Accounting for “fat tails” in portfolio
risk management:
NZSF case study
IFSWF Meeting, Beijing May 10-13
Aaron Drew, Macro Strategist, NZSF
William Kinlaw, Head of Portfolio and Risk Management
Group, State Street Associates
Outline
• Motivation: why should we account for “fat tails” in
portfolio risk management?
• Contrast two broad approaches for modeling fat tails:
(i) Structural
(ii) Statistical
• Applications of these approaches to the NZSF’s
Reference Portfolio
Motivation
•
The basic risk-profile choice that must be taken to suit the
investment purpose of a fund relies on there being a “reasonable”
ex-ante description of the distribution of asset returns.
•
It is desirable stakeholder’s are prepared for the full range of
outcomes that may occur, particularly downside losses.
•
Internal management should similarly be prepared and know
implications for fund liquidity, re-balancing, etc.
•
Post GFC of course we are much more cogniscent of these issues.
The challenge is to formally embed them into our portfolio decisions.
Motivation
•
Challenges to the “traditional” mean-variance approach for
describing downside risk:
I.
Asset returns are clearly fat tailed: so-called “extreme” events are much
more statistically likely than what would occur assuming returns are
from a normal distribution.
II. Return correlations are shock specific: using historic average
correlations may overstate portfolio diversification benefits in times of
stress.
III. Historical risk and return patterns may not be a good guide for the
future.
Accounting for fat tails
1. Structural approach: returns are modeled as a function of underlying
macroeconomic (and possibly other) drivers. Fat tails in history or
simulation are largely seen as the outcome of extreme events
(scenarios) occurring.
 This was the approach taken by the NZSF for its recent
Reference Portfolio Review.
2. Statistical approach: as in traditional approach returns are modeled
using historical data, but methods try to account for fat-tails and
differences in co-movement in times of historical “stress”.
 This is the approach taken by State Street Associates in
application to the NZSF’s Reference Portfolio
•
We see the two approaches as complementary…
Accounting for fat tails
Structural approaches
Statistical approaches
Strengths
Weaknesses
Strengths
Weaknesses
• Aids understanding of
underlying economic drivers of
risk and returns. Return
outcomes are shock specific
and conditional on modeled
linkages.
• Relatively complicated to
build and estimate models especially at higher
frequencies (monthly or
greater)
• Relatively easy to estimate
and ‘close’ to the historical
data – less need for
judgmental input and
identification of what
constitutes an “extreme event”.
• Does not unpick sources of
historical extreme events and
generally ‘lumps’ such events
together (i.e. two state view of
the world – normal or
“extreme”.)
• Useful tool for “what if”
scenario analysis and
consideration of portfolio
protection strategies to such
scenarios
• Heavy requirement for
judgmental and /or theoretical
inputs given weak empirical
linkages (identification
problems).
• Can estimate at higher
frequencies - enables
examination of “within horizon”
risk
• More difficult to embed views
on how future may differ from
past.
• Can embed views of how
“shocks” and macro-financial
linkages (shock propagation)
may differ going forward from
the past .
• Not all extreme market
movements are result of welldefined shocks (e.g. 1987
“flash-crash”, accounting
scandals)
• Relatively straight-forward
extension of traditional asset
allocation and VaR problems
• Can calibrate model to match
important non-normal features
• Can incorporate important
non-normal features of the
Application: NZSF Reference Portfolio
The Idea
The reference portfolio is
an equilibrium concept:
Expected
excess
return
2
1
Value Adding
Activities
Reference Portfolio
Expected risk
 based on assumptions
of what the long-term
value of the various
asset classes should be
 disregards what is
actually happening to
those values in any
given market conditions
 responses to these
valuation changes are
part of the Fund’s valueadding activities
Slide 7
Application: NZSF Reference Portfolio
Composition
• Delivery of the Reference Portfolio
•
•
•
•
Low-cost, passive portfolio which can achieve Fund objective
Appropriate degree of risk for long-term investor (80:20)
Smaller over-weight allocation to NZ equities and global listed property
No allocation to commodities or to foreign currency
• Both blueprint and benchmark
• Public assessment of whether we are adding value with active investment
Application: NZSF Reference Portfolio
NZSF structural approach to modeling returns
• Simulation model developed for the NZSF’s 2010 Reference Portfolio
Review that incorporated: macro-financial linkages, extreme shocks and
mean reversion in risk-premia.
