Question

We have a bond such that, YTM = 6%, coupon rate = 5%, maturity = 10 years and it pays coupon semiannually. Now suppose YTM goes from 6% to 8%, how the bond price will change?

It will increase by $29.47
		It will increase by $129.47
		It will decrease by $129.47
		It will decrease by $29.47

Answer 1

Suppose the face value of the bond be $1000
Coupon rate is 5%.
As the coupon is paid semiannually, the semiannual coupon payment=Annual coupon payment/2
=(Coupon rate)*(Face value)/2=5%*1000/2=25
Yield to maturity is 6%, for semiannual compounding, the rate will be 6%/2=3%
Time to maturity= 10 years
As the coupon is paid semiannually, the number of periods is 10*2=20

The present value at 6% YTM is $925.61
Similarly, the present value at 8% YTM is $796.15

Change in price=796.15-925.61 =-129.46

Answer: It will decrease by $129.47