Immunization is one of the more difficult topics in the curriculum (in my opinion). There are a couple of terms/intricacies that have sort of confused me. Perhaps somebody can help me out point by point or summarize the different issues in a paragraph. Barbell vs. bullet portfolios: Please describe both if possible and explain whether the bullets or barbells have more reinvestment risk. I read in one place that barbells have higher reinvestment risk and in another place that bullets have higher reinvestment risk. Not sure which is right. I would assume that since barbell portfolios have bonds with higher durations (which have higher interest rate sensitivity) and greater possibility of declining interest rates then they would have greater reinvestment risk. Matching the horizon vs. around the horizon: I don’t really understand what the horizon date refers to. Is it the date at which a liability/bond matures? And in which context would we match the horizon vs. around the horizon? Would we match the horizon of a bullet portfolio because it has lower convexity adjustments and around the horizon dates for barbell portfolios because they have higher convexity adjustments (and therefore less accuracy when immunizing)? Sorry for the wordiness, but I just want to put immunization to bed.
Immunization means that your goal is to “immunize” your bond portfolio to changes in the yield curve. This is done by making sure the duration of your assets matches the duration of your liabilities. Thus when the yield curve shifts, the value of your assets moves by the same amount as your liabilities. A perfectly immunized portfolio would consist of zero-coupon bonds maturing at the exact time that liabilities are due and with a face value equal to each liability payment. A barbell portfolio would be exposed to more reinvestment risk than a bullet portfolio because the shorter duration bond would mature and have to be reinvested at the prevailing interest rate.
So what is the best way to handle reinvestment risk? Do you invest in bonds with the same duration as the reinvested bond at prevailing interest rates or is there a way to handle the reinvestment risk at the onset without having to reinvest your bonds when the short term bond (liability) matures. Is the best strategy to invest in two bonds with durations in between that of the short term and long term bonds in the barbell right away and then forget about it?
zero coupon bond with the same maturity as liability eliminates reinvestment risk, and therefore, immunization risk. The catch with barbell and bullet is this: as bullet cash flow moves away from the liability maturity and as barbell moves closer, bullet will not be such a great way to reduce reinvestment risk while barbell would be the better choice. Essentially, both strategies can be used to reduce immunization risk, all depending all the maturity date of the bonds used…
Just to add, you want to minimize maturity variance (M squared)
phBOOM Wrote: ------------------------------------------------------- > Just to add, you want to minimize maturity > variance (M squared) Not to be confused with the M squared measure in equity management that is the RFR + the Sharpe Ratio * Std Dev of the Mkt Index. 
Dwight Wrote: ------------------------------------------------------- > phBOOM Wrote: > -------------------------------------------------- > ----- > > Just to add, you want to minimize maturity > > variance (M squared) > > > Not to be confused with the M squared measure in > equity management that is the RFR + the Sharpe > Ratio * Std Dev of the Mkt Index. > > right.