Chapter 36: Valuing Liabilities II

Question 1

Describe the traditional discounted cashflow approach

Answer 1

Both assets and liabilities are valued by discounting the future expected cashflows using a long-term rate of interest.

Question 2

2 Market-related approaches to valuation

Answer 2

Asset-based discount rate approach

Replicating portfolio approaches

Question 3

Asset-based discount rate approach

Answer 3

For all of the market-related approaches, assets are taken at market value. 
An implied market discount rate is determined for each asset class, e.g. using the gross redemption yield for a government bond.
Liabilities are discounted at a rate that is calculated as the weighted average of the individual discount rates. The weights are based on the proportions invested in each asset class using either the actual investment portfolio, or - if this is not representative of the usual strategy - the strategic benchmark.

Question 4

2 Replicating portfolio approaches

Answer 4

• Mark-to-market approach

- Replicating portfolio bond-yields plus risk premium method

Question 5

Mark-to-market approach

Answer 5

As for the asset-based approach, 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.
If corporate bonds are used, the credit risk premium should be stripped out.

Ideally term-standard discount rates would be used.

Question 6

Replicating portfolio bond-yields plus risk premium method

Answer 6

As for the mark-to-market approach, but the liability rate is adjusted by adding an equity risk premium.

However, some actuaries think that taking account of the extra return from equities is unsound unless extra account of the extra risk; and that the equity risk premium should not be used.

Question 7

Why has there been a move in many countries towards the market-value approaches and away from the traditional cashflow approach in pension schemes

Answer 7

Mainly due to requirements from regulatory and accounting standards requiring more realistic reporting.

Question 8

Fair value

Answer 8

The amount for which an asset can be exchanged or a liability settled between two knowledgable, willing parties in an arms’ length transaction.

Question 9

Why might it be difficult to determine the fair value of liabilities?

Answer 9

Most insurance company or pension scheme liabilities are not actively traded.

Question 10

A way to determine the fair value of a set of liabilities

Answer 10

Start by determining the risk-free fair value, by:
- discounting the liability values using the pre-tax market yield on risk-free assets, e.g. government bonds of a suitable duration.

Then we would need to consider how to allow for the various risks associated with the liabilities:

• financial risks can be allowed for either by
• – the replicating portfolio market value approach, or by
• — using a stochastic model with a suitably calibrated asset model.
• Mismatching risk is generally ignored, since it is a general principle of fair value that the liabilities should be independent of the actual assets held.
• Non-financial risks such as demographic risk, expense risk, withdrawal risk, compliance risk and operational risk can be allowed for either by adjusting the expected future cashflows or via an adjustment to the discount rate used.

Question 11

3 Approaches to allowing for risk in cashflows

Answer 11

• adopt a best-estimate plus margins basis, building a risk margin into each assumption
• apply a contingency loading, increasing the liability value by a certain percentage
• discounting the cashflows at a risk premium. Cashflows are valued on a best-estimate basis, but the discount rate reflects the overall risk in the project or liability.