Chapter 21 & 22: Setting assumptions Flashcards

Question

Profit requirements: Explain what is meant by the term risk discount rate (5)

Answer 1

1. Composition: A risk discount rate is the expected rate of return that investors demand, which is equal to the risk-free rate plus a risk premium. 2. Shareholder Return: It reflects the return required by the shareholders on the capital they invest in the insurance company. 3. Compensation for Risk: The risk premium component is required to compensate the investor for the risks inherent in investing in a life insurance company, such as risks of commercial failure and default. 4. Pricing Tool: The RDR is a number that is simply used as a criterion in profit testing within pricing models. 5. Risk Reflection and Standard: The risk discount rate must be higher than the risk-free rate, and the margin between these two rates should attempt to reflect all sources of risk in the product. It is set to ensure that the rate of return from the product is satisfactory, given the inherent variability of the return and the required return on capital

Answer 2

1) the CAPM result provides the overall rate of return ($\text{E}_i$) that shareholders expect from investing in the company as a whole to compensate for systematic risk. 2) 1. Lack of historical data: This increases parameter risk regarding future experience assumptions. 2. High guarantees: Products offering high guarantees expose the company to greater liability risk. 3. Policyholder options: These features (e.g., options to surrender or switch funds) introduce anti-selection risk and uncertainty regarding future cashflows. 4. Overhead costs: Products involving significant or uncertain overhead costs increase financial risk. 5. Complexity of design: Complex products are harder to model, administer, and understand, potentially increasing operational and parameter risk. 6. Untested market: Launching a product into an untested market carries high commercial risk and uncertainty regarding expected volumes and persistency.

Answer 3

1. Analytical Assessment of Parameter Variances: The statistical risk ($\text{Var}[R]$) can be quantified analytically by considering the variances of the individual parameter values used (such as interest, mortality, withdrawal levels, and expense inflation). This method determines the variance of the rate of return by assessing how the variance of these important parameters influences the projected profit. 2. Stochastic Models and Simulation: This method involves using stochastic models for some, or all, of the parameter values and simulation. The important parameter values are varied stochastically according to their assumed probability distribution, and the rate of return is re-computed for each new scenario. Repeating this process many times (e.g., 1,000 times) provides a good indication of the variance of the rate of return. This approach is the numerical equivalent of the analytical approach. 3. Deterministic Sensitivity Analysis: This approach utilizes sensitivity analyses with deterministically assessed variations in the parameter values. The method determines which changes in assumptions (e.g., an increase or decrease in mortality rates) the profits are most susceptible to. The actuary then identifies the increased parameter value that subjectively corresponds to a specific low probability level (e.g., 5% probability level) and tests whether the return on capital under this scenario is still greater than the minimum acceptable return. 4. Comparison with Market Data: The level of statistical risk determined through other means could also be assessed by comparison with any available market data.

Answer 4

Published results Supervisory reserves Internal management accounts Embedded values

Answer 5

Broadly speaking, determined as PV of Future benefit outgo plus claims expenses (including commission) plus taxes (if appropriate) less future premiums

Answer 6

Impact of changes in the discount rate all things being equal, decreasing (increasing) the discount rate, will increase (decrease) degree of prudence for a positive reserve decreasing (increasing) the discount rate, will decrease (increase) degree of prudence for a negative reserve, where this is permitted

Answer 7

For country concerned, consider +legislation +accounting principles Matters to consider (1) going concern or break-up basis (2) required to show a true and fair value? (3) best estimate basis or some other basis? (4) precisely how terms used are to be interpreted

Answer 8

Key driver should be discussion with insurance company about the principles to follow, based on the purpose for which the internal accounts are required Most likely aim is to have best estimates of the company’s financial performance, based on realistic assumptions.

