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The Actuary The magazine of the Institute & Faculty of Actuaries

Insurance: Judgment call

Over the past decade, actuarial methods for rigorously taking account of the complex forms of financial market risk that can be embedded in insurance liabilities have been revolutionised. The concept of ‘mark-to-market’ for insurance liabilities has been crucial to this transformation. Indeed, mark-to-market valuation is now an essential element of actuarial risk management thinking and practice. It underpins UK insurance regulatory capital and will similarly form part of the Europe-wide Solvency II implementation. Insurance groups use it to measure economic capital requirements, to price and design products and to inform capital management strategy. Rating agencies use it to justify changes in the credit ratings of global insurance groups.

‘Mark-to-market’ sounds straightforward and objective — it is a matter of working out how to deconstruct insurance liabilities into an equivalent portfolio of financial instruments and then take the cost of this portfolio to be the liability market value. However, mark-to-market is not so simple in long-term, complex insurance liabilities. This gives rise to the concept of a ‘market-consistent valuation’ — a piece of jargon that simultaneously aspires to a market-value basis while recognising that there may not always be a market price available.

Insurance liabilities can differ from typical market-traded securities in a number of ways. Firstly, they are often highly illiquid. Secondly, the cash flows may not only be a function of financial market outcomes, but can also depend on policyholder behaviour and decisions made by management — neither of which may be entirely rational or predictable. These unique characteristics create the need for actuarial judgment in the market-consistent valuation process. This need for judgment falls into three areas:

1 Illiquidity premium
Insurance liabilities are often inherently illiquid. For example, an annuity writer can assume there is no circumstance under which the annuity premium will have to be returned to the annuitant as a lump sum at short notice. Does the market price of a liquid fixed cash flow differ from an illiquid one, and thereby justify placing a lower value on illiquid cash flows on the insurance balance sheet?

Given how difficult it is to observe any illiquid price ‘almost by definition’, how can you tell? Traders and portfolio managers generally accept that the more illiquid an asset is, the less it is worth; the illiquidity premium. Economic models have been developed to estimate this illiquidity premium, and these have been used to adjust market-consistent liability values downwards. Inevitably, they involve difficult parameter estimation, and judgment may be required in considering to what extent such adjustments should be made to market-consistent liability values. This issue is very topical — currently there is much discussion about the extent to which adjustments for illiquidity should be made for the purpose of estimating Market- Consistent Embedded Value.

2 Extrapolation of observable market prices
Market consistency for insurance liabilities means that the valuation should be consistent with prices of assets with similar characteristics. For fixed insurance liabilities or cash flows with option-like features guarantees, for example, these values should be consistent with market option prices and the prices of long-dated bonds. However, the required interest rates and/or option prices may fall beyond the maturities observable in markets. This issue is most acute in economies where capital markets are less developed. However, in practice it arises in every market, including the world’s deepest, broadest capital markets. Just try to find a quote for an out-of-the-money, 30-year S&P 500 option. Therefore, actuarial judgment and technical expertise is required to estimate reasonable and consistent ‘mark-to-model’ prices for these long-term exposures.

3 Market-consistent assumptions for highly complex forms of market risks
Future policyholder and management actions, which may be contingent on future financial market behaviour, can generate very complex, path-dependent forms of optionality in insurance liabilities such as with-profit policies or variable annuity contracts. Market-consistent valuation can often involve using models to (subjectively) infer what ‘vanilla’ option prices might imply for much more complex forms of market-risk optionality. It is important for the actuary to consider the potential ramifications of this in the valuation process. For example, it may mean that using a model that produces a better fit to vanilla prices could feasibly produce a less market-consistent liability valuation — if the model produces a less appropriate description of the non-vanilla risk features that are important to the liability.

So what does this all mean?
We can draw a number of conclusions. Actuarial judgment must form a crucial part of market-consistent insurance liability valuations — the subjectivity of the challenge requires the deep ‘domain knowledge’ that is unique to actuaries. Stochastic models and financial economics are also vital parts of the valuation methodology. Over the last decade, the level of expertise within the actuarial profession in how to apply the insights and power of these ideas and techniques to insurance business has grown hugely. The publicity surrounding the valuation challenges of the recent financial turmoil has heightened awareness that this will continue to be a fast-developing and strategically important area of practice for the global profession.

Craig Turnbull is the regional head for Barrie & Hibbert in North America