Question

a. What is the convexity of a 10 year bond with a coupon of 6% and a yield of 7.82%?

b. For the 11th coupon, what is the present value times t times t+1?

c. A bond has a MD of 6.50 years and trades at a price of 118.08. The YTM is 3.40%. Its CX factor is 50.68. Using MD and CX, what is the new price when the YTM increases to 5.1%?

Answer 1

Convexity is like a companion to the bond holder. We know that, when the yield in the market of a bond increases the bond price decreases but when the yield decreases the bond price increases. But due to convexity, the increase in yield will have a lesser impact on the decrease in bond price whereas the decrease in yield will have a greater impact on the increase in the bond price.  

By formulae, Convexity = (V-+V+-2V0)/2*V0*deltaY2  

where V-= value of the bond when the yield is decreased, V+= value of the bond when the yield is increased, V0= value of the bond at the given yield and Y= the % increase or decrease in bond yield (in the below example taken at 1%)

We have to assume the Face Value of the bond to be $1000. The following will give us a clear idea about the convexity of the bond. The calculation of convexity is done for better understanding.