Immunization Using dv01

DV01-based techniques are just as appropriate as duration-based techniques for achiev-

ing immunization. If the duration of the portfolio matches the duration of a zero-coupon

bond with (1) a maturity equal to the horizon date and (2) a price equal to that of the

portfolio, then the DV01of a long position in the portfolio and a short position in the

bond is zero. Maintaining a DV01of zero for this combined position also guarantees

a fixed value portfolio at the horizon date.¹⁴

¹⁴We

can easily extend this analysis to asset-liability management.

Grinblatt1686Titman: Financial	VI. Risk Management	23. Interest Rate Risk	© The McGraw1686Hill
Markets and Corporate		Management	Companies, 2002
Strategy, Second Edition

838Part VIRisk Management

Practical Issues to Consider

Although immunization techniques are widely used in bond portfolio and asset-liability

management, they cannot perfectly guarantee a value at the horizon date. First, trans-

action costs make it prohibitively expensive to continually rebalance the portfolio (or

the assets and liabilities) to maintain the proper duration, which is constantly declin-

ing. For this reason, the necessary rebalancing is done only when the duration match

is off by a critical amount. Second, immunization techniques assume that the term struc-

ture of interest rates is flat. This is rare even in an approximate sense and, when

observed, tends to quickly evolve into upward or (less frequently) downward sloping

or oddly shaped yield curves. In spite of these impediments, immunization seems to

work well in most instances as a risk-reduction tool. As a consequence, it is popular

despite its imperfection.

Contingent Immunization

Contingent immunization is the bond portfolio equivalent of portfolio insurance (which,

as illustrated in Chapter 8, is generally used to insure equity portfolios). Contingent

immunizationsets a target value for the bond portfolio at the horizon date that is

smaller than the face value of a zero-coupon bond with the same market value as the

portfolio. This target value is regarded as a floor below which the future value of the

bond portfolio should not fall. The bond portfolio is managed actively without regard

for duration until its value falls to a critical level. From that point on, an immuniza-

tion strategy is followed. In this sense, immunization is contingent on a decline in the

bond portfolio to a prespecified critical point.

We can regard the critical level in contingent immunization as the market value of

a zero-coupon bond maturing on the horizon date with a face value equal to the floor

value. Hence, this critical value tends to rise over time, although it may fall when inter-

est rates increase.