Question

Consider the 2-year, 1000 USD T-note with a coupon rate of 4.5% and a YTM of 1.42% If the YTM increases from 1.42% to 1.5%, by approximately how much does the bond price fall (in percent)?

Answer 1

Case 1- When YTM-1.42%

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=2

r-YTM-1.42%

Face value =1000

Coupon payment=Coupon rate*face value=4.5%*1000=45

Putting values in formula

Price of bond=45*((1-(1/(1+.0142)^2))/.0142)+1000/(1+.0142)^2

=1060.31

Case 2- YTM-1.5%

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=2

r-YTM-1.5%

Face value =1000

Coupon payment=Coupon rate*face value=4.5%*1000=45

Putting values in formula

Price of bond=45*((1-(1/(1+.015)^2))/.015)+1000/(1+.015)^2

=1058.68

Therefore change in price of bond=(1058.68/1060.31-1)*100=-.00154

=.154%(Fall in price of bond)

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