Preliminary results - 12 months ended 31 December 2005
Principal economic assumptions – 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”.
This section describes the models used to generate future investment simulations, and gives some sample statistics for the simulations used. Two separate models have been used, for the UK businesses and for the Europe (excluding UK) and International businesses, as each of these models better reflect the characteristics of the businesses.
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 means and standard deviations (StDev) of future returns at 31 December 2005 for the three most significant asset classes. Interest rates are assumed to have a lognormal distribution with an annualised standard deviation of 13% p.a. for the natural logarithm of the interest rate.
| Mean1 | StDev2 | |
|---|---|---|
| Equities | 7.1% | 20% |
| Property | 6.1% | 15% |
| Government Bonds | 4.1% | 3.25-4.75%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 1).
- 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.
Europe (excluding UK) and 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 1 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 returns at 31 December 2005 for the three most significant asset classes: equities, short-term bonds (defined to be of 1 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 9 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 | |
| Short Government Bonds | 3.0% | 1.5% | 3.2% | 2.9% | 3.5% | 5.3% |
| Long Government Bonds | 3.5% | 3.8% | 3.7% | 3.0% | 3.9% | 3.3% |
| Equities | 6.2% | 19.5% | 6.4% | 19.3% | 6.5% | 19.0% |
