Question

When is duration appropriate for estimating the bond’s sensitivity to changes in interest rates.

Answer 1

Duration is a good measure of interest rate sensitivity because the calculation includes multiple bond characteristics, such as coupon payments and maturity.

Generally, the longer the maturity of the asset, the more sensitive the asset to changes in interest rates. Changes in interest rates are watched closely by bond and fixed-income traders, as the resulting price fluctuations affect the overall yield of the securities. Investors who understand the concept of duration can immunize their fixed-income portfolios to changes in short-term interest rates.

Types of Interest Rate Sensitivity

There are four widely used duration measurements to determine a fixed-income security's interest-rate sensitivity—the Macaulay duration, modified duration, effective duration, and key rate duration.

To calculate the Macaulay duration certain metrics must be known, including the time to maturity, remaining cash flows, required yield, cash flow payment, par value, and bond price.

The modified duration is a modified calculation of the Macaulay duration that incorporates yield to maturity (YTM). It determines how much the duration would change for each percentage point change in the yield.

The effective duration is used to calculate the duration of bonds with embedded options. It determines the approximate price decline for a bond if interest rates rise instantaneously by 1%. Effective duration is the sensitivity of a bond. The bond issuer borrows capital from the bondholder and makes fixed payments to them at a fixed (or variable) interest rate for a specified period.'s price against the benchmark yield curve. ... The effective duration figure is used for hybrid securities.

The key rate duration determines a fixed-income security's or fixed-income portfolio's duration at a specific maturity on the yield curve.

Certain factors can affect a bond’s duration, including:

• Time to maturity. The longer the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but have different maturities. A bond that matures faster – say, in one year – would repay its true cost faster than a bond that matures in 10 years. Consequently, the shorter-maturity bond would have a lower duration and less risk.
• Coupon rate. A bond’s coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception on their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk.

How Duration Works

Duration measures how long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows. At the same time, duration is a measure of sensitivity of a bond's or fixed income portfolio's price to changes in interest rates. In general, the higher the duration, the more a bond's price will drop as interest rates rise (and the greater the interest rate risk). As a general rule, for every 1% change in interest rates (increase or decrease), a bond’s price will change approximately 1% in the opposite direction, for every year of duration. If a bond has a duration of five years and interest rates increase 1%, the bond’s price will drop by approximately 5% (1% X 5 years). Likewise, if interest rates fall by 1%, the same bond’s price will increase by about 5% (1% X 5 years).

A bond's duration can be split into two different features. The Macauley duration is the weighted average time to receive all the bond's cash flows and is expressed in years. A bond's modified duration converts the Macauley duration into an estimate of how much the bond's price will rise or fall with a 1% change in the yield to maturity. A bond with a long time to maturity will have larger duration than a short-term bond. As a bond's duration rises, its interest rate risk also rises because the impact of a change in the interest rate environment is larger than it would be for a bond with a smaller duration.