## Bond Immunization: Duration and Duration Matching

*Duration represents the approximate period—a number of years—required for cash flows from a bond to recoup its listed face value (par value) price.*

- Duration assumes to measure the risk of a bond, since longer duration—more time required for repayment, or longer time without full money recovery from the investment—implies greater risk.
- Based on that assumption, duration measures the sensitivity of bond price to changes in interest rate. Sensitivity here refers to the extent interest rate influences bond price (how much bond price changes due to changes in interest rate).
- Longer bond maturity generally assumes greater bond price sensitivity because of many cash flows to discount. Thus, greater duration assumes greater sensitivity risk to interest rate fluctuations.

** Duration matching**—a type of immunization strategy used to “match” bond duration value with the duration value for future investment liabilities (debt obligations assumed in repayment).

- In other words, assuming a flat interest-rate term structure, duration matching “matches” the
**market value**for the**duration of future obligations**with**bond duration value**by offsetting**both values**to**equal each other.** - Therefore, duration matching serves the purpose of immunizing (equalizing payoff at some specific future date) fluctuating interest rate risks by setting
**bond duration value**to**equal duration value for future obligations**.__Example__:**Asset Market Value = Liability Market Value** - “If you have a 7-year obligation whose present value is $1,000, how would you immunize this obligation against interest rate risk?”

** Answer: **Immunizing interest rate risk with matching duration assumes:

(1) Knowledge of the bond’s duration in a portfolio; and

(2) Adjusting portfolio’s duration to equal investment time horizon.

Here, the facts provide a 7-year duration for a $1,000 present value. To synchronize the portfolio duration with a 7-year obligation, we may immunize by selecting bonds that equal $1,000 in seven years regardless of interest rate. We may achieve this outcome in one of two ways:

- Purchase one
**zero-coupon bond**that equals $1,000 assuming a 7-year yield to maturity; or - Purchase several coupon bonds on the assumption each bond averages a 7-year duration. [i]

Therefore, these two options __might__ immunize the interest rate risk through duration matching—assuming we can synchronize our 7-year obligation with a 7-year YTM bond duration, while simultaneously ensuring 1,000 present value **equals** our expected return.

[i] Morning Star, Inc., “What is Bond Immunization?” p.2, 2015, http://news.morningstar.com/classroom2/course.asp?docId=5397&page=2&CN=com.