Question

Details of a semiannual bond:

Par value = 1000

Maturity = 4 years

Yield to Maturity = 11% per annum

Coupon Rate = 8% per year paid semiannually

Find the duration, modified duration, and convexity of the bond.

Answer 1

Semiannual coupon = 8%*1000/2 = 40

Price of bond = 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

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