In this article, we will look into an important concept in bond investments, which is immunizing a bond portfolio, assume that you have a future obligation (or a financial need) to meet with your current bond investments and ensure that the future obligation is met irrespective of market conditions (changes in yield/interest rates), or in other words you want to immunize your bond portfolio against changes in yield.
Immunizing a bond portfolio is something which has practical applications in investment science in that it can be mathematically proven that when you immunize your bond portfolio, you will be protected against changes in yield (whether they go up or down), though we don't need to dig deep into the mathematics of it, in this article we will see the necessary conditions to be met for immunizing your bond portfolio.
It can be easily said that zero coupon bonds are the first choice solution for immunizing without having a portfolio, if you have a financial obligation of F after a duration of D years, you can buy a zero coupon bond with it's present value P which will pay it's face value F after D years, but assume that zero coupon bonds are not available, in which case you need to invest in a bond portfolio to meet your needs.
For the sake of simplicity, assume that there are two bonds available with
Immunizing a bond portfolio is something which has practical applications in investment science in that it can be mathematically proven that when you immunize your bond portfolio, you will be protected against changes in yield (whether they go up or down), though we don't need to dig deep into the mathematics of it, in this article we will see the necessary conditions to be met for immunizing your bond portfolio.
It can be easily said that zero coupon bonds are the first choice solution for immunizing without having a portfolio, if you have a financial obligation of F after a duration of D years, you can buy a zero coupon bond with it's present value P which will pay it's face value F after D years, but assume that zero coupon bonds are not available, in which case you need to invest in a bond portfolio to meet your needs.
For the sake of simplicity, assume that there are two bonds available with
Bond 1: Price = P1 , Duration = D1
Bond 2: Price = P2 , Duration = D2
Consider that you have an obligation F (with a present value of P) after D years which you wish to meet by investing in the above two bonds, then the required conditions for bond portfolio immunization are
Step 1: The duration of the obligation D should be such that
Step 1: The duration of the obligation D should be such that
(The weighted duration of the bonds should be greater than or equal to the duration of the obligation)
Step 2: Compute the present value of the obligation
Where 'm' is the number of coupon periods in an year, λ is the market yield.
Step 3: Buy 'x' shares of Bond 1 and 'y' shares of bond 2 such that
Step 3: Buy 'x' shares of Bond 1 and 'y' shares of bond 2 such that
Therefore based on the above equations, if you have a future obligation F with a present value of P and duration D, you can meet your obligation by investing in 'x' shares of Bond 1 and 'y' shares of Bond 2 subject to the above constraints to protect against changes in yield, the above criteria for bond portfolio immunization can easily be extended to 'n' bonds.
I know it's may not be easy to understand this important concept without an example, we will look into a more practical example on how to immunize a bond portfolio in the next article.
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