Notes on the EEV basis results
2. Economic assumptions
(a) Deterministic assumptions
In most countries, the long-term expected rates of return on investments and risk discount rates are set by reference to period end rates of return on cash or fixed interest securities. This ‘active’ basis of assumption setting has been applied in preparing the results of all the Group’s UK and US long-term business operations. For the Group’s Asian operations, the active basis is appropriate for business written in Japan, Korea and US dollar denominated business written in Hong Kong.
An exception to this general rule is that for countries where long-term fixed interest markets are less established, investment return assumptions and risk discount rates are based on an assessment of longer-term economic conditions. Except for the countries listed above, this basis is appropriate for the Group’s Asian operations.
Expected returns on equity and property asset classes are derived by adding a risk premium, also based on the long-term view of Prudential’s economists in respect of each territory, to the risk-free rate. In the UK and the US, the equity risk premium is 4.0 per cent above risk-free rates for all periods for which results are prepared in this report. In Asia, equity risk premiums range from 3.0 per cent to 5.8 per cent for all periods for which results are prepared in this report. Best estimate assumptions for other asset classes, such as corporate bond spreads, are set consistently.
Assumed investment returns reflect the expected future returns on the assets held and allocated to the covered business at the valuation date.
The table below summarises the principal financial assumptions:
| 30 Jun 2007 % |
30 Jun 2006 % |
31 Dec 2006 % |
|
|---|---|---|---|
| UK insurance operations | |||
| Risk discount rate: | |||
| New business | 8.7 | 8.0 | 7.8 |
| In force | 8.6 | 8.2 | 8.0 |
| Pre-tax expected long-term nominal rates of investment return: | |||
| UK equities | 9.3 | 8.7 | 8.6 |
| Overseas equities | |||
| Property | 7.8 | 7.2 | 7.1 |
| Gilts | 5.3 | 4.7 | 4.6 |
| Corporate bonds | 6.0 | 5.4 | 5.3 |
| Expected long-term rate of inflation | 3.1 | 3.0 | 3.1 |
| Post-tax expected long-term nominal rate of return for the with-profits fund: | |||
| Pension business (where no tax applies) | 8.3 | 7.7 | 7.5 |
| Life business | 7.4 | 6.85 | 6.6 |
| US operations (Jackson) | |||
| Risk discount rate: | |||
| New business (note) | 7.9 | 8.0 | 7.6 |
| In force (note) | 7.3 | 7.1 | 6.7 |
| Expected long-term spread between earned rate and rate credited to policyholders for single premium deferred annuity business | 1.75 | 1.75 | 1.75 |
| US 10 year treasury bond rate at end of period | 5.1 | 5.2 | 4.8 |
| Pre-tax expected long-term nominal rate of return for US equities | 9.1 | 9.2 | 8.8 |
| Expected long-term rate of inflation | 2.4 | 2.7 | 2.5 |
Note:
US operations – risk discount rates
The risk discount rates at 30 June 2007 for new business and business in force for US operations reflect weighted rates based on underlying rates of 8.8% for variable annuity
business and 5.9% for other business. The increase in the weighted discount rate for business in force from 31 December 2006 of 6.7% to 30 June 2007 of 7.3% reflects the
increase in the US 10-year treasury bond rate and the increasing proportion of variable annuity business.
Asian operations
| 30 Jun 2007 | China % |
Hong Kong (notes iii,iv,v) % |
India % |
Indonesia % |
Japan % |
Korea % |
Malaysia (notes iv,v) % |
Philippines % |
Singapore (notes iv,v) % |
Taiwan (notes ii,v) % |
Thailand % |
Vietnam % |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Risk discount rate: | ||||||||||||
| New business | 12.0 | 6.5 | 16.5 | 17.5 | 5.3 | 10.1 | 9.7 | 16.5 | 7.1 | 8.6 | 13.75 | 16.5 |
| In force | 12.0 | 6.7 | 16.5 | 17.5 | 5.3 | 10.1 | 9.3 | 16.5 | 6.3 | 9.3 | 13.75 | 16.5 |
| Expected long-term rate of inflation | 4.0 | 2.25 | 5.5 | 6.5 | 0.0 | 2.75 | 3.0 | 5.5 | 1.75 | 2.25 | 3.75 | 5.5 |
| Government bond yield | 9.0 | 5.1 | 10.5 | 11.5 | 2.2 | 5.6 | 7.0 | 10.5 | 4.5 | 5.5 | 7.75 | 10.5 |
| 30 Jun 2006 | China % |
Hong Kong (notes iii,iv,v) % |
India % |
Indonesia % |
Japan % |
Korea % |
Malaysia (notes iv,v) % |
Philippines % |
Singapore (notes iv,v) % |
Taiwan (notes ii,v) % |
Thailand % |
Vietnam % |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Risk discount rate: | ||||||||||||
| New business | 12.0 | 6.6 | 16.5 | 17.5 | 5.3 | 9.7 | 9.5 | 16.5 | 6.7 | 8.9 | 13.75 | 16.5 |
| In force | 12.0 | 6.9 | 16.5 | 17.5 | 5.3 | 9.7 | 9.1 | 16.5 | 6.8 | 9.5 | 13.75 | 16.5 |
| Expected long-term rate of inflation | 4.0 | 2.25 | 5.5 | 6.5 | 0.0 | 2.75 | 3.0 | 5.5 | 1.75 | 2.25 | 3.75 | 5.5 |
| Government bond yield | 9.0 | 5.3 | 10.5 | 11.5 | 2.1 | 5.2 | 7.0 | 10.5 | 4.5 | 5.5 | 7.75 | 10.5 |
| 31 Dec 2006 | China % |
Hong Kong (notes iii,iv,v) % |
India % |
Indonesia % |
Japan % |
Korea % |
Malaysia (notes iv,v) % |
Philippines % |
Singapore (notes iv,v) % |
Taiwan (notes ii,v) % |
Thailand % |
Vietnam % |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Risk discount rate: | ||||||||||||
| New business | 12.0 | 6.6 | 16.5 | 17.5 | 5.3 | 9.5 | 9.5 | 16.5 | 6.9 | 8.8 | 13.75 | 16.5 |
| In force | 12.0 | 6.8 | 16.5 | 17.5 | 5.3 | 9.5 | 9.2 | 16.5 | 6.9 | 9.3 | 13.75 | 16.5 |
| Expected long-term rate of inflation | 4.0 | 2.25 | 5.5 | 6.5 | 0.0 | 2.75 | 3.0 | 5.5 | 1.75 | 2.25 | 3.75 | 5.5 |
| Government bond yield | 9.0 | 4.7 | 10.5 | 11.5 | 2.1 | 5.0 | 7.0 | 10.5 | 4.5 | 5.5 | 7.75 | 10.5 |
| Asia total 30 Jun 2007 % |
Asia total 30 Jun 2006 % |
Asia total 31 Dec 2006 % |
|
|---|---|---|---|
| Weighted risk discount rate (note i) | |||
| New business | 10.1 | 9.9 | 9.8 |
| In force | 8.7 | 8.9 | 8.8 |
Notes:
Asian operations – economic assumptions
(i) The weighted risk discount rates for the Asian operations shown above have been determined by weighting each country’s risk discount rates by reference to the EEV basis operating result for new business and the closing value of in-force business.
(ii) For traditional business in Taiwan, the economic scenarios used to calculate the half year 2007 EEV basis results continue to reflect the assumption of a phased progression of the bond yields from the current rates applying to the assets held to the long-term expected rates. The projections assume that in the average scenario, the current bond yields of around 2.5% trend towards 5.5% at 31 December 2013 (half year 2006: 2% towards 5.5% at 31 December 2012, full year 2006: 2% towards 5.5% at 31 December 2013).
The projections for the Fund Earned Rate reflect the same approach as applied for the full year 2006 results, with allowance made for the mix of assets in the fund, future investment strategy and further market depreciation of bonds held as a result of assumed future yield increases. The projections for the Fund Earned Rate alter for changes to these factors and the effects of movements in interest rates from period to period.
