There's a lot going on here and the answer very much depends on what we mean by profit. So it's worth taking a step back to consider what we mean by profit and the factors that affect it.

We can think about the profit emerging at the following times:

The profit emerging on day one of the contract.

The profit emerging each year over the life of the contract.

The total profit (day one, plus the subsequent years).

These profit calculations depend on three things:

the pricing basis

the valuation basis

the actual experience.

The total profit depends only on the pricing basis and the actual experience. If actual experience is better than assumed in the pricing, then we make a profit. Basically the bigger the premium, the bigger the profit. The premium could be big because we made prudent assumptions (for simplicity of explanation we'll assume this is the case), or because we added an explicit profit loading. This is the first type of profit that you mentioned.

In practice, insurers use many different valuation bases. However they have no impact on the total profit (because that only depends on the premium and the actual experience). But, the valuation basis can affect the timing of the profit as follows.

The profit emerging on day one depends on the pricing basis and the valuation basis. If the valuation basis is stronger than the pricing basis, then the initial premium won't be enough to cover the initial reserves and expenses and we record a loss on day 1.

The profit emerging each year then depends on the difference between the valuation basis and the actual experience. If the actual experience is better than assumed in the valuation basis, then we make profits in future years. This is the second type of profit that you mention.

Note that the stronger the valuation basis, the bigger the day one loss, but the higher the year on year profits will be. However, the bigger day one loss is balanced by the higher year on year profits so that the total profitability is unchanged.

Now let's consider what happens if we do an expense analysis and increase our valuation assumption as you suggest. Let's assume that our old expense assumption was 3 for each of the next ten years, and the new assumption has been increased to 4. What happens depends on the actual experience as follows.

Reserves will increase by 10 (ignoring discounting for simplicity), as we have an extra 1 of expenses for 10 years. So we make an immediate loss of 10.

If expenses actually turn out to be 4, then no profit will emerge over the remaining 10 years. **The extra reserves will exactly cancel out the higher actual expenses.**

However, if the expenses turn out to be 3 after all (so the stronger reserves were unnecessary), **then the profit will be 1 in each of the next 10 years, because we had reserves to pay 4 expenses, but only had to pay 3. Note that the profit still emerges year on year, even though the reserves aren't fully released until the end of the contract.** So in this case the total profit hasn't changed, but the timing has as you've suggested.

Finally let's take your point on the risk adjustment. Let's say that the pricing expense assumption was 2. You've said that actual expenses are worse than the pricing basis, so let's say the actual expenses are 3. You've split the valuation basis into two parts, let's say our best estimate is 3 and then there's a risk adjustment of 1, giving a total valuation assumption of 4. Let's assume a 10 year policy.

The total profit is -10. The premium expense loading of 2 is not enough to cover the actual expenses of 3. So we lose 1 for each of the ten years.

The day one profit is -20. We need to set up reserves to cover expenses of 4 every year, but only have premium loadings of 2.

Then the year on year profit is 1. The risk adjustment is released each year as profit because we have reserved for 4, but have actual expenses of 3.

So profits are -20 followed by 1 for the next ten years, giving a total of -10 as required.

I hope this numerical example helps to show how the various factors impact the different components of the profit.

Best wishes

Mark

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