Aviva 2005 Annual Report Download - page 219

Principal economic assumptions – deterministic calculations continued
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 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 returns at 31 December 2005 for the three most
significant asset classes: equities, 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 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 UK.
5-year return 10-year return 20-year return
Mean1StDev2Mean1StDev2Mean1StDev2
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%
1. 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).
2. 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.
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.
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.
Financial statements
Aviva plc 2005
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