SIR i have two questions..
(1st highlight) – The pv01 for asset & liab is not same.. there is a bit of difference, even though the solution says its matching (only The money duration is exactly matching). SO IS THIS AMT OF DIFFERENCE in PV01 BE CONSIDERED SAME?
(2nd highlight) – due to difference in convexity, when rates are rising, assets having lower convexity, will fall more than the liabilities with higher convexity. So in essence, liabilities will fall (change) less due to its higher convexity. BUT IN SOLUTION IT SAY THAT THE CHANGE IN LIABILITIES WILL BE MORE??? HOW COME??
Firstly for immunization the money duration of liability portfolio should match the money duration of asset portfolio not the pv01’s. That is for a parallel change the asset and liab should move by same amount. Which is exactly the case here if yield curve shifts by 1% both the asset and liab portfolio would fall by same amount.
Whereas a non parallel shift is expected here to immunize which the convexity of the asset portfolio should be just higher or equal to the convexity of the liability portfolio so that the dispersion is minimal.
Convexity is the unique property that reduces the fall in the bond prices when the yields rises in a non parallel fashion (think of gamma in derivatives). Given a higher convexity for liabilities, the liability porfolio would fall by a lower amount compared to the asset portfolio thereby adding to the underfunded status of the plan.
On the contrary if the convexity of assets was just higher or equal to the convexity of the liability the immunization would have been effective.
hi. yes i understood your expalnation. But my qs was regarding what the solution states regarding..
1) PV01 being same (but pv01 is not same.. thre is a difference in numbers in the table) &
2) Liabilities falling by a Higher Amt as mentioned in the solution?? (You menationed that liabilities will fall less due to higher convexity.. which i agree. But why is the solution saying that liability will fall more?) can you pls explain that.
or do you mean the solution is wrong?