• Extreme shocks included:
(i) a global negative supply shock ;
(ii) a global financial crisis and
(iii) a NZ specific shock.
 Correlations under these shocks change markedly relative to average
seen under normally distributed returns (increase between growth assets).
 Shocks resulted in negative skew and kurtosis in returns close to
observed historical data
• Simulation results presented to the Board of the NZSF as input into the
risk profile decision for the Reference Portfolio.
.
Application: NZSF Reference Portfolio
NZSF structural approach to modeling returns
• For differing growth-income allocations distributions (1st to 99th percentile
outcomes) for various performance metrics over 1 to 30-year horizons
were presented, such as:
o
o
o
o
Nominal and real returns
Probability returns exceeded thresholds (NZ T-Bills and inflation)
Probability returns fell short of thresholds
NZ dollar value-added relative to NZ T-Bills (metric shown in this
presentation over page, see annex for simple graphical
representation)
•Various sensitivities examined, including changing: equilbrium risk premia
assumptions, degree of mean reversion, FX hedging, extreme shocks (fat
tails), and capital contributions.
• Key trade-off elicited: tolerance for short-term losses vs. longer run gains
as growth allocation increased. Incorporation of extreme shocks (fat-tails)
makes the choice tougher…
Application: NZSF Reference Portfolio
NZSF structural approach to modeling returns
Estimated tail-losses under normal (purple) & fat-tailed (black) returns
(1st percentile excess return of portfolio relative to T-bills after 5-years as % of initial Fund value)
0.0%
1
2
3
-10.0%
-20.0%
-30.0%
-40.0%
-50.0%
-60.0%
Lower risk
profile (60:40)
Reference
Portfolio
(80:20)
Higher risk
profile
(90:10)
Application: NZSF Reference Portfolio
NZSF structural approach to modeling returns
Expected long-term outcomes under normal (purple) & fat-tailed (black) returns
(mean excess return of portfolio relative to T-bills after 30-years as % of initial Fund value)
450.0%
400.0%
350.0%
300.0%
250.0%
200.0%
150.0%
100.0%
50.0%
0.0%
1
Lower risk
profile
(60:40)
2
Reference
Portfolio
(80:20)
3
Higher risk
profile
(90:10)
Application: NZSF Reference Portfolio
State Street Associates statistical approach to modeling returns
•
Monthly historical returns for assets comprising the Reference Portfolio
decomposed into two regimes: normal and “turbulent” periods. Historic
data does not include the GFC period forward.
•
A multivariate return outliers technique is used to estimate turbulent
periods. In these periods the cross-section of returns is unusual from a
correlation or returns perspective (see Annex for graphical
representation).
•
Over the turbulent months correlations between growth assets and
standard deviations of returns are generally higher than non-turbulent
periods (see Annex).
Application: NZSF Reference Portfolio
State Street Associates statistical approach to modeling returns
• Risk metrics are calculated given:
(i) The conventional mean-variance approach
(ii) The variance-covariance matrix of the turbulent months (20% and
30% thresholds are examined).
• Key finding is that the conventional approach underestimates the “true”
downside loss exposure, as proxied by the GFC period.
•Tail outcomes using the turbulent months are more consistent with losses
the Reference Portfolio would have experienced in the GFC.
Application: NZSF Reference Portfolio
State Street Associates statistical approach to modeling returns
Risk metric
What does it measure?
Inputs & methodology
Conventional value at risk
(5-year, 95%)
The most that an investor can expect
to lose at the end of a 5-year period
with 95% confidence. Losses should
exceed this threshold one out of twenty
5-year periods (5% of the time).
•Long-term average standard
deviations
•Long-term average correlations
•Ignores interim losses
The most that an investor can expect
to lose at any time throughout a 5-year
turbulent period with 95% confidence.
Losses should exceed this threshold
one out of twenty 5-year periods.
