Question

3. Suppose that you’re given a 8-year 7.2%-coupon bond with $1,000 face value that pays the semi-annual coupon payments, the bond price in the market is $886 per bond, answer the following questions:

a) What is the yield to maturity? What is the idea of yield to maturity? Explain the difference between your bond’s yield to maturity versus the term structure of interest rates.

b) Suppose you are about to apply the immunization strategy for the bond portfolio what is the optimal holding period for the bond portfolio? What are the limitations of the immunization strategy?

c) What is the convexity of a bond? Suppose the interest rate is about to change 4 basis points, what will be the change of bond price?

d) Suppose you’re considering the other 8-year 10%-coupon bond with $1,000 face value that pays the semi-annual payments, the bond price is $682 per bond in the market. What is the duration of this bond given that the interest rate is to change 4 basis points?

e) Is this bond subject to higher convexity or not following the same interest rate change in c)? Which bond is better in your perspective to immunize the interest rate risk? Graph your result to show their differences in convexity.

f) What are the limitations in using duration and convexity to analyze the interest rate risk for the fixed income portfolio?

Answer 1

a)Yeild to maturity= i+(f-p)/n

---------------

(f+p)/2

= [36+(1000-886)/16]÷(1000+886)/2

=4.57%i.e 9.14% pa

Yeild to maturity is bonds IRR.

Term structure is a relationship between spot rates and maturity and spot rate refers to the Ytm of zero coupon bond.

b)Optimal holding period of bond portfolio is its duration.

Duration=(current yeild/Ytm)×pvaf of Ytm×Ytm factor+1-(current yeild/ Ytm)

=[(36/886)×100]÷4.57×11.1772×1.0457+(1-.8891)

=10.5 half years or 5.25 years

c)Convexity= duration/periodic Ytm factor

5.25/1.0457= 5.02%

If interest rate will change by 4 basis point then the price will change by 5.02×.04 =20.08% in opposite direction.