Question

# A Treasury bond that settles on October 18, 2016, matures on March 30, 2035. The coupon...

A Treasury bond that settles on October 18, 2016, matures on March 30, 2035. The coupon rate is 5.55 percent and the bond has a yield to maturity of 4.80 percent. What are the Macaulay duration and modified duration?

Macaulay duration:

Modified duration:

Solution.>

The Macaulay duration can be calculated by using excel formla =DURATION (settlement, maturity, coupon, yld, freq)

where:

settlement - Settlement date of the security, maturity - Maturity date of the security, coupon - The security's annual coupon rate, yld - The security's annual yield, freq - Number of coupon payments per year (annual = 1, semi-annual = 2, quarterly = 4).

 Particular Date/Value Settlement Date(s) 18-10-2016 Maturity Date(m) 30-03-2035 Coupon(c) 5.5% Yield(y) 4.8% Frequency(f) 1 Macaulay Duration is calculated as Macaulay Duration 11.99 =DURATION(s,m,c,y,f)

Macaulay duration = 11.99

Modified Duration = Macaulay duration/ (1+YTM)

= 11.99/1+4.8%

= 11.44

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