Preliminary results year ended 31 December 2008
05 March 2009
M24 – Principal economic assumptions
(a) Economic assumptions – Deterministic calculations
Economic assumptions are derived actively, based on market yields on risk-free fixed interest assets at the end of each reporting period.
In setting the risk-free rate we have, wherever possible used the mid-price swap yield curve for an AA-rated bank.
The curve is extrapolated if necessary to get rates suitable to the liabilities. For markets in which there is no reliable swap yield curve the relevant government bond yields are used.
Required capital is shown as a multiple of the EU statutory minimum solvency margin or equivalent.
The adjustments made to swap rates to derive a risk-free rate for UK and Netherlands immediate annuities and immediate annuities, deferred annuities and all other US business are shown below the reference rate table.
The principal economic assumptions used are as follows:
Reference rate and expense inflation
| United Kingdom | Eurozone (excluding the Netherlands) | ||||
|---|---|---|---|---|---|
| 2008 | 2007 | 2008 | 2007 | ||
| Reference rate – term 1 year | 2.8% | 5.7% | 2.5% | 4.8% | |
| Reference rate – term 5 years | 3.2% | 5.1% | 3.3% | 4.6% | |
| Reference rate – term 10 years | 3.5% | 5.0% | 3.8% | 4.7% | |
| Reference rate – term 15 years | 3.8% | 4.9% | 3.9% | 4.9% | |
| Reference rate – term 20 years | 3.8% | 4.8% | 3.9% | 4.9% | |
| Expense inflation | 3.5% | 3.6% | 2.1% | 2.9% | |
| Netherlands1 | Poland | ||||
|---|---|---|---|---|---|
| 2008 | 2007 | 2008 | 2007 | ||
| Reference rate – term 1 year | 2.5% | 4.7% | 4.4% | 6.2% | |
| Reference rate – term 5 years | 3.3% | 4.6% | 4.3% | 5.8% | |
| Reference rate – term 10 years | 3.8% | 4.7% | 4.2% | 5.5% | |
| Reference rate – term 15 years | 4.0% | 4.9% | 4.1% | 5.4% | |
| Reference rate – term 20 years | 3.9% | 5.0% | 4.0% | 5.4% | |
| Expense inflation | 2.5% | 3.0% | 2.9% | 4.7% | |
| United States | ||
|---|---|---|
| 2008 | 2007 | |
| Reference rate – term 1 year | 1.3% | 4.2% |
| Reference rate – term 5 years | 2.2% | 4.2% |
| Reference rate – term 10 years | 2.6% | 4.7% |
| Reference rate – term 15 years | 2.9% | 4.9% |
| Reference rate – term 20 years | 2.9% | 5.0% |
| Expense inflation | 3.0% | 3.5% |
- The economic assumptions used in the Netherlands differ from those in the Eurozone as the Dutch bank swap rate is used in the Netherlands.
For service companies, expense inflation relates to the underlying expenses rather than the fees charged to the life company.
In current markets, the following adjustments are made to the swap rate for UK and Netherlands immediate annuities and all US contracts. The risk-free rate is taken as the swap yield curve for the currency of the liability, adjusted by:
| New business |
Embedded value |
|||||
|---|---|---|---|---|---|---|
| Fourth Quarter 2008 |
Third Quarter 2008 |
First half 2008 |
Second half 2007 |
2008 | 2007 | |
| UK and Netherlands immediate annuities | 1.45% | 0.85% | 0.55% | 0.25% | 1.50% | 0.50% |
| US immediate annuities | 2.00% | 0.65% | 0.55% | 0.25% | 3.00% | 0.50% |
| US deferred annuities and all other contracts | 1.50% | 0.65% | 0.55% | 0.25% | 2.50% | 0.50% |
Risk premium – used for operating profit, Implied Discount Rates (IDR), Internal Rates of Return (IRR) and payback period
For life and pensions operating earnings, Aviva uses normalised investment returns, which are generally expressed as one-year swap returns plus an asset risk premium. The use of asset risk premia only impacts operating earnings as expected returns reflect management’s long-term expectations of asset returns in excess of the reference rate from investing in different asset classes. This assumption does not impact the balance sheet embedded value or value of new business as asset risk premia are not recognised until earned. The asset risk premia set out in the table below are added to the one-year swap rate to calculate expected returns.
| All territories | ||
|---|---|---|
| 2008 | 2007 | |
| Equity risk premium | 3.5% | 3.5% |
| Property risk premium | 2.0% | 2.0% |
Future returns on corporate fixed interest investments are calculated from prospective yields less an adjustment for credit risk.
