Can someone explain the resaon why a bullet portfolio consisting of a single coupon bond must mature after the investment horizon for it to be immunized against the effect of a parallel shift in the yeild curve. Additionally what benefit is this strategy when the liability matures before the bond?
The portfolio to be immunized has only one coupon bond?
Perhaps to eliminate re-investment risk. If the liability matures before you need to figure out a way to re-invest.
I’m assuming it’s in case you have a downward parallel shift in the Yield curve, and therefore since your bond has a higher duration than your liability it’s price will appreciate more than your liability plus you have a higher coupon rate than would be offered currently in the mkt after the shift. If you had an increase in rates you could either sell the bond and buy a new one at teh higher rate or just reinvest your coupons at that higher rate.
To immunize yourself against a parallel shift in the yield curve, you want the duration of your liabilities to equal the duration of your portfolio. Any bond that has a coupon will have a shorter duration than it’s time remaining to maturity. Therefore, for a bond to have the same duration as a given liability, it must mature after the liability “matures”.
A related question: when they mention duration, w/o qualifying it, do they mean Mac. Duration or Modified Duration? When you say that duration of liabilities & assets match, you mean that the cash flows from the assets be available when liabilities are due. To me, this sounds like Mac. Duration. If it were Modified, then an increase in interest rates will reduce the value of the assets, but the liability remains the same (what you promised investors). So, it cannot be that modified duration of assets equals modified duration of liabilities?
I think they mean something like “interest rate sensitivity” and you can calculate it using either modified duration, effective duration, MacCauley, etc…