Sep 2017 Q5 ii

[dimitris13]

Hi there ,
two small qs.
the solutions mention that (in section other assumptions) that there will be a reduction in earning and followed by small contributions to earnings as the expected investment returns are earned. how the latter is derived ? maybe some sort of eqs would be helpful.

similarly in rdr section it says that earnings will increase (ok) followed by small -ve contributions to future earnings as the unwind of rdr will be less under mkt consistent. the latter in what sense? bc the rf is lower than the rdr ?

thanks

 

[Mark Willder]

Hi there ,

similarly in rdr section it says that earnings will increase (ok) followed by small -ve contributions to future earnings as the unwind of rdr will be less under mkt consistent. the latter in what sense? bc the rf is lower than the rdr ?

thanks

I will answer your two points separately. I'll take your second point on RDR here.

A numerical example might help. Under the passive approach the RDR is set to be a return to reward investors for the risk they are taking on. Let's say the investors require a return of 8%. So the old RDR is 8%.

Under the new market consistent approach, the RDR will be related to the risk-free rate. We might take the yield on government bonds as the risk-free rate, so in this case the RDR might be 2% say. Alternatively, we might take the risk-free rate as the return on corporate bonds less an allowance for default risk, so in this case the RDR might be 2.5% say (maybe 3% yield on the corporate bond less 0.5% for credit risk). Either way, the new RDR is less than the old RDR of 8%.

So at the time the change is made, the present value of future profits goes up. The profits are unchanged but we are discounting them at a lower rate.

Whenever changing the assumptions, a good general point to make is that if we make a bigger embedded value profit now, then we must make a lower embedded value profit in the future. This will always be true if the actual experience is unchanged. We make the same amount of profit over the term of the contract, but we change the timing when the profit is recognised.

We can demonstrate this as follows. Let's say there is a profit in ten years of 10. The present value of this profit now is 10 / (1 + RDR)^10. The present value of this profit in one year's time is 10 / (1 + RDR)^9 as the profit is now one year nearer to being realised. So the present value of the profit in one year is (1 + RDR) bigger than at time zero (ie it's discounted for 9 years instead of 10) - this is called the unwinding of the RDR. As the new RDR is smaller under the new approach then the future profit (1 + RDR) must be smaller too.

I hope this helps.

Mark

 

[Mark Willder]

Hi there ,
two small qs.
the solutions mention that (in section other assumptions) that there will be a reduction in earning and followed by small contributions to earnings as the expected investment returns are earned. how the latter is derived ? maybe some sort of eqs would be helpful.

thanks

I'll now look at your first point.

To calculate the present value of future profits of the EV we need to project what the profits will be each year.

The equations are different depending on the type of business.

For conventional without profits, the profit formula is:

Premiums - Claims - Expenses - Increase in reserves + Interest on reserves.

For unit-linked it is:

Charges - Claims in excess of unit fund - Expenses - Increase in non-unit reserve + Interest on non-unit reserves.

In this question the calculation of interest on reserves has changed. The passive approach used the expected return on assets. The new market-consistent approach uses a risk-free rate. The new approach will have lower investment returns as we deduct an allowance for default risk from the expected return on assets. So the projected profits each year are lower and hence the EV is lower.

So the EV today is lower due to the change in assumptions. Now we can consider what will happen to EV in future years.

The point I made in the previous reply is still relevant here: a good general point to make is that if we make a bigger embedded value profit now, then we must make a lower embedded value profit in the future. In this case, as the EV profit now is lower, then the reverse happens, so we make higher EV profits in future years.

We have calculated the projected profits assuming that we only earn the risk-free rate. However, we actually expect to earn more than the risk-free rate from the assets chosen. So actual experience is likely to be better than assumed, so we make profits in later years.

I hope this helps.

Mark

 

[dimitris13]

Hi Mark,

i am reading the syllabus again and i see the following.

PVIF(t+1)-PVIF(t)=PVIF(t)*v-S(t)

the syllabus says "the 1st ellement of this expression represents the unwind of discount rate, being the discount rate multiplied by the PVIF at the start of the period".
I am a bit confused now.
is unwind of disc rate the PVIF(t+1)-PVIF(t)
or PVIF(t)*v?
(in S2 may be the same i understand).

To this direction if we wanted to formalize the CSM unwind what would be the "general" equation ? CSM(t)*v or sth else?

thanks in advance

 

[Mark Willder]

Hi Dimitris

I think you are taking this from Chapter 20 of the SA1 Course Notes. So anyone taking SP1 doesn't need to worry about this just yet.

The formula you have quoted isn't the one in the Course Notes. The v should be replaced with an r, where v=1/(1+r). So we have

PVIF(t+1)-PVIF(t)=PVIF(t)*r-S(t)

Or equivalently

PVIF(t+1)=PVIF(t)(1+r)-S(t)

so in words we have that the present value of the surplus emerging from time t+1 onwards is equal to the present value of the surplus emerging from time t onwards, rolled up for one year at the risk discount rate, plus the surplus emerging at time t.

The unwinding of the risk discount rate is the PVIF(t)*r term, ie it is the present value of the surplus emerging from time t onwards, rolled up for one year at the risk discount rate.

Yes, we'd have a similar formula under Solvency II for the best estimate liability with

BEL(t+1)-BEL(t)=BEL(t)*i-CF(t)

where CF(t) is the cashflow at time t and i is our SII discount rate.

Note that the above two calculations (PVIF and BEL) are prospective calculations. We have projected future surpluses for the PVIF (and future cashflows for the BEL) and discounted them back.

The contractual service margin under IFRS17 is quite different. We calculate the CSM as the balancing item to set the time zero profit to zero. We then roll this forwards, so it is a retrospective calculation. We then need to run off the CSM in line with some coverage unit (perhaps the number of remaining contracts).

This level of detail about the CSM is going beyond the SA1 syllabus, but there were some good talks at the Life Conference in 2017 which covered this topic. You can download them from the profession's website along with many other CPD videos.

Best wishes

Mark