Question

I have a portfolio of bond and I know a 10% increase in the interest rate will cause a 2% decrease in the value of the bond portfolio. Also, I know that a 10% decrease in the interest rate will cause a 4 % increase in the value of the portfolio.

a) What is your approximation for the modified duration and convexity of the portfolio?

b) What will be the change in your answers if the decrease and increase are 4% and 2% for the same amount of change in the interest rate?

Answer 1

a)

Let the par value of the bond (V0)) be 100

Value of the bond when interest increase by 10% (V+) = 98

Value of the bond when interest decrease by 10% (V-) = 104

Approx Mod duration = (V- - V+) / ( 2* V0 * interest change )

= ( 104 - 98 ) / (2*100 * 0.1)

= 0.3

Approx convexity = (V- + V+ - 2*V0) / ( V0 * interest change^2 )

= (104+98- 200) / (100*0.1^2)

= 2 / 1

= 2

b)

Similarly,if the decrease and increase are 4% and 2% for the same amount of change in the interest rate

Approx Mod duration = (V- - V+) / ( 2* V0 * interest change )

= ( 102 - 96 ) / (2*100 * 0.1)

= 0.3

Approx convexity = (V- + V+ - 2*V0) / ( V0 * interest change^2 )

= (102+96- 200) / (100*0.1^2)

= -2 / 1

= -2