Ch 33: Valuation of liabilities

Question 1

What is the most important factors to consider when setting the discount rates used to value the assets and liabilities?

Answer 1

CONSISTENCY between the rates used for asset and liability valuations.

Question 2

Describe the traditional discounted cashflow method of valuing assets and liabilites

Answer 2

Both assets and liabilities are valued by discounting the future cashflows using a rate that reflects the long-term future investment return expected.

The rates and assumptions are based on actuarial judgement.

Question 3

What is the major criticism of the traditional discounted cashflow method of valuing assets and liabilities?

Answer 3

It provides a value of the assets that is different from the market value. It is difficult to explain to clients.

(Consequently, there has been a move towards market-related methods of valuing assets and liabilities)

Question 4

Give two definitions of “fair value”

Answer 4

1. The amount for which an asset could be exchanged or a liability settled between knowledgeable, willing parties in an arm’s length transaction.
2. The amount that the enterprise would have to pay a third party to take over the liability

*note: fair values implies that a market-related approach is used

Question 5

Give 2 examples of financial contracts for which it might be fairly straightforward to determine a fair value.

Answer 5

1. Unit linked contracts - the value of the liability is effectively known since it is the value of the units and the unit price is determined on a frequent basis.
2. The pensions in payment liabilities of a benefit scheme - there may be an active ‘buyout’ market consisting of insurance companies and other financial organizations that are prepared to provide immediate annuities to cover pensions in payment.

Question 6

What is the major difficulty in determining the fair value of a provider’s liabilities?

Answer 6

There is no liquid secondary market in most of the liabilities that actuaries are required to value, so the identification of fair amounts from the market is not practical. As a result, fair values of liabilities need to be “estimated” using market-based assumptions.

Question 7

Describe the replicating portfolio - mark-to-market (market value) method of valuing assets and liabilities

Answer 7

Market information provides assumptions: inflation and discount rate, and related assumptions.

1. Assets are taken at MARKET VALUE
2. Liabilities are DISCOUNTED at yields on investments that MATCH the liabilities (often bonds)
   
   • May be government or corporate bonds - but adjust corporate bonds to allow for credit risk
3. The (market rate of) inflation can be taken as the DIFFERENCE between YIELDS on suitable portfolios of fixed and index-linked bonds

*note: a better way would be to use the discount rates provided by the yield curve.

Question 8

Describe the replicating portfolio - bond yields plus risk premium method of valuing assets and liabilities

Answer 8

The method is similar to the mark to market method with:

1. Assets taken at MARKET value
2. Liabilities discounted at the ADJUSTED YIELDS on investments that closely replicate the duration and risk characteristics of the liabilities - often bonds.
   2.1 The discount rate used is found by adjusting bond yields by the addition of a constant/variable Equity Risk
   Premium

However, some actuaries think that taking account of the extra return from other assets is unsound unless account is also taken of the extra risk, and that a risk premium should not be used.

*Note: This methods starts by using a DISCOUNT rate based on BONDS YIELDS as in “mark to market methods”, but then ADJUSTS DISCOUNT RATE to take into account the expected returns on other assets classes.

Question 9

Describe the asset-based discount rate approach for valuing assets and liabilities

Answer 9

1. Assets are taken at MARKET value.

An IMPLIED market discount rate is determined for each asset class.
(e.g. fixed interest assets = GRY; equities = discount rate implied by market price and the expected dividends and sale proceeds)

The liabilities are valued using a discount rate calculated as the weighted average of the individual discount rates based on the proportions invested in each asset class.

The discount rate could be determined using the distribution of the actual investment portfolio or the scheme’s strategic benchmark (if the current asset allocation is not representative of the scheme’s usual investment strategy)

Question 10

Outline how the fair value of liabilities can be determined by performing a “risk-neutral” market-consistent valuation.

Answer 10

The value is determined as the present value of future liability cashflows, discounted at the pre-tax market yield on risk-free assets.

Such assets might be swaps or government bonds.

Question 11

Outline the factors to consider when valuing guarantees

Answer 11

1. In general, a CAUTIOUS approach is taken
2. However, unless all guarantees are in the money, assuming the worst case scenario in every case will build in too much caution.
3. A STOCHASTIC model should be used for valuing guarantees (taking the class of business as a whole), to show the likelihood of the guarantees biting and the associated cost. Parameter values should reflect the purpose for which the results are required.
4. Guarantees may become more or less onerous over time.
5. The value of guarantees and their influences on consumer behavior will vary widely according to the economic scenarios and the sophistication of the market.

