CP1 September 2017 Paper 2 Q5 (ii)

[o.menary11]

Hi All,

Could i have help with the following question please? i don't understand the answer provided nor how to formulate my own answer. Any help would be greatly appreciated.

Question:
Contracts are priced using a traditional equation of value approach. The company has set up the equations to calculate the risk premiums. It now needs to incorporate the theoretical expense loadings into the equations.
Describe, for each of the following, how the expense loadings should be incorporated into the equation of value. You should ignore allowances for tax and reserving.
(a) expenses of paying level immediate annuities
(b) investment expenses of endowment assurances
(c) underwriting expenses of term assurances
(d) underwriting expenses of long term care contracts.

Summary of answer in examiners report:
(a)Treat as an extra annuity per annum per policy, but use reduced interest rate to allow for future expenses inflation.
(b) Reduce interest rate. In this case, on both sides of the equation.
(c) Add to fixed initial costs per policy.
(d) Add initial underwriting to fixed initial costs per policy or as % of benefit.


Thanks!

 

[Tim12345]

What do you not understand about this question? The formulation of the what it's asking, or specifically how expenses should be allowed for in an equation of value?

Equations of value are PV Income = PV Outgo. PV Outgo can be broken down into PV benefits + PV expenses.
Therefore the question is asking how it should allow for (a)-(d) in this equation.

(a) are expenses that are paid whenever annuities benefits are paid. So the appropriate allowance for this is to model the expenses as an uplift to the annuity benefits. Therefore these expenses should also be an annuity that are paid at the same time as the annuity benefits. When it speaks about future expenses inflation - this can be modelled either by directly uplifting the expense cashflow projection using a projected inflation curve, or by reducing the interest rate (or use a real discount rate) to allow for the fact that future expenses will increase with inflation (note that a real discount rate is (nominal rate)/(expected inflation) ).

(b) When investing in assets, let's say you on average get 3% return on the assets. Normally you have to pay investment expenses to pay fund managers, or investment admin fees such as transactional costs. Normally this is charged by just slightly reducing the return you get from the investment, if this is 0.5% charge, then the net investment return will be 3%-0.5%=2.5%. Therefore investment expenses can be modelled as just a deduction to the interest rate as the interest rate is just the return earned on invested assets.

(c) Underwriting is performed at the start of a contract, so these should be modelled as initial expenses.

(d) basically the same concept as (c)