
Bonds  Duration
Bond duration is a measure of the sensitivity of the price (the value of principal) of a fixedincome investment to a change in interest rates. Duration is expressed as a number of years. Rising interest rates mean falling bond prices, while declining interest rates mean rising bond prices.
The duration number is a complicated calculation involving present value, yield, coupon, final maturity and call features. Fortunately for investors, this indicator is a standard data point provided in the presentation of comprehensive bond and bond mutual fund information. The bigger the duration number, the greater the interestrate risk or reward for bond prices.
It is a common misconception among nonprofessional investors that bonds and bond funds are riskfree. They are not. As you learned in the last section, investors need to be aware of two main risks that can affect a bond's investment value: credit risk (default) and interest rate risk (rate fluctuations). The duration indicator addresses the latter issue.
The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.
For each of the two basic types of bonds the duration is the following:
1. ZeroCoupon Bond  Duration is equal to its time to maturity.
2. Vanilla Bond  Duration will always be less than its time to maturity.
Let's first work through some visual models that demonstrate the properties of duration for a zerocoupon bond and a vanilla bond.
Duration of a ZeroCoupon Bond
The red lever above represents the fouryear time period it takes for a zerocoupon bond to mature. The money bag balancing on the far right represents the future value of the bond  the amount that will be paid to the bondholder at maturity. The fulcrum, or the point holding the lever, represents duration, which must be positioned where the red lever is balanced. The fulcrum balances the red lever at the point on the time line at which the amount paid for the bond and the cash flow received from the bond are equal. The entire cash flow of a zerocoupon bond occurs at maturity, so the fulcrum is located directly below this one payment.
Duration of a Vanilla or Straight Bond
Consider a vanilla or straight bond that pays coupons annually and matures in five years. Its cash flows consist of five annual coupon payments and the last payment includes the face value of the bond.
The money bags represent the cash flows you will receive over the fiveyear period. To balance the red lever at the point where total cash flows equal the amount paid for the bond, the fulcrum must be farther to the left, at a point before maturity. Unlike the zerocoupon bond, the straight bond pays coupon payments throughout its life and therefore repays the full amount paid for the bond sooner.
Factors Affecting Duration
It is important to note, however, that duration changes as the coupons are paid to the bondholder. As the bondholder receives a coupon payment, the amount of the cash flow is no longer on the time line, which means it is no longer counted as a future cash flow that goes towards repaying the bondholder. Our model of the fulcrum demonstrates this: as the first coupon payment is removed from the red lever and paid to the bondholder, the lever is no longer in balance because the coupon payment is no longer counted as a future cash flow.
The fulcrum must now move to the right in order to balance the lever again:
Duration: Other Factors
Besides the movement of time and the payment of coupons, there are other factors that affect a bond's duration, including the coupon rate and its yield. Bonds with high coupon rates and, in turn, high yields will tend to have lower durations than bonds that pay low coupon rates or offer low yields. This makes empirical sense, because when a bond pays a higher coupon rate or has a high yield, the holder of the security receives repayment for the security at a faster rate.
Types of Duration
There are four main types of duration calculations, each of which differ in the way they account for factors such as interest rate changes and the bond's embedded options or redemption features. The four types of durations are Macaulay duration, modified duration, effective duration and keyrate duration.
Macaulay Duration The formula usually used to calculate a bond\'s basic duration is the Macaulay duration, which was created by Frederick Macaulay in 1938, although it was not commonly used until the 1970s. Macaulay duration is calculated by adding the results of multiplying the present value of each cash flow by the time it is received and dividing by the total price of the security. The formula for Macaulay duration is as follows:
Example 1: Betty holds a fiveyear bond with a par value of $1,000 and coupon rate of 5%. For simplicity, let's assume that the coupon is paid annually and that interest rates are 5%. What is the Macaulay duration of the bond?

