Question

Consider the following bond:

US Gov't Strip (Zero) Bond due May 15, 2029 trading at a YTM of 0.718%. Assume a settlement date of May 22nd, 2020.

Face value = 100$

Calculate the bond's Macaulay Duration, Modified Duration and the Convexity Measure. Note, you must calculate the full market price of each bond to arrive at the duration and convexity figures (do not back out accrued interest).

Assume that for the US treasury bonds the actual/actual day count convention applies. For the actual/actual day count convention use the actual days in the 6 month period for the denominator (for example: 181 days).

Answer 1

Year to maturity = 9 years

Macaulay duration of a zero coupon bond is always equlas to it's maturity period.

Hence Macaulay duration = 9 years

Modified duration (MD) = Macaulay duration/ 1+YTM

= 9/(1+.718%)

= 8.94

Explanation: bond duration is 8.94 means if interest rate increases by 1% then bond price will fall by 8.94 or vice versa.

Current price (P0) = 100

Price if inst.rate increase by 1% (P+) = 91.06

Price if inst. fall by 1%(P-) = 108.94

Bond convexity=

( P+) +(P-) - 2P0/(2P0* (CHANGE IN INST.) ^2