The Key To Duration: Sensitivity To Changing Interest Rates

by: Adam Hoffman, CFA


The Fed is expected to raise interest rates on June 14th.

Bond prices fall when yields increase.

Duration estimates the change in price for a bond given a change in yield.

Effective duration measures the change in price when the entire yield curve shifts.

Key Rate Duration measures the change in price when only one spot on the yield curve changes.

On June 14th, the Federal Reserve will conclude their policy meeting and announce the targeted Federal Funds rate. There possibly could be no change, a very likely chance of an increase, and very little to no chance of a decrease in this benchmark interest rate. While we do believe it is very likely that Janet Yellen will proclaim higher rates, we do not believe it is the time to join the highly acclaimed fixed income analyst Chicken Little in panicked chants of "the rates are rising, the rates are rising, and the sky is falling, too". Now is not the time to panic and take action driven by emotion. The time prior to the eight scheduled meetings of the Fed is a good time to reevaluate the risk exposure of a fixed income portfolio and reconcile this with required returns and tolerance for risk. The evaluation of the portfolio should be coupled with an examination of the metrics used to evaluate risk.

Beginning with the most basic concept of bond pricing: prices move inversely to yields. If yields increase, bond prices go down and vice versa. The price of a used car is analogous to bond prices in a rising rate environment. For example, an auto enthusiast is trying to sell a two year old car with 30,000 miles and squeaky brakes. A new car with the latest safety features, better performance, and zero miles can be purchased for $35,000. In order for our auto enthusiast to sell his used car, it would have to be priced less than $35,000. Much in the same way a bond that pays $40 a year would have to be priced lower to entice a buyer if new bonds pay $50 a year. In the auto market, Manheim Market Reports can be utilized to estimate the depreciation of a vehicle. Fixed income enthusiasts utilize duration to gauge the price change of a bond due to a change in yields.

Duration is a measure of how much the price of a bond, individual or fund, will move given a small change in yield. For example, if an intermediate-term bond fund has duration of 6.5 and yields increase by 0.5%, the price is expected to decline by ~3.25%. The longer the maturity of a bond, the greater the duration due to more interest rate risk. The duration figure that is cited most commonly for ETFs and mutual funds is effective duration. Effective duration is the interest rate risk metric that is primarily used since it accounts for the likelihood of a bond being called prior to maturity. Going forward in this paper, when duration is referenced it is effective duration. The primary limitation of duration is that it assumes all yields across all maturities change by the same amount. This duration measurement accounts for a parallel shift in the yield curve.

The equal and simultaneous requirement of duration with respect to yield changes might not offer a true reflection of a portfolio's interest rate risk. It is very likely to overestimate the decline in fixed income prices and lead to erroneous allocations. Although the future cannot be divined, the past can assist in preparation for time's inevitable passage.

The Federal Reserve in 2008 took drastic measures to try and spur economic growth out of the collapse of the housing market. On December 16, 2008, the Fed slashed the Federal Funds rate to effectively 0%. In addition, the Fed also started purchasing longer-dated fixed income securities in the open market to lower longer-term interest rates. The steady narrative that began on December 17 was that at some point the Federal Reserve would have to raise rates and lower rates could not last for longer. At some point the Fed would have to raise interest rates, which would drive the price of bonds and bond funds down. The thought at that time was to move to short-term fixed income instruments or cash to avoid a drop in price caused by increased rates.

Seven years later . . .

December 2015, the Federal Reserve raised interest rates by a quarter of a point. The narrative that the Fed would have to continue to raise rates continued. Lower cannot last longer.

One year later . . .

December 2016, the Federal Reserve raised interest rates by additional 25 basis points to a targeted rate of between 0.5% and 0.75%. This rate increase was followed three months later by another 25 basis points bringing the target range from 0.75% to 1.00%. According to data from the Chicago Mercantile Exchange, the market expects that the Fed will increase rates in June by another 0.25% with ~100% probability.

Table 1 outlines the probabilities for various Fed action based upon price of Fed Fund Futures contracts as of June 8, 2017. The grey column corresponds to the odds of no interest rate hike and the red column is the odds for one rate hike. The data also shows that the market believes that there is ~23% chance that the Fed will raise rates a third time in 2017 at their September meeting.

Returning to our assumption of a rate increase in June, we know one thing with certainty: the targeted Feds Fund rate will be higher. This may raise rates across the yield curve, maybe only some yields increase, and possibly yields may actually decline. Figure 1 is the change in the Treasury curve from the beginning to end of the month in which the Fed increased rates.

Figure 2 below is the change in Treasury yields from the end of the month in which the Fed took action to June 7.

On the surface, these charts seem a bit odd considering that the Fed has increased rates three times since 2015. However, the Fed has only increased the Federal Funds Rate, which is the interest rate that depository institutions charge one another for overnight loans. This rate then affects yields on the rest of the curve. However, its influence abates further out on the curve. The value of current economic data is replaced by expectations of the future: real interest rates, inflation, economic growth, etc. The Fed simply influences the short-end of the curve when they announce a change to the Federal Funds Rate.