Duration and Bond Price Volatility
We have established that when interest rates rise, bond prices fall, and vice versa. But how does one determine the degree of a price change when interest rates change? Generally, bonds with a high duration will have a higher price fluctuation than bonds with a low duration. But it is important to know that there are also three other factors that determine how sensitive a bond's price is to changes in interest rates. These factors are term to maturity, coupon rate and yield to maturity. Knowing what affects a bond's volatility is important to investors who use durationbased immunization strategies, which we discuss below, in their portfolios.
Factors 1 and 2: Coupon Rate and Term to Maturity If term to maturity and a bond\'s initial price remain constant, the higher the coupon, the lower the volatility, and the lower the coupon, the higher the volatility. If the coupon rate and the bond\'s initial price are constant, the bond with a longer term to maturity will display higher price volatility and a bond with a shorter term to maturity will display lower price volatility. Therefore, if you would like to invest in a bond with minimal interest rate risk, a bond with high coupon payments and a short term to maturity would be optimal. An investor who predicts that interest rates will decline would best potentially capitalize on a bond with low coupon payments and a long term to maturity, since these factors would magnify a bond\'s price increase. Factor 3: Yield to Maturity (YTM) The sensitivity of a bond\'s price to changes in interest rates also depends on its yield to maturity. A bond with a high yield to maturity will display lower price volatility than a bond with a lower yield to maturity, but a similar coupon rate and term to maturity. Yield to maturity is affected by the bond\'s credit rating, so bonds with poor credit ratings will have higher yields than bonds with excellent credit ratings. Therefore, bonds with poor credit ratings typically display lower price volatility than bonds with excellent credit ratings. 
All three factors affect the degree to which bond price will be altered in the face of a change in prevailing interest rates. These factors work together and against each other.
So, if a bond has both a short term to maturity and a low coupon rate, its characteristics have opposite effects on its volatility: the low coupon raises volatility and the short term to maturity lowers volatility. The bond's volatility would then be an average of these two opposite effects.
Immunization
As we mentioned in the above section, the interrelated factors of duration, coupon rate, term to maturity and price volatility are important for those investors employing durationbased immunization strategies. These strategies aim to match the durations of assets and liabilities within a portfolio for the purpose of minimizing the impact of interest rates on the net worth. To create these strategies, portfolio managers use Macaulay duration.
For example, say a bond has a twoyear term with four coupons of $50 and a par value of $1,000. If the investor did not reinvest his or her proceeds at some interest rate, he or she would have received a total of $1,200 at the end of two years. However, if the investor were to reinvest each of the bond cash flows until maturity, he or she would have more than $1,200 in two years. Therefore, the extra interest accumulated on the reinvested coupons would allow the bondholder to satisfy a future $1,200 obligation in less time than the maturity of the bond.
Understanding what duration is, how it is used and what factors affect it will help you to determine a bond's price volatility. Volatility is an important factor in determining your strategy for capitalizing on interest rate movements. Furthermore, duration will also help you to determine how you can protect your portfolio from interest rate risk.


Bonds & Fixed Income
Use Duration And Convexity To Measure Bond Risk
Find out how this measure can help fixedincome investors manage their portfolios. 
Professionals
Yield Terms
FINRA Series 6 Exam Study Guide  Yield Terms. This section distinguishes three types of yield calculations for bonds. 
Investing
Watch Your Duration When Rates Rise
While recent market volatility is leading investors to look for the nearest exit, here are some suggestions for bond exposure in attractive sectors. 
Financial Advisors
Why You Should Avoid Fixating on Bond Duration
Financial advisors and their clients should then focus on a bond fundâ€™s portfolio rather than relying on any single metric like duration. 
Professionals
Duration and Stock Risks
FINRA/NASAA Series 66: Section 5 Duration and Stock Risks. This section discusses duration and risks associated with investing in the stock markets: systematic, unsystematic, business, regulatory ... 
Bonds & Fixed Income
What Does Duration Mean?
Duration measures a fixedincomeâ€™s sensitivity to changes in interest rates. 
Professionals
Effective, Modified, and Macaulay Duration
CFA Level 1  Duration. Learn the differences between effective, modified and Macaulay duration. Shows how to apply a weighted duration to a portfolio of bonds. 
Professionals
Bond Risks and Duration
NASAA Series 65: Section 16 Bond Risks and Duration. In this section types of bond risks and duration. 
Investing Basics
Calculating the Macaulay Duration
The weighted average term to maturity of the cash flows from a bond. 
Options & Futures
Immunization Inoculates Against Interest Rate Risk
Bigmoney investors can hedge against bond portfolio losses caused by rate fluctuations.

Duration
A measure of the sensitivity of the price (the value of principal) ... 
Dollar Duration
Dollar duration measures the dollar change in a bond's value ... 
Effective Duration
A duration calculation for bonds with embedded options. Effective ... 
Macaulay Duration
The weighted average term to maturity of the cash flows from ... 
Bond
A debt investment in which an investor loans money to an entity ... 
Empirical Duration
The calculation of a bond's duration based on historical data. ...

How can I use a bond's duration to predict its return?
Learn how the concept of duration is used to determine when future cash flows for a bond will equal the amount paid for the ... Read Answer >> 
What is the relationship between modified duration and interest rates?
Learn about modified duration and Macaulay duration, how to calculate the durations of bonds, and how interest rates and ... Read Answer >> 
Which is a better metric, modified duration or Macaulay duration?
Learn why the modified duration is a more useful metric than the Macaulay duration, and understand how the measures are different ... Read Answer >> 
What is the average profit margin of a company in the chemicals sector?
Learn more about the Macaulay duration and the modified duration, how to calculate a bond's Macaulay duration and modified ... Read Answer >> 
What is the risk return tradeoff for bonds?
Find out more about the Macaulay duration and modified duration, how to calculate them and the difference between the Macaulay ... Read Answer >> 
How does duration impact bond funds?
Learn how duration for a bond fund measures the risk the bond portfolio has to a rise in interest rates, and see how managers ... Read Answer >>