Question

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

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)

Homework Answers

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

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