Question

What are the three Duration Principles?

Answer 1

What is Duration

Duration is one of the fundamental characteristics of a fixed-income security (e.g., a bond) alongside maturity, yield, coupon, and call features. It is a tool used in the assessment of the price volatility of a fixed-income security.

For example, a bond with 10 years till maturity and a 7% coupon trading at par to yield 7% has a duration of 7.355 years. At a yield of 6% (price 107 14/32), its duration is 7.461 years.

The duration is several types. The most common types are the Macaulay duration, modified duration, and effective duration.

The Macaulay duration calculates the weighted average time before a bondholder would receive the bond's cash flows. The Macaulay duration is measured in units of time (e.g., years).

The Modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity. The modified duration figure indicates the percentage change in the bond’s value given an X% interest rate change. Unlike the Macaulay duration, modified duration is measured in percentages.

The Effective duration is a measure of the duration for bonds with embedded options (e.g.is callable bonds). Unlike the modified duration and Macaulay duration, effective duration considers fluctuations in the bond’s price movements relative to the changes in the bond’s yield to maturity (YTM).

The formula for effective duration contains four variables. They are: P(0) = the bond's original price per $100 worth of par value. P(1) = the price of the bond if the yield were to decrease by Y percent.