Aon Global Asset Model

Growth Asset Model10 March 2010Andrew Claringbold MA FIAMark Jeavons BSc MA MSc FRSSIvor Krol BSc

Outline of Presentation

• Background/ Objectives

• Model Structure

• How we use the model

Background

• Pension fund investment market has developed significantlyØOverseas asset classes have taken on greater importance.ØMore investment in alternative asset classesØMore detailed matching policies and products, which move

some of the investment risk on the liabilities without having to disinvest significantly from return seeking assets (LDI)

ØGreater focus on short-term movementsØGreater need to have a consistent global model for multi-

national companies

Background (continued)

• To capture the risks it is crucial to have the following model features:ØAbility to capture short periods of higher volatility in

return seeking assets, whilst retaining the long-term volatility.ØRecognise asset returns are not normally distributed

and are negatively skewed (i.e. fat left tails).ØRecognise that asset returns are not independent.ØRecognise that correlations between asset classes

change depending on market conditions.

Distributions are not Normal and Independent

0%

5%

10%

15%

20%

25%

30%

US Equities EuropeanEquities

Commodities Hedge Funds

Annualised Monthly (assumingNormality and independence)Annual (Rolling average)

Standard Deviations

Where Divergence Failed

Objectives

• To assess and quantify risk through projections• For a wide range of asset classes• Consistency between assets and liabilities• Output must be consistent with history and economic theory.• Model not purely data driven.• The model should be flexible and adaptable.• The underlying model should be tractable.• The model should be global and work consistently across all

markets we are interested in.

Objectives (Continued)

• The model must:Ø capture “short” periods of higher volatility, whilst retaining long

term volatility. Ø recognise asset returns are not Normally distributed and are

typically negatively skewedØ allow asset class correlations to change under conditions of

stressØ recognise that asset returns are not necessarily independent

over timeØ match historic performance for combinations of assets

Model Structure

Yield Curve Models

Government Bond Yield

CurveInflation

Index-Linked Bond Yield

Curve

Domestic Corporate

Bonds

Domestic Equities REITS

High Yield Bonds

Foreign Equities Property

Foreign Bonds

Emerging Markets Commodities

Infrastructure

Hedge Funds

Regime Switching Model

•Inflation and Govt Bond Yield Curve models at top of cascade

•Corporate bond spreads and growth assets modelled in regime switching structure

•Correlations and volatilities different under each regime

Regime Switching Model

• Assume there are 2 regimes (St):ØStable regime (St=1):ØUnstable regime (St=2)

• We assume that the regimes are unobservable and one needs to infer:ØPr(St=s\St-1) transition probabilitiesØPr(St=s) where s={1,2} unconditional

probabilities

tStS

Transition Probability

• Probability transition matrix (monthly):

• In the long-term, around 75% of the time spent in the “Stable” regime and 25% of the time in the “Unstable” regime.

(St-1,St) Stable UnstableStable 0.971 0.029

Unstable 0.087 0.913

Probability of Being in Stable State

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Feb-70

Jan-72

Dec-73

Nov-75

Oct-77

Sep-79

Aug-81

Jul-83

Jun-85

May-87

Apr-89

Mar-91

Feb-93

Jan-95

Dec-96

Nov-98

Oct-00

Sep-02

Aug-04

Jul-06

Jun-08

Regime Switching Model Structure

ttStSSt retHzGcretttt

e+++= -1

where

rett is an (N 1) vector that contains the returns for N assets at time t

cS is an (N 1) vector containing the level shift term that depends on the state St.

zt is a (K 1) vector of K explanatory variables

GS (an (N K) matrix) and HS (an (N N) matrix) contain parameters to estimate that depend on the state St.

ΣS is an (N N) variance-covariance matrix that depends on the state St.

),0(~tSt N Se

US Equities model

Stable UnstableLevel shift (c) 1.22% -0.74%Link to government bond yields (γ)

-4.4 0

Standard deviation (σ)

3.21% 6.57%

USttSSt dgiltcreteqtyus

tteg ++=__ ),0(~

tSt N Se

US Equity Model Output

Statistic Model History

Annual Arithmetic Mean 10.8% 11.2%

Annual Geometric Mean 9.8% 9.5%

Annual Standard Deviation 18.2% 17.9%

5th percentile -20.9% -22.3%

Average return in worst 5% of cases

-29.4% -30.1%

Adjusted US Equities Model

Stable UnstableLevel shift (c) 1.05% -0.74%Link to government bond yields (γ)