As we can see from Figures 1 and 2, there was not a parallel shift in the yield curve. Yields on longer maturities have actually declined, increasing their price. The opposite occurred on the short end with yields increasing and prices falling. This returns to the main limitation of duration. It is not able to provide a good approximation for changing bond prices when the curve performs a gymnastic routine worthy of a perfect score.

Key Rate Duration (KRD) is able to account for twists and flips of the yield curve. KRD similar to duration measures the change in the price of a bond for a small change in yield. However, KRD assumes that only one yield on the curve changes, not all of them. KRD breaks down the duration of the portfolio by its component parts. Stated differently, duration is the sum of the individual KRDs across the yield curve. The most common key rates are the on-the-run Treasury yields.

The primary limitation of KRD is that is assumes only one spot on the yield curve will change and all other points will remain the same. A change in the yield of the 2 year will likely influence the yield of 1 year and 3 year rates. Figure 3, visualizes the yield curve changes that effective duration and KRD most accurately measure. As we can see, effective duration is the best measurement if the entire yield curve moves by the same amount. KRDs best measure if only one spot on the yield curve changes.

Figure 4, below, outlines the current treasury yield along with the yields from the end of 2015 and 2016. As we have seen in Figures 1 and 2, the curve did not evenly shift upwards when the Fed increased rates. The curve twisted with the short-end increasing and the far-end declining in yield. In this scenario, KRDs would have provided a better measurement for the risk of rising interest rates on a fixed income portfolio.

Table 2 below presents the KRDs for 3 iShares ETFs representing short, inter, and long-term bond portfolios. The durations for CSJ-OLD, CRED-OLD, and CLY-OLD are 1.92, 6.99, and 13.24. This duration equals the sum of the component KRDs. Examining the 10 year key rate, KRD is 1.65 and 1.96 for CRED and CLY, respectively. Meaning that if the yield on the 10 year changed by 1%, we would expect the price to change for CRED by ~1.65% and CLY ~1.96%. We would expect no change in price for CSJ, since this fund does not hold bonds with a maturity of 10 years or longer and thus no exposure to the long end of the yield curve.

Examining the 1 year key rate, which is likely to change based upon an increase by the Fed, CSJ has the largest KRD. Intuitively, this makes sense because ~95% of the portfolio is in short term bonds. The short-term bond ETF has the highest sensitivity to changes in short-term yields even though it has the lowest overall duration. The intermediate and long-term bond ETFs have fewer short-term holdings and thus their overall sensitivity to changes on the short end of the yield curve are less.

With an assumed increase in the 1 year key rate of 0.5%, we would expect that CSJ, CRED, and CLY would decline by approximately 0.165%, 0.04%, and 0.01%, respectively.

Price change = KRD x -Yield Change

Table 3 below is the breakdown of the ETF's portfolios by maturity. The maturity weightings of an ETF or mutual fund provides another means of evaluating key points of interest sensitivity without having to perform calculations to derive key rates.

As we can see from the Table, CSJ's portfolio is primarily invested in bonds with maturities of 1 to 3 years and the resulting average maturity of 1.96 years. This information can be used as short-cut to gauge interest rate sensitivity to various parts of the yield curve. Just using the data from Table 3, we can interpret that this fund will be most sensitive to changes in the 2 year yield. Examining CLY, the majority of its holdings have maturities of 20 to 30 years and an average maturity of 23.14 years. This indicates the fund will be most sensitive to changes in yields on the curve between 20 and 30 years. CLY will not be too sensitive to changes on the short-end of the curve. Returning to the KRDs in Table 2, the mathematics verifies this simplification. For CSJ, a majority of its duration is explained by changes in the 2 year yield. For CLY, its duration is primarily driven by changes in the 20 and 30 year yields.

Broader based funds such as CRED, which hold bonds across all maturities, will be exposed to changes in yield across the curve. The weightings of the portfolio will provide more relevance than average maturity since it does not hold a concentrated position around one maturity. CRED is approximately 40% short-term (1-5 years), 30% intermediate (5-10 years), and 30% long-term (10+ years). Utilizing other more concentrated funds to reconstruct the portfolio can help in evaluating interest rate risk. For example, CRED can be thought of as holding 40% CSJ, 30% CIU-OLD and, 30% CLY. If only short-term rates change by 1%, the price impact to CRED can be approximated by the duration of CSJ multiplied by 40%. 1.96 x 1% x 40% = 0.78.

Utilizing basic math can produce representative KRDs without having to do the computational steps to calculate the actual KRDs. The methods we will outline will both utilize the portfolio weightings of the respective funds. In one method, we will utilize the portfolio's effective duration and the other will utilize the duration of zero coupon bonds. Both of these methods will not properly calculate KRD due to estimation errors caused by the duration inputs; however, both will provide insight into where the ETF or fund has the most sensitivity to changes in interest rates. In other terms, these alternatives will give the location of sensitivity, but not the amount of sensitivity.

The first method simply takes the effective duration of the portfolio and multiplies this by the maturity breakdown. The overall portfolio duration will cause the KRDs less than the average maturity to be overstated. KRDs will be understated for maturities greater than average maturity. Examining CRED, the true KRDs for 20 and 30 years are 1.03 and 2.12, respectively. The estimated KRDs for this period is 1.34.

