Sensitivity of a Bond With Respect to Changes in Desired Yield Rate

Interest rate sensitivity is a measure of how much the price of a fixed-income asset will fluctuate as a result of changes in the interest rate environment.

Securities that are more sensitive have greater price fluctuations than those with less sensitivity.

This type of sensitivity must be taken into account when selecting a bond or other fixed-income instrument the investor may sell in the secondary market.

Fixed-income securities and interest rates are inversely correlated. Therefore, as interest rates rise, prices of fixed-income securities tend to fall.

One way to determine how interest rates affect a fixed-income security’s portfolio is to determine the duration. The higher a bond or bond fund’s duration, the more sensitive the bond or bond fund to changes in interest rates.

The duration of fixed-income securities gives investors an idea of the sensitivity to potential interest rate changes. Duration is a good measure of interest rate sensitivity because the calculation includes multiple bond characteristics, such as coupon payments and maturity.

Sensitivity of Bond

 Sensitivity = [latex]\dfrac {\sum n.PV}{1+i}[/latex]

Duration of a Bond

Common Misconceptions

The term duration is generally misunderstood as the life of bond or remaining maturity of the bond. Duration of bond does not mean the life of the bond or remaining, maturity of the bond.

Correct Meaning of Duration

Duration of a bond indicates a period over which the investment is recovered. In other words, Duration of a bond can be considered as payback period of a bond. However, the method of determining the duration of the bond is completely different from the calculation of payback period.

Calculation of Duration

Duration of the bond can be determined by the following methods:

• Macaulay’s Duration

• Modified Duration (Volatility of Bond)

Note

As per ICAI the duration means Macaulay’s Duration only. Therefore, if the question requires calculation of duration, it should be considered as Macaulay’s Duration. Modified Duration should be computed only when the question specifies calculation of Modified Duration or Volatility.

Macaulay’s Duration = [latex]\dfrac { \sum { n.PV } }{ Bond\quad Value }[/latex]

Modified Duration = [latex]\dfrac {Macaulay’s\quad Duration}{\left( 1+i\right) }[/latex]

[latex]\dfrac {Macaulay’s\quad Duration}{\left( 1+i\right) }[/latex] = [latex]\dfrac { \left( \dfrac { \sum { n.PV } }{ Intrinsic\quad Value } \right) }{ \left( 1+i \right) }[/latex]

         = [latex]\dfrac { \sum { n.PV } }{ \left( Intrinsic\quad Value \right) \times \left( 1+i \right) }[/latex]

                = [latex]\dfrac { 1 }{ Intrinsic\quad Value } \times \dfrac { \sum { n.PV } }{ \left( 1+i \right) }[/latex]

               = [latex]\dfrac { Sensitivity }{ Intrinsic\quad Value }[/latex]

Interpretation of Volatility

It is sensitivity in terms of per rupee of bond value. In other words, when sensitivity of the bond is expressed for each rupee of its intrinsic value it is called volatility.