Fixed Income Duration & its relationship with yield change

Hello,

Please help me to understand the below-mentioned relationship.

Option Free Bonds
D increases as r declines
C is always positive

Callable Bonds
D first increases and then decreases as r declines
C is first positive and then negative

Putable Bonds
D increases as r declines
C is always positive and can exceed the C of an OFB

What, exactly, don’t you understand about them? Everything you’ve written is correct.

(Note: it’s Fixed Income, not Fixed Asset; I’ve corrected the title of your thread. Fixed assets are PP&E: buildings, machinery, tools, vehicles, and so on.)

Thank you for correcting it.

If rate declines value increase then further I am not able to connect it to duration. My understanding says if value increase then duration has to decrease because now he will get the value early because of price effect.

I understand duration is time weighted present value of cashflows and it is less than the maturity in coupon bearing bond compared to zero coupon bond.