Required capital and tax
| Tax rates1 | Required capital (% EU minimum or equivalent) |
||||
|---|---|---|---|---|---|
| 2008 | 2007 | 2008 | 2007 | ||
| United Kingdom | 28.0% | 28.0% | 100% / 110% | 100% / 110% | |
| France | 34.4% | 34.4% | 110% | 110% | |
| Ireland | 12.5% | 12.5% | 150% | 150% | |
| Italy | 32.4% | 32.4% | 115% / 184% | 115% / 184% | |
| Netherlands | 25.5% | 25.5% | 168% | 188% | |
| Poland | 19.0% | 19.0% | 150% | 150% | |
| Spain | 30.0% | 30.0% | 110% / 125% | 110% / 125% | |
| United States | 35.0% | 35.0% | 325% | 325% | |
- The required capital in the United Kingdom under MCEV is 100% for unit-linked and other non-participating business and 110% for annuity business.
- Required capital in Italy under MCEV is 184% of the EU minimum for Eurovita and 115% for other companies
- Required capital in the Netherlands is 168%. This capital level is the aggregate capital required for the Netherlands.
- Required capital in Spain is 125% of the EU minimum for Aviva Vida y Pensiones and 110% for bancassurance companies.
- Correct tax legislation and rates have been assumed to continue unaltered except where changes in future tax rates have been announced.
Other economic assumptions
Required capital relating to with-profit business is assumed to be covered by the surplus within the with-profit funds and no effect has been attributed to shareholders. Bonus rates on participating business have been set at levels consistent with the economic assumptions. The distribution of profit between policyholders and shareholders within the with-profit funds assumes that the shareholder interest in conventional with-profit business in the United Kingdom and Ireland continues at the current rate of one-ninth of the cost of bonus.
(b) Economic Assumptions – Stochastic calculations
The calculation of time value of options and guarantees allows for expected management and policyholder actions in response to varying future investment conditions. The management actions modelled include changes to asset mix, bonus rates and rates of interest and other guarantees granted to policyholders. Modelled policyholder actions are described under "Other assumptions".
The embedded value of the US spread based products anticipates the application of management discretion allowed for contractually within the policies, subject to contractual guarantees. This includes the ability to change the crediting rates and indexed strategies available within the policy. Consideration is taken of the economic environment assumed in future projections and returns in excess of the reference rate are not assumed. Anticipated market and policyholder reaction to management action has been considered. The anticipated management action is consistent with current decision rules and has been approved and signed off by management and legal counsel.
Model – United Kingdom, Europe (excluding Delta Lloyd) and North America
Swap rates are generated by a model, the Libor Market Model (LMM), that projects a full swap curve at monthly intervals. Forward rates are assumed to have a log-normal distribution which guarantees non-negative interest rates. The model is calibrated to at-the-money swaptions of a variety of terms and tenors. Swaption volatilities are taken from Bloomberg. Tests have been performed to ensure that sufficient scenarios have been used that the result converges to the stochastic value of the business being valued.
The total annual return on equities is calculated as the return on one-year swaps plus an excess return. This excess return is modelled using a log-normal model where volatility varies by time horizon. This allows the model to capture the term structure of implied volatilities. The model is calibrated to at-the-money options of a variety of terms. Option volatilities are taken from a survey of investment banks.
The model also generates property total returns and real yield curves, although these are not significant asset classes for Aviva outside the UK. In the absence of liquid market data, the volatilities of these asset classes are based on historic data.
Assumptions for correlations between asset classes have been set based on historic data.
Model – Netherlands
In the Netherlands, yield curves are based on De Nederlandsche Bank (DNB) yield curve data.
