Question

Below are details of a semiannual bond.

Par value = 1000; Maturity 4 years; Market rate if interest (yield to Maturity) = 11% per annum; Coupon rate = 8% per year paid semiannually. Show steps in finding all three of the parameters below:

1. Find the Duration, modified duration, and Convexity of the bond.

Answer 1

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Answer:

Given that coupon rate = 8%

Semiannual payments = 80/2 = 40

PV of the bond is the discounting of cashflows at 11%

= 40/(1+11%/2)^1+40/(1+11%/2)^2+40/(1+11%/2)^3+..........+40/(1+11%/2)^7+1040/(1+11%/2)^8

=904.98

Duration = (40*1/(1+11%/2)^1+40*2/(1+11%/2)^2+40*3/(1+11%/2)^3+40*4/(1+11%/2)^4+40*5/(1+11%/2)^5+40*6/(1+11%/2)^6+40*7/(1+11%/2)^7+1040*8/(1+11%/2)^8)/904.98 = 6.94

Modified duration is chaneg in price of bond for an increase and decrease in 1%

Lets assume yield to maturity = 12%

Price of bond(P-) = $ 875.80

for YTM = 10%

Price of bond(P+) = $ 935.37

Modified Duration = P+ - P-/(2*0.01*P) = (935.37-875.80)/(2*0.01*904.98) = 3.291

Convexity =

=> (935.37+875.80-2*904.98)/(2*0.01^2*904.98) = 6.685