-4.4 0

Standard deviation (σ)

3.21% 6.57%

USttSSt dgiltcreteqtyus

tteg ++=__ ),0(~

tSt N Se

Adjusted US Equity Model Output

Statistic Model History

Annual Arithmetic Mean 9.1% 11.2%

Annual “Geometric” Mean over 10 years

8.0% 9.5%

Annual Standard Deviation 17.7% 17.9%

5th percentile -21.4% -22.3%

Average return in worst 5% of cases

-29.6% -30.1%

Summary of Individual Equity Markets

US UK Canada Europe Japan Australia

Arithmetic Mean 9.1% 9.4% 9.3% 8.8% 9.3% 9.5%

“Geometric” Mean over 10 years

8.0% 8.0% 8.0% 8.0% 7.0% 8.0%

Standard Deviation

17.7% 19.7% 19.3% 18.6% 24.3% 21.1%

5th percentile -21.4% -24.5% -23.8% -26.2% -27.3% -25.9%

Average return in worst 5% of cases

-29.6% -33.5% -32.9% -35.1% -36.9% -34.8%

Monthly Equity Correlations Stable State

Stable US UK Canada Europe Japan Austr.

US 1.00 0.40 0.75 0.60 0.30 0.75

UK 0.40 1.00 0.45 0.60 0.20 0.70

Canada 0.75 0.45 1.00 0.65 0.25 0.70

Europe 0.60 0.65 0.65 1.00 0.30 0.80

Japan 0.30 0.25 0.25 0.30 1.00 0.60

Australia 0.75 0.70 0.70 0.80 0.60 1.00

Monthly Equity CorrelationsUnstable State

Unstable US UK Canada Europe Japan Austr.

US 1.00 0.90 0.90 0.90 0.75 0.85

UK 0.90 1.00 0.90 0.90 0.75 0.90

Canada 0.90 0.90 1.00 0.85 0.75 0.85

Europe 0.90 0.90 0.85 1.00 0.75 0.85

Japan 0.75 0.75 0.75 0.85 1.00 0.75

Australia 0.85 0.90 0.85 0.75 0.75 1.00

Annual Correlations from the Model

US UK Canada Europe Japan Austr. US 100% 71% 86% 83% 52% 83% UK 71% 100% 74% 67% 51% 80%

Canada 86% 74% 100% 78% 51% 79% Europe 83% 67% 78% 100% 51% 79% Japan 52% 51% 51% 51% 100% 66%

Australia 83% 80% 79% 79% 66% 100%

How we use the model

• A client asked us to build an optimal portfolio that gave the same expected return as the current growth portfolio (95% equities, 5% property) but with less risk

• We minimised the downside risk at the 5% level subject to the geometric mean being at least that of the current strategy over 10 years

• The portfolio produced was broadly 55% equities, 10% emerging markets, 15% hedge funds, 15% high yield bonds and 5% properties

How we use the model

Distributions of simulations from our model vs LogNormal distribution

0%

1%

2%

3%

4%

-40% -30% -20% -10% 0% 10% 20% 30% 40%

LogNormalRegime Switch

How we use the modelImpact on risk profile

-259

-50

-123

-211

-300 -250 -200 -150 -100 -50 0

Total

Mortality

Liability Risk

Growth Assets

-239

-50

-123

-188

-300 -250 -200 -150 -100 -50 0

Total

Mortality

Liability Risk

Growth Assets

Current Investment Strategy Diversifying Growth Assets

• Diversification reduces risk by around £20m over 1 year

SummaryHave the objectives been met?

• The model must:Ø capture “short” periods of higher volatility, whilst retaining long

term volatility. Ø recognise asset returns are not Normally distributed and are

typically negatively skewedØ allow asset class correlations to change under conditions of

stressØ recognise that asset returns are not necessarily independent

over timeØ match historic performance for combinations of assets

Further Extensions

• Considered a range of alternative asset classes.• Developing a new exchange rate model.• Direct property market value obtained in two

different ways:– Unsmooth the reported direct property values– Remove some of the noise from REITS which comes

through gearing and through correlation with the equity market sentiment.

• Other

Contact Details

Andrew Claringbold and Mark Jeavons

Aon Consulting

+44 208 970 4510 (Andrew)

+44 207 086 8078 (Mark)

Andrew.Claringbold@aonconsulting.co.uk

Mark.Jeavons@aonconsulting.co.uk

Determining the Model Parameters

• The most efficient way to set the parameters was to adopt a staged approach as follows:1. Determine the global transitional probabilities for moving

from one state to the other.2. Calculate the best-fit parameters for each region based

on the global transitional probabilities.3. Build up the links between the asset classes/regions

through the error terms having fixed all the local parameters.

