The QIC Factor Model

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The QIC Factor Model
QIC Strategy 5 October 2006
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Introduction/Overview

• Overview of Queensland Investment Corporation
  (QIC)
• Overview
• Alpha Beta Approach
• What the Factor Model is and where it fits in
• Why the Factor Model?
• Factor Model Design Principles
• Generation of economic factor paths
• Asset yield/return models
• Portfolio construction based upon client
  investment objectives

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Introduction/Overview (cont)

• Economic Scenario Generation
• Asset Models
• Discussion of Academia vs the real world
• Strengths and weakness (general accusations)
• Specific examples of some of the real world
  issues
• Our attempt to capture the best of both worlds
• Our Approach aiming for the best of both worlds

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Section 1.

• Overview of QIC

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QIC

• QIC is a wholesale funds manager
• 50 Billion under management
• Approximately 80 clients
• Major clients are QSuper and Queensland Treasury
• Government owned but independent from Government
  Influence
• Pursuing alpha beta separation for our major
  client

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Alpha Beta

• ?eta
• A return derived from a broad market or otherwise
  defined universe of assets or securities
• It is accessible via mechanistic processes which
  are transparent and readily defined
• All investors receive equivalent returns before
  fees and tax
• Generally equivalent to market return
• Alpha
• A return derived from skillfully selecting among
  markets or securities to build unique portfolios
• It is accessible only via proprietary processes
  developed and maintained by portfolio managers
• Each investor receives a unique return (allowing
  for collective investment)
• Generally equivalent to active return

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Implications of Alpha Beta

• Alpha Committee
• Decide allocation of alpha risk budget, in line
  with client objectives and constraints
• Limits on
• Capital used
• Fees (MER)
• Correlation with beta
• Beta Management (Strategy)
• Selection and investment in various betas to meet
  client objectives within client constraints
• Limits on
• Capital used
• Fees (MER)
• Asset Allocation ranges

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Section 2.

• What the Factor Model is
• and where it fits in

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The QIC Factor Model

• Produces a set of possible return forecasts
  (1,000 per asset class)

Australian Equities cumulative return forecasts
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Forecasts are required for portfolio
construction
Client Objectives Scorecard
Asset Return Forecasts
Portfolio Return Forecasts
Potential Portfolios
etc
Asset Allocations
US Equity
AU Equity
AU 3yr Bonds
Sensitivity Analysis / Portfolio Improvement
Cash
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Factor Modeling Overview

• Economic Scenarios
• (paths of cash, inf., growth)
• Asset Return Distributions
• Portfolio Construction
• (vs client scorecard objectives)

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Section 3.

• Why the Factor Model?
• The problems with the existing approach

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Problems with the existing approach

• Markowitz (1952) represents the standard approach
• Many acknowledged weaknesses with the approach
• Assumed IID (at the height of a bubble it could
  go either way)
• Equilibrium numbers ignore current prices
• Diversification controlled by correlation
  correlations change
• over time i.e. different periods e.g. 1960-1980,
  1980-2000
• over the same time period if measure differently
  eg 1yr vs 5yr steps
• because of paradigms change (e.g. post Volcker)
• Performance above CPI not intuitively managed

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Correlations change over time
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Correlations change if step size changes.
US 1980-2004
US 1980-2004
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Standard approach replaced with?

• A yield based approach
• With common drivers (factors) affecting asset
  yields e.g.
• expected inflation, expected cash, expected
  growth.
• We treat returns not related to these factors as
  idiosyncratic to the asset class.
• With such an approach
• Correlations can change over time consider the
  correlation between cash and 3 year bonds, with a
  rate hike
• over 1 year - negative correlation
• over 5 years - positive correlation
• Scenarios are considered consistently across all
  asset classes e.g. increase in inflation,
  increase in inflation risk premium.
• Diversification (or lack of) more accurately
  modeled

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Section 4.

• Factor Model
• Design Principles

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Design Principles

• Based upon yield modeling (returns are not
  modeled directly)
• As discussed
• Module Plug Play
• Can change various models, scenarios,
  assumptions, sensitivities. Most differences in
  valuations can be traced to differences in
  assumptions we want to be able to capture this.
  This approach also leaves room to grow.
• Fair Value model
• Presents a model fair value for any scenario
• If prices double what do we expect for returns
  going forward
• Consistent across asset classes
• Uniform treatment of increased inflation or
  increased volatility of inflation.

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Factor Modeling Overview

• Economic Scenarios
• (paths of cash, inf., growth)
• Asset Return Distributions
• Portfolio Construction
• (vs scorecard objectives)

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Economic Scenario Modeling

• Step1. Create future paths of inflation, cash,
  growth for various countries
• Expectations and volatilities of the economic
  factor paths are provided by the QIC economics
  team. 1000 paths are simulated for each country.
• Step 2. Validate scenarios
• For each simulation
• Ensure sensible intra-country relationships
  between real GDP, inflation and real cash.
• Ensure sensible inter-country relationship
  between real GDP, inflation and real cash..

• 1. Economic Scenarios
• 2. Asset Return Distributions
• 3. Portfolio Construction

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Asset Return Modeling

• 1. Economic Scenarios
• 2. Asset Return Distributions
• 3. Portfolio Construction

Step 1. Specify asset return yield models
(standard theory). Step 2. Specify values or
models for parameters Step3. Use economic
scenarios to generate yield and return paths
for assets
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Portfolio Construction

• 1. Economic Scenarios
• 2. Asset Return Distributions
• 3. Portfolio Construction

Step 1. Map asset return paths into Investment
Objectives Scorecard Step 2. Measure
performance of various portfolios against
scorecard objectives Step 3. Repeat process
changing scenarios/models/parameters to assess
the robustness of portfolios to various
assumptions.
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Section 5.

