Ch33: Valuation of liabilities

Question 1

Three methods for valuation

Answer 1

• Traditional DCF based on long-term assumptions
• Market-based that reflect assets held; current value and yield
• Fair value approaches

Question 2

Traditional DCF method description

Answer 2

• Long-term assumptions are set using actuarial judgement
• Key assumption is future expected investment returns
• For consistency: Assets also valued by discounting cashflows
• Criticism: Different value on assets than the market value, introduces risk + inappropriate for short-term valuations such as a break-up valuation

Question 3

Market-based approach reflecting assets held description

Answer 3

• Liabilities are valued using a discount rate that reflects the weighted average yield on the backing assets held, where this yield is based on the current implied market discount rates
• E.g for fixed-interest securities it would be GRY
• E.g for equities might involve estimating yield implied by current market price and expected dividend and/or sale proceeds
• Often would be a deduction from expected return to allow for risk
• Not fair value since under this approach since valuation of liabilities reflect actual assets held. For fair value, value of liabilities should be independent of assets held to back them.

Question 4

Fair valuation description

Answer 4

• First assets are valued at market value provided it is available and meets definition of fair value.
• Then these methods seek to place a market value on the liabilities
• Two definitions of fair value are:
  + The amount for which an asset could be exchanged or a liability settled between knowledgeable, willing parties in an arm’s length transaction.
  + The amount that the enterprise would have to pay a third party to take over the liability
• Two approaches to estimating fair value of liabilities:
  + Replicating portfolio approach and Risk-neutral market-consistent approach

Question 5

Two fair value approaches to estimating value of liabilities

Answer 5

Replicating portfolio approach:
- Find replicating portfolio of assets that most closely replicates the duration and market risk characteristics of the liabilities
- Fair value of liabilities is then taken as the market value of the the replicating assets.

Risk neutral market-consistent approach
- Discounting future liability cashflows at the pre-tax market yield on risk-free assets, such as government bonds or swaps
- Any credit or default risk element in the yields should be stripped out

Question 6

Valuing options

Answer 6

• Necessary to make assumptions about the proportion who will exercise an option at each point in time at which exercise is available
• When setting provisions, may be appropriate to assume that the highest cost option is always exercised
• However may build too much caution into the valuation (option with very high cost may be one that is unlikely to be most valuable to an individual)
• Biases: Attraction of cash; tax benefits
• With options, risk of selection against provider. Mitigate by setting eligibility criteria for option or by setting terms that favor one option over the other.
• Other factors affecting value of options:
  + Assumptions to value option depend on:
  * State of the economy
  * Demographic factors such as age, health and employment status
  * Cultural bias
  * Consumer sophistication
  + Aim is to value option by finding a market option that will close out the option in the policy

Question 7

Valuing guarantees

Answer 7

• Risk that the guarantee will apply and so costs will be greater than would otherwise have been the case
• Unless all guarantees are in the money, providing for the worst-case scenario for every contract will mean that unnecessarily large provisions are made
• Usually best valued by a stochastic approach

Question 8

Allowance for risk in DCF valuation (3)

Answer 8

• Best estimate and margin
  + Risk margin built into each assumption by using best estimate assumptions together with an
  explicit margin for caution
  + Assessment of necessary margins depend on the risk involved, and its materiality to the
  final result
  + Care should be taken considering the overall effect when introducing margins, as multiple
  small margins may lead to a cumulative effect of the basis being stronger than intended
• Contingency loading
  + Approach is to increase the liability value by a certain percentage
  + Degree of contingency loading is in effect another assumption and should ideally reflect the
  degree of uncertainty that exists
• Discounting cashflows at a risk premium
  + Cashflows are assessed at best estimate basis, then discounted at a rate of return that
  reflects the overall risk of a project or liability
  + Frequently risk discount rate is not associated with the cashflow but rather the opportunity
  cost of the firm not pursuing some other business opportunity

Question 9

Allowance for risk in a fair valuation

Answer 9

• Financial risk
  + Normally allowed for in a market-consistent manner either by a replicating portfolio or
  through stochastic modelling and the use of a suitably calibrated asset model
  + If replicating portfolio has been found, financial risk is allowed for implicitly by taking the
  market value of the replicating assets, since the market value will reflect the risk associated
  with those equivalent assets
  + If stochastic modelling is used, financial risk is allowed for through the volatility assumption
  used to generate investment outputs
• Non-financial risk
  + Allowed for by either adjusting the expected future cashflows or by adjustment to rate used
  to discount cashflows.
  + Alternatively an extra provision or capital requirement can be held for non-financial risks.

Question 10

Methods of calculating provisions for general insurers(4)

Answer 10

• Statistical analysis
  + Mathematical approach using normal distribution
• Case-by-case estimates
  + In the case where insured risks are rare events and have high variability in outcome, then
  statistical analysis may break down.
• Proportionate approach
  + Provisions for risks which provider has accepted but risk event has not yet occurred, is to
  set provisions based on the assumption that the premium charged is a fair assessment of
  the cost of risk, expenses and profit
  + say 75% of premium covers risks equally throughout the period of the policy
• Equalization reserves
  + Provider wishes to exhibit stable results from year to year
  + Establish a claims equalization reserve in years when no claim arises, with a view to use the
  reserves to smooth results when a claim does occur.