Investment

Chapter 18 – Problem 5

A bond for the Chelle Corporation has the following characteristics :

Maturity – 12 years, Coupon – 10%, Yield to maturity – 9.5%, Macaulay duration – 5.7 years, Conxevity – 48, Noncallable

a. Calculate the approximate price change for this bond using only its duration, assuming its yield to maturity increased by 150 basis points. Discuss (without calculation) the impact when you include the convexity effect.

b. Calculate the approximate price change for this bond (using only its duration) if its yield to maturity declined by 300 basis points. Discuss (without calculation) what would happen to your estimate of the price change if this was a callable point.

Answers :

Step 1 of 6

a) Computation of approximate price change (using only its duration ) assuming its YTM increased by 150 basic points:

Given data are :

Period (n) = 12 years

Cash flows = $100

i = 9.5%

Dmod = 5.7 years

Convexity = 48

For finding the approximate price changes, we we have to find the current price of the bond.

The current price of the bond can be computed as below:

Bond Price = $100 x PVIFA (9.5%. 12Periods) + $1000 x PVIFA (9.5%. 12Periods)

= $100 x 6.983 + $1000 x 2.97

= $ 1034.92

Step 2 of 6

The estimated percentage change in the price of the bond can be computed by using the formula :

% ∆P = - Dmod x ∆i

Where,

Dmod = the modified duration of the bond.

∆ i = the yield change in the basic points divided by 100.

Substitusing the variables in the above formula, we get:

= (5.70) x +150

100

= (5.70) x 1.50

= (8.55)

This indicates the bond price should decrease by approximately 8.55% in response to the 150 basis points increase in the YTM.

After the change, the bond price would be changed to:

= 1+(-0.0855)) x Existing Bond Price

= 0.9145 x Existing Bond...