Question

can we say that prices of bonds are equally sensitive to the same percentage increases or decreases of the market interest rate (ytm)? Explain. (i.e. Market interest rates increases, say, from 4% to 6% or decreases from 6% to 4%)

Please explain the impact of coupon amount (say $30 coupon vs. $$85 coupon) on the interest rate sensitivity of a bond. In other words, if the market interest rate changes, which bond's price will change more, the one with the low or high coupon? (assuming other things are identical.)

What is the relationship between the time to maturity and interest rate sensitivity of bonds?

Answer 1

Price of the bonds are sensitive to the increase or decrease of the market interest rate but not equally proportional as the price of the bond also depends on the duration of the bond. Higher the interest rate, the lower will the price of the bond because the bond price gets discounted by the market interest rate.

Lets take an example to get into the concept:-

Assuming the coupon rate at 3% and YTM be 4%

Par Value	1,000
Coupon Rate	3%
YTM bonds	4.00%

Year	Coupon	PV
1	$30.00	$28.85
2	$30.00	$27.74
3	$30.00	$26.67
4	$30.00	$25.64
5	$1,030.00	$846.58
Bond Present Value		$955.48

Assuming the coupon rate at 3% and YTM be 6%

Par Value	1,000
Coupon Rate	3%
YTM bonds	6.00%

Year	Coupon	PV
1	$30.00	$28.30
2	$30.00	$26.70
3	$30.00	$25.19
4	$30.00	$23.76
5	$1,030.00	$769.68
Bond Present Value		$873.63

we can see from the above example that as the YTM increases the bond value decreases simultaneously. The change in the is 50% increase (6%-4%/4%), and the change in bond price be ((955-873.63)/955.48) 8.57%. so the percentage of change also determine on the duration of the bond for which an investor holds it.

The relation between the time to maturity and interest rate sensitivity is directly proportional in nature. As the time to maturity increases the bond price sensitivity increases.