What are the two main approaches to valuing liabilities?

- Discounted cashflow approach based on long-term assumptions
- Market-related or fair value approaches
- Important to use consistent methods to value assets & liabilities

Discounted cashflow method outline:

- Long-term assumption of future expected investment return is needed
- Future liability cashflows are discounted to present value using this rate
- For consistency, assets are also valued using the same approach, future cashflows discounted

Major criticisms of DCF method:

- It places a value on assets different from mkt. value which introduces another element of risk
- This method is inappropriate for short-term valuations eg. discontinuance valuation for benefit scheme or break-up valuation for insurance company

What are the two defns of fair value?

- Amt. for which an asset could be exchanged or a liability settled b/w two knowledgeable willing parties in an arm’s length transaction
- Amt. that the enterprise would have to pay a 3rd party to take over a liability

Why is identification of fair values/market values not practical for liabilities? What is done as a result?

- Because there is no secondary market for many of the liabilities that actuaries are meant to value
- As a result, mkt. based approaches such as replicating and option valuing techniques are used

Outline the mark to market method of valuing A/Ls:

- Assets are taken at mkt. value
- Liabilities are discounted at yields on investments that match the liabilities wrt term, currency & nature - often bonds
- Bond yield may be based on govt. or corporate bonds -> latter allows for credit risk

o Term-standard discount rates could be used to vary rates over time to reflect yield curve

o Mkt. rate of inflation derived as diff. b/w yields on suitable portfolios of FI & IL bonds - This tends to be conservative approach to valuation since its based on bond yields

Outline bond yields + risk premium method of valuing A/Ls:

- Assets taken at market value
- Discount rate found by adjusting bond yields by adding a constant/variable ERP
- Adding constant ERP gives same result as mark to mkt method except this usually results in lower value placed on liabilities
- Adding variable ERP using mkt info & actuarial judgment gives a optimistic estimate of liabs

Outline the asset-based discount rate method of valuation:

- Assets are taken at market value
- Implied market discount rate calculated for each asset class eg

o For FI securities it may by GRY

o For equities it involves estimating discount rate implied by current mkt price & expected div/sale proceeds

o Might be subjective for assets like property - Liabs are valued at the discount rate calculated as the weighted avg. of discount rates based on proportion of different asset classes held
- Discount rate could also be determined using scheme’s strategic benchmark or the dbn of actual investment portfolio

Under what circumstances can an option/guarantee be exercised?

- In situations where the guarantees make the option more financially advantageous (in the money)
- Sometimes options are exercised even when the alternative would be better for the client financially eg. surrendering a LI policy because of having a better immediate use for the money

Why might a p/h exercise an option even if its not in their best financial interest?

- Better immediate use for lump sum of cash eg. mortgage, financing home improvements, car, holiday
- Beneficial tax treatment in the hands of the individual

How to value options & guarantees prudently?

- Assuming that options will only be exercised “in the money” is highly prudent even for solvency calculation
- Take up rate of the option will be set according to the level of prudence required

What are the factors affecting the value of options?

- State of the economy (options must be scenario specific)
- Consumer sophistication
- Demographic factors eg. age, health, employment status
- Cultural bias eg. preference for cash to spend immediately

Which method is the best for estimating the price of guarantees?

- A stochastic approach which takes the class of business as a whole

What is sensitivity analysis used for?

- Used to determine the risk margins to place on assumptions used to set provisions

o While taking solvency capital into account - Used to determine the global provisions to be kept aside for potential future adverse experiences

Outline how to carry out sensitivity analysis:

- Start with a set of central assumptions
- Change one assumption at a time in a logical manner
- Quantify the effect of assumption changes
- Then test the effects of multiple assumption changes
- Assumptions are usually neither independent nor fully correlated

=> Effect of applying two tests simultaneously will be less or greater than sum of individual effects

What are the methods of allowing for risk in cashflows of a DCF valuation?

- Best estimate and margin
- Contingency loading
- Discounting cashflows at a risk premium

Outline the best estimate & margin approach:

- Risk margin built in by taking the best estimate assumptions and adding an explicit margin for the risk
- Assessment of the risk margins depends on the risk involved (stability & nature) and its materiality to the final result
- If all assumptions have small margins, the overall effect might result in an overly strong basis

Outline the contingency loading approach:

- Increase the liability value by a certain percentage
- The contingency loading should reflect the degree of uncertainty that exists in the liability
- Seen as arbitrary given the available methods

Outline the discounting CFs at a risk premium approach and its characteristics:

- Traditional DCF approach, CFs are assessed on best estimate basis
- CFs are then discounted @ a rate of return which reflects the overall risk of the project or liability
- Discount rate found is:
- > Somewhat arbitrary
- > Prescribed by firm’s governing body
- > Frequently based on the opportunity cost of the firm not pursuing other business ventures
- If discount rates are high, it can affect near and remote CFs disproportionately to the actual risk of the CFs

What types of risks need to be allowed for in market consistent or fair valuation?

- Financial risk

- Non-financial risk

How to allow for financial risk in liability cashflow wrt market consistent approach?

- Replicating portfolio approach implicitly allows for financial risk by taking mkt value of replicating assets
- Stochastic modelling and the use of a suitably calibrated model

o Allows for risk through a mkt. consistent volatility assumption used to generate investment outputs - Exclude risks associated w mismatched A/Ls when finding fair value

o Fair value of liabs calculated should be independent of the assets held to meet liabs

How to allow for non-financial risk in liability cashflow wrt market consistent approach?

- Adjusting expected future CFs
- Adjusting discount rate used
- Holding extra provisions or capital req. (risk margin in Solvency II) against non-financial risks

Adjustments depend on:

- The amount of risk
- Cost of risk implied by mkt risk preferences

What are the different methods of calculating provisions?

- Statistical analysis
- Case-by-case estimates
- Proportionate approach
- Equalization reserves

Outline statistical analysis approach for calculating provisions:

- Large population exposed to similar risk
- Consequence of the risk follows a certain distribution approximately
- Mathematical approach can be used to determine provisions at a given ruin probability

Outline case-by-case estimate approach for calculating provisions:

- Insured events are rare w large variability in outcome
- Involves a claims assessor examining individual reported claims and assessing likely cost of settling the claim (case estimates)

Outline proportionate approach for calculating provisions:

- Provisions are made based on assumption that premium charged was a fair assessment of cost of risks, expenses and profits
- x% of the premium allows for expenses & profits & (1-x)% of premium covers risk equally throughout policy period

Outline equalization approach for calculating provisions:

- For companies that have low probability risks with a highly volatile financial outcome
- To smooth results a company establishes equalization reserves
- It sets aside the profits from years without claims to smooth results when the claims actually occur

o Not all regulatory regimes recognize equalisation reserves -> It is seen as a method to defer profits & hence taxes