Chapter 33 - Valuation of liabilities Flashcards
What are the two primary methods of valuation of liabilities.
Traditional discounted cashflow (TDCF) based on long-term assumptions
Market-consistent value or fair value (FV)
- This value should be independent of assets held
Note:
- Techniques for these are not necessarily different
- Rather method for determining assumptions are different (notably the discount rate)
What is the main principle for valuing assets and liabilities.
Asset and liability valuation should be consistent
- May be difficult to achieve with traditional method if market value used to value assets
- Asset and liability values should, however, still be valued independently
List the main differences between TDCF and FV approaches to valuation.
TDCF vs FV:
Passive | Active
Long-term assumptions | Current assumptions
Update infrequently | Frequently updated
Stable results | Volatile results
DCF or other method | DCF
Assets not at market value | Assets at market value
Aims to smooth market fluctuations | Aims to follow the market
Subjective | Less subjective
Define the fair value of liabilities.
The amount for which a liability could be settled between knowledgeable, willing parties in an arm’s length transaction
OR
The amount that an enterprise would have to pay a third party to take over the liability
Discuss how the discount rate is determined for fair valuation of liabilities
Liability values not observable in the market
- Or at least not in a deep and liquid market
Estimation techniques are required such as:
Option pricing techniques (slightly outdated)
- Treat liabilities as options and use option pricing techniques such as Black-Scholes
Replicating portfolio (see also practice question at end of chapter)
- Value of liabilities is the value of a portfolio of assets that most closely replicate the duration and market risk characteristics of the liabilities
- Market inflation taken as difference in yields on suitable portfolios of fixed-interest and index-linked bonds
- Better, more complicated method would be to use term-standard discount rates which vary over time to reflect shape of the yield curve
- Two approaches are
1) Mark to market
- A @ market value
- L discounted @ yields on investments that match liabilities, often bonds (use corporate or government depending on credit risk)
2) Bond yields plus risk premium
- A @ market value
- L discounted @ discount rate found by adjusting bond yields (or other) by adding constant/variable equity risk premium
- More common to use variable risk premium, which is derived from market information and actuarial judgement
Asset-based discounting
- Uses split of assets backing the liabilities - either actual or strategic benchmark
- Discount rate is weighted average of expected returns per relevant asset class
- Different ways in theory to determine expected returns such as
1) Implied rates from the market
2) Bond yield plus adjustments - Could argue this is not a fair value of liabilities, since valuation of liabilities is clearly not independent of the assets
(Market) risk neutral
- Returns on assets above risk-free come with risk and so should allow for that risk
- Liabilities discounted using risk-free curve (bond yield or swap)
- Removes market risk from the liability discounting, so
allowance is made for this elsewhere
- Advantage is lack of reliance on asset values for valuation
Discuss how to allow for risk in liability valuations.
!Go through slides and section 5 and see if you can improve this card!
Ways to include risk
1) Implicit in reserves
2) Explicit risk adjustment or risk margin in assumptions
3) Explicit contingency loading/provisions
4) Some combination of the above
Implicit risk adjustments can be via:
- Best estimate + margin in each assumption
- Discounting at a risk discount rate/risk premium
Several sources of risk in model
- Data
- Model
- Assumptions
- Possible short-term fluctuations due to random nature of values
“How much” allowance to make depends on
- Variability and riskiness of cashflows
- Risk appetite
- Capital requirements
- Opportunity cost of holding capital
Can assess with sensitivity analysis and similar types of tests.
Discuss how options and guarantees are allowed for in liability valuations.
Need to determine when in or out of the money
Also need to assume take up in case of options when options are in the money
- i.e. assume worst case scenario
- Could rather assume some margin, so if options are significantly in the money then assume they will be exercised
- Take up is very dependent on policy holder behaviour which is difficult to predict and so have to make subjective assumptions
Need to consider the dynamics of the option or guarantee under different scenarios such as
- economic states
- stochastic modelling of investment guarantees
- Inter-dependency between certain options & guarantees
Recap: List the main types of options and guarantees
Surrender/Withdrawal
Extend term or defer maturity payment
Reduce or increase premiums
- Includes paid-up value where premiums are stopped but policy is still in force
Extend the term on guaranteed terms (is this guaranteed insurability?)
- Could be with or without renewed evidence of health
Investment guarantees, such as
- Guaranteed minimum death, surrender or maturity value
- Guaranteed minimum bonus rate, or smoothed returns with zero minimum
- Guaranteed minimum pension increase
- Fixed maturity value
- Minimum investment return
- Could be several other examples
List the main factors which determine when a policyholder/member would take up an option.
Economic state
Policyholder preferences
Tax treatment
Ability to select against insurer
- Latter 3 are related to:
1) Demographic factors such as age, health and employment status
2) Cultural bias (What could this include?)
3) Consumer sophistication
Briefly discuss some alternative liability valuation techniques.
Statistical analysis
- E.g., If population exposed to a risk is large and severity of risk approximately normally distributed
- This or other cases may lead to simple mathematical approach giving valid valuations
Case-by-case estimates
- If insured risks are rare and have large variability
- Essentially difficult to calculate provisions, so prudence of assumptions may be advisable
Proportionate approach
- Set provision on basis that premium charged is fair assessment of cost of risk, expenses and profit
- See example p.19
Equalisation reserves
- If company wishes to smooth future profits in light of possible high variability
- Establish equalisation reserves in years with profits to smooth results in future years when claims are excessive
- Do no fit with definition of provision
- Possible disadvantages:
1) Not recognised under some regulatory regimes, e.g. solvency II
2) Tax authorities may not be prepared to acknowledge these as reserves as they may be seen as a way of deferring profits and hence tax.
