Bonds are specific types of loans to governments and corporations. The interest for these loans can either be fixed i.e. unchanging or floating (changing) and is paid out at specific time intervals. Bonds can also be convertible to other financial instruments, have the face value paid along with interest or not, and are exchanged in secondary markets such as the Chicago Board of Trade. Two important features of bonds are their maturity dates and duration. This article will discuss the difference between bond maturity and duration.

## Bond maturity

Bond maturity is fairly simple to understand in comparison to duration. Since bonds are like loans, at some point the principle of the loan has to be paid back. For example, if a bond had a 30 year life in which "coupons" i.e. the interest rate on the face value of the loan were paid, the face value of that bond could either be paid along with the coupons or bought back early as in the case with "call bonds". However, other bonds do not pay back the face value until the end of the established term of the loan. This end of bond life is known as "maturity" and is the point by which the face value of the bond must be paid back.

## Bond duration

Duration is an important financial equation that measures risk of return due to fluctuations in market interest rates. For example, since bonds are loans made from companies or governments to individuals or other companies or governments and new bonds are issued frequently, the benefits of older bonds may rise or decline in relation to new bonds. In other words, if interest rates rise on new bonds, the old bonds won't be as valuable in secondary exchanges because the new bonds are a better deal. The risk of this happening is termed interest rate risk and is measurable by the duration equation. One type of duration equation is Macaulay's duration, which is explained in the video below:

Duration is a very useful equation to investors because of its ability to quantify interest rate risk. This quantification assists in the investment decision making process and does so by expressing the relation between interest, time, and price variables of the bond. The result becomes an "interest rate sensitivity" i.e. risk level. Logically speaking, duration is a time value that either equals, is lower or greater than the original interest payments. In other words, when interest rates fluctuate old bond prices change, causing the duration value to also change. Since duration is a weighted average function of time, the greater the difference between original duration and new duration, the more risk is present in the bond.

## Bond duration equation

The duration equation is a sophisticated combination of variables that each have a unique meaning unto themselves. However, one might consider the most important aspect of the duration equation to be the outcome rather than how it is calculated. This is because it is the outcome that helps indicate investment risk. Nevertheless, understanding the logic and the relationships between the bond variables helps clarify the dynamics and depth of understanding between the variables. This gives one a greater appreciation for the nature of the bond market and investments within it. A few key variables in bond duration are the following:

Important variables:

• Present value of payments: Value of interest payments in proportion to face value, bond price in secondary markets. Also known as discount rate.

• Bond price: Current bond price for used bonds

• Interest rate: i.e. coupon rate

• Face value of bond: The future value at maturity

• Future value of bond: The future value if other than face value

• Time i.e. number of interest remaining in the life of the bond

• Bond price: Current bond price for used bonds

• Interest rate: i.e. coupon rate

• Face value of bond: The future value at maturity

• Future value of bond: The future value if other than face value

• Time i.e. number of interest remaining in the life of the bond

Duration can be calculated by adding the sum of the present value of coupons and multiplying that by the weight of that coupon in proportion to total payments including face value. There are a lot of concepts built into that last sentence. Of particular relevance is weighted average; this is the present value of coupon rates i.e. (adjusted interest payments based on current bond prices) divided by the latest bond pricing.

Essentially, in this case, weighted average is a concept within a concept that contains another concept i.e. present value which is calculated by inputting remaining payments, new interest rate, payment amounts and future value i.e. final bond payment into a financial calculator, spreadsheet application or by hand. The result becomes a time value that is either lower, higher or the same as the original bond duration i..e time between payments and term of the bond. If the duration is lower the risk is also thought lower and if the duration is higher than original bond duration, the risk is thought higher.

Calculating duration is a way to double check accuracy in bond pricing as well as determine price risk. For the most part, adjustments in bond prices are efficiently adjusted for in the secondary bond markets through market efficiency. However, some bonds may be at greater risk to opportunity cost i.e. the risk of obtaining higher yields from alternative investments. This being the case the duration equation is a necessary tool to bond traders and investors.

Since the duration equation can be complicated and conceptually advanced, it can be a good idea to break it down in terms of its sub-components and relationships. This can help make the final equation make more sense. Following this underlying understanding, the duration equation can be simplified and expedited through the use of financial calculators and spreadsheets.

Sources:

1. Bodie, Kane and Marcus. 'Investments 5th ed.' Boston. McGraw-Hill Irwin, 2002. p.485-492

2. Brigham and Erhardt 'Financial Management: Theory and Practice 10th ed' Mason, Ohio SouthWestern, 2002 p.352-357

3. http://en.wikipedia.org/wiki/Bond_duration

4. http://www.investopedia.com/university/advancedbond/advancedbond5.asp