C32 : Valuation of liabilities

Question 1

List two main approaches to valuing liabilities and assets

Answer 1

There are two main groups of approaches to carrying out a valuation of assets and liabilities:
1. ‘traditional’ discounted cashflow approaches based on long-term assumptions
2. market-related or ‘fair value’ approaches.

valuation of assets and liabilities should be consistent.

Question 2

Describe the Traditional discounted cashflow method of valuing assets and liabilties

Answer 2

• Assets and liabilities valued by discounting the future expected cashflows
• Discount rate = long term rate of interest (Inv return)

Criticism:
- Produces a value of assets that is different to market value
- Introduces an added element of risk and it is difficult to explain the difference to clients

Question 3

Define ‘fair value’

Answer 3

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

Question 4

Give an example of a case where a fair value of a liability is straightforward

Answer 4

• If a contract provides that it can be terminated at various points in time for predetermined values, with no discretion on the part of the product provider, then those values are necessarily the fair values of the liability.

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. Pensions in payment liabilities of a benefit scheme – there may be an active ‘buyout’ market consisting of insurance companies and other financial organisations that are prepared to provide immediate annuities to cover pensions in payments

Question 5

Difficulty in determining fair value of provider’s liabilities and the methods used for calculating fair value

Answer 5

• No liquid secondary market in most of the liabilities that actuaries are required to value
• So identification of fair value amounts form the market is not practical
• As a result fair values of liabilities need to be estimated using market-based assumptions

Methods:
1. Consider the liabilities as a series of financial options, and to use option pricing techniques to assess a value.
2. Another approach to obtaining a fair value of liabilities is to use a ‘replicating portfolio’.
3. A further approach values liabilities using an asset-based discount rate.

Question 6

Describe the replicating portfolio ‘market value’ method of valuing assets and liabilities

Answer 6

‘replicating portfolio’ approach involves
1. Taking the fair (ie 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.
2. The replicating portfolio can be established by using stochastic optimisation techniques, ie a form of asset / liability modelling.

Question 7

Describe Replicating portfolio method 1:
Mark to market (or market value) method

Answer 7

• Assets are taken at market value.
• Liabilities discounted at yields on investments that closely replicate the duration and risk characteristics of the liabilities – often bonds.
• Replicating portfolio can be determined using stochastic optimisation techniques (ALM)
• If corporate bonds are used credit risk premium should be stripped out.
• Ideally, term specific discount rates would be used to reflect shape of yield curve
• Market rate of inflation is derived as difference between yields on suitable fixed-interest and index-linked government bonds

Question 8

Describe Replicating portfolio method 2:
Bond yields plus risk premium

Answer 8

Method similar to mark to market:
- Assets are taken at market value.
- Liabilities discounted at yields on investments that closely replicate the duration and risk characteristics of the liabilities – often bonds.
- However, liability discount rate is adjusted (usually increased) to reflect an ERP (if equities are held)
- ERP may be constant of variable
- However, some actuaries think taking account of the extra return from equities is unsound unless account is also taken of the extra risk and ERP should not be used.

Question 9

Describe Asset-based discount rate method for valuing assets and liabilities

Answer 9

• Assets are taken at market value.
• An implied market discount rate is determined for each asset class, eg for fixed-interest securities it may be the gross redemption yield, for equities it involves
  estimating the discount rate implied by the current market price and the expected dividend and/or 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 ( or strategic asset allocation)

Question 10

Describe how the risk-neutral market-consistent value is determined

Answer 10

• Present value based on discounting future
  liability cashflows at the pre-tax market yield on risk-free assets (govt bonds)

Question 11

Discuss the general considerations involved in valuing options

Answer 11

1. Cautious approach is taken e.g. assume the highest cost option is taken
2. This can build up too much caution cost depends on: cultural bias, state of the economy, demographic factors, consumer sophistication
3. Allow for anti-selection risk when valuing options
4. Options and guarantees are not independent

Question 12

Discuss the issues surrounding the assumptions to be used for valuing guarantees

Answer 12

• Cautious approach is taken e.g. assume a high probability that the guarantee will bite
• Assuming worse case scenario in every case can build in too much caution
• Guarantees may be assessed on global basis
• Stochastic or deterministic model with scenario testing should be used for valuing guarantees to show the likelihood of the guarantee biting and the associated expected cost
• Value of guarantees and their influences on consumer behaviour will vary widely according to the economic scenarios and the sophistication of the market

Question 13

Explain why sensitivity analysis in necessary in setting provisions, and how it should be carried out

Answer 13

• 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.
• Sensitivity analysis can be used to determine these
  margins.
  -Sensitivity analysis could also be used to assess the extent of any global provisions.
• Start with a central set of assumptions, and then to
  vary each item in turn, to quantify the effect of assumption changes.
• also necessary to test the effect of multiple assumption change.

