Ch 20 and Ch 21 Doubts - Core reading

[Kamal Sardana]

Ques 1 - Ch20 - Valuing mortality option --I did not understand the italic line here --

" " " An alternative assumption would therefore be that the mortality of those who do not take up the option is such that average mortality for all lives remains at the base expected level. The assumed mortality of those who do not take up the option would then be lower than this base level" " "

Correct me if am wrong, they are saying that if i purchase policy at age 40, then exercise my option at age 45. So my mortality will be of age 50 (say) but those other people with me who did not exercise the option at age 45 (there mortality will be of age 42 (i.e. lower than base mortality of age 45). So that on an average mortality at age 45 will be standard base mortality ?????

Ques 2 - Ch21 - Embedded Value -- I did not understand the italic line here --
" " "
Part A = If the assumptions used to calculate the supervisory reserves were exactly the same as those used to calculate the future cashflows in the EV calculation, then the profit emerging each year (and hence the PVFP) would be zero. This is because net cashflow, plus investment income on the reserves would equal the release of reserves in each year.

Part B = Therefore, the extent to which the two bases are different will be reflected in the PVFP calculation. In the (more realistic) EV calculation, estimated future cashflows are likely to be higher than in the (more prudent) reserving basis. Hence, future profits will arise. " " "

Kindly explain for Part A, how PVFP would be zero, any example please....
for Part B, are they saying that if reserving basis is prudent then release of margins will be high, hence profit will be high (but in my view if reserves are high then my Net assets will be low, hence overall impact on EV will be very small.
Kindly shed some light on both these topics

 

[Mark Willder]

Ques 1 - Ch20 - Valuing mortality option --I did not understand the italic line here --

" " " An alternative assumption would therefore be that the mortality of those who do not take up the option is such that average mortality for all lives remains at the base expected level. The assumed mortality of those who do not take up the option would then be lower than this base level" " "

Correct me if am wrong, they are saying that if i purchase policy at age 40, then exercise my option at age 45. So my mortality will be of age 50 (say) but those other people with me who did not exercise the option at age 45 (there mortality will be of age 42 (i.e. lower than base mortality of age 45). So that on an average mortality at age 45 will be standard base mortality ?????

Ques 2 - Ch21 - Embedded Value -- I did not understand the italic line here --
" " "
Part A = If the assumptions used to calculate the supervisory reserves were exactly the same as those used to calculate the future cashflows in the EV calculation, then the profit emerging each year (and hence the PVFP) would be zero. This is because net cashflow, plus investment income on the reserves would equal the release of reserves in each year.

Part B = Therefore, the extent to which the two bases are different will be reflected in the PVFP calculation. In the (more realistic) EV calculation, estimated future cashflows are likely to be higher than in the (more prudent) reserving basis. Hence, future profits will arise. " " "

Kindly explain for Part A, how PVFP would be zero, any example please....
for Part B, are they saying that if reserving basis is prudent then release of margins will be high, hence profit will be high (but in my view if reserves are high then my Net assets will be low, hence overall impact on EV will be very small.
Kindly shed some light on both these topics

Hi Kamal

Q1. Yes your example is exactly what the notes are saying here. Note that when the contract was taken out the average mortality would have been 40 select, but when the option is taken the average mortality is 45 ultimate.

Q2A. Let's consider a really simple one year contract. Reserves are calculated just before the premium now due. Profit in the PVFP calculation is given by:

Premiums - Expenses - Claims + Investment + release of reserves.

Let's say the premium is 90. In the reserving basis we assume that investment return is 10%, claims at end of year are 200, expenses at end of year are 20. Then the reserve at the start of year just before the premium is paid is

(200 + 20) / 1.1 - 100 = 110

The reserve at the end of the year is zero as the contract has now finished.

In part A we have the case where the EV projection basis is the same as the valuation basis, so again we assume 10% investment, claims of 200 and expenses of 20.

So

Profit = Premiums - Expenses - Claims + Investment + release of reserves

= 90 - 20 - 200 + (110 + 90) x 0.1 - 110 = 90 - 20 - 200 + 20 + 110 = 0

So profits are zero as required. Fundamentally, reserves are the amount of money we need if experience follows the reserving basis. So if actual experience does follow the reserving basis then we have exactly the right amount of money and so no profit or loss.

Q2B. Yes, you're right that if reserves are prudent then PVFP will be high. And yes, you're right that the net asset will be low. So yes, the overall impact on the EV may be small. However, there could be some impact on the EV. Shareholders will prefer money now to money later. Net assets are money now. But the PVFP represents money later (when the reserves are released). If the interest earned on the reserves is lower than the shareholders required return then there is a cost of capital. For example if reserves go up by 100, then net asset go down by 100. But the PVFP goes up because we release the reserves and the interest earned on them, say 100 x 1.1 =110 using the example in A. But the value of that release of reserves needs to be discounted at the risk discount rate, this will be less than 100 if the RDR is more than 10%, ie 100 x 1.1 / (1 +RDR) < 100 if RDR > 10%.

Best wishes

Mark