Chapter 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

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

Answer 2

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 3

Give two definitions of “fair value”

Answer 3

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 4

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

Answer 4

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 5

Describe the replicating portfolio approach to valuing liabilities

Answer 5

• find a ‘ replicating portfolio’ of assets that most closely replicates the duration and risk characteristics of the liabilities
• the fair value of the portfolio of liabilities is then taken as the market value of the replicating assets
• these assets might include non-traded derivatives, so option pricing techniques or stochastic modelling might be required to assess the value

Question 6

Describe the traditional discounted cashflow method of valuing assets and liabilites

Answer 6

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

Question 7

Describe the risk-neutral market-consistent approach to valuing liabilities

Answer 7

• It involves discounting future liability cashflows at the pre-taxed market yield on risk-free assets, such as government bonds or swops

( effectively replicating the projected liability cashflows by using a hypothetical series of zero-coupon risk-free bonds)

( when setting the risk-free discount rate using government bond yields or swops, any default risk element in those yields should be striped out)

Question 8

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

Answer 8

• it may be appropriate to assume the highest cost option is always exercised
  ( the holder will always exercise an in-the-money and never exercise an out-of-money option)
• however, this might build too much caution into the valuation
• an option with a very high cost may be one that is unlikely to be the most valuable for the individual or chosen the most
• options are heavily dependant on the option holder’s behaviour, i.e some holders may fail to exercise in-the-money options, and some will exercise out-of-money options
• if market-traded derivatives (e.g put or call options) can be found which replicates the option in the liability, then the value of the policy option can be taken as the market value of that derivative)
• if a derivative is not available, it may be possible to construct a theoretical derivative that would replicate the option in the liability and then value that derivative using a model or ‘ closed form’ solution such as the black scholes formula

Question 9

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

Answer 9

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

Question 10

Outline the factors to consider when valuing guarantees

Answer 10

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 11

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

Answer 11

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 12

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

Answer 12

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.