Aviva 2007 Annual Report Download - page 267
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Please find page 267 of the 2007 Aviva annual report below. You can navigate through the pages in the report by either clicking on the pages listed below, or by using the keyword search tool below to find specific information within the annual report.Principal economic assumptions continued
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 the 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 31 December 2007 for the
three most significant asset classes. Interest rates are assumed to have a lognormal distribution with an annualised
standard deviation of 11.5% 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 one).
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.
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 31 December 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 ten year zero coupon bonds). In the accumulation of ten year bonds, it is
assumed that these are held for one year, sold as nine year bonds then the proceeds are reinvested in ten 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
Mean1StDev2Mean1StDev2Mean1StDev2
Euro
Short Government Bonds 4.0% 1.9% 4.1% 3.7% 4.4% 6.6%
Long Government Bonds 4.7% 4.8% 4.7% 3.6% 4.7% 3.9%
Equities 7.3% 19.5% 7.3% 19.2% 7.3% 19.2%
US dollar
Short Government Bonds 3.4% 1.7% 3.9% 3.7% 4.3% 6.6%
Long Government Bonds 4.2% 4.9% 4.6% 3.6% 4.8% 4.1%
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 one).
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 (nth years) and taking the square root. This makes the
result comparable to implied volatilities quoted in investment markets.
Aviva plc
Annual Report and
Accounts 2007
263
Financial
statements