• Economic Scenario Generation
• The Creation of Sensible Future Economic Factor
  Paths

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Economic Factor Path Generation
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Step 1. GDP and GDP Heat
GDPt GDPt-1 MRgdp. (GDPLR - GDPt-1) MRgdp x
GDP Heatt-1 x N(0,1) GDP Heatt a.
(GDPt GDPLR) (1-b) x GDP Heatt-1
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Inter-country GDP Contagion
Contagion effects are applied to real GDP as
follows
The new path for GDP (including contagion) is
used to recalculate GDP Heat (which is then used
to estimate inflation).
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Step 2. Inflation

• Inflation is simulated as a function of GDP heat
  (output gap).

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Step 2. Inflation
A traditional Monte Carlo simulation is used to
estimate smoothed inflation (1 yr average) based
upon economists expectations and volatility
bands. Inflation contagion across regions can
then be applied using the same approach as used
for GDP. Final inflation paths are re-adjusted to
fit within economists beliefs.
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Step 3. Real Cash
To obtain real cash we first estimate nominal
cash via a Taylor Rule (based upon Central Bank
policy)
Where inflation heat is defined similar to GDP
heat.
Nominal cash is estimated as a weighted average
of Taylor Cash and cash estimated from a Monte
Carlo Simulation based upon economist forecasts.
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Step 4. Feedback Loop
Finally, we feedback the effects of real cash on
inflation and real GDP
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Example
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Section 6.

• Asset Modeling
• How economics drives asset prices return
  distributions

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Is the term premium zero now?
10year Bonds 5
3year Bonds 5
Cash 5
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Term premium is not zero if expected cash is
lower than current levels
10year Bonds 5
3year Bonds 5
Cash 5
Expected Level of cash
Expected average cash over 10yrs 4 therefore
TP 10yr 1.0
Expected average cash over 3yrs 4.5 therefore
TP 3yr 0.5
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Return on Assets Nominal Bonds

• Return on Bonds for a period
• expected inflation over the period
• expected real cash over the period
• inflation risk premium for the period
• real cash risk premium for the period
• risk premium/discount other
• Bond Yield Expected Return over the life of the
  bond

Expected nominal cash
Bond risk premium
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Return on Assets Inflation Linked Bonds (ILBs)

• Expected Return on ILB for a period
• expected inflation over the period
• expected real cash over the period
• real cash risk premium for the period
• risk premium/discount other

Expected nominal cash
ILB risk premium
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Return on Assets Equity

• Expected Return on Equity for a period
• expected inflation over the period
• expected real cash over the period
• inflation risk premium for the period
• real cash premium for the period
• growth risk premium for the period
• risk premium/discount other
• Also EY (constant) expected non-retained
  earnings growth for the period

Expected nominal cash
Equity risk premium
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Equity Returns other

• Model EY as above
• Model Earnings using trend line (with Dividend
  reinvested)
• Combine these to get a price series (returns then
  are just accounting)

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PE and E Relationship
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EY Model
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Model Forecast
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Consistent Risk Premium from Factor Analysis

• Risk Premia are by definition compensation for
  risk.
• If two assets have an exposure to a risk factor
  then the relative risk premium for each asset
  should be proportional to the exposure to that
  factor.
• Similarly, the more volatile the factor the
  higher the risk premium required.
• So risk premium in the factor model can change
  over time.

Risk Premium from Factor Analysis
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Modeling asset distributions

• By inputting various scenarios for economic
  drivers, we get model paths of asset yields and
  returns.
• We assume reversion to the model consistent with
  history i.e. the same historical distribution
  (other models could be imposed).
• We apply the same historical correlation between
  model errors to recreate known relationships ie
  5yr and 10yr bonds tend to move together,
  modeling totally uncorrelated reversion to
  similar models would not be correct.

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Example of modeling
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Small change approach, for radical in change in
approach

• Weve discussed the difference in outcome, but is
  the approach too radically different (and perhaps
  risky)
• Yield vs return biggest difference, after that
  still informed by history (though not dominated
  by it we want to explain history not rely on it
  to repeat).
• Basic approach relatively similar after this
  change, and changing yields to returns is
  relatively simple.
• Need to implement this yield vs return approach
  in a intelligent and disciplined way. The same
  challenge really!

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Summary

• We have developed a yield based approach that
• considers changes to the common drivers of
  returns (factors) consistently between asset
  classes
• uses historical correlations between yield model
  errors (the bit not explained by the common
  factor model)
• creates time varying risk premium
• takes into account current prices

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Section 7.

• Academia vs the real world

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General Accusations

• Academia
• ( Quant. processes)
• Narrow focus
• Impracticable (eg Markowitz)
• Disciplined
• Only as good as its assumptions
• Appearance of certainty

• Market Practice
• Unscientific
• Ill-disciplined
• Broad scope
• Practical
• More snake-oil than substance
• Appearance of certainty

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Real World Problems

• The Tech bubble Being right isnt enough
• Multiple objectives Quantification is subjective
• The Economic Herd
• Attribution focus not right (s/be on process)
• Forecasts not what they seem

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Forecasts arent forecasts
You need to be aware of the how why of some
information
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Section 8.

• Our Approach
• Aiming for the best of both worlds, as we all do

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Our approach

• Try to start with the right questions (not the
  available answers)
• Happy to be approximately right rather than
  precisely wrong
• Aim for Consistency
• across asset classes time
• Focus effort towards the most material issues
• And dont get carried away with precision, if
  available precision is swamped by unknowns
• Try to be aware of own weaknesses

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Some of our questions

• Inflation real cash duration of equities?
• Asset price inflation and CPI inflation?
• Where is asset pricing headed to?
• What should we do differently?

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• Discussion!