The interest rate model used is a short rate G2++ model. The model is calibrated to the DNB yield curve and the swaption implied volatilities. Swaption implied volatilities are taken from Bloomberg.
The equity model is a Heston model. The model considers an equity volatility surface in the market and covers strike levels between 0.8 and 1.2. The model is calibrated to the same DNB curves used in interest rate model. The option volatilities used for year-end 2007 are DJ Eurostoxx 50-quotes taken from Bloomberg. For 2008 the model was calibrated to DJ Eurostoxx 50-quotes (end August 2008) provided by a market maker.
The inflation model used is based on the standard Jarrow-Yildirim inflation model which connects real and nominal yields and an inflation index. This is calibrated to ZCII quotes on HICPxT-index.
Asset classes
The significant asset classes for UK participating business are equities, property and long-term fixed rate bonds. The most significant assumption is the distribution of future long-term interest rates, since this is the most important factor in the cost of guaranteed annuity options.
For many businesses, including US, France and Netherlands, the most important assets are fixed rate bonds of various durations.
Summary statistics
Swaption implied volatilities
The implied volatility is that determined by Black-Scholes' formula to reproduce the market price of the option. The following table sets out the model swaption implied volatilities.
| 20081 Swap length | 2007 Swap length | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Option length | 10 years | 15 years | 20 years | 25 years | 10 years | 15 years | 20 years | 25 years | |
| UK sterling | |||||||||
| 10 years | n/a | n/a | 11.8% | n/a | n/a | n/a | 10.9% | n/a | |
| 15 years | n/a | n/a | 11.9% | n/a | n/a | n/a | 10.8% | n/a | |
| 20 years | n/a | n/a | 12.1% | n/a | n/a | n/a | 10.8% | n/a | |
| 25 years | n/a | n/a | 12.4% | n/a | n/a | n/a | 10.9% | n/a | |
| Euro | |||||||||
| 10 years | 11.7% | 11.7% | 11.7% | 11.8% | 11.7% | 11.1% | 10.6% | 10.3% | |
| 15 years | 10.9% | 10.9% | 10.4% | 10.9% | 11.4% | 10.9% | 10.5% | 10.2% | |
| 20 years | 10.5% | 10.4% | 10.4% | 10.3% | 10.6% | 10.2% | 9.9% | 9.7% | |
| 25 years | 10.0% | 10.0% | 9.9% | 9.5% | 10.3% | 9.9% | 9.6% | 9.4% | |
| Netherlands | |||||||||
| 10 years | 11.6% | 11.6% | 11.7% | 11.7% | 11.1% | 10.9% | 10.7% | 10.7% | |
| 15 years | 10.8% | 10.7% | 10.6% | 10.8% | 10.7% | 10.4% | 10.2% | 10.3% | |
| 20 years | 10.5% | 10.3% | 10.2% | 10.3% | 10.3% | 10.0% | 9.8% | 9.8% | |
| 25 years | 10.0% | 9.8% | 9.8% | 9.7% | 10.1% | 9.8% | 9.4% | 9.4% | |
| US dollar | |||||||||
| 10 years | 15.2% | 14.4% | 14.0% | 14.0% | 17.1% | 15.0% | 13.4% | 12.2% | |
| 15 years | 13.9% | 13.0% | 12.8% | 12.7% | 15.0% | 13.2% | 11.9% | 10.9% | |
| 20 years | 13.3% | 12.4% | 12.1% | 12.1% | 13.3% | 11.8% | 10.7% | 10.0% | |
| 25 years | 12.9% | 11.9% | 11.6% | 11.7% | 12.4% | 11.2% | 10.3% | 9.8% | |
Equity implied volatilities
The implied volatility is that determined by the Black-Scholes’ formula to reproduce the market price of the option. The following tables sets out the model equity implied volatilities.
