Immunizing with coupon-bearing bonds entails continuously matching the portfolio Macaulay duration with the Macaulay duration of the zero-coupon bond over time and as the yield curve shifts, even though the zero-coupon bond could be hypothetical and not exist in reality. Also, the bond portfolio’s initial market value has to match or exceed the present value of the zero-coupon bond. The Macaulay duration of that, perhaps hypothetical, zero-coupon bond always matches the investment horizon. Immunization will be achieved if any ensuing change in the cash flow yield on the bond portfolio is equal to the change in the yield to maturity on the zero-coupon bond. That equivalence will ensure that the change in the bond portfolio’s market value is close to the change in the market value of the zero-coupon bond. Therefore, at the end of the six-year investment horizon, the bond portfolio’s market value should meet or exceed the face value of the zero-coupon bond, regardless of the path for interest rates over the six years.
Can someone please explain what is the logic of Interest Rate Immunization as Zero Replication?
Why the bond portfolio’s initial market value has to match or exceed the present value of the zero-coupon bond?
Why i__mmunization will be achieved if any ensuing change in the cash flow yield on the bond portfolio is equal to the change in the yield to maturity on the zero-coupon bond?
when interest rates change 2 things happen with a Bond Portfolio…
interest rate increases - coupon payments increase - but the terminal value of the portfolio falls.
When rates drop - coupon payments drop - but terminal value increases.
With immunization you are trying to ensure that the decrease of one stream (interest rate payments when rates drop or final balloon payment) matches or offsets the increase in the other stream.
If you had a zero coupon bond - there is NO coupon over the life of the portfolio - and you are ensuring you receive the face value at the portfolio horizon. And there is absolutely no variation in your expectations from the portfolio (you get what you wanted to get) - and by immunization you are trying to get to the same spot… hence the “zero replication - you are trying to replicate the returns of a zero coupon bond portfolio”.
============================
You are setting up the portfolio to meet some liability stream. So to ensure you get what you want - you need to exceed the present value of the zero coupon bond - so you have that much amount of money - whether rates increase or drop during your portfolio’s life.
But why the bond portfolio’s initial market value has to match or exceed the present value of the zero-coupon bond? Is this because at the end of investment horizon, market value of the bond portfolio can exceed the face value of zero coupon bond, in order to meet liability?
And why immunization will be achieved if any ensuing change in the cash flow yield on the bond portfolio is equal to the change in the yield to maturity on the zero-coupon bond?
you want to set up the portfolio to meet the ultimate liability. You have a Liability to meet in N years. You can do it two ways – agree to buy a Zero Coupon Bond today that meets that liability - or else buy a coupon paying bond. With a Coupon PAying Bond - you have to deal with the ups and downs caused by interest rate fluctuations … which cannot be avoided. In order to give yourself a cushion - you need to get into buying a Bond Portfolio that is a little bigger than the liability - so that if interest rates go against you - you are still covered.
In all this - you are trying to ensure that Price Return = Coupon (Interest) Return. This is the entire function of immunization.