Tutorial 1 and 2 exercises.

Hi

I've answered your questions in turn.

Tutorial 1

1. You appear to be suggesting that the premiums for TA are all profit as the claims and reserves are so small. But remember that the premiums are correspondingly small too. Profit for any type of conventional without-profits business is premiums less claims less expenses plus investment return less increase in reserves.

We can calculate an asset share for any contact. Its the accumulated value of premiums less claims less expenses. Given the small regular premiums for TA we'd expect the asset share to be small too, and usually negative at first.

3. All endowment assurances will have a sum assured. If it's a with-profits policy, then this sum assured may also increase with bonuses. So yes, if the policyholder dies early on there is a large sum at risk. Note that the question is not concerned with company profit, but instead looks at the impact on asset share. If the death benefit is larger than the asset share, then this loss reduces the asset share of the surviving policies.

4. I agree that for without-profits annuities, the benefits of the surviving policyholders are unaltered by the death. But we can still calculate the asset share. Asset shares have many uses: measuring profit, determining surrender values, determining bonuses. I agree that these reasons aren't so strong for annuities as some other contracts, but although rare, surrender values and with-profits annuities are possible.

5. Yes, that's right. The policyholder's asset share receives investment income in proportion to their contribution. So a policy with twice the asset share will receive twice the investment income, all other things being equal. But we should also consider what assets are backing the policy. Some polices may be backed by mostly equities, while other contracts may be backed by bonds. So we should consider the source of the income and allocate it to the appropriate policies.

Tutorial 2

No I wouldn't say that this flowchart is trying to present a prudent approach (although I agree that if we had a lower discount rate and hence a higher value for liabilities then this would be more prudent).

Instead the flowchart is trying to present a market-consistent approach to valuing an insurer, ie what would be a fair valuation of its assets and liabilities. In that sense it is neither prudent nor optimistic, but just right.

The market-consistent approach is used in many countries, eg in the EU and the UK we use Solvency II which is a market consistent approach. As solvency calculations are usually prudent to provide protection to policyholders, but a market-consistent approach isn't prudent, then we need to add solvency capital requirements on top.

A fair value is the price that would be exchanged for cashflows in an arms length transaction between two knowledgeable and willing parties. Hence this will be the market price (where this exists) and so we have the name market-consistent. As most assets have a readily available market price we just use that. It is usually more difficult to find a market price for liabilities, but we know from Subject CM2 that prices can be obtained by discounting using the risk-free rate, so that's a good starting point. However, nobody would want to take on liabilities at their best estimate value as there would be a 50% chance of a loss, so we add a risk margin to the liability value to bring the value up to an amount that the market would be willing to accept to take on the liabilities.

So in conclusion, it's all about what the market believes is a fair value of the assets and liabilities.

I hope this helps to provide the logic behind the approach.

Best wishes

Mark

 

Hi

Again, I've answered your questions in turn.

Q1. A paid up conventional with-profits policy could continue to receive bonuses. The bonus rate would be the same as for other policies, but the amount would be smaller as you suggest because the sum assured would be reduced when the policy is paid up.

Chapter 22 describes how to perform alterations for without-profits policies. It describes two approaches to make a policy paid up. The proportionate paid up approach would reduce the sum assured in direct proportion to the unpaid premiums, ie if 25% of the premiums were unpaid then the sum assured would reduce by 25%. A more accurate approach would be to equate policies values, equating the value of the old policy with premiums and a higher sum assured with the value of the new policy with no premiums and the lower sum assured.

Q2. Yes, these assumptions are used to value the liabilities. Basically the entire flowchart in the tutorial concerns liabilities. The assets are simply valued at market value.

Q3. Chapter 17 is looking at the investment return assumption needed to value liabilities. We don't need any assumptions to value assets with an observable market price.

The key thing to remember about market-consistent valuations is they are trying to be consistent with market prices. So we always use market values for assets where we can.

In fact, in life insurance, we'd generally use the market value of assets even where we are not valuing liabilities in a market consistent way. I think what might be confusing you is Subject CP1 where it talks about valuing assets as discounted cashflows. While using discounted cashflows to value assets has been common to value defined benefit pensions, it's not something that's done in life insurance (at least not in the UK or in the exams).

Best wishes

Mark