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Profit modelling for pleasure

A major form of entertainment for actuaries in life offices is profit testing. The “beneficiaries” of this work may see it as a black art but the process is actually very straightforward. In essence, all it involves is a comparison of income and outgoings.

If the former exc eeds the latter by a suitable margin you have happy with-profit policyholders and share holders. Otherwise, long faces.

Profit modelling is carried out both before and after products are sold. The work in advance is to predict the likely profit position and to assist in setting the price of the products. The analysis after the fact is to see what actually happened.

The models used by actuaries could be applied to any industry. The principles are universal.

The first stage is to determine cashflow to and from the provider. This is done by type of cashflow and for each time period, often month by month.

The principal inflow of cash is obviously premium income. It is not the only inc ome, however. Receipt of tax relief, capital growth, investment income and other items may also feature depending on the product. The outgoings include expenses, the cost of claims (maturity, death, critical illness, etc), commission, tax and the reserves which must be set up.

Although it may be clear what items make up the cashflow, it may be more difficult to be precise regarding the amounts. Premium amounts are straightforward but other items such as expenses will require estimation.

This estimation will be based on previous experience of selling and servicing similar products. Due to the need to spread the development and other costs, anticipated costs will be dep endent on the volume sold.

If the office is optimistic and assumes a high volume of sales this will spread the costs thinly, resulting in a lower price to the consumer (or a higher anticipated profit).

If those volume sales don&#39t appear, however, the actual profit may be lower than expected or may turn into a loss. The office quantifies the impact of actual experience differing from expectations by scenario and sensitivity testing on a range of different assumptions.

The next stage is to determine the expected cashflow in each time period and to discount them back to the start of the policy to calculate a current or present value.

Many assumptions are required. On the investment side, there are the anticipated levels of income and capital growth. On the experience side, the anticipated levels of deaths, critical illness claims, surrenders and withdrawals.

Like the expenses mentioned, actuaries base their expectations of future claim levels on past experience. If entering a new market, this process will often be assisted by input from reassurers and from national experience surveys of assured lives.

There may be a slight tendency to be on the cautious side but market competitiveness has reduced such conservatism in many areas.

Various profit measures can be drawn from considering these cash flows. The discounted value of future profits is exactly what is says – the cashflow are discoun ted at whatever rate of interest the company chooses.

This interest rate would usually be the rate which the office believes it could earn from less risky activities than launching new products (for example, investing elsewhere) plus a margin.

An alternative measure is the internal rate of return. This is the rate of interest which, when applied to discount the cashflow, results in the sum of those discounted cashflow being zero.

It is effectively therefore the rate of return earned by the product provider for their investment.

Often the cashflow in the early months or years of products are negative. It may take several years for positive cash flows to come through after the issue of a policy to wipe out that initial negative.

The break-even period is defined as the time a policy has to be in force for the sum of the discounted cashflow to be zero.

The principal use of profit modelling before a product goes on sale is to assist in the setting of the price for that product and to determine capital requirements.

The principal use once a portfolio of business exists is to measure the value of that business.

The profit testing of financial products may be a little bit more complicated than in some other businesses but the major principles remain the same.

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