios themselves. However, their concentration makes their duration and dependence on a single interest rate a bit more believable. Additionally, these ETFs are constant maturity portfolios that periodically roll over their holdings into new bonds. To some extent, this can mitigate the impact of rising rates depending on how fast they rise as we discussed in this post.

The speed and magnitude of interest rate increases along the yield curve will ultimately determine portfolio performance, but this simplified analysis may serve as a good rule-of-thumb for understanding the possible impacts to fixed income portfolios based on your current market outlook. However, always bear in mind the underlying assumptions of any analysis: just because you calculate that there is a benefit to adding SHY to your IEF position does not mean that you should necessarily switch fully over to SHY, despite the formula outputting that that would yield the largest benefit.

While the commonly held belief in the marketplace is that short-term rates will rise more quickly than long-term rates, we believe that the best course of action is to take advantage of diversification in fixed income across different durations and credit qualities.  Keep the nuances of duration in mind, and be aware that shortening duration may simply be shifting risk factors rather than positioning a portfolio to achieve its desired outcome.

### Nathan Faber Nathan is a Portfolio Manager at Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team. Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software. Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.