Reference no: EM133072502

A bond has the par value $1000. The yield to maturity is 2% anuually. The bond pays $20 coupon annually. The maturity of the bond is 5 years, in the end of which the bond pays back the par value.

(a) What is the price of the bond?

(b) What are the duration and the modified duration of this bond?

(c) If the yield increases from 2% to 2.1%, what is the price change based on modified duration?

(d) What is the actual price change? [Hint, recalculate the price of the bond using 2.1% yield].

(e) Do (c) and (d) differ a lot?

(f) Repeat (c)-(e), assuming that the yield increased from 2% to 4%.

(g) Can you reliably rely on (modified) duration method to estimate price changes when the yield moves a lot? Why? [Hint: Using the fact that modified duration is the first-order derivative of the bond price as a function of the yiled. Combine this with Taylor expansion.]

(h) What are the duration and the modified duration of a 4-year discount bond, assuming a flat term structure (i.e., spot rates are equal to 2% at all matures)?

(i) You can include the 4-year discount bond to your portfolio in order to hedge interest risk. Describe your portfolio composition.

(j) When the yield change from 2.0% to 2.1%, how much does each position in your portfolio change in value? How much does the portfolio change in value?

(k) Realistically, interest rates at different maturities do not move up and down at the same time; and even when they do, they move by different amounts. Now assume that 4-year yield increases from 2% to 2.2% whereas the 5-year yield only increases from 2% to 2.1%. In this scenario, what is the change in value of your portfolio based on modified duration?