Question

A 5-year, $1,000 face bond with a 3% coupon is currently selling with a 4% YTM (yield to maturity). What is the purchase price of the bond?

Immediately after you purchase the bond, the reinvestment rate in the market drops to 3%. What is your realized yield on your bond investment?

What is the duration of the bond in Question?

If market yields were to drop by 1%, what is the approximate percentage change in price you would expect, based on the bond’s duration?

How long should you hold the bond, if you want to earn the 4% YTM that you thought you would get when you bought the bond?

Assume that market yields rise by 40 basis points. What do you expect to happen to the bond’s price, using modified duration?

Answer 1

1.
Price of the bond=Present value of cash flows=3%*1000/4%*(1-1/1.04^5)+1000/1.04^5=955.4817767

2.

=((3%*1000/3%*(1.03^5-1)+1000)/955.4817767)^(1/5)-1
=3.9424%

3.

Duration=(1*3%*1000/1.04+2*3%*1000/1.04^2+3*3%*1000/1.04^3+4*3%*1000/1.04^4+5*3%*1000/1.04^5+5*1000/1.04^5)/955.4817767
=4.709488356

4.
=-Modified Duration*change in yields
=-Macaulay Duration/(1+ytm)*change in yield
=-4.709488356/1.04*(-1%)

=4.5284%

5.

5 years i.e., till maturity

6.

=-4.709488356/1.04*(0.40%)

=-1.8113%

Price falls by 1.8113%