Hi,
can someone please explain by two eqs if possible the following two:
1. if prudential basis the emergence of prud margins =pvif
2. if bea pvif= 0.
i remember from st2 that pvif = pv netCf + res(t)-res(t+1) + int on reserve.
thanks
Hi
It may help to think of the following:
The PVIF is the present value of future profits on the in-force business. These profits arise from the release of the assets backing the reserves, over and above those which are needed to pay the net
outward cashflows (NCF) arising on the business.
If we project those cashflows on the same basis (best estimate) as the reserves are calculated then there should be no excess assets to form the PVIF.
I’ll try and explain using your terminology:
· Let’s say
res(t) represents supervisory reserves calculated on a best estimate, market-consistent basis at the start of year t
·
int = interest rate which under market-consistent assumptions (as SII will be)
int = discount rate = risk-free rate
· Assume
NCF(t) occur at the start of the year t, and that these are projected on the same best estimate, market-consistent basis
Since res(t) = NCF(t) + NCF(t+1).v + NCF(t+2).v2 + … and res(t+1) = NCF(t+1) + NCF(t+2).v + …
then we have
· (1+i)res(t) = (1+i)NCF(t) + res(t+1)
which means that:
· (1+i)NCF(t)+res(t+1)-(1+i)res(t)=0
In other words, the investment return earned on the reserves held at the start of the year (= i.res(t)) plus the release of reserves over the year (= res(t) – res(t+1)) is exactly enough to cover the net outward cashflows arising during the year. So no ‘profit’ arises.
We can also see this as follows:
Profit arising in year t = net cashflows to the company (ie net
inwards cashflows) + investment return earned on reserves held at start of year and on net cashflows received – increase in reserves over the year
= – NCF(t) + i.{res(t) – NCF(t)} – res(t+1) + res(t)
= – NCF(t).(1+i) + (1+i)res(t) – res(t+1)
Which, from the equivalent statement above, is zero.
So profit arising in year t = 0, for all years t. Thus PVIF = 0.
Does that help?