18 ASSUMPTIONS.


UK assumptions

The assumed future pre-tax returns on fixed interest and RPI linked securities are set by reference to the portfolio yield on the relevant backing assets held at market value at the end of the reporting period. The calculated return takes account of derivatives and other credit instruments in the investment portfolio. Indicative yields on the portfolio, excluding annuities within Legal & General Pensions Limited (LGPL), but after allowance for long term default risk, are shown below.

For LGPL annuities, separate returns are calculated for new and existing business. Indicative combined yields, after allowance for long term default risk and the following additional assumptions, are also shown below. These additional assumptions are:

i. Where cash balances are held at the reporting date in excess of, or below strategic investment guidelines, then it is assumed that these cash balances are immediately invested or disinvested at current yields.

ii. Where interest rate swaps are used to reduce risk, it is assumed that these swaps will be sold before expiry and the proceeds reinvested in corporate bonds with a redemption yield 0.70% p.a. (0.70% p.a. at 31 December 2010) greater than the swap rate at that time (i.e. the long term credit rate).

iii. Where reinvestment or disinvestment is necessary to rebalance the asset portfolio in line with projected outgo, this is also assumed to take place at the long term credit rate above the swap rate at that time.

The returns on fixed and index-linked securities are calculated net of an allowance for default risk which takes account of the credit rating, outstanding term of the securities, and increase in the expectation of credit defaults over the economic cycle. The allowance for corporate securities expressed as a level rate deduction from the expected returns for annuities was 26bps at 31 December 2011 (29bps at 31 December 2010).

Economic assumptions

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As at 31 December

2011
% p.a.

2010
% p.a.

2009
% p.a.

1.

The risk free rate is the gross redemption yield on the 15 year gilt index (15 year gilt index for 31 December 2010; 20 year gilt index for 31 December 2009).

Equity risk premium

3.3

3.5

3.5

Property risk premium

2.0

2.0

2.0

Investment return (excluding annuities in LGPL)

 

 

 

– Gilts:

 

 

 

– Fixed interest

1.8 – 2.5

3.4 – 4.0

4.0

– RPI linked

2.6

4.1

4.5

– Non gilts:

 

 

 

– Fixed interest

3.0 – 4.6

3.6 – 5.0

4.4 – 6.2

– Equities

5.8

7.5

8.0

– Property

4.5

6.0

6.5

Long term rate of return on non profit annuities in LGPL

5.0

5.5

6.1

Risk free rate1

2.5

4.0

4.5

Risk margin

3.7

3.3

3.5

Risk discount rate (net of tax)

6.2

7.3

8.0

Inflation

 

 

 

– Expenses/earnings

3.5

4.1

4.6

– Indexation

3.0

3.6

3.6

UK covered business

i. Assets are valued at market value.

ii. Future bonus rates have been set at levels which would fully utilise the assets supporting the policyholders’ portion of the with-profits business. The proportion of profits derived from with-profits business allocated to shareholders has been assumed to be 10% throughout.

iii. The value of in-force business reflects the cost, including administration expenses, of providing for benefit enhancement or compensation in relation to certain products.

iv. Other actuarial assumptions have been set at levels commensurate with recent operating experience, including those for mortality, morbidity, persistency and maintenance expenses (excluding the development costs referred to below). These are normally reviewed annually.

An allowance is made for future improvements in annuitant mortality based on experience and externally published data. Male annuitant mortality is assumed to improve in accordance with 100% of CMI2009 Working Paper 41, with a Long Term Rate of improvement of 1.5% for future experience, and 2.0% for statutory reserving. Female annuitant mortality is assumed to improve in accordance with 100% of CMI2009, with a Long Term Rate of improvement of 1.0% for future experience and 1.5% for statutory reserving. In each case, the annual improvement is assumed to reduce linearly after age 85 to zero at age 120.

On this basis, the best estimate of the expectation of life for a new 65 year old Male CPA annuitant is 24.2 years (31 December 2010: 24.3 years). The expectation of life on the regulatory reserving basis is 25.8 years (31 December 2010: 26.0 years).

v. Development costs relate to investment in strategic systems and development capability that are charged to the covered business. Projects charged to the non-covered business are included within Investment projects in Group capital and financing.

International

vi. Key assumptions:

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As at 31 December

2011
% p.a.

2010
% p.a.

2009
% p.a.

1.

The LGA risk free rate is the 10 year US Treasury effective yield (10 year US Treasury effective yield for 31 December 2010 and 2009). The Europe risk free rate is the 10 year ECB AAA-rated euro area central government bond par yield (10 year ECB AAA-rated euro area central government bond par yield for 31 December 2010 and 2009).

LGA

 

 

 

Reinvestment rate

4.2

5.5

5.1

Risk free rate1

1.9

3.3

3.9

Risk margin

3.7

3.3

3.5

Risk discount rate (net of tax)

5.6

6.6

7.4

 

 

 

 

Europe

 

 

 

Risk free rate1

2.6

3.2

3.6

Risk margin

3.7

3.3

3.5

Risk discount rate (net of tax)

6.3

6.5

7.1

vii. Other actuarial assumptions have been set at levels commensurate with recent operating experience, including those for mortality, morbidity, persistency and maintenance expenses.

