EV - impact of strengthening reserving basis

I'll add some numbers to Anacts formula to show how this would impact EV. Thank you Anacts for the helpful post above.

Let's say that strengthening the mortality basis adds 100 to the reserves. So the net assets go down by 100. If we then look at the insurer's balance sheet we may then think that the insurer's value has dropped by 100. However, if our expectations of the actual experience is unchanged (so it's only our reserves that have changed) then the prudence in the reserves will be released as 100 of profit at some point in the future.

Let's follow Anacts and assume that the profit emerges in one year. The assets backing the reserves of 100 roll up with interest, let's say i=4%. Then we have assets of 100x1.04=104. As the reserves are higher than required, then all of these margins emerge as a profit of 104.

The value to the shareholders of these profits depends upon their risk discount rate. If r=4%, then the PVFP (present value of future profits) is 104/1.04=100. So the net assets went down by 100 and the PVFP went up by 100, so the EV is unchanged.

However, often the shareholders will demand a higher risk discount rate than the investment return that they earn on the assets (the assets may be invested in safe bonds with a low return, but the shareholders capital is invested in the insurance business which is more risky and demands a higher return). Let's say r=8%, then PVFP is 104/1.08 = 96.3. So PVFP has gone up by 96.3, but net assets have gone down by 100, so strengthening the reserves makes the EV fall by 96.3-100=3.7.

I hope this example makes the calculation of EV clearer.

Good luck with the exam

Mark

 

I'll look at Q2 here and come back to Q1 in my next post.

In the example above, holding 100 of extra reserves meant a decrease in net assets of 100 and increase in PVFP of 96.3. So at time 0 the EV profit is -3.7.

At time 1 the reserves are released with interest, so net assets go up by 104. The PVFP is now zero (there are no future profits to discount), so PVFP goes down by 96.3. So at time 1 the EV profit is 104 - 96.3 = 7.7. So total profit is 7.7 - 3.7 = 4.

If we had not set up the extra reserve then the net assets of 100 would have rolled up with interest to give a profit at time 1 of 4.

So the total profit is unchanged by strengthening the reserves. However, we see that the profit emerges later with stronger reserves.

Best wishes

Mark

 

Yes, on page 7 of Chapter 18 the Core Reading states that:

For without-profits business, embedded value is effectively the release of any margins within the supervisory reserves relative to the assumptions used within the embedded value calculation.

Unfortunately this isn't quite right. The Core Reading above is only referring to the PVFP. We should also add the net assets to this value.

Thank you for pointing this out. We'll ask the profession to update the Core Reading in the future.

Best wishes

Mark

 

EV has two parts: net assets and PVFP. The net assets are largely the same as the surplus. So yes an analysis of EV is very similar to an analysis of surplus. However we analyse the PVFP too under an analysis of EV.

Best wishes

Mark

PS

I'm sorry for the delay in replying to your queries. We are very busy at the moment teaching the block tutorials so it may take a few days to reply to some of your queries.

 

To answer these two questions fully we would have to go beyond the ST2 syllabus and use ideas from SA2.

The PVFP for with-profits business depends on when the bonuses are declared. So in this sense it is different to the calculation of EV for without-profits business - without-profits business looks at the release of margins in the reserves so is directly affected by the strength of the reserving basis.

The assumptions used in the EV published in the accounts has varied over time (and varies between countries). In the UK, the assumptions used to be on the prudent side, then more recently best estimates have been used, and today some companies would use a market-consistent basis. Which approach is the best is open to debate.

Best wishes

Mark

 

Hi

The relationship between the discount rate and assumed future investment return assumptions is relevant to the new business contribution in the EV, but isn't the reason for that contribution being positive. You would expect there to be a positive impact on the EV from writing new business if, as would normally be the case, the business has been priced to generate profit.

Simplistically:

The company would price the product so that:
PV{Premiums} = Initial expenses + PV{Renewal expenses + Claims} + Profit loading

The immediate impact on the EV from writing new business would be as follows:
Impact on net assets = + First premium - Initial expenses - Initial reserve
Impact on PVFP = + PV{Premiums excluding first premium} - PV{Renewal expenses + Claims} + Release of initial reserve over time (including investment return earned on reserves)

So total impact on EV = PV{All premiums} - Initial expenses - PV{Renewal expenses + Claims} - Initial reserve + Release of initial reserve (including investment return earned)

Assuming that the EV experience basis is in line with the pricing basis, substituting in the pricing equation gives:
Impact of new business on EV = Profit loading + {Release of initial reserve (including investment return earned) - initial reserve}

The final component in this equation will be negative if discount rate > assumed investment return. It basically represents the 'lock-in' cost of having capital tied up supporting the reserves, which erodes the value.

However, we would expect the overall impact to be positive due to the profit loading.

In other words, writing new business adds value to the company due to the profits that we expect to generate from it.

Hope that helps.

 

Hi - to answer quickly: my example above described the net asset and PVFP position immediately AFTER receipt of the first premium and AFTER the initial expenses are incurred. In other words, the position on the very first day of the policy after the initial cashflows have been incurred. So the first premium and initial expenses are recognised in net assets, not in the value of future profits (because they have already happened).

The example that you mention first calculates the position immediately BEFORE receipt of the first premium and BEFORE the initial expenses are incurred. In which case, the premium and initial expenses are still (just) in the future (they have not yet happened) and so are part of the PVFP. It's just a slightly different way of looking at this.

Whichever approach is taken (immediately before or immediately after these cashflows actually happen) the overall EV impact is the same. The only difference is whether those particular cashflows are included in the net assets component or are included in the PVFP component. If they are included in the PVFP, they won't be discounted because they are just about to happen. So it adds up to the same thing.

 

Hello Anaayaa

Don't worry about this post. It refers to an old version of the Core Reading that has since been corrected.

Embedded values have two parts: the net assets and the present value of the future profits. For without-profits business these future profits occur because the reserves are prudently high and so set asset more money than we really expect to be needed to pay the liabilities.

Best wishes

Mark