Hello, Can someone please help me understanding the last sentence of this text from schweser ?
« For a large parallel increase in the curve , the immediate decrease in portfolio value will be less than the decrease in the PVL due to the positive convexity effect. With the parallel increase, the new portfolio IRR will increase by basically the same amount as the increase in discount rate for the PVL. In other words, the future rate of increase in A and L are still the same, but starting from a new PVA that is relatively higher than the PVL, the FVA will exceed the FVL »
It says that for an equal change in interest rate between asset and liability, thanks to convexity the PVA > PVL, with IRR Asset = Discount rate Liability. But the FVA (future value of asset) should not be superior to FVL (future value of liability) as the cash flows remain the same. At bond maturity, we don’t care about the change in yield curve what is paid is the par… thanks !
Oh maybe i should account for the reinvesment yield that will be higher ? thus the future value of my asset (with coupon reinvested) will be higher than the future value of my liabilty… I don’t know
Take this example. If PVL falls by 10% and PVA falls by 7%, the IRR goes up if rates go up because of the positive convexity effect. Your assets falling by a lower % than your liabs is still valuable as against assets with -ve convexity which can lower your IRR.
When rates go down, the up move for assets starts from its low (which it reached due to rate increase) and same with liabs, leading to a higher FVA than FVL.
Page 69 (CFA book volume 4) - immunizing multiple liabilities
In second paragraph they have mentioned due to structural change (steepening twist), asset portfolio loss(change in market value) is higher than change in liability reduction ( i got this) but how did they get positive change in cash flow yield by 10.04bps? and why there is a positive change?
No im sorry i don’t understand. Maybe i don’t understand what is FVA and FVL