Bond Investing Basics – Duration


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:

  1. Higher interest rates
  2. Longer maturity
  3. 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.

Risk Management

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:

  1. Amortization or cash flow sweep payments (the model assumes a bullet payment)
  2. Interest Payment dates if anything other than quarterly payments
  3. Call or Put options embedded in the bond structure
  4. 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!

Bond Investing Basics – Credit Ratings


Today’s lesson will focus on credit ratings and how to utilize them in order to manage your portfolio and potentially select strategies that will enhance returns.

Credit Rating Definitions

There are generally two credit rating agencies that investors pay attention to: Standard & Poor’s and Moody’s. Credit rating categories range (in the case of S&P) from AAA (highest rating) to D (lowest rating). See below for each company’s credit categories and corresponding definitions:

  1. Moody’s
  2. S&P

One important consideration is the separation of “investment grade” and “high yield” bonds. Investment grade bonds (categorized typically as AAA through BBB rated bonds using the S&P categories and Aaa through Baa3 using the Moody’s categories) are generally “safer” investments than high yield bonds. More risk, in the case of bonds, refers to the increased probability of default. Given this perspective, a few key differences exit between the two:

  1. Investors will demand a higher expected return high yields to make up for the additional risk of the investments. Please refer to our latest market update to see the yield differentials for each credit rating.
  2. High yield instruments will generally have more restrictive financial covenants set by lenders. Breach of the covenants could lead to an increase in the interest rate, triggering of additional fees, or even be considered an event of default (in which case the lenders may choose to take control of the assets to either replace the management team or sell the assets in order to recoup their principal).
  3. Given the greater yield on high yield instruments, these bonds will experience greater volatility and sensitivity to movements in interest rate changes. From the lesson on the relationship between bond prices and yields (namely, they are inversely related), the magnitude of the impact of changing yields will be greater for riskier investments. This is measured by ‘duration’ and ‘convexity’ (we will discuss these in later posts).
  4. The maturities of investment grade bonds are typically longer given the relative trustworthiness of the company.

Risk Management

There are generally two ways to incorporate credit ratings of bonds into risk management strategies.

First, for a portfolio of bonds, each individual bond will typically have an individual credit rating. Based on a weighted average approach, an investor can view the overall risk of the portfolio by calculating an assumed “portfolio credit rating.” There are two steps in this process.  

Assign an ordinal indicator to each credit rating category. For example, in the case of S&P credit ratings, we have assigned a figure to each credit rating category:

Next, we can find the assumed numerical weighting based on the credit rating of each bond. In the chart below, we have inserted random credit ratings to the dollar amount of each individual bond. Based on the weighted average of each portfolio position (dividing each holding amount by the total dollar amount held) and the numerical rating of each position, we can estimate the weighted average contribution in the “Weighted Avg Rating” column. After summing all of these rating contributions, we calculate a numerical rating of 3.8 for the portfolio. Looking back above at point 1, this implies a credit rating in between A and BBB.

The second way to incorporate credit ratings into risk management is by observing changes over time. Over time, as credit ratings increase or decrease, the investor can make adjustments to fine tune the portfolio. For example, in the case above, if the investor wants to keep a rating of A as the minimum for the portfolio, they may consider selling lower rated bonds (such as Bond 6, Bond 3, or Bond 4) and purchasing other bonds with higher credit ratings.

Total Return Perspective

One key element of utilizing credit ratings is to find potential cases where an investor believes a bond will receive a credit upgrade in the future. For example, a bond may be upgraded from a BBB to an A. Ratings upgrades occur when recent performance, the macroeconomic backdrop, or some other factor occurs and the credit rating agency determines it has materially lessened the company’s probability of default. For example, see the link here for a recent Moody’s upgrade of Anglo American.  

When this occurs, investors are willing to acquire the bond at a greater price given the risk reduction in the position. The key to this strategy is to predict when and if a company will experience a ratings upgrade. If an investor is successful with this strategy, they are able to lock in a higher return by selling the bond at a higher price than they acquired it for.


Credit ratings are an important component of risk management and bond investment strategy. Investors must be aware of various strategies they can deploy to take advantage of changes in the company’s rating. For example, a recent rating downgrade may provide an investor to take advantage of a lower price. However, the investor must be willing to either take on the additional risk or believe that some change will occur to reverse this trend sometime in the future.