Answer 9

If separate accounts required during process solvency supervision process , rules for preparation of separate accounts may/may not be same as rules for published accounts… Key considerations +for example may be required to use different basis (going-concern/break-up basis) +Should reference rules & guidance which was issued needing interpretation +will most likely be certain assumption restrictions which are either specific (valuation interest rates must equal premium basis rate) general (do valuation as wish, subject to not lower than X basis) +usually require prudent basis, some jurisdictions moved to market consistent approach

Answer 10

going concern assume insurer continues issuing new business into future break-up +assume new business cease immediately, or at some point in future e.g …closed fund by company, or.. …transfer liabilities to another insurer, who will administer/process claims until book runs down

Answer 11

Key difference is that in force policies can provide important information for setting reserving assumptions (compared to pricing assumptions)

Answer 12

Demographic assumptions +already know who PHs are => good info about class of lives +historical experience investigation likely to indicate future experience well (if data volume credible) +hence less uncertainty in assumption than for pricing’ Expense assumptions +should be easier to assess for reserving because no future initial expenses +less uncertainty over volume/mix of future business +but share of fixed expenses covered by existing PHs affected by new policies expected… +…so expense assumption still has some uncertainty

Answer 13

In some countries, standard practice uses prudent assumptions for pricing/premiums, then same assumptions or supervisory reserving

Answer 14

For WP products, surplus will emerge from actual experience being better than that assumed in prudent assumptions ie. even if margins are high, surpluses from experience can be given back to PHs through bonuses

Answer 15

Less appropriate for without-profits products as overly high margins => uncompetitive, hence usually small margins are used, meaning pricing basis cannot be used for supervisory solvency

Answer 16

Embededed value is defined as sum of: +shareholder-owned share of net assets +present value of future shareholder profits from existing business, including release of shareholder assets EV essentially recognises value of assets in excess of reserves and value to shareholders of future margin releases from reserves

Answer 17

May need embedded values for +published accounts as supplementary info +internal management accounts

Answer 18

Net assets are defined as the excess of assets held over those required to meet liabilities. These assets may be valued at market value or may be discounted to reflect lock-in, e.g. if they are required to be retained within the fund to cover solvency capital requirements. The value of the reserves (used in NAV) needs to be consistent with the assumption used in determining the emergence of future profit.

Answer 19

1. The Application or Purpose of the Basis: The most important determinant is the application, or purpose, of the basis for which the assumptions are being set. The sources explicitly list "ongoing profitability measurement" as one such application, which requires certain considerations (such as the extent to which margins for adverse future experience are needed). 2. Expected Future Experience (Best Estimates): The core part of the process is the determination of what future experience is expected. The derivation of assumptions for future experience follows a framework where historical estimates are adjusted to determine the best estimates of the assumptions, given the expected future commercial and economic conditions. These best estimates serve as the starting point for setting the value of any parameter. 3. Principle of Consistency: The assumptions need to be considered in their totality, guided by the principle of consistency. This means ensuring that realistic allowance is made for the way variables behave together where correlations exist between them. For example, the expense inflation assumption must be consistent with the future investment income assumption, and the long-term relationship between the rate of expense inflation and the rates of return on different asset types must be valid.

Answer 20

1. A basis reflecting the Best Estimates of future experience. This involves investigating historical experience and determining the most likely values given expected future conditions. 2. A basis incorporating margins for prudence. The best estimates may need to be adjusted in order to include a margin for prudence. The size of any margin incorporated depends on the purpose for which the model is required, which in this context is ongoing profitability measurement.

Answer 21

1. Allowing for Risk through the Core Assumptions (The "Best Estimate" Basis) The core assumptions for future cashflows (like mortality, expenses, and persistency) must be determined based on expected future experience. Risk can be incorporated here using parameter margins: * Applying Margins to Expected Values: The actuary can choose to assess what margins to apply to the expected values of individual parameters. Under this approach, margins are incorporated into the assumptions for each individual parameter, and the risk discount rate would theoretically be the risk-free rate. * Use of Stochastic Models (for Risk Quantification): Although used primarily to determine the required return (RDR), stochastic models can be used to set the parameter values themselves. The parameter would take a range of values from a probability distribution, and the resulting price or profit metric could be chosen based on a specific percentile (e.g., the 60th percentile) to allow for risk. 2. Allowing for Risk through the Discount Rate / Valuation Method (The "Risk/Discounting" Basis) The risk associated with the timing and uncertainty of the future cashflows is typically managed through the discount rate or an explicit risk adjustment: * Using a Risk Discount Rate (RDR): The risk can be allowed for through the risk element of the risk discount rate. This involves using best estimates for the individual parameters but including margins for risk by assuming a higher risk discount rate than the risk-free rate. The margin between the RDR and the risk-free rate should attempt to reflect all sources of risk in the product. * Using a Market-Consistent Valuation (Risk Margin): An alternative approach is to perform a market-consistent valuation of the cashflows using the "risk neutral" approach. This involves using risk-free interest rates for the discount rates. Risk allowance is then made by including some form of margin in respect of other parameters (such as expenses, persistency, and mortality) to allow for the inherent risks in their estimation. This approach may also involve calculating a specific risk margin.