The second method to estimate KRDs utilizes the properties of zero coupon bonds and the maturity weightings of the ETF or mutual fund to locate interest rate sensitivity. The duration of a zero coupon bond is equal to its maturity since there are no intermittent coupon payments. The only cash flow a zero coupon provides is the payment of its principal at maturity. For example, a five year zero has duration of 5. Since the interest rate sensitivity of a zero coupon bond is directly linked to its maturity date, the zero coupon bond will only have one key rate which will be equal to its time to maturity and duration.

Using the properties of the zero coupon bond, KRDs can be approximated by taking the portfolio weights and multiplying them by the duration of a zero coupon bond with the same maturity. For example, CRED has ~19% of its portfolio invested in maturities of 7 to 10 years and this is multiplied by 8.5 to approximate the mid-point of the 7 to 10 year maturity category. Table 5 presents the KRDs estimated by this approach.

From the table, we see that the short-term bond's duration is most sensitive to changes in yields between 1 and 3 years. Returning to table 2, the sum of the KRDs for 1 year, 2 year, and 3 year is 1.90. CRED provides similar results to the actual calculations of KRDs prior to 20 years. Utilizing zero coupon bonds to approximate KRDs becomes less and less accurate farther out on the maturity spectrum. This deviation is driven by the fact that for a given bond maturity, the duration of a coupon paying bond will always be less than zero coupon bond. This discrepancy is seen in CLY were the approximation of KRDs sum to 22.70, which is significantly greater than the duration of the ETF. KRDs sum to the duration of the portfolio and this relationship breaks down due to the overestimate of the portfolios duration by utilizing zero coupon bonds as a proxy for longer-term bonds. This method still highlights the spots on the yield curve that present the most interest rate risk for a portfolio, but the estimated KRDs are inaccurate.

Although the two methods of approximating KRDs are flawed in respect to their calculation of bond price changes with respect to change in one yield, they still provide useful information in regards to where a portfolio is most sensitive to a change in the yield structure. This evaluation of where the risk is located can help improve allocation decisions for fixed income. A large duration figure should not necessarily be a deterrent to investing in fixed income, but the location of the interest rate risk and the willingness to take that risk should guide the allocation decisions.

Transitioning a portfolio to lower duration also has its costs. Returning to 2010, an investor believed that with rates these low, they must go up. Our investor moves from an intermediate-term bond index fund to a short-term index fund. At the beginning of 2010, the investor moved $10,000 from Vanguards Intermediate-term bond index (MUTF:VBIIX) to the short-term bond index fund (MUTF:VBISX). The first set of columns illustrates the difference in income that was generated by the funds and the last two columns show the compounded growth of $10,000.

This change from intermediate-term to short-term resulted in ~$1,200 less in interest income and resulted in an overall portfolio value ~$2,500 lower. Over seven years, this accounts for nearly a 10% difference in interest income received and ~25% in total overall return by moving to a shorter maturity fund.

It is important for investors to understand what duration measures and the assumptions duration requires in order to provide an accurate representation of interest rate risk and bond pricing. We urge investors to look beyond the reported duration for a portfolio and dive deeper to contemplate how the Fed's action will impact the yield curve prior to taking any investment action. When the Fed raises the target rate, this is likely to only move yields on the short-end of the curve. KRDs will provide a better estimate of bond prices for a twist in the curve than duration. Although, KRDs are limited by the assumption that only one yield changes, we believe that this is a better measurement of a portfolio's sensitivity to interest rate risk for a change in the Federal Funds Rate. We believe that the long-end of the curve will not react to the action taken on June 14th.

The Federal Reserve, in concert with cutting the Federal Funds Rate, has also engaged in unconventional open market operations to reduce interest rates across the entire curve. The Federal Reserve engaged in large-scale asset purchases (LSAPs) and a maturity extension program (MEP). Through these two programs, the Fed purchased long-term fixed income securities, primarily Treasuries and agency mortgage-backed securities, in an effort to decrease supply and decrease yield. As of now, the Fed has given no firm indication that these programs will be reduced, which will likely lead to a broad increase in yields along the entire curve. The Federal Reserve estimates that the yield on the 10 year Treasury has been reduced by ~1% from these operations[1]. It is very likely when the Fed begins to "unwind" these programs; there will be a broad shift in the yield curve making effective duration a better measurement of interest rate risk than KRDs.

Adam Hoffman, CFA, CAIA

[1]Bonis, Brian, Jane Ihrig, and Min Wei. (2017, April). "The Effect of the Federal Reserve's Securities Holdings on Longer-term Interest Rates. Retrieved from

Disclosure: I am/we are long VTI, VXUS, VCSH, VCIT, VMBS, VFIIX.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: Peak Capital Research & Management's clients are long the following positions in either Vanguard ETFs or Mutual Funds or utilizing a similar iShares ETF. Broad US Index, Broad International Index, short-term corporate bonds, intermediate-term corporate bonds, and GNMAs.