Question 12

Outline the factors to consider when assessing the cost of an option from the perspective of the provider

Answer 12

1. In general, a cautious approach is taken
2. However, this can build in too much caution.
3. For example, a policyholder may not exercise the highest cost option despite it being financially better for them to do so.
4. It is necessary to allow for anti-selection risk when valuing options, or to mitigate this risk using eligibility criteria for exercising the option.
5. Options and guarantees are not necessarily independent; some guarantees may make options more valuable in certain circumstances.
6. Deterministic and closed-form (e.g. Black Scholes) methods could be used.

Question 13

State 4 factors on which the option exercise rate assumption will depend

Answer 13

1. The state of the economy
2. Demographic factors, e.g. age, health, employment status
3. Cultural bias
4. Consumer sophistication

Question 14

State 2 examples of where an assumption of the policyholders always exercising an option that is in-the-money from the provider’s perspective may not be appropriate

Answer 14

1. The policyholder prefers to take the alternative benefit as it is paid as a lump sum cash amount.
   - -> cash-in-hand has a powerful influence on an individual’s decision.
2. The policyholder receives beneficial tax treatment on the alternative benefit.
   - -> e.g. taking a % lump sum of pension, as it is tax-free. Uses rest of pension to purchase annuity-based income (which is taxed)

Question 15

Describe 3 approaches to ALLOWING FOR RISK in the cashflows used for valuing liabilites

Answer 15

1. Best estimate + Margin - a margin is explicitly built into each assumption. The size of the margin reflects the amount of risk involved and its materiality to the final result.
2. Contingency loading - the liabilities are increased by a certain percentage. The size of the margin reflects the uncertainty involved. This method is very arbitrary.
3. Discount rate - the discount rate is adjusted by a risk premium that reflects the overall risk of the liability.
   - -> usually defined by governing bodies. (risk discount rate)

Question 16

Outline how risk can be allowed for in a market-consistent or fair valuation of liabilities

Answer 16

Financial risk - implicitly allowed for by using a REPLICATING PORTFOLIO or STOCHASTIC modelling approach. Mismatching risk is typically ignored, as the fair value of the liabilities should be independent of the assets held.

Non-financial risk - allowed for by adjusting the expected cashflows or by adjusting the discount rate. Alternatively, an extra provision or capital requirement can be held (such as the risk margin under Solvency II). These adjustments depend on:
- the amount of the risk
- and the costs of the risk implied by the market.

Question 17

Outline 4 methods that an insurance company might use for establishing provisions, particularly a general insurance company.

Answer 17

1. Statistical analysis - used where many claims following a known pattern/distribution. The provision could be set equal to the amount that keeps the probability of ruin below a certain level.
2. Case-by-case estimates - used if the insured risk is rare or there is large variability in the outcome, such as for personal injury claims.
3. Proportionate approach - used for risks that have been accepted but for which the risk event has not yet occurred. Provision is a proportion of the part of the premium designed to cover claims. The proportion will represent the unexpected period of cover.
4. Equalization reserves - used to smooth profits from year to year. May not be recognized by the regulator, and can be perceived by the tax authorities as a way of deferring profit and thus tax.

Question 18

The role of Sensitivity Analysis in the valuation of liabilities?

Answer 18

The assumptions used for setting provisions are estimates of future experience, taking any requirements for solvency capital into account. They are the expected values plus risk margins for adverse future experience..

These PROVISIONS are EXPECTED VALUES plus RISK MARGINS for adverse future experience.
-> Sensitivity analysis can be used to determine these margins.

Sensitivity testing could also be used to calculate global provisions that may need to be set up to cover potential future adverse experience.

Question 19

Describe a “replicating portfolio” in the contest of liability valuation.

Answer 19

Using a “replicating portfolio” approach involves taking the fair (i.e. market) value of the liabilities as…
the MARKET VALUE of the PORTFOLIO of ASSETS that…
most closely replicates the DURATION and RISK characteristics of the liabilities.

This can be done by using stochastic optimisation techniques - i.e. a form of asset-liability modelling.