Bond Immunization: Explain with Example, Know the concept - financebrother

Bond Immunization
Immunization of the bond is the process of making the bond portfolio immune from interest rate risk and reinvestment risk, through which these risks are either eliminated or minimized.

Important Note: Immunization process of the bond cannot be obtained from only a single bond. Hence, creating a bond portfolio is a must for the bond immunization.

Let us understand the bond immunization process as an example:

Suppose, you are required to immunize your bond portfolio for a targeted period of 4 years. For this purpose you want to invest INR 500,000 at present and have identified two bonds X and Y

       Particulars           Bond X          Bond Y
       Face Value           1,000             1,000
       Market Price           980             1,050
       Duration              5 years         2 years

You are required to calculate the following:

•  Amount of money to be invested in each of the two bonds.
• Number of units to be purchased on each bond.

Steps to be followed are as follows:

Step 1: Identify the target period of the investment.
Step 2: Select the bonds for making a bond portfolio in such a way that at least one bond should have its duration less than the target investment period and at least one bond should have its duration greater than the target investment period.
Step3: Examine the Optimum Weights.

The optimum weights should be determined to keep in mind that the duration of the bond portfolio is equal to the target investment period of 4 years.

So, Let W(X) and W(Y) are the weights of Bond X and Bond Y respectively.

We know that W(X) and W(Y) = 1
Hence, W(Y) = 1 – W(X)

The duration of the bond portfolio will be:

D(P) = D(X)*W(X) + D(Y)*W(Y)
4 = 5 * W(X) + 2(1 – W(X))
4 = 5 * W(X) + 2 – 2W(X)
4 – 2 = 5 * W(X) – 2W(X)
2 = 3W(X)
W(X) = 2/3

i.e., W(Y) = 1 - W(X)
1 – 2/3 = 1/3
W(Y) = 1/3

Total Amount invested in Bond X = 500,000 * 2/3 = 333,333
Total Amount invested in Bond Y = 500,000 * 1/3 = 166,667

Number of units to be purchased for each bond:

Bond X = INR 333,333 / INR 980
Units to be purchased for Bond X = 340.13 or 340 Units

Bond Y = INR 166,667 / INR 1,050
Units to be purchased for Bond Y = 158.73 or 159 Units