Question

Consider a 2-year coupon bond that pays coupon annually with a coupon rate of 3%, face value $1000, a yield to maturity of 4%.

(a) What is the approximated bond price estimated by both duration and convexity if the yield is increased by 0.5%?

(b) Suppose you purchased 1 unit of the above coupon bond mentioned above and is worried if the interest rate will increase. You are considering taking short position on a zero coupon bond. The zero coupon bond has a maturity of 2 years, face value of 1000 and a yield to maturity of 3.5%. How many zero coupon bonds do you need to short to match the duration?

Answer 1

1.
Convexity=((1^2+1)*1000*3%/1.04+(2^2+2)*(1000*3%+1000)/1.04^2)/981.1390533*1/1.04^2=5.438606958

Duration=(1*1000*3%/1.04+2*(1000*3%+1000)/1.04^2)/981.1390533=1.970599321

Approximate bond price=981.1390533*(1-1.970599321/1.04*0.5%+5.438606958*(0.5%)^2*0.5)=971.9104077

2.
=((1.970599321/1.04)*981.1390533)/((2/1.035)*1000/1.035^2)
=1.030591618