In a perfect world, interest rates would not fluctuate and the value of the bonds in your portfolio would not change over time.

Unfortunately, we live in a world where interest rates move up and downâ€¦sometimes dramaticallyâ€¦over the course of a bond's term. This movement can have a meaningful impact on your portfolio, if not taken into account in the day-to-day management of your fixed income assets says **Emad A Zikry**, Chief Executive Officer of Vanderbilt Avenue Asset Management.

One of the ways we help to insulate your portfolio from negative interest rate moves and to take advantage of those that are positive, is to carefully monitor its duration. In what follows, we will examine the concept of duration and its applicability as an interest rate risk management tool.

**Duration as a risk measure:**

There is an inverse relationship between the price of a bond and its yield. The yield on a bond is the discount rate that makes the present value of the bond's cash flows equal to its price. Thus, as the bond's price declines, its yield increases, a direct reflection of the discount between the bond's par value and the price investors are willing to pay for it.

In a rising interest rate environment investors demand greater yields, which can only be provided by lowering the asking price for the bond. Conversely, in a decreasing interest rate environment, the bond's fixed rate of return may make it very attractive to investors, causing its price to rise (a reflection of increased demand) and its yield to decline.

Obviously, this kind of price variability can play havoc on the value of a fixed income portfolio at any given point in time, unless the portfolio is carefully monitored and positioned to defend against or take advantage of changes in the interest rate environment.

Duration, which measures the price sensitivity of bonds to a variable yield environment, enables us to do just that, notes **Emad A Zikry**, Chief Executive Officer of Vanderbilt Avenue Asset Management.

There are three primary duration calculations: Macaulay Duration, Modified Duration and Effective Duration.

**Macaulay Duration:**

In 1938, Frederick Macaulay introduced the concept now known as "Duration". Named after its founder, Macaulay Duration is a calculation of the approximate sensitivity of a bond's price to changes in interest rates.

In general, Macaulay Duration is used to determine the point in time, measured in years, at which half of a bond's total cash flows will be received. However, to make it more usable as a mathematical calculation of risk, Macaulay Duration has been modified slightly, giving rise to a more modern interpretation known as "Modified Duration".

**Modified Duration:**

Modified Duration equals Macaulay Duration divided by one plus the yield to maturity. Since Modified Duration and Macaulay Duration essentially measure the same thing (i.e., sensitivity of a bond's price to changes in yields or interest rates), one measure is not strictly preferable to the other. However, for estimating price changes, Modified Duration is easier to use, as can be seen in the following equation.

As determined by the Modified Duration method, duration is the approximate percentage change in a given bond's price for each 100 basis point (bp) shift in the yield curve. For example, if a bond's duration is 4.0, this means a 1.0% (100 basis point) decrease in interest rates will result in a price increase of approximately 4.0%. By the same token, a 50 basis point increase in yields will result in a price decline of approximately 2.0%.

**Effective Duration:**

Modified Duration is a good way to measure bonds that have fixed cash flows and maturity dates, but it can't accurately measure the price/interest rate sensitivity of bonds that have embedded options, such as mortgage backed securities and callable corporate bonds.

Mortgages backed securities are complicated by the fact that homeowners have the *option* of refinancing their mortgages when interest rates drop. When this option is exercised, investors in mortgage backed securities get their principal back much earlier than expected and are faced with having to reinvest the proceeds in lower yielding instruments.

Similarly, with callable corporate bonds, issuers have the right to call, or redeem, the bond prior to maturity. As with the homeowner, corporations tend to call these bonds when interest rates fall, in order to reduce the borrowing cost of the loan. Again, the investor must reinvest in lower yielding instruments.

We have to quantify and adjust for redemption-related risk when analyzing the characteristics of a bond with embedded options. Modified Duration does not take into account this risk of optionality, if you will, because it assumes the yield to maturity is not affected by changes in interest rates, states **Emad A Zikry**, Chief Executive Officer of Vanderbilt Avenue Asset Management.

The only duration formula that can measure the risk of bonds that have embedded options is called "Effective Duration," or "Option Adjusted Duration". Effective Duration adjusts the riskiness of bonds by taking into account the relative sensitivity of bonds with different coupon rates and terms to prevailing interest rates. It can gauge the likelihood of the call being exercised, or a mortgage being refinanced, and thereby help to measure the risk represented by these securities in various yield, or interest rate, environments. We would note that Effective Duration should be equal to or close to Modified Duration for bulleted bonds, (i.e. those without option risk).