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.

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.

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

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 method of valuing assets and liabilties

Answer 7

Assets are taken at market value.

Liabilities are discounted at the yields on investments that closely replicate the duration and risk characteristics of the liabilities - often bonds. The replicating portfolio can be determined using stochastic optimization techniques (asset-liability modelling)

Ideally, term-specific discount rates would be used to reflect the shape of the yield curve.

Other assumptions should also be market related, for example the market rate of inflation is derived as the difference between the yields on fixed interest and index-lined government bonds of an appropriate term.

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 assets taken at market value and the liabilities discounted at the yields on investments that closely replicate the duration and risk characteristics of the liabilities- often bonds.

However, the liability discount rate is adjusted to reflect a risk premium.

The risk premium may be constant or variable.

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.

Question 9

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

Answer 9

Assets are taken at market value.

An implied market discount rate is determined for each asset class.

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 asst 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, 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.
2. The policyholder receives beneficial tax treatment on the alternative benefit.

Question 15

Describe 3 approaches to allowing for risk in the cashflows used for valuing liabilites

Answer 15

1. Best estimate and 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 DECREASED by a risk premium that reflects the overall risk of the liability.

Question 16

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

Answer 16

Financial risk - 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. 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. 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.