Aviva 2006 Annual Report Download - page 242

Aviva plc
Annual Report and Accounts 2006 238Financial statements continued
Alternative method of reporting long-term business profits continued
Principal economic assumptions – deterministic calculations continued
Spain US
2006 2005 2004 2006* 2005 2004
Risk discount rate 6.7% 6.0% 6.4% 7.4% 7.2% 7.1%
Pre-tax investment returns:
Base government fixed interest 4.0% 3.3% 3.7% 4.7% 4.5% 4.4%
Ordinary shares 7.0% 6.3% 6.7% n/ a n/a n/a
Property 6.0% 5.3% 5.7% n/ a n/a n/a
Future expense inflation 2.5% 2.5% 2.5% 3.0% 3.0% 3.0%
Tax rate 30.0% 35.0% 35.0% 35.0% 35.0% 35.0%
Required Capital (% EU minimum or equivalent) 125% / 125% / 125% / 250% 200% 200%
110% 110% 110%
* 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’smedium-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.
Principal economic assumptions – stochastic calculations
The time value of options and guarantees calculation allows for expected management and policyholder actions in response to varying
futureinvestment 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 futureinvestment simulations, and gives some sample statistics for the simulations
used. Two separate models have been used, for the UK businesses and for 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 futurelong-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 2006 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.
Mean1StDev2
Equities 7.6% 20%
Property 6.6% 15%
Government Bonds 4.6% 3.25-4.5% 3
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.
3. Depending on the duration of the portfolio.