Corporate Finance: Instructor\'s Manual Applied Corporate Finance

Aswath Damodaran 400

Why the coefficient on the regression is duration..

! The duration of a straight bond or loan issued by a company can be written in

terms of the coupons (interest payments) on the bond (loan) and the face

value of the bond to be –

! The duration of a bond measures how much the price of the bond changes for

a unit change in interest rates.

! Holding other factors constant, the duration of a bond will increase with the

maturity of the bond, and decrease with the coupon rate on the bond.

Duration of Bond = ddPr//rP =

t*Coupont

t= 1 (^1 +r)t

t=N

! +N*(F 1 a+cer^ V)Nalue

"

#$$

%

&''

Coupont

t= 1 (^1 +r)t

t=N

! +Fa(c 1 +e^ Vr)aNlue

"

#

$$ %^

&

'' (^)

This is a traditional Macaulay duration. It is a measure of the percentage change

in the bond price for a 1% change in interest rates.

Equivalently, it can be viewed as the maturity of a zero-coupon bond with the

same sensitivity to interest rate changes.

Note, in the regression on the previous page, the coefficient on the change in

interest rates, measures the percentage change in firm value for a 1% change in

interest rates. Thus, the regression coefficient also measures duration.