Question

Using excel, illustrate and check the following observations on bonds and interest rate sensitivity.

You can use any set of a given bond's characteristics of your choosing.

1. Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds.

2. Bond prices' sensitivity to changes in yields increases at a decreasing rate as maturity increases.

3. Interest rate risk is inversely related to the bond's coupon rate. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds.

4. The sensitivity of a bond's price to a change in its yield to maturity is inversely related to the yield to maturity at which the bond is currently selling.

You can make up the excel macros.

Answer 1

Bond prices are sensitive to changes in Interest rates, they are inversely related to the interest rates. The intensity of the price sensitivity depends on bonds maturity and coupon rate. The longer the maturity of bond the higher its sensitivity to the interest rate change.Similarly the price of bond with low coupon rate will be more sensitive to the interest rate change.

Let us considered two bonds with 5 yrs Maturity. The first one with 8.5% rate bond of Rs 1000 face value, and current market value of Rs 954.74 and YTM of 10%. The second one with 11.5% rate bond of Rs 1000 face value and current market value 1044.57 and YTM is 10.6%.

	8.5% Bond
Year	Cash Flow	Present Value @ 10%	Proportn of Bond Price	Poportion of Bond       Price * Time
1	85	77.27	0.082	0.082
2	85	70.25	0.074	0.149
3	85	63.86	0.068	0.203
4	85	58.06	0.062	0.246
5	1085	673.7	0.714	3.572
		943.14	1	4.252

	11.5% Bond
Year	Cash Flow	Present Value @ 10%	Proportn of Bond Price	Poportion of Bond       Price * Time
1	115	103.98	0.101	0.101
2	115	94.01	0.091	0.182
3	115	85	0.082	0.247
4	115	76.86	0.074	0.297
5	1115	673.75	0.652	3.259
		1033.6	1	4.086

Volatility of bond=Duration/(1+YTM)

Volatility of 8.5% Bond=4.252/(1.100)=3.87

Volatility of 11.5% Bond=4.086/(1.106)=3.69

The 8.5% Bond has higher volatilty. If YTM increase b y 1% this will result in 3.87% decrease in the price of 8.5% bond in respect to 3.69% decrease of 11.5% bond.