1. Immunization Riccardo Colacito

2. Uses of Duration • Summary measure of length or effective maturity for a portfolio • Measure of price sensitivity for changes in interest rate • Immunization of interest rate risk

3. Example • An insurance company issues a Guaranteed Investment Contract (GIC) for $10,000. • The GIC has a maturity of 5 years • The GIC guarantees an interest rate of 8% per year (i.e. $14,693.28 at maturity)

4. The strategy • Suppose that the insurance company funds its obligation with a • 6 years bond • Selling at par value equal to $10,000 • Carrying an 8% annual coupon • Will this protect the insurance company from interest rate risk?

5. If the market interest rate does not change: yes! • The bank can reinvest coupon payments at 8% • In year 5 the bond will still sell at par

6. What if market interest rate increases or decreases? • In this case the insurance company can always repay its obligation

7. Graphically

8. Is this always the case? • Suppose that coupon rate is 4.0981% instead of 8%

9. Graphically Price benefit dominates reinvestment risk Price risk dominates reinvestment benefits

10. A higher coupon rate • Suppose that coupon rate is 11.7195% instead of 8%

11. Condition for immunization • For a horizon equal to the portfolio’s duration, price risk and reinvestment risk exactly cancel out • In other words, the insurance company should construct a portfolio whose duration equals the time of the promised payoff.

12. In our example

13. An equivalent definition for immunization • A strategy that matches the durations of assets and liabilities, thereby minimizing the impact of interest rates on the net worth.

14. Real life examples • Large banks must protect their current net worth • Pension funds have the obligation of payments after a number of years. • These institutions are both concerned about protecting the future value of their portfolios and therefore have the problem of dealing with uncertain future interest rates. • By using an immunization technique, large institutions can protect (immunize) their firm from exposure to interest rate fluctuations. • A perfect immunization strategy establishes a virtually zero-risk profile in which interest rate movements have no impact on the value of a firm.

15. Rebalancing • Every year the duration of the bond portfolio changes simply because the maturity changes. • Portfolio manager must rebalance in such a way that duration still matches investment horizon.

16. Example • Insurance company must finance this obligation • Payment of $19,487 • Horizon is 7 years • Interest rate is 10% per year • Hence present value of the obligation is $10,000 • Fund the obligation with • Three year zero coupon bond and • Perpetuities paying annual coupons of 10%

17. Matching duration and horizon at date zero • Calculate durations of underlying assets • Pick portfolio weights in such a way that portfolio duration equals horizon

18. Matching duration and horizon after one year • Calculate durations of underlying assets • Pick portfolio weights in such a way that portfolio duration equals horizon

19. Questions • How many dollars are invested in the zero coupon bond and in the annuity at time zero? • How much after 1 year? Answer: Time 0: $5,000 in each security Time 1: $6,111.11 in zero and $4888.88 in annuity

20. Contingent Immunization • Allow the managers to actively manage until the bond portfolio falls to a threshold level • Once the threshold value is hit the manager must then immunize the portfolio • Active with a floor loss level

21. Figure 10-8 Contingent Immunization

22. Active Bond Management: Swapping Strategies • Substitution swap: exchange of a bond for a bond with similar attributes but more attractively priced • Intermarket swap: switching from one segment of the bond market to another • Rate anticipation swap: a switch made in response to forecasts of interest rate changes • Pure yield pickup: moving to higher yield bond, usually with longer maturities • Tax swap: swapping two similar bonds tp receive a tax benefit