Tax

viii. The profits on the covered business, except for the profits on the [Society] shareholder capital held outside the long term fund, are calculated on an after tax basis and are grossed up by the notional attributed tax rate for presentation in the income statement. For the UK, the after tax basis assumes the annualised current tax rate of 26.5% and the subsequent planned future reductions in corporation tax to 25% from 1 April 2012, 24% from 1 April 2013, and 23% from 1 April 2014 (previously a single tax rate was used; 31 December 2010: 27%). The tax rate used for grossing up is the long term corporate tax rate in the territory concerned, which for the UK is 23% (31 December 2010: 27%) taking into account the expected further rate reductions to 23% by 1 April 2014. The profits on the Society shareholder capital held outside the long term fund are calculated before tax and therefore tax is calculated on an actual basis.

Stochastic calculations

ix. The time value of options and guarantees is calculated using economic and non-economic assumptions consistent with those used for the deterministic embedded value calculations.

This section describes the models used to generate future investment simulations, and gives some sample statistics for the simulations used. A single model has been used for UK and international business, with different economic assumptions for each territory.

Government nominal interest rates are generated using a LIBOR Market Model projecting full yield curves at annual intervals. The model provides a good fit to the initial yield curve.

The total annual returns on equities and property are calculated as the return on 1 year bonds plus an excess return. The excess return is assumed to have a lognormal distribution. Corporate bonds are modelled separately by credit rating using stochastic credit spreads over the risk free rates, transition matrices and default recovery rates. The real yield curve model assumes that the real short rate follows a mean-reverting process subject to two normally distributed random shocks.

Asset classes

The significant asset classes are:

  • UK with-profits business – equities, property and fixed rate bonds of various durations;
  • UK annuity business – fixed rate and index-linked bonds of various durations; and
  • International business – fixed rate bonds of various durations.

Summary statistics:

The following table sets out means and standard deviations (StDev) of future returns as at 31 December 2011 for the most significant asset classes. Correlations between asset classes have been set based on an internal assessment of historical data.

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10-year return

20-year return

1.

For asset classes other than for equities and property, mean returns are calculated as the mean return in excess of 1 year government bonds plus the mean return on 1 year government bonds. Mean excess returns for the equities and property are calculated as the mean return in excess of 1 year government bonds. Each mean return is derived by calculating the accumulated value of a unit asset invested to time n years for each simulation, averaging the resultant values across all simulations, then calculating the equivalent annual return required to give this average accumulation (by taking the nth root of the average accumulation and deducting 1).

2.

Standard deviations are calculated by accumulating a unit investment for n years in each simulation, taking the natural logarithm of the result, calculating the variance of this statistic, dividing by n and taking the square root. Equities and property values use excess returns. The results are comparable to implied volatilities quoted in investment markets.

3.

Long term bonds are defined to be 10 year par-coupon bonds.

4.

Short term bonds are defined to be 1 year duration bonds.

 

Mean1

StDev2

Mean1

StDev2

UK Business (Sterling)

 

 

 

 

Government bonds

2.2%

3.1%

3.3%

3.3%

Corporate bonds

4.5%

3.6%

5.1%

3.8%

Property (excess returns)

2.0%

15.0%

2.1%

15.2%

Equities (excess returns)

3.3%

20.1%

3.4%

20.6%

European Business (Euro)

 

 

 

 

Long Government bonds3

2.7%

3.8%

3.2%

3.8%

Short Government bonds4

2.7%

3.2%

3.2%

5.8%

US Business (US Dollar)

 

 

 

 

Long Government bonds3

2.0%

4.3%

3.1%

4.5%

Risk discount rate:

The risk discount rate is scenario dependent within the stochastic projection. It is calculated by applying the deterministic risk margin to the risk free rate in each stochastic projection.

Sensitivity calculations

x. A number of sensitivities have been produced on alternative assumption sets to reflect the sensitivity of the embedded value and the new business contribution to changes in key assumptions. Relevant details relating to each sensitivity are:

  • 1% variation in discount rate – a one percentage point increase/decrease in the risk margin has been assumed in each case (for example a 1% increase in the risk margin would result in a 4.7% risk margin).
  • 1% variation in interest rate environment – a one percentage point increased/decreased parallel shift in the risk free curve with consequential impacts on fixed asset market values, investment return assumptions, risk discount rate, including consequential changes to valuation bases.
  • 1% higher equity/property yields – a one percentage point increase in the assumed equity/property investment returns, excluding any consequential changes, for example, to risk discount rates or valuation bases, has been assumed in each case (for example a 1% increase in equity returns would increase assumed total equity returns from 5.8% to 6.8%).
  • 10% lower equity/property market values – an immediate 10% reduction in equity and property asset values.
  • 10% lower maintenance expenses, excluding any consequential changes, for example, to valuation expense bases or potentially reviewable policy fees (a 10% decrease on a base assumption of £10 per annum would result in a £9 per annum expense assumption).
  • 10% lower assumed persistency experience rates, excluding any consequential changes to valuation bases, incorporating a 10% decrease in lapse, surrender and premium cessation assumptions (a 10% decrease on a base assumption of 7% would result in a 6.3% lapse assumption).
  • 5% lower mortality and morbidity rates, excluding any consequential changes to valuation bases but including assumed product repricing action where appropriate (for example if base experienced mortality is 90% of a standard mortality table then, for this sensitivity, the assumption is set to 85.5% of the standard table).

The sensitivities for covered business allow for any material changes to the cost of financial options and guarantees but do not allow for any changes to reserving bases or capital requirements within the sensitivity calculation, unless indicated otherwise above.

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