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29th May 2012

31 MAY 2012 | RICHARD PURCELL; GARETH MEE

Under the current realistic solvency regime, insurers are required to hold assets in excess of their best-estimate liabilities and capital. With the advent of Solvency II, insurers will need to hold an additional 'risk margin' (RM) on their balance sheet.

This risk margin is designed to represent the amount an insurance company would require to take on the obligations of a given insurance company. It effectively means that if an insurer were, as a result of a shock, to use up all its free surplus and capital, then it would still have sufficient assets to safely wind-up and transfer its obligations to a third party.

The risk margin, according to the latest draft of the Solvency II text, is to be calculated using a cost of capital approach; a firm must project its solvency capital requirement (SCR) in respect of non-hedgeable risks, and apply a prescribed cost of capital charge of 6% pa. This charge is then discounted at the risk-free rate to determine the risk margin. The risk margin will be relatively large for insurers with significant non-hedgeable risks, such as longevity, and that have a long duration (duration being a measure for interest rate sensitivity).

It can be seen that the risk margin, like the best-estimate liabilities (BEL), is sensitive to interest rate changes. Insurers may currently choose to hedge the interest rate risk of their liabilities by constructing a portfolio of assets that match any movement in the value of liabilities resulting from a change in interest rates. By doing so, insurers expect to reduce their balance sheet volatility. In the remainder of this article, we investigate how insurers may choose to manage the additional interest rate risk brought about by the introduction of a risk margin.

For insurers with an asset portfolio hedging the interest rate risk on their liabilities, they could easily immunise the risk margin from interest rate changes by 'extending' their hedging portfolio - for instance, by buying more interest-rate-sensitive assets. This approach should see insurers protect their overall balance sheet from changes in interest rates.

However, the capital impact on the insurer should also be considered. The SCR, according to the Solvency II standard formula, should capture the 1-in-200-year interest rate risk of a firm's assets and best estimate liabilities only. The actual capital will be determined by the difference in value of the assets and best estimate liabilities resulting from the prescribed stress in interest rates. Under stress, the best-estimate liabilities will be less sensitive than the hedging portfolio, since the hedging portfolio is now designed to cover changes in interest rates across both the best-estimate liabilities and risk margin. Therefore, additional interest rate capital will be required.

So it appears that insurers have a dilemma:

- Hedge the risk margin to increase the stability of their balance sheet at the expense of holding more regulatory capital; or,

- Decide not to hedge the risk margin to optimise capital but accept some volatility in the balance sheet.

In short, they must choose between balance sheet stability and capital optimisation.

We note that, in some ways, this is not a new problem. Companies already face a choice of whether to hedge just their best estimate liabilities, prudent liabilities or their capital as well. The risk margin simply makes it a more important decision. To further illustrate it, we next consider some stylised examples looking at the effect of hedging the risk margin.

Consider the example in Figure 1, which tabulates an example balance sheet with and without risk margin hedging. When the risk margin is not hedged, one can observe the volatility in the balance sheet arising from changes in interest rates (for simplicity, we have assumed that the SCR is not interest-rate sensitive). Figure 1 also illustrates that extending the hedge to include the risk margin increases the SCR slightly and reduces the solvency ratio. It is observed in Figure 2 that, once the hedges have been extended, further extreme changes in interest rates do not have a material effect on the solvency ratio, as expected.

The risk margin, according to the latest draft of the Solvency II text, is to be calculated using a cost of capital approach; a firm must project its solvency capital requirement (SCR) in respect of non-hedgeable risks, and apply a prescribed cost of capital charge of 6% pa. This charge is then discounted at the risk-free rate to determine the risk margin. The risk margin will be relatively large for insurers with significant non-hedgeable risks, such as longevity, and that have a long duration (duration being a measure for interest rate sensitivity).

It can be seen that the risk margin, like the best-estimate liabilities (BEL), is sensitive to interest rate changes. Insurers may currently choose to hedge the interest rate risk of their liabilities by constructing a portfolio of assets that match any movement in the value of liabilities resulting from a change in interest rates. By doing so, insurers expect to reduce their balance sheet volatility. In the remainder of this article, we investigate how insurers may choose to manage the additional interest rate risk brought about by the introduction of a risk margin.

**Stability v optimisation?**For insurers with an asset portfolio hedging the interest rate risk on their liabilities, they could easily immunise the risk margin from interest rate changes by 'extending' their hedging portfolio - for instance, by buying more interest-rate-sensitive assets. This approach should see insurers protect their overall balance sheet from changes in interest rates.

