1. Suppose that you’re given a 10-year 6.8%-coupon bond with $1,000 face value that pays the semi-annual coupon payments, the bond price in the market is $879 per bond, answer the following questions:
a) What is the yield to maturity? What is the idea of yield to maturity? Is this the same as holding period return?
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 0.05% now, what will be the change of bond price?
d) Suppose you’re considering the other 5-year 6.6%-coupon bond with $1,000 face value that pays the semi-annual payments, the bond price is $782 per bond in the market. 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.
e) What are the limitations in using duration and convexity to analyze the interest rate risk for the fixed income portfolio?
2. Suppose you own a bank that consists of both bonds in question 2. You have 3050 bonds in the 6.8%-coupon bonds as interest-sensitive assets, and 3000 bonds in the bonds of 2 d) as interest-sensitive liabilities. Answer the following questions;
a) What is the duration and convexity of your bond portfolio? What assumption do you apply for these measurements of interest rate risk?
b) What is the duration GAP for your bank?
c) What is the change of Economic Value of Equity (EVE) for the bank if the interest rate increases with 0.15%?
d) What are the assumptions for analysis in using change of EVE to measure interest rate risk?