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Bond Valuation

Duration analysis is used to quantify the interest rate risk associated with bonds. The duration (also called "Macaulay duration") is the average period of capital commitment. Unlike the simple term to maturity, it takes account of the capital commitment of all the individual payment flows. Duration analysis can be applied to entire bond portfolios. It can also be used to hedge bonds against unfavourable yield trends.

There is an inverse relationship between market rates and bond prices - the direct result of rising yields is dropping prices. On the other hand, coupon payments can be invested more profitably, which increases the future value of the portfolio. The duration is usually expressed in years and indicates the period after which these two effects cancel each other out.

This figure allows investors to compare bonds with different terms to maturity, interest coupons and repayment frequencies. The concept of duration suggests that investors should choose the average commitment period of a bond or bond portfolio in accordance with their individual investment horizons.

The duration can be calculated using the following formula:


D: duration (average period of capital commitment) in years
Zt: payment at point in time t
r: market rate
t: time

Bond price 97.327%
Duration 3 years
Coupon 5%
Market rate 6%

Calculation of duration:

As the positive and negative effects of interest rate changes cancel each other out at the time of the duration, interest rate changes have no bearing on the value of the investment at this point in time. It should be noted that the concept assumes a flat yield curve and a parallel movement of the curve, i.e. that the rate change will be the same for all maturities.

The duration expresses the interest-rate sensitivity of a bond issue in a single figure. The relative risk of a bond is indicated by changes in the duration or differences between the durations of different bonds.

The duration of a bond depends on the features that determine its price. It will be shorter

  • The shorter the term to maturity,
  • the higher the market yield, and
  • the higher the coupon,

The duration can be used to calculate an approximative price change:

Calculation of an approximative price change in the event of a rate increase by 0.01%: