Interim results - 6 months ended 30 June 2007
EEV Basis
12. Principal economic assumptions
(a) Deterministic calculations
Economic assumptions are derived actively, based on market yields on risk-free fixed interest assets at the end of each reporting period. The same margins are applied on a consistent basis across the Group to gross risk-free yields to obtain investment return assumptions for ordinary shares and property and to produce risk discount rates. Additional country-specific risk margins are applied to smaller businesses to reflect additional economic, political and business-specific risk, which result in the application of risk margins ranging from 3.7% to 8.7% in our eastern European and Asian business operations. Expense inflation is derived as a fixed margin above a local measure of long-term price inflation. Risk free rates and price inflation have been harmonised across territories within the Euro currency zone, except for expense inflation in Ireland where significant differences remain. Required capital is shown as a multiple of the EU statutory minimum solvency margin or equivalent.
Investment return assumptions are generally derived by major product class, based on hypothecating the assets at the valuation date. Future assumed reinvestment rates are consistent with implied market returns at 30 June 2007. Rates have been derived using rates from the current yield curve at a duration based on the term of the liabilities, or directly from forward yield curves where considered appropriate. Assumptions about future investment mix are consistent with long-term plans. In most cases, the investment mix is assumed to continue unchanged throughout the projection period. The changes in assumptions between reporting dates reflect the actual movements in risk free yields in the United Kingdom, the Eurozone and other territories. The principal economic assumptions used are as follows:
| United Kingdom | France | |||||||
|---|---|---|---|---|---|---|---|---|
| 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | |
| Risk discount rate | 8.0% | 7.3% | 7.4% | 6.8% | 7.3% | 6.7% | 6.8% | 6.0% |
| Pre-tax investment returns: | ||||||||
| Base government fixed interest | 5.3% | 4.6% | 4.7% | 4.1% | 4.6% | 4.0% | 4.1% | 3.3% |
| Ordinary shares | 8.3% | 7.6% | 7.7% | 7.1% | 7.6% | 7.0% | 7.1% | 6.3% |
| Property | 7.3% | 6.6% | 6.7% | 6.1% | 6.6% | 6.0% | 6.1% | 5.3% |
| Future expense inflation | 3.5% | 3.4% | 3.3% | 3.2% | 2.5% | 2.5% | 2.5% | 2.5% |
| Tax rate | 28.0% | 30.0% | 30.0% | 30.0% | 34.4% | 34.4% | 34.4% | 34.4% |
| Required Capital (% EU minimum) | 150% / 100% | 150% / 100% | 150% / 100% | 150% / 100% | 115% | 115% | 115% | 115% |
| Ireland | Italy | |||||||
|---|---|---|---|---|---|---|---|---|
| 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | |
| Risk | 7.3% | 6.7% | 6.8% | 6.0% | 7.3% | 6.7% | 6.8% | 6.0% |
| Pre-tax investment returns: | ||||||||
| Base government fixed interest | 4.6% | 4.0% | 4.1% | 3.3% | 4.6% | 4.0% | 4.1% | 3.3% |
| Ordinary shares | AAA | AAA | AAA | AAA | AAA | AAA | AAA | AAA |
| Property | 7.6% | 7.0% | 7.1% | 6.3% | 7.6% | 7.0% | 7.1% | 6.3% |
| Future expense inflation | 4.0% | 4.0% | 4.0% | 4.0% | 2.5% | 2.5% | 2.5% | 2.5% |
| Tax rate | 12.5% | 12.5% | 12.5% | 12.5% | 38.3% | 38.3% | 38.3% | 38.3% |
| Required Capital (% EU minimum) | 150% | 150% | 150% | 150% | 115% | 115% | 115% | 115% |
| Netherlands | Poland | |||||||
|---|---|---|---|---|---|---|---|---|
| 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | |
| Risk discount rate | 7.3% | 6.7% | 6.8% | 6.0% | 9.2% | 8.7% | 8.8% | 8.6% |
| Pre-tax investment returns: | ||||||||
| Base government fixed interest | 4.6% | 4.0% | 4.1% | 3.3% | 5.5% | 5.0% | 5.1% | 4.9% |
| Ordinary shares | 7.6% | 7.0% | 7.1% | 6.3% | 8.5% | 8.0% | 8.1% | 7.9% |
| Property | 6.6% | 6.0% | 6.1% | 5.3% | n/a | n/a | n/a | n/a |
| Future expense inflation | 2.5% | 2.5% | 2.5% | 2.5% | 3.9% | 3.4% | 3.5% | 3.3% |
| Tax rate | 25.5% | 25.5% | 29.1% | 29.1% | 19.0% | 19.0% | 19.0% | 19.0% |
| Required Capital (% EU minimum) | 150% | 150% | 150% | 150% | 150% | 150% | 150% | 150% |
| Spain | United States | |||||||
|---|---|---|---|---|---|---|---|---|
| 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | 30 June 2007 | 31 Dec 2006 | 30 June 2006 | 31 Dec 2005 | |
| Risk discount rate | 7.3% | 6.7% | 6.8% | 6.0% | 7.7% | 7.4% | 7.8% | 7.2% |
| Pre-tax investment returns: | ||||||||
| Base government fixed interest | 4.6% | 4.0% | 4.1% | 3.3% | 5.0% | 4.7% | 5.1% | 4.5% |
| Ordinary shares | 7.6% | 7.0% | 7.0% | 6.3% | 8.0% | 7.7% | n/a | n/a |
| Property | 6.6% | 6.0% | 6.1% | 5.3% | n/a | n/a | n/a | n/a |
| Future expense inflation | 2.5% | 2.5% | 2.5% | 2.5% | 3.0% | 3.0% | 3.0% | 3.0% |
| Tax rate | 30.0% | 30.0% | 30.0% | 30.0% | 35.0% | 35.0% | 35.0% | 35.0% |
| Required Capital (% EU minimum) | 125% / 110% | 125% / 110% | 125% / 110% | 125% / 110% | 250% | 250% | 200% | 200% |
* The principal economic assumptions used for AmerUs Group Co. at the date of acquisition were as follows: risk discount rate of 7.2%, pre-tax investment returns of 4.6% for base government fixed interest and required capital of 250%.
For service companies, expense inflation relates to the underlying expenses rather than the fees charged to the life company. Future returns on corporate fixed interest investments are calculated from prospective yields less an adjustment for credit risk. Required capital in the United Kingdom is 150% EU minimum for Norwich Union Annuity Limited and 100% for other companies. Required capital in Spain is 125% EU minimum for Aviva Vida y Pensiones and 110% for bancassurance companies. The level of required capital for the US business is 250% of the risk based capital, at the company action level, set by the National Association of Insurance Commissioners. The required capital is equivalent to 5% of the insurance liabilities on a local regulatory basis which is broadly equivalent to the required capital we hold for our main European businesses.
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 and Aviva's medium-term bonus plans. 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) Stochastic calculations
The time value of options and guarantees calculation allows for expected management and policyholder actions in response to varying future investment conditions. The management actions modelled include changes to asset mix and bonus rates. Modelled policyholder actions are described under "Other assumptions".
The time value of options and guarantees calculation allows for expected management and policyholder actions in response to varying future investment conditions. The management actions modelled include changes to asset mix and bonus rates. Modelled policyholder actions are described under "Other assumptions".
United Kingdom
Model
Overall asset returns have been generated assuming that the portfolio total return has a lognormal distribution. The mean and standard deviation of the overall asset return have been calculated using the evolving asset mix of the fund and assumptions over the mean and standard deviation of each asset class, together with correlations between them.
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.
Summary Statistics
The following table sets out the mean and standard deviations (StDev) of future returns at 30 June 2007 for the three most significant asset classes. Interest rates are assumed to have a lognormal distribution with an annualised standard deviation of 12.5% p.a. for the natural logarithm of the interest rate.
| Mean1 | StDev2 | |
|---|---|---|
| Equities | 8.3% | 20% |
| Property | 7.3% | 15% |
| Government Bonds | 5.3% | 3.25% - 4.5%3 |
- Means have been calculated by accumulating a unit investment for the required number of years in each simulation, averaging the accumulation across all simulations, and converting the result to an equivalent annual rate (by taking the nth root of the average accumulation minus one).
- Standard deviations have been calculated by accumulating a unit investment for the required number of years in each simulation, taking the natural logarithm of the result, calculating the variance of this statistic, dividing by the projection period (n years) and taking the square root. This makes the result comparable to implied volatilities quoted in investment markets.
- Depending on the duration of the portfolio.
For the UK, the statistics are the same over all projection horizons. Assumptions are also required for correlations between asset classes. These have been set based on an assessment of historical data. Returns for corporate fixed interest investments in each scenario are equal to the return on Government bonds plus a fixed additional amount, based on current spreads less a margin for credit risk.
International
Model
Government nominal interest rates are generated by a model that projects a full yield curve at annual intervals. The model assumes that the logarithm of the short rate follows a mean reverting process subject to two normally distributed random shocks. This ensures that nominal interest rates are always positive, the distribution of future interest rates remains credible, and the model can be calibrated to give a good fit to the initial yield curve.
The total annual return on equities is calculated as the return on one year bonds plus an excess return. The excess return is assumed to have a lognormal distribution. The model also generates property total returns and real yield curves, although these are not significant asset classes for Aviva outside the UK.
Asset Classes
The most important assets are fixed rate bonds of various durations. In some businesses equities are also an important asset class.
Summary Statistics
The following table sets out the means and standard deviations of future euro and US dollar returns at 30 June 2007 for the three most significant asset classes: equities (in the case of euro), short-term bonds (defined to be of one year duration) and long-term bonds (defined to be 10 year zero coupon bonds). In the accumulation of 10 year bonds, it is assumed that these are held for one year, sold as nine year bonds then the proceeds are reinvested in 10 year bonds, although in practice businesses follow more complex asset strategies or tend to adopt a buy and hold strategy. Correlations between asset classes have been set using the same approach as described for the United Kingdom.
| 5 - year return | 10 - year return | 20 - year return | ||||
|---|---|---|---|---|---|---|
| Mean1 | StDev2 | Mean1 | StDev2 | Mean1 | StDev2 | |
| Euro | ||||||
| Short Government Bonds | 4.4% | 2.0% | 4.4% | 3.5% | 4.5% | 6.1% |
| Long Government Bonds | 5.0% | 4.4% | 4.6% | 3.3% | 4.8% | 3.7% |
| Equities | 7.7% | 19.7% | 7.6% | 19.3% | 7.5% | 19.1% |
| US dollar | ||||||
| Short Government Bonds | 4.7% | 2.1% | 4.7% | 3.7% | 5.0% | 7.2% |
| Long Government Bonds | 5.2% | 4.9% | 5.0% | 4.0% | 5.3% | 4.7% |
- Means have been calculated by accumulating a unit investment for the required number of years in each simulation, averaging the accumulation across all simulations, and converting the result to an equivalent annual rate (by taking the nth root of the average accumulation minus one).
- Standard deviations have been calculated by accumulating a unit investment for the required number of years in each simulation, taking the natural logarithm of the result, calculating the variance of this statistic, dividing by the projection period (n years) and taking the square root. This makes the result comparable to implied volatilities quoted in investment markets.
(c) Other assumptions
Taxation
Current tax legislation and rates have been assumed to continue unaltered, except where changes in future tax rates have been announced.
Demographic assumptions
Assumed future mortality, morbidity and lapse rates have been derived from an analysis of Aviva's recent operating experience. Where appropriate, 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.
Expense assumptions
Management expenses and operating expenses of holding companies attributed to life and related businesses have been included in the EEV 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 businesses included in the European Embedded Value calculations, the value of profits or losses arising from these services have been included in the embedded value and new business contribution.
Valuation of debt
Borrowings in the EEV consolidated balance sheet are valued on an IFRS basis, consistent with the primary financial statements. At 30 June 2007 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 £5,696 million (31 December 2006: £5,991 million).
| 30 June 2007 £m | 30 June 2006 £m | 31 December 2006 £m | |
|---|---|---|---|
| Borrowings per summarised consolidated balance sheet - EEV basis | 12,196 | 11,070 | 12,137 |
| Add: amount included within held for sale | 11 | - | - |
| Less: Securitised mortgage funding | (6,825) | (6,689) | (7,068) |
| Borrowings excluding non-recourse funding - EEV basis | 5,382 | 4,381 | 5,069 |
| Less: Operational financing by businesses | (1,176) | (1,176) | (874) |
| External debt and subordinated debt - EEV basis | 4,206 | 3,619 | 4,195 |
| Add: Preference shares (including General Accident plc) and direct capital instrument | 1,440 | 1,440 | 1,440 |
| External debt, subordinated debt, preference shares and direct capital instrument - EEV basis | 5,646 | 5,059 | 5,635 |
| Effect of marking these instruments to market | 50 | 354 | 356 |
| Market value of external debt, subordinated debt, preference shares and direct capital instrument | 5,696 | 5,413 | 5,991 |
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.
