Lecture Notes 6

Lecture Notes 6 1

Profit testingProfit testing•Remember our aim, as a life assurance company, is to make a profit (so long as we have shareholders; if we are only a mutual we don't have shareholders although our policyholders will share in any profits). •Therefore, we now consider the policy as an investment on the part of the company. •The company now tries to look at the profit from each policy in every future year.

Lecture Notes 6 2

Profit testingProfit testing•By 'Profit Testing' we mean the process of designing, and pricing (determining premiums) for new products. The steps are broadly as follows:• decide on the type of product, and when premiums are payable• model the future cashflows in or out at all future timeperiods (monthly,

annually, etc – depends on product)• decide on the profit criterion (i.e. what level of profit we need) and which

return we require (risk discount rate – see later)• choose a basis (probably a best estimate basis) to work out the premiums

needed. See if this meets the profit criterion. Vary the premiums to meet the criterion; and compare against what we can actually charge bearing in mind the other players in the market;

• sensitivity test to see what the profitability is if some of the basis entries change to see the resilience of our product

Lecture Notes 6 3

Future CashflowsFuture Cashflows•For any policies, we may wish to calculate expected cashflows to enable us to profit test. Normally we divide the policy up into a series of time periods (non-overlapping). We normally start at the beginning of the time period under consideration; rather than at inception. •We might wish to have shorter periods when there are likely to be many cashflows (start of policy); and longer ones when there is not much happening. •We then construct a revenue account per contract for each time period. The revenue account is simply all the inflows, less all the outflows.

Lecture Notes 6 4

Projecting cashflowsProjecting cashflowsPremiums + investment income - expenses- benefit payments - increase in reserves - tax= profit net of tax

Lecture Notes 6 5

Future CashflowsFuture Cashflows•To calculate an expected present value, remember we simply take the cashflow, discount it, and multiply by the probability of payment. If we have complicated cashflows, such as under a unit linked policy (later in the notes), it might make sense to work those out first each year, and then do the discounting and probability parts afterward. Also, if we want to see the profit (or cashflow) “emerging” every year; rather than just summarised 'EPV'; we will need to project cashflows forward. Note that if there are multiple possible states at any point in time, all of which can generate cashflows, we need to consider all the possibilities.

The balancing item in the revenue account is profit (or loss!).

Lecture Notes 6 6

Future CashflowsFuture Cashflows•To see why cashflows, rather than just expected present values, are needed; consider the following. A life office issues a term assurance policy to a group of policyholders. You calculate that the expected present value of the profit from this group is £45,284; assuming an interest rate of 5%. Great! Clearly a profit from this group (if our assumptions are correct, clearly!). Then we examine the (hypothetical) cashflows:

Lecture Notes 6 7

1

-15000

-10000

-5000

0

5000

10000

15000

CashflowEPV

Lecture Notes 6 8

Future CashflowsFuture Cashflows•Even though we have a large outflow in the first two years; the policy overall is still expected to be profitable. However, we need to know the cashflow pattern to enable us to predict correctly the extra money we will need to borrow (either from our own reserves or from elsewhere) in order to pay out in the first few years.•Additionally, if we have shareholders (and if we don't, but are a mutual who returns profit to members instead) we need to decide how much profit to distribute when. Remember that the final profit is never known until the final policyholder has died; which could be about 100 years into the future. Shareholders generally have a somewhat shorter time horizon. Therefore we can work out the profit arising each year; based on comparing the expected future outflows and expected future inflows. Remember profit comes after the transfer to reserves.. ...which cover expected future outflows

Lecture Notes 6 9

Future CashflowsFuture Cashflows•To calculate our future cashflows we need:

• Premium payment details (£ and timing)• Expected expenses (£ and timing)• Benefits payable (£ and timing). • Other payments (taxes)• Other receipts (management charges)• Reserves required at the start and end of each period.

• Remember we here consider both the benefits payable from the unit fund and any guarantees payable from the non-unit fund

• Also remember that a valuation basis (for reserves) doesn't need to be the same as a basis used to predict the cashflows. Generally speaking reserves need to be prudent, whereas cashflow prediction can be realistic

Lecture Notes 6 10

Expected Future CashflowsExpected Future Cashflows•To calculate our expected future cashflows we need:

• Full details of the cashflows; plus full details of the probability of each particular cashflow occurring.

• The balance of the revenue account at any given time will be invested (probably in a fairly liquid asset class); and any balance will earn interest/return. We then need to work out the expected investment return at the end of each period as well.