After taking into account current bond yields, the assumption of the phased progression in bond yields and the factors described above, the average assumed Fund Earned Rate remains below 1.2% until 2010 (due to the depreciation of bond values as yields rise) and fluctuates around a target of 5.9% after 2013.
Consistent with EEV methodology, a constant discount rate has been applied to the projected cash flows.
(iii) The assumptions shown are for US dollar denominated business which comprises the largest proportion of the in-force Hong Kong business.
(iv) Assumed equity returns
The mean equity return assumptions for the most significant equity holdings in the Asian operations were:
| 30 Jun 2007 % |
30 Jun 2006 % |
31 Dec 2006 % |
|
|---|---|---|---|
| Hong Kong | 9.1 | 9.2 | 8.7 |
| Malaysia | 12.8 | 12.8 | 12.8 |
| Singapore | 9.3 | 9.3 | 9.3 |
To obtain the mean, an average over all simulations of the accumulated return at the end of the projection period is calculated. The annual average return is then calculated by taking the root of the average accumulated return minus 1.
(v) For Hong Kong, Malaysia, Singapore and Taiwan, bond yields have been used in setting the risk discount rates for half year 2007 reporting. For half year and full year 2006, cash rates were used in setting the risk discount rates for these operations.
(b) Stochastic assumptions
The economic assumptions used for the stochastic calculations are consistent with those used for the deterministic calculations described above. Assumptions specific to the stochastic calculations such as the volatilities of asset returns reflect local market conditions and are based on a combination of actual market data, historic market data and an assessment of longer-term economic conditions. Common principles have been adopted across the Group for the stochastic asset models, for example, separate modelling of individual asset classes but with allowance for correlation between the various asset classes.
Details are given below of the key characteristics and calibrations of each model.
UK insurance operations
- Interest rates are projected using a two-factor model calibrated to actual market data;
- the risk premium on equity assets is assumed to follow a log-normal distribution;
- the corporate bond return is calculated as the return on a zero-coupon bond plus a spread. The spread process is a mean reverting stochastic process; and
- property returns are modelled in a similar fashion to corporate bonds, namely as the return on a riskless bond, plus a risk premium, plus a process representative of the change in residual values and the change in value of the call option on rents.
The rates to which the model has been calibrated are set out below.
Mean returns have been derived as the annualised arithmetic average return across all simulations and durations.
Standard deviations have been calculated by taking the annualised variance of the returns over all the simulations, taking the square root and averaging over all durations in the projection. For bonds, the standard deviations relate to the yields on bonds of the average portfolio duration. For equity and property, they relate to the total return on these assets. The standard deviations applied to all periods presented in these statements are as follows:
% |
|
|---|---|
| Government bond yield | 2.0 |
| Corporate bond yield | 5.5 |
| Equities: | |
| UK | 18.0 |
| Overseas | 16.0 |
| Property | 15.0 |
US operations (Jackson)
- Interest rates are projected using a log-normal generator calibrated to actual market data;
- corporate bond returns are based on Treasury securities plus a spread that has been calibrated to current market conditions and varies by credit quality; and
- variable annuity equity and bond returns have been stochastically generated using a regime-switching log-normal model with parameters determined by reference to historical data. The volatility of equity fund returns ranges from 19.2 per cent to 28.6 per cent (half year 2006 and full year 2006: 18.6 per cent to 28.1 per cent), depending on risk class, and the volatility of bond funds ranges from 1.4 per cent to 2.0 per cent for all periods presented in this report.
Asian operations
The same asset return model, as used in the UK, appropriately calibrated, has been used for the Asian operations.
The stochastic cost of guarantees are only of significance for the Hong Kong, Malaysia, Singapore and Taiwan operations.
The mean stochastic returns are consistent with the mean deterministic returns for each country. The volatility of equity returns ranges from 18 per cent to 25 per cent (half year 2006: 18 per cent to 26 per cent, full year 2006: 18 per cent to 25 per cent), and the volatility of government bond yields ranges from 1.4 per cent to 2.5 per cent (half year 2006: 1.2 per cent to 2.2 per cent, full year 2006: 1.4 per cent to 2.5 per cent).
