Question

18. What is the duration of a 10 year, 4% coupon bond with a 4% YTM (face value=1000)?

if its YTM drops by 0.25%, what happens to the bond’s price?

Answer 1

It is assumed that the frequency of coupon payments is annual.

Duration of the bond is 8.5087 years as shown below:

(Columns related to years 6 through 9 , being identical to earlier ones, are hidden for convenience).

L21 F K L 1 fic =SUM(B21:K21) AB C D E (All amounts in Dollar) 2 Face Value 1000 3 Coupon rate 4% Semiannual interest= B2*B3/F5 = Term (No. of years) 10 5 Frequency Annual No. of times a year (k) 6 Annual Interest Rate(Y) 6% Semiannual discount rate (n)= B6/2 = 40 4 0.03 7 5 8 Cash Flow Period (i) 1 2 3 4 10 Total 9 Interest 40 40 40 40 40 40 10 Redemption 1000 11 Total cash flow (CF) 40 40 40 40 40 1040 12 Present value 13 Formula CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i 14 Cell reference B11/(1+F6)^B8 C11/(1+F6)^C8 D11/(1+F6)^D8 E11/(1+F6)^E8 F11/(1+F6)^F8 G11/(1+F6)^K8 value 38.83495146 37.70383637 36.60566637 35.53948192 34.50435138 773.8576715 1085.302 16 17 Proportion of PV 18 Cell ref B15/L15 C15/L15 D15/L15 E15/L15 F15/L15 K15/L15 19 Value 0.035782621 0.034740409 0.033728552 0.032746167 0.031792396 0.713034392 20 21 Time* proprtion of PV 0.035782621 0.069480818 0.101185657 0.13098467 0.158961978 7.130343916 8.50869 22 Macaulay Duration (Years) =L21/F5= 8.508690304 15

As a general rule, for every drop in YTM by 1%, price will increase by approximately 1% for every year of Duration. Hence, if the YTM drops by 0.25%, price will increase by 2.1272% as follows:

Price change= Duration * Change in YTM= 8.5087 Years *0.25% = 2.1272%