Lecture Notes 6 11

Expected Future CashflowsExpected Future Cashflows•For our first example we'll consider a 'conventional' whole life assurance. We throw in a complication: policyholders don't only leave through death, but also through surrender (when they will be paid some benefits); so we need a multiple decrement table or another method of calculating dependent decrement rates. •At any policy duration, we have:

Lecture Notes 6 12

Profit TestingProfit Testing•Once we have worked out our expected cashflows for each future year; we can work out a profit vector – this is a vector with each value being the profit for year t, per policy in force at the beginning of the policy year. The profit vector is denoted (PRO) t

•The profit vector might depend on the policyholder's status at the start of the year (eg healthy/sick in a policy which pays out while sick)

•The profit signature is the vector of expected profits per policy issued – so we need to include the possibility of death/withdrawal before t to calculate this. •We denote the profit signature by (PS) t

Lecture Notes 6 13

Profit TestingProfit Testing•A profit vector or signature is useful, but it's still often preferable to summarise values into one 'number'. We can do this as an EPV

•or we can work out the profit margin

Lecture Notes 6 14

Risk Discount RateRisk Discount Rate•Both the NPV and EPV premiums (used to calculate the Profit Margin) on the previous slide are discounted at what we call the risk discount rate. This is the 'cost of capital' rate - i.e. the rate at which funds can be borrowed if needed; or alternately which funds could earn if invested elsewhere. This is often calculated using an underlying risk free rate (usually government bonds, or possibly swaps); and adding a margin for the extra risk taken on.•Alternately, we could work out the IRR / MWRR (internal rate of return) - i.e. the i solving NPV = 0. This is the return that is earned on the 'capital' the company has invested in the policy.

Lecture Notes 6 15

Premiums using profit testingPremiums using profit testing•We can calculate the premium for any policy using a profit criterion. This is a required expected level of profit which we include when calculating the premiums payable by the policyholder. Examples include:

•NPV of profit = x% of initial commission payable•Profit margin = y% of the NPV of expected premium income

Lecture Notes 6 16

Unit Linked ContractsUnit Linked Contracts•A common type of policy now issued is a unit-linked contract. All the policies covered until now have been non-unit-linked, which we call conventional. A unit-linked policy pays benefits directly linked to the underlying investments held – specifically for the particular policyholder. There is no pooling of risk, or share in profits from anything other than investment returns. Note the policyholder takes on risk here – there is a chance that the returns could be low. •A specified proportion – the allocation percentage – of each premium is used to buy units in an investment fund chosen by the policyholder. Units here simply means that the fund is divided into small portions – similar to shares in a company – which then increase or decrease in value when the underlying investments change value.

Lecture Notes 6 17

Unit Linked ContractsUnit Linked Contracts•A record is then kept of the total number of units that belong to the policyholder. When the policyholder dies, or the term is up (in an endowment assurance, term assurance, or pure endowment) the total number of units is calculated, and the current price per unit is applied, to work out the sum assured. At any point in time the unit account is the term for the total value invested (so # units * price per unit). •Because at first, the sum assured worked out this way will be very small, there is often a minimum guaranteed sum assured. This also can provide some protection against exceptionally poor investment returns.•To price and value unit-linked contracts we need to know the allocation percentage and assume the future growth of the unit price.

Lecture Notes 6 18

Unit Linked ContractsUnit Linked Contracts•It is common for units to operate a 'bid/offer spread'. This is when the price quoted for selling units (eg on maturity, when the sum assured becomes payable) is not the same as the price quoted for buying units (eg on payment of each premium). It is common to confuse bid and offer. The terms relate to the market maker's bid/offer – in this case the life company. The trick to remember is 'market makers buy at bid'.If a market maker is buying units, it means that the policyholder is selling the units back to the market maker.•Generally, the bid price is lower than the offer price. It is common to have a bid price of 95% of the offer price.

Lecture Notes 6 19

Unit Linked ContractsUnit Linked Contracts•It is also common for the life company to deduct charges regularly – perhaps monthly or annually. This can cover both expenses (those directly associated with investment, such as investment management charges, and those not – such as policy administration) and the cost of any guarantees to sum assureds. The company usually reserves the right to alter these charges if necessary.

Lecture Notes 6 20

Premiums

Allocated Premiums

Unallocated Premiums

Cost of Allocation Non Unit Fund

Unit Fund

Bid/Offer spread

Unit Fund Charges

Company Expenses Profit

Non unit benefitsto policyholder

Unit benefits to policyholder

Lecture Notes 6 21

Projecting cashflows Projecting cashflows (unit linked)(unit linked)

•For unit linked contracts we need to project the non-unit fund and the unit fund. The non-unit fund is projected as:Premiums less cost of allocation (i.e premiums into the non-unit fund)+ investment income on non unit fund only - expenses- benefit payments coming from non unit fund only+ management charge= profitThe unit fund is projected similarly to the previous conventional

projection.