FIN701 Financial Institutions Management
CHAPTER 9 Interest Rate Risk II
INTRODUCTION
Book value accounting – assets and liabilities of FI recorded at historic values
Market value accounting – assets and liabilities of FI revalued according to current level of interest rates
Marking to market – valuing securities at current market price
DURATION: A SIMPLE INTRODUCTION
Duration is a more complete measure of asset’s or liability’s interest rate sensitivity than maturity because it takes into
account time of arrival (or payment) of all cash flows and maturity
Duration – weighted-average time to maturity on an investment
o On time value of money basis, measure period of time required to recover initial investment on the loan
After that time, the FI earns a profit, or return, on the loan
When cash flows are limited to one payment at the end of the period with no intervening cash flows, duration equals
maturity
A GENERAL FORMULA FOR DURATION
Calculate duration (or Macaulay’s duration) for any fixed-income security that pays interest annually
( )
Assumes that yield curve or term structure of interest rates is flat and that when rates change, yield curve shifts in parallel
fashion and assumes no default risk
The Duration of a Zero-Coupon Bond
Bonds sell at a discount from face value on issue, pay face value on maturity, and have no intervening cash flows between
issue and maturity
Because there are no intervening cash flows, duration of zero-coupon bond equals its maturity ( )
The Duration of a Consol Bond (Perpetuities)
Consol bond – bond that pays fixed coupon each year forever
o Feature of this bond is that it never matures
While maturity is infinite, duration is finite to recover initial investment
FEATURES OF DURATION
Features of duration
o Duration increases with maturity of fixed-income asset or liability, but at decreasing rate
o Duration decreases as yield on a security increases
Higher yields discount later cash flows more heavily and relative importance, or weights, of those later
cash flows decline when compared with earlier cash flows on asset or liability
o Duration decreases as coupon or interest payment increases
Larger coupons or promised interest payments means cash flows are received more quickly and the
higher are the present value weights of those cash flows in duration calculation
THE ECONOMIC MEANING OF DURATION
Duration is a direct measure of the interest rate sensitivity, or elasticity, of an asset or liability
o The larger the numerical value of C, the more sensitive the price is to changes or shocks in interest rates
Taking the derivative of the bond’s price (P) with respect to yield to matur

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