FM for Actuaries

Bond Management 279
5. Immunization is the technique to neutralize the interest-rate risk of a business.
Target-date immunization is used when an obligation with a known
amount at a fixed date is to be met. Duration-matching immunization neutralizes
the interest-rate risk of a series of liabilities by a portfolio of bonds.
Redington immunization requires the asset convexity to be larger than the
liability convexity. Full immunization ensures net-worth to be non-negative
under any flat term structure.
6. Traditional duration matching has drawbacks in that it assumes (a) the term
structure is flat, (b) the term structure shifts in a parallel manner, and (c) the
cash flows are fixed.
7. Fisher-Weil duration is a generalization of Macaulay duration. Immunization
strategy assuming parallel shifts to a nonflat term structure may be based on
matching the Fisher-Weil duration.
8. When an asset involves cash flows that are contingent on some random events,
the effective duration may be estimated numerically by evaluating the asset
prices at perturbed interest rates. The computed asset prices should take account
of the embedded options in the asset.
9. Passive bond investment involves tracking the performance of a bond index.
Managers may attempt to achieve higher returns than the index using horizon
analysis, which involves comparing the holding-period yield of the bond
under different forecasts of interest-rate movements.
Exercises
8.1 Calculate the modified duration and convexity of the cash-flow stream as
shown below. Use i =6%.
t
C t
1 0
2 2
3 0
4 4
5 0
6 6