However, the capital impact on the insurer should also be considered. The SCR, according to the Solvency II standard formula, should capture the 1-in-200-year interest rate risk of a firm's assets and best estimate liabilities only. The actual capital will be determined by the difference in value of the assets and best estimate liabilities resulting from the prescribed stress in interest rates. Under stress, the best-estimate liabilities will be less sensitive than the hedging portfolio, since the hedging portfolio is now designed to cover changes in interest rates across both the best-estimate liabilities and risk margin. Therefore, additional interest rate capital will be required.

So it appears that insurers have a dilemma:

- Hedge the risk margin to increase the stability of their balance sheet at the expense of holding more regulatory capital; or,

- Decide not to hedge the risk margin to optimise capital but accept some volatility in the balance sheet.

In short, they must choose between balance sheet stability and capital optimisation.

We note that, in some ways, this is not a new problem. Companies already face a choice of whether to hedge just their best estimate liabilities, prudent liabilities or their capital as well. The risk margin simply makes it a more important decision. To further illustrate it, we next consider some stylised examples looking at the effect of hedging the risk margin.

**Hedging in practice**Consider the example in Figure 1, which tabulates an example balance sheet with and without risk margin hedging. When the risk margin is not hedged, one can observe the volatility in the balance sheet arising from changes in interest rates (for simplicity, we have assumed that the SCR is not interest-rate sensitive). Figure 1 also illustrates that extending the hedge to include the risk margin increases the SCR slightly and reduces the solvency ratio. It is observed in Figure 2 that, once the hedges have been extended, further extreme changes in interest rates do not have a material effect on the solvency ratio, as expected.

Based on the above example, an insurer might reasonably decide not to hedge the risk margin, since any balance sheet volatility results in a higher average solvency ratio compared with the scenario where it is hedged.

So far, our analysis has relied on the standard formula definition of the SCR stress - applying a stress only to the best estimate liabilities. If firms choose to define their interest rate stresses differently within their internal model - by, for example, setting the interest rate stress to consider also the sensitivity within the risk margin - the results are different.

**Using an internal model**So far, our analysis has relied on the standard formula definition of the SCR stress - applying a stress only to the best estimate liabilities. If firms choose to define their interest rate stresses differently within their internal model - by, for example, setting the interest rate stress to consider also the sensitivity within the risk margin - the results are different.

Figure 3 shows that with this new stress definition there is a higher initial SCR and lower solvency ratio in the unhedged base case, since the hedging assets only match the best estimate liabilities.

However, once the hedge is extended to cover the risk margin, there is by construction, no hedging mismatch under the stress and the SCR reduces by 4%. As before, the balance sheet will now be resilient to any further changes in interest rates.

In this case, the unhedged balance sheet is similarly volatile, but the solvency ratio is, on average, below that of the fully hedged scenario. So, in contrast to the earlier example, insurers would reasonably consider hedging the risk margin. In deciding whether to hedge the risk margin in either case insurers should also consider their own expectations of short-term interest rate trends.

The above examples make a number of simplifying assumptions and therefore the analysis will be different for each insurer. However, we believe that insurers should carefully consider the definition of their internal model interest rate stresses and their appetite for capital optimisation compared with balance sheet stability.

However, once the hedge is extended to cover the risk margin, there is by construction, no hedging mismatch under the stress and the SCR reduces by 4%. As before, the balance sheet will now be resilient to any further changes in interest rates.

In this case, the unhedged balance sheet is similarly volatile, but the solvency ratio is, on average, below that of the fully hedged scenario. So, in contrast to the earlier example, insurers would reasonably consider hedging the risk margin. In deciding whether to hedge the risk margin in either case insurers should also consider their own expectations of short-term interest rate trends.

**Conclusion**The above examples make a number of simplifying assumptions and therefore the analysis will be different for each insurer. However, we believe that insurers should carefully consider the definition of their internal model interest rate stresses and their appetite for capital optimisation compared with balance sheet stability.

*The views expressed in this article are the views of the authors, and not their employers*

Richard Purcell is a senior actuary at Pension Corporation, focusing on risk management and Solvency II

Gareth Mee is a senior manager within Ernst & Young's European actuarial services and is responsible for capital markets and longevity solutions for life insurance clientsRichard Purcell is a senior actuary at Pension Corporation, focusing on risk management and Solvency II

Gareth Mee is a senior manager within Ernst & Young's European actuarial services and is responsible for capital markets and longevity solutions for life insurance clients

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