4. If future mean returns are expected to be different from past mean returns then the means will be adjusted accordingly.

Historic Monthly Equity Correlations

US UK Canada Europe Japan World US 1.00 0.65 0.69 0.75 0.41 0.91 UK 0.65 1.00 0.45 0.56 0.34 0.71

Canada 0.69 0.45 1.00 0.69 0.54 0.77 Europe 0.75 0.56 0.69 1.00 0.50 0.87 Japan 0.41 0.34 0.54 0.50 1.00 0.65 World 0.91 0.71 0.77 0.87 0.65 1.00

Combining Equity Asset Classes

Statistic US UK Canada Europe Japan Australia World Combined Geometric Mean

9.5% 11.7% 10.3% 9.3% 6.0% 10.4% 8.6% 9.8%

Arithmetic Mean

11.2% 15.0% 11.8% 11.8% 9.4% 13.0% 10.2% 11.4%

Standard Dev

17.9% 22.7% 20.6% 21.3% 25.3% 22.9% 17.2% 17.1%

Skewness -41% 81% 26% -3% 69% 36% -57% -61% Percentiles US UK Canada Europe Japan Australia World Combined

2.5 -27.2% -30.2% -30.1% -31.4% -34.5% -29.9% -27.5% -26.9% 5 -22.3% -23.1% -21.9% -25.0% -27.6% -24.7% -23.7% -21.6% 25 0.6% 1.8% -0.4% -1.1% -10.1% -0.8% 0.2% 2.5% 50 12.6% 15.1% 11.6% 11.2% 9.2% 11.2% 13.1% 14.2% 75 23.0% 26.9% 23.5% 25.5% 23.1% 26.6% 21.5% 22.6% 95 37.7% 41.5% 46.4% 47.3% 49.0% 50.8% 35.3% 36.0%

Average of worst 5%

-30.1% -33.8% -30.1% -33.5% -35.6% -31.2% -30.1% -29.5%

Model Output for Hedged Equities

50% US, 20% Eur, 15% Jap, 10% UK, 5% Can

History

50% US, 20% Eur, 15% Jap, 10% UK, 5% Can

Model (Adjusted)

Geometric Mean 9.6% 8.3%

Arithmetic Mean 11.1% 9.1%

Standard Deviation 17.1% 16.9%

5th percentile -21.6% -21.8%

Average return in worst 5% of cases

-29.8% -30.6%

What happened in real life?

Region Proportion of asset Geometric Mean Arithmetic Mean

US 45% 9.5% 11.2%

UK 10% 11.7% 15.0%

Canada 5% 10.3% 11.8%

Europe ex UK 20% 9.3% 11.8%

Japan 15% 6.0% 9.4%

Australia 5% 10.4% 13.0%

Weighted Average 9.25% 11.55%

Historical performance of weights above

9.8% 11.4%

Why a Regime Switching Model?

• Mathematics are based on a mixture of Normal Distributions

• Allows for negatively skewed distributions• Provide a simple framework to incorporate different

correlations.• While we assume independence of monthly returns

in a particular state, there is regime switching between regimes such that the overall returns are not independent.

• The models capture the downside risks over many assets and regions.

Geometric vs Arithmetic Means

• When simulating a pension scheme we are interested in compound returns, i.e. geometric means.

• We are not interested in the arithmetic mean.

• E.g. an asset loses 50% in one year and then doubles the year after– Geometric mean = [(1-50%)(1+100%)]^(1/2)-1 = 0%– Arithmetic mean = (-50%+100%)/2 = 25%

Geometric vs Arithmetic Means

• It is important we get the distributions right.• Normal distributions (Log Normal distributions) are

not adequate.• Combining asset classes will significantly add to the

expected “geometric” returns and reduce the risk, if asset classes are not perfectly correlated.

• The fact that markets are negatively skewed and are more closely correlated in downturns, means that combined simulations of returns in a Normal environment are far too optimistic.

An Extended RS Model

• Considered multiple asset classes across a number of regions – jointly modelling multiple series.

• Considered autoregressive terms and considered explanatory variables, e.g. equity link to government bonds.

• Using a state space model structure which allows a building block approach when putting asset classes together.

• Lots of extensions easily considered: more regimes, non-parametric terms, missing values, probability model, heteroskedasticity, etc.