Chapter33-Valuation of liabilities

Question 1

Framework

Answer 1

1 Important factor in valuing assets and liabilities
2 Traditional discounted cash flow method
3 Drawbacks of DCF
4 Two definitions of fair value
5 Examples of straightforward fair value valuation of assets
6 Difficulty of valuing liabilities using fair value
7 Mark-to-Market method
8 Bond yield plus risk premium method
9 Asset-based discount rate approach
10 Risk -neutral market consistent valuation
11 Valuing guarantees
12 Valuing options
13 Option exercise rate and reasons for not exercising options that are in the money
14 Allowing for risk in cash flows
15 Allowing for risk in cash flows using market consistent method
16 Establishing provisions - general insurer

Question 2

Traditional discounted cash flow method

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

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

Mark-to-Market method

Answer 4

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 optimisation 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-linked government bonds of an appropriate term.

Question 5

Bond yield plus risk premium method (4)

Answer 5

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 (eg an equity risk premium if equities are part of the replicating portfolio).

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 6

Asset-based discount rate approach

Answer 6

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.

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 7

Risk -neutral market consistent valuation

Answer 7

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 (eg in the UK) or government bonds.

Question 8

Establishing provisions - general insurer

Answer 8

1. Statistical analysis – used where many claims following a known pattern, eg if claim numbers and claim amounts follow a recognised distribution, the provision could be set equal to the amount that keeps the probability of ruin below a specified 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 unexpired period of cover.
4. Equalisation reserves – used to smooth profits from year to year. May not be recognised by the regulator, and can be perceived by the tax authorities as a way of deferring profit and thus tax.