Consider a bond whose annual coupon rate is 10% and coupons are paid twice a year evenly. Its face-value is $100,000 and maturity is 2 years. Yield-to-maturity is 10% (annual) (fixed). What are the duration (in years) and convexity of the bond?
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =2x2 |
Bond Price =∑ [(10*100000/200)/(1 + 10/200)^k] + 100000/(1 + 10/200)^2x2 |
k=1 |
Bond Price = 100000 |
Period | Cash Flow | Discounting factor | PV Cash Flow | Duration Calc | Convexity Calc |
0 | ($100,000.00) | =(1+YTM/number of coupon payments in the year)^period | =cashflow/discounting factor | =PV cashflow*period | =duration calc*(1+period)/(1+YTM/N)^2 |
1 | 5,000.00 | 1.05 | 4,761.90 | 4,761.90 | 8,638.38 |
2 | 5,000.00 | 1.10 | 4,535.15 | 9,070.29 | 24,681.07 |
3 | 5,000.00 | 1.16 | 4,319.19 | 12,957.56 | 47,011.57 |
4 | 105,000.00 | 1.22 | 86,383.76 | 345,535.04 | 1,567,052.33 |
Total | 372,324.80 | 1,647,383.35 |
Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year) |
=372324.8/(100000*2) |
=1.861624 |
Modified duration = Macaulay duration/(1+YTM) |
=1.86/(1+0.1) |
=1.772975 |
Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2) |
=1647383.35/(100000*2^2) |
=4.12 |
Consider a bond whose annual coupon rate is 10% and coupons are paid twice a year...
Consider a bond whose annual coupon rate is 10% and coupons are paid twice a year evenly. Its face-value is $100,000 and maturity is 2 years. Yield-to-maturity is 10% (annual) (fixed). What are the duration (in years) and convexity of the bond?
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