DURATION Chapter 25 Duration is a measure of

DURATION (Chapter 25) • Duration is a measure of the sensitivity of the price of a bond to changes in the interest rate • Risk measure. • Consider a bond with payments Ci: the first n-1 are interest payments, the last one is the last interest payment + repayment of the principal • Macauley Duration (flat term structure)

DURATION • DURATION(settlement; maturity; coupon; yield; frequency; basis) • Important: For the dates, use the function DATE(year; month; day) • Settlement: purchase date. • maturity of the bond. • coupon nominal interest rate for the coupon. • Yield (annual basis) • Frequency (number of coupon payments per year) • Basis (day count basis, default 30/360)

• DATES: • Are serial numbers • 1 January 1900 / 1 January 1904

Modified duration:

Modified duration: Elasticity of the price to the interest rate: Volatility of the price:

MDURATION • MDURATION(settlement; maturity; coupon; yield; frequency; basis) • Duration/(1+r)

Immunization strategies • If a portfolio has the same payoff at some specific future date no matter what interest rate structure prevail, then it is said to be immunized. • Present value of the obligations: V 0 • Present value of the assets: VB

Immunization strategies • If the duration of the asset equals the duration of the obligation. • An obligation against which an asset of that type is held is said to be immunized • Immunization applies only to a first order approximation