Hi, I’m just trying to knuckle down a couple of key points. When calculating the safety net on a contingent immunization i’m confused as to which interest rates i need to use when I calc the TV and the PV of the asset and the which rate I need to use to calc the PV of the bond… Is the below correct?
TV = PV(of bond) * (1+x)^n where x=acceptable rate
Then PV of the TV i.e. PV = TV/(1+x)^n where x = immunized rate
Then calc the PV of the bond using the immunized rated…
Where does the new rate come in…i.e. when rates change immediately after…?
Im not clear on the actual question but the immunization rate is the rate in which the PV of the liability matches the PV of the asset.
The X = acceptable rate is the return in which you believe you can achieve in the market
This means the asset will grow from today’s to the future value of said assets amount. This is what you can reasonably expect to have in your possession when the liability comes due.
“Then PV of the TV i.e. PV = TV/(1+x)^n where x = immunized rate”
This is just saying your future asset is worth x today. This 'x' value of worth today should match your of liability. Said differently, this is the amount of liability you can have today which is satisified by your assets.