Answer 22

1) 1. Reflecting Expected Future Experience: The key part of the process is the determination of what future experience is expected. The derivation process involves determining what the best estimates of assumptions will be. 2. Reliance on Historical and Future Conditions: Assumptions are based on investigating historical experience to make best estimates, which are then adjusted considering expected future commercial and economic conditions. 3. Exclusion of Prudence Margins (Generally): This basis represents the core estimate of future values (like the interest rate $i'$) before any margin for prudence is explicitly included. 2) 1. Application Dependence: The basis is dictated by the specific application, which is ongoing profitability measurement. 2. Inclusion of Prudence Margins: The best estimates may need to be adjusted in order to include a margin for prudence. The inclusion of margins (whether in individual parameters, the discount rate, or chosen percentile) is necessary to ensure the resulting profit emergence is satisfactory given the inherent risk. 3. Consistency Requirement: It requires strict adherence to the principle of consistency, meaning that assumptions must be considered in their totality, making realistic allowance for how variables behave together (e.g., correlations between investment return, inflation, and tax treatment).

Answer 23

1.  The expense assumptions will be very different to those for your existing product.  However, the total expenses may end up being similar.  You do not need to make an allowance for commission.  You need an estimate of the total marketing costs for the period over which you are doing the pricing.  The take-up of policies per campaign / per Rand spent on marketing is a key assumption.  The sums insured will be lower than for the existing product, so you will need to consider carefully how to spread the expense per policy.  The underwriting expenses will be significantly less than for the existing product.  You will need to make an allowance for the cost of the IT development of the on-line offering, and the cost of the call centre. 2.  The lapses are likely to be significantly different from those on the existing product.  There are no intermediaries to keep the relationship with policyholders “warm”.  It is likely that there will be a high percentage of Not Taken Ups (NTUs).  The existing product’s lapse rates can be used as a starting point, but some margins should be built in to this.  Consider the lapse rates of any other limited underwriting / direct product offerings the company has.  Reinsurers may also be able to assist with setting this assumption 3.  This could be similar to the existing product.  A good starting point could be CPI or salary inflation. 4.  There are likely to be very little data in the sub-Saharan country.  You could consider the company’s existing data to detect any macro trends.  It would be worth looking at trends in the country.  You could approach a reinsurer for assistance. 5.  There is a lot more risk in the new product, so higher margins than used for the existing product would be required.  Higher margins will be required in respect of the assumptions where there is the most uncertainty. However, this will be restricted by the need to make the new product competitive.  If the business is reinsured this may reduce the need for margins. 6.  As above, you would want to load this, but within reason.  The profit margin could be the same as that for the existing product if you have allowed for sufficient risk margins.  It will also depend on the value placed on getting a foothold in this market.  Consideration should also be given as to the impact on the existing product. 7.  Some sensible assumption for the mix will be required.  Sensitivity testing should be carried out. 8.  Consider the existing sales volumes and consult with the company’s marketing staff to get an initial estimate.  Consider how well such business has been doing in the country as a whole.  Reinsurers may be able to provide input on this.  Sensitivity testing will be important. 9.  The current average sum assured would give an upper limit to the estimate.  It might be possible to work backwards from an expected affordable premium.  Sensitivity testing should be carried out.

Chapter 21 & 22: Setting assumptions Flashcards

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