Question

Consider a 3-year 8% semiannual coupon bond. The YTM of this bond is 6%. Compute the following

a) Macaulay Duration (use  Mac Duration

b) Modified Duration

c) Effective duration (assume a ±50 BP change of Yield)

d) Convexity Factor (use

e) Effective Convexity Factor (assume a ±50 BP change of Yield)

Answer 1

1.Let the coupon face value be 1000

Coupon Rate	8%	8%	8%	8%	8%	8%
Maturity Period	6 months	1 year	1.5 year	2 year	2.5 year	3 year
Discount Factor	0.9615	0.9246	0.8890	0.8548	0.8219	0.7903
Cash flow	40	40	40	40	40	1040
Present value of cashflows	38.46154	73.9645	106.68	136.7687	164.3854	4931.563
current bond price	5451.82
bond value		1000
macauley duration	5.45182

discount factor = 1/(1+r)ⁿ

2.

The modified duration formula is:

Modified Duration=Macauley Duration/1+(YTM/n)

where n =number of coupons period per year

=5.45/[1+6/2)]

=5.45/4

=1.3625 years

3