Bond Investing Basics – Setting Your Goals


In this section, we will discuss setting goals for investing in bonds. This section is not designed to give you a primer on bonds given the plethora of sources out there that provide sufficient overviews (I have provided links to some of the better ones below). Instead, we will focus on the key components of choosing an investment that matches your personal goals and strategy.

Background Knowledge

If you do not have a good background in bond investing, I suggest reading through the following sources:

  1. Investopedia – “Bonds”
  2. The Motley Fool – “How to Invest in Bonds: A Step-by-Step Guide”
  3. Project Invested – “What Factors Should You Consider When Investing in Bonds”

Furthermore, if you are not interested in investing in individual bonds (given the time and knowledge commitment required to get there), review some of the differences in investing in bonds and bond funds below (my only specific suggestion is to play close attention to bond fund fees, that could also be a critical factor outside of the actual management of the portfolio):

  1. CNBC – “Bonds vs Bond Funds: What you Need to Know Now”
  2. Fidelity – “Bonds vs Bond Funds”
  3. The Balance – “Investing in Bonds versus Bond Funds”

Setting Goals for Bond Investing

The sheer size of the global bond market (estimated to be over $100 trillion) provides investors with numerous investment options. Some of these investments have traditionally been seen as “safer” than investing in stocks. Some of these investments have funky features (such as call/put options, conversion features, etc.). Some of these investments provide certain tax advantages (e.g., municipal bonds). As part of your investment plan, we will focus today’s discussion on a few items:

  1. Time Horizon
  2. Risk Taking and Risk Management

Time Horizon

Bonds can be structured to have short-term maturities (0-5 years), medium-term maturities (5-10 years), and long-term maturities (10+ years). Different investors may differentiate the categories for maturity length, but this summary should suffice to get the point across.

In the case of figuring out your time horizon, it can be as simple as counting the years until your child goes off to college to as difficult as figuring out how many bonds you will need to provide income through your retirement. A few suggestions:

  1. Be honest and conservative in your assumptions
  2. There are always multiple time horizons for your savings plan, make a plan for each one
  3. Think about potential scenarios where you may need money
  4. Think about inflation over the long run and if it will impact your time horizon assumptions
  5. Your emergency fund is your best friend, time horizons are meaningless if you do not have a reserve in case the market drops really fast

Risk Taking and Risk Management

For individuals entering into retirement, traditional investment theory dictates most of your portfolio should be allocated towards investment grade (discussed below in the risk taking and risk management section) bonds. A rule of thumb often portrayed is to subtract your age from 100 to determine the percentage allocation in your portfolio (e.g., if I am 75, then 75% of my portfolio should be in bonds).

However, as you will often note, real world application of finance theory often falls flat in real world applications. For example, if the size of the portfolio relative to retirement needs is quite large, an investor will often elect to invest more in stocks in order to potentially maximize their estate. In addition, different portfolios may have different goals, such as saving for an expensive purchase (Harley or a boat), children’s education, or an emergency reserve.

Although we will discuss some of the strategies in later posts, here are some of the risk-based items you will need to think through:

  1. Credit Rating / Default risk – What is the rating of the company and where do you expect this to trend in the future or over your time horizon?
  2. Credit Spread relative to comparable credits and market indices – Are you getting a good deal at the price you are paying?
  3. Financial and operating leverage of the company – Can small swings in the company impact your investment?
  4. Industry of the company – What are certain industry drivers and what part of the business cycle is the industry currently experiencing?
  5. Duration / Interest rate risk – How quickly will rates rise (obviously you will need to consider the opposite as well, but our low interest rate environment contributes to this specific discussion)?
  6. Inflation risk – Is nominal or real return more important to you?
  7. Liquidity – Will you be able to sell when you need to?


There are obviously a lot of factors to consider when setting up a strategy. The issue some investors have is that they read online for various bond investing strategies and try to fit their personal situation to fit the strategy. Rather, you should think more about your situation and pick the appropriate strategies to meet your goals. This will also allow you to make the right sacrifices, correctly set your risk parameters, and focus your attention on specific details you will need to succeed.