Today, we will talk about the concept of duration. The discussion will include a basic overview of the concept of duration, different methods to calculate duration, and how to incorporate duration into both strategy and risk management.
What is Duration?
Duration measures the sensitivity of a bond’s price to changes in interest rates. Since bond prices have an inverse relationship to bond yields, an increase in interest rates will reduce a bond’s price (and vice versa). For a more basic overview, please visit “Bond Investing Basics – Setting Your Goals” for links related to basic bond concepts. Duration measures (or, more precisely, attempts to estimate) the magnitude of that change.
How to Find Duration
Most brokerage firms that allow you to trade bonds have both screening tools and tearsheets in order to find a suitable bond based on the desired level of duration. Below, I have used the E*Trade platform to find for a position’s duration. First, click on Trading –> Bonds to pull up the Bond Overview page.
In the box labelled “CUSIP,” (CUSIP stands for Committee on Uniform Security Identification Procedures and represents a 9 digit identifier for bonds) type in any identifier for the bond. For the purpose of this post, we have used the CUSIP “665859AL8,” which is a CUSIP for a bond issued by Northern Trust Corp.
From here, click on the actual issue (in this case, it is clicking on “Northern Trust Corp” in the Issue column) to bring up further details on this specific bond. Looking at the bottom right, you can see the Macaulay duration to be 2.848.
There are a few different measures for duration outlined on this page (in addition to convexity, which we will not be covered today), that we will cover in a later post. The duration figure represents the number of years it will take an investor recover the cost of a bond (after accounting for discounting, the purchase price, and remaining cash flows). The higher the duration, the higher the interest rate risk. Generally speaking, a bond’s duration will be higher with:
- Higher interest rates
- Longer maturity
- Lower bond prices
One general strategy is to consider where interest rates are expected to move in the future. If an investor expects interest rates to move up (hence, prices to move down), he or she may consider “shortening” duration in order to reduce interest rate risk. This will make the bond portfolio’s value to be more resilient to increases in the interest rate. If an investor expects interest rates to decline (hence, price move up), he or she may consider “lengthening” duration in order to take advantage of a bond’s sensitivity to interest rates. The most sensitive the portfolio is, the more likely that the bond’s price will move up.
The first step in the process is to determine what you can benchmark your portfolio to. There are several different benchmarks released by companies such as S&P, Merrill Lynch, etc. In addition, the benchmarks can be tied to the tenor of bonds, industry, credit rating, structure, etc. Using more specific benchmarks can help investors tie their performance and uncover key drivers of under or over performance. As an example, for the purpose of our post, we will be using the general S&P US Aggregate Bond Index (click here for the S&P summary page). As indicated in the name, this index represents broad coverage of US-based investment grade fixed income. First, click on “Factsheet” and then download the Month-End report.
After, flip to page 3 of the downloaded document where you can find the index characteristics below:
As you can see, when comparing to the Northern Trust Corp. specific data, the general US investment grade market has a higher duration (5.50 versus 2.848). While we have just used the duration figure here, you will be able to benchmark a few factors relative to the general index (such as yield, tenor, etc.). A more appropriate benchmark to Northern Trust Corp. may have a portfolio duration closer to the subject company.
Risk Management Modelling
Please download the duration model here
This model is intended to provide a broad view of how to manage duration risk in a portfolio. We start off with noting key elements of your bond portfolio (such as the invested amount, price per bond, maturity date, and the coupon rate). The model automatically calculates the duration (using the Macaulay formula) and the implied yield on the bond. After all the individual data has been input, the model will calculate the portfolio figures in the bottom row:
From here, we can calculate potential changes to each position. Changes in the price, based on the duration of the bond is generally presented as:
Change in the Bond Price = Duration * Change in Yield
The sensitivity table below shows the percentage changes in the bond price based on assumed changes in interest rates:
Based on this analysis, investors can choose whether or not they need to adjust the portfolio for expected changes in the interest rate in the future (i.e., to take advantage of declining interest rates by lengthening duration or vice versa).
Just to note, the model is a simplified tool. In order to truly understand your portfolio, adjustments would need to be made for:
- Amortization or cash flow sweep payments (the model assumes a bullet payment)
- Interest Payment dates if anything other than quarterly payments
- Call or Put options embedded in the bond structure
- Unique structures
Another way to look at the model’s output is to determine the total dollars at risk. If you expect for rates to decline 2% over the next year, you can see the potential impact to your portfolio. Investors can find ways to hedge the portfolio or change strategy. Again, investors need to pay attention to their specific strategies; the model is just a tool to help you along the way!
Duration is a foundational concept to understand when building your bond investment strategy. Bonds have a built-in structure that enables investors to have more clarity relative to general equity investments. Taking advantage of these structures may be difficult to understand, but are rewarding to figure out!