Question 14

List methods of allowing for risk in cashflows in traditional discounted CF approach

Answer 14

1. Best estimate and margin
2. Contingency loading
3. Discounting cashflows at a risk premium

Question 15

Discuss the method of allowing for risk in cashflows:

Best estimate and margin

Answer 15

• A risk margin is built in to each assumption by using ‘best estimate’ assumptions together with an explicit margin for caution.
• size of margins depends on the risk involved
• Where a risk factor has been stable for many years, the margin may be a simple percentage loading.
• Where there is more uncertainty, the margin may be determined stochastically in order to meet a specific risk tolerance.

Question 16

Discuss the method of allowing for risk in cashflows:

Contingency loading

Answer 16

• Liabilities are increase by a certain percentage. Size of margin reflects uncertainty involved.
• This method is very arbitrary and is falling out of favour.

Question 17

Discuss the method of allowing for risk in cashflows:

Discounting cashflows at a risk premium

Answer 17

– the discount rate is increased by a risk premium that reflects the overall risk of the liability (in a similar way to the discount rate used for capital project appraisal)

Question 18

Describe how Financial risk is normally allowed for in a
market-consistent or fair valuation

Answer 18

1. Replicating portfolio: market value of the replicating assets, will reflect the inherent risk associated with those equivalent assets.
2. Stochastic modelling and the use of a suitably calibrated asset model - through use of volatility assumption used to generate investment outputs.

The risks associated with the general mismatching of assets and liabilities are on the whole excluded from fair value calculations. This is because inclusion of this risk would be inconsistent with the general principle that the fair value of liabilities should be independent
of the assets held to meet the liabilities.

Question 19

Describe how Non- Financial risk is normally allowed for in a market-consistent or fair valuation

Answer 19

Different ways to allow for non-financial risk
1. Adjusting the expected future cashflows
2. Adjustment to the rate used to discount cashflows.
3. Extra provision or a capital requirement,

These adjustments will depend on:
1. the amount of the risk
2. the cost of the risk implied by market risk preferences.

Question 20

List the approaches an insurer may take to in calculating provisions for claims

Answer 20

1. Statistical analysis
2. Proportionate approach
3. Equalisation reserves
4. Case-by-case estimates

Question 21

Describe the approach an general insurer may take to in calculating provisions for claims:

Statistical analysis

Answer 21

A mathematical approach to establishing a
provision for the risk will give a valid answer if:
1. population exposed to a risk is large enough
2. consequence of a risk event is approximately normally distributed

• Provision could be set equal to the amount that keeps the probability of ruin below a specified level

e.g. provision for notified theft claims under a household contents =
number of notified claims * average cost of a claim in the last year,

plus margin for prudence using normal distribution

Question 22

Describe the approach an general insurer may take to in calculating provisions for claims:

Proportionate approach

Answer 22

• used for risks that have been accepted but for which the risk event has not yet occurred.
• set a provision on the basis that the premium charged is a fair assessment of the cost of the risk, expenses, and profit.

e.g.
- If a premium basis allows for 25% of the premium to cover expenses, commissions and profit,
- Establish a provision for the unexpired part of a year’s cover by assuming that 75% of the premium covers risks equally through the period of the policy.
- A provision for the unexpired duration can be set by a simple proportion of this 75%.

Question 23

Describe the approach an general insurer may take to in calculating provisions for claims:

Claim equalisation reserve

Answer 23

Claims equalisation reserves – used to smooth profits from year to year. Can be perceived by tax authorities as a way of deferring profit / tax

Question 24

Describe the approach an general insurer may take to in calculating provisions for claims:

Case-by-case estimates

Answer 24

• Appropriate when insured risks are rare events, and large variability in outcome (claims)
• the claims assessor examines each individual claim file for the reported claims and assesses the likely cost of settling each claim.