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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)
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.