DURATION

Duration is the measurement of how long in years it takes the price of a bond to be repaid by its internal cash flows, and is expressed as a weighted average. Duration is an important measurement function for investors, as bonds with higher duration are riskier with higher price volatility. Imagine the following see-saw diagram:

The above example shows a five-year bond with annual coupon payments, the see-saw is balanced nicely, but when a payment is made the balance will tip, so in order to balance again we have to move the duration base to the right. Hence duration will change over time as coupon payments are made to the bond holder, because future cash flows have changed. Duration decreases over time as time moves closer to maturity, although it does increase momentarily on the day a cash flow payment is made and removed from the future cash flows. This will occur until duration eventually converges with maturity. Zero-coupon bonds remember would only have the duration base at maturity because no coupons payments are made.

Besides time and payment of coupons that affect a bonds duration there are other factors to consider in duration they are coupon rate and yield. High coupon rates and in turn high yields tend to have lower duration than bonds that pay low coupon rates, or offer a low yield.

The following diagram shows this principle.

There are four types of duration calculations, which all differ in their approach to individual factors such as interest rate changes, or the bonds features, their four methods are:

Macaulay Duration

Created by Frederick Macaulay in 1938, it is calculated by adding the results of multiplying present value of each coupon payment by the time it is received, and dividing by the total price of the security.

Modified Duration

A modified version of Macaulay that accounts for changing interest rates, because they affect yield, in turn fluctuating interest rates will affect duration. In short Modified duration shows how much duration changes for each % change in yield.

Effective Duration

Both of the above methods assume that cash flows remain constant, even if rates change, which is effective for option free fixed income securities. Although some securities come with cash flow options that change with interest rates, effective duration calculations using binomial trees work best in these products but the formulas are very complicated.

Key-Rate Duration

Calculates spot durations at 11 key maturities along a spot curve, being 3 months, 1, 2, 3, 4, 5, 7, 10, 15, 20, 25, and 30 years. It is most commonly used for fixed income securities with differing maturities.

In summary then duration has five key uses and points:

• Measure of sensitivity
• Zero-coupon bonds will have a duration exactly equal to its maturity
• Coupon paying bonds will have a duration less than its maturity
• Duration is a parameter in constructing portfolios for fund managers
• Allows bonds of different maturities and coupon rates to be compared directly