Hello, I just want to clarify somethings 1. WP Bel can thought of as Smoothed asset share(RB + TB+SUM ASSURED) + cost of guarantee. The cost of guarantee will depend if the asset share is higher than the guarantee amount? 2. If more policies than expected where to surrender, asset will reduce due to the surrender payouts. 3. The value of surrender is roughly the asset share. 4. If the BEL is higher than asset share, in another words if the the cost of guarantee bites. Then BEL could decrease at a bigger rate then asset as bel will lose the cost of guarantee in addition to the asset share component. In this case Surplus will incrase? 5. If the asset share is higher than RB+TB, then BEL will roughly be the asset share and in this case reduction in asset will be met with similar reduction in bel. Surplus will stay the same? 6. If WP policies are surrendered at early duration, surrender value is not going to be asset share (since it will be negative). Surrender value could be e.g. premiums paid, in which case BEL could be quite substantial. This will results in an increase in surplus? 7. If few policies surrender than expected, asset will reduce due to the surrender payout. The rate at which BEL decrease will depend on the BEL value relative to the premiums paid out? This is not something that will be obvious. Thanks for your time
OK - there's a lot of things going on here, so I'll answer each area in turn. Sounds like you are referring to an exercise that we work through in the tutorials and Online Classroom? Basically, the BEL is a provision held to meet future obligations to policyholders, so should equal (for conventional business) the present value of future benefits plus future expenses minus future premiums (if any). For WP business, this would give us something that approximates to the current (unsmoothed) asset share + cost of guarantees + cost of smoothing. Yes, the cost of guarantees would most likely be higher for a product where the guarantee is biting (ie guaranteed benefits > asset share) but there will (almost always) be a cost of guarantee: don't forget the 'time value' of the guarantee, which reflects the possibility that the guarantee can come into the money between now and the guarantee date.
Be a little careful here: sum assured + RB + TB = smoothed asset share (approximately) only at the point of claim, ie you only add a terminal bonus at the point at which a policy becomes a claim.
When a policy surrenders, assets will reduce by the amount of surrender value (SV) paid out and the overall BEL will reduce by the BEL for that policy. As you say, the SV would typically be set to target the asset share (AS). If we disregard cost of smoothing (which could go in either direction, depending on where we currently are in the smoothing cycle - so let's assume we are at mid-point and that the company applies a cost-neutral policy for smoothing), we have BEL > AS (since COG > 0). Note that the cost of guarantee (COG) exists irrespective of the current comparison between AS and guaranteed benefits, as mentioned above. Hence an additional surrender of a WP contract will cause {assets - BEL} to increase. This reflects the release of the COG part of the BEL. In other words, the surrender is beneficial for the company because it only has to pay out (approx) asset share and no longer has to worry about the possibility of having to pay out the guaranteed benefits on that policy if these were to bite. If we instead consider surplus to equal {assets - technical provisions} or {assets - {TP + SCR}} then there would also be a release of the risk margin or RM + SCR respectively, in relation to the surrendered policy. Hence surplus would be further improved: no longer any need to put capital aside to back that policy that has surrendered.
No - it will be as above, as there is still (probably) a COG, reflecting the time value of the guarantee. [Also I think you might mean to be comparing asset share with SA+RB (the guaranteed bits) rather than RB+TB?]
At early durations for regular premium business, where AS is some way below zero, then this is a good example of a situation where we might have BEL < 0 and so would have SV > BEL. In that case, we have the opposite situation to what I have described above, if we consider 'surplus' as just {assets - BEL}. In this case, assets will stay the same if the policy has no surrender value (or will reduce a little by whatever SV is paid) and the overall BEL will increase (no longer holding a negative BEL for it). This is worse for the company ('surplus' as defined here would reduce) - effectively because it was not good for the company for that policy to surrender before the initial expenses have been recouped. If we extend the definition of 'surplus' to take into consideration the risk margin and possibly also the SCR, then their release would offset this.
If fewer policies surrender than expected over a period, the end period BEL will be bigger than it was expected to be: we have to hold BEL for the policies we expected to surrender but which didn't. [Assuming a positive BEL here.] But the end period assets will also be bigger than we expected them to be, as we didn't have to pay out so many surrender values. So the overall impact depends again on BEL vs SV. If BEL > SV (as was the most likely situation as described above) then this overall situation is worse for the company. Stepping back from the details, in this case the company is still having to set aside monies to support the COG, risk margin, SCR etc (whatever we are 'counting' in our analysis) for the policies that it thought would surrender but which didn't. Hope that helps.
All you have explained really make sense and help me to consolidate my understanding. I just want to clarity one more thing. Bel <0 during early duration because the future premiums and investment income will more than offset the expected benefit and expenses. At later dates, There will be fewer premiums and a claim is more likely to occur. So the combined effect of increasing expected benefit payout and fewer future premiums received may lead to BEL >0 at later durations? Thanks,
Great, so glad this helped. And yes, you are right about the BEL becoming positive (for RP business) at later durations, although it's about comparing the future premiums with the future benefits & expenses (not the investment income). Remember that BEL = PV{Benefits + Expenses - Premiums}. For RP business, at early durations you would expect PV{Future premiums}>PV{Future benefits & expenses} because the premiums not only have to be sufficient to meet those benefits and expenses, they will also include a profit loading and will also partly be loaded up to recover initial expenses. Over time, as you say, there will be fewer future premiums to take credit for but still a fairly high expectation of future benefits. For SP business, the BEL will always be positive of course: no future premiums to deduct.
