FM for Actuaries

Bond Management 251
To use the modified duration as a measure of the sensitivity of the price of the
investment with respect to the rate of interest, note that if the modified duration is
expressed in terms of the number of payment periods, then the interest rate quoted
must also be per payment period. Thus, in the above example, the value of the
bond drops by 3.7920% per 1 percentage point increase (not percentage increase)
in the rate of interest per half-year. Alternatively, we can state that the bond drops
by 1.896% in value per 1 percentage point increase in the rate of interest per year.
Excel provides the function DURATION to compute the Macaulay duration and
the function MDURATION to compute the modified duration of a bond. The bond
is assumed to be redeemable at par. The specifications of these functions are given
as follows:
Excel functions: DURATION/MDURATION (smt,mty,crt,yld,frq,basis)
smt = settlement date
mty = maturity date
crt = coupon rate of interest per annum
yld = annualized bond yield
frq = number of coupon payments per year
basis = day count, 30/360 if omitted (or set to 0) and actual/actual if set to 1
Output = Macaulay/modified duration of the bond in years
Exhibit 8.1 illustrates the use of the DURATION and MDURATION functions to
compute the answers for Examples 8.1 through 8.4. Note that we have arbitrarily
fixed the settlement date as January 1, 2001, and the maturity date is then entered
based on the given time to maturity of the bond.
Exhibit 8.1:
Use of DURATION and MDURATION