| 20081 | Country | ||||||
|---|---|---|---|---|---|---|---|
| Option length | UK | France | Italy | Ireland | Netherlands | Spain | US |
| 5 years | 25.8% | 24.9% | 24.4% | 24.5% | 26.1% | 26.3% | 24.6% |
| 10 years | 27.2% | 26.3% | n/a | 26.2% | 26.8% | 28.8% | 27.3% |
| 15 years | 27.7% | n/a | n/a | 27.0% | 27.1% | n/a | 25.9% |
| 2007 | Country | ||||||
|---|---|---|---|---|---|---|---|
| Option length | UK | France | Italy | Ireland | Netherlands | Spain | US |
| 5 years | 23.7% | 26.2% | 23.7% | 24.6% | 26.5% | 25.5% | 23.4% |
| 10 years | 25.2% | 27.5% | 26.0% | 26.7% | 28.9% | 27.2% | 25.1% |
| 15 years | 25.8% | 29.1% | 26.0% | 28.2% | 29.5% | 28.3% | 27.0% |
- Volatilities are calibrated to end August 2008.
Property implied volatilities
Best estimate levels of volatility have been used, in the absence of meaningful option prices from which implied levels of volatility can be derived.
For the UK and the Netherlands, model property implied volatility is 15% for 31 December 2008 (31 December 2007:15%).
Demographic assumptions
Assumed future mortality, morbidity and lapse rates have been derived from an analysis of Aviva’s recent operating experience with a view to giving a best estimate of future experience. We have anticipated future changes in experience where that is appropriate, eg we have allowed for improvements in future policyholder longevity.
We have set the assumptions based on a best estimate of outcome of shareholder outcomes. In particular, where the policyholder behaviour varies with economic experience, we have set assumptions which are dynamic, ie vary depending on the economic assumptions. For example, surrender and option take up rate assumptions that vary according to the investment scenario under consideration have been used in the calculation of the time value of options and guarantees, based on our assessment of likely policyholder behaviour in different investment scenarios.
Additionally, where demographic experience is not driven by economic scenarios but is asymmetric on a stand-alone basis, the best estimate assumption considers the weighted-average expected experience, not simply the median or most likely outcome.
Expense assumptions
Management expenses and operating expenses of holding companies attributed to life and related businesses have been included in the MCEV calculations and split between expenses relating to the acquisition of new business, the maintenance of business in-force and project expenses. Future expense assumptions include an allowance for maintenance expenses and a proportion of recurring project expenses. Certain expenses of an exceptional nature, when they occur, are identified separately and are generally charged as incurred. No future productivity gains have been anticipated.
Where subsidiary companies provide administration, investment management or other services to our life businesses, the value of profits or losses arising from these services have been included in the embedded value and value of new business.
Non-hedgeable risk
A charge of 2.5% has been applied to the Group-diversified capital required on a 1-in-200 one-year basis over the remaining lifetime of in-force business.
(c) Other assumptions
Valuation of debt
Borrowings in the MCEV consolidated balance sheet are valued on an IFRS basis, consistent with the primary financial statements. At 31 December 2008 the market value of the Group’s external debt, subordinated debt, preference shares including General Accident plc preference shares of £250 million (classified as minority interests) and direct capital instrument was £4,911 million (31 December 2007: £5,774 million).
| 2008 £m |
2007 £m |
|
|---|---|---|
| Borrowings per summarised consolidated balance sheet – MCEV basis | 15,201 | 12,657 |
| Add: amount included within held for sale | – | 12 |
| Less: Securitised mortgage funding | (7,785) | (7,295) |
| Borrowings excluding non-recourse funding – MCEV basis | 7,416 | 5,374 |
| Less: Operational financing by businesses | (1,891) | (1,063) |
| External debt and subordinated debt – MCEV basis | 5,525 | 4,311 |
| Add: Preference shares (including General Accident plc) and direct capital instrument | 1,440 | 1,440 |
| External debt, subordinated debt, preference shares and direct capital instrument – MCEV basis | 6,965 | 5,751 |
| Effect of marking these instruments to market | (2,054) | 23 |
| Market value of external debt, subordinated debt, preference shares and direct capital instrument | 4,911 | 5,774 |
Other
It has been assumed that there will be no changes to the methods and bases used to calculate the statutory technical provisions and current surrender values, except where driven by varying future investment conditions under stochastic economic scenarios.