•Standard deviations during the 20%
most turbulent months
•Correlations during the 20% most
turbulent months
•Models interim losses
The amount than an investor should
expect to lose when value at risk is
breached at any time throughout a 5year turbulent period.
•Same as above, and…
•Measures expected loss once VaR is
breached
Within-horizon, turbulent
value at risk
(5-year, 95%)
Conditional within-horizon,
turbulent value at risk
(5-year, 95%)
Application: NZSF Reference Portfolio
State Street Associates statistical approach to modeling returns
Value-at-risk estimates and hypothetical Reference Portfolio loss during the crisis
(5-year 95% confidence interval)
Staasdasdasd
Source: State Street Associates
Managing tail risk at the NZSF
• NZSF Board and stakeholders recognise that large losses are possible
with risk profile choice – no pressure to change this post-GFC
• We have changed the way we measure and manage Fund liquidity to
better prepare for extreme events.
• Active part of current research is examining the portfolio’s exposure to welldefined extreme downside risks and approaches to mitigate these e.g.:
o via portfolio ‘tilts’ to assets less prone to risks
o and/or via implementing tail-risk option protection strategies
Annex
NZSFs value-adding strategies anchored to
beliefs
Value Adding Activities
Reference
Portfolio
+
=
Strategic
Tilting
Capture Active Returns
NZ Direct
Timber
2. Asset
allocation
is key.
Private
Equity
Property
Infrastructure
Public
mkts
active
Non
market
cap
Other
Tilting
Portfolio
Completion
Actual
Portfolio
5. True manager skill is rare.
STRATEGIES
10. Managing
fees and costs
can prevent
unnecessary
cost.
6. Some strategies are conducive to the generation of excess returns.
7. Identifying the life-cycle of an investment is important.
9. Improving ESG can improve a company's financial performance.
Policies
and
procedu
res
Portfolio
completion
3. A long-term horizon investor can outperform.
4. Returns can mean revert.
Governance
BELIEFS
1. Good
governance adds
value.
8. Responsible
asset owner has
concern for ESG
issues.
NZSF performance against initial expectations
Cumulative Fund Return
To 28 February 2011
3.3
2.8
Returns (post fees)
Initial Upper
Expectation (95%
Confidence Interval)
1.8
09/10 SOI Upper Exp.
09/10 SOI Median Exp.
1.3
09/10 SOI Lower Exp.
NZSF Actual (Net of Fees)
NZSF Initial Expectation
NZ T-Bills
NZ T-Bills +2.5%
Dec-10
Sep-10
Jun-10
Mar-10
Dec-09
Sep-09
Jun-09
Mar-09
Sep-08
Jun-08
Mar-08
Dec-07
Sep-07
Jun-07
Mar-07
Dec-06
Sep-06
Jun-06
Mar-06
Dec-05
Sep-05
Jun-05
Mar-05
Dec-04
Sep-04
Jun-04
Mar-04
Dec-03
0.8
Dec-08
Initial Lower Expectation (95%
Confidence Interval)
Sep-03
Index
2.3
Reference Portfolio
Moments of asset class returns
Structural approach
Global
Equities
New Zealand
Equities
Property
Fixed
Interest
Mean (long-run)
9.5%
8.5%
8.6%
6.6%
Std deviation (single year)
15%
16%
15%
4.0%
Skew (single year)
0.0
0.0
0.0
0.0
Kurtosis (single year)
3.0
3.0
3.0
3.0
Normal shocks
Normal plus extreme shocks (base case model for Reference Portfolio Review)
Mean
9.1%
8.4%
8.6%
6.7%
Std deviation (single year)
16%
18%
16%
5.0%
Skew (single year)
-0.5
-0.3
-0.2
-0.5
Kurtosis (single year)
4.3
3.6
3.4
5.9
Measuring returns
Structural approach
Hypothetical fund returns
150
125
100
T-Bills
Expected Fund Returns
75
Bad draw
50
1
2
3
4
5
Excess returns relative to T-Bills as % of initial fund value
25.0%
0.0%
1
-25.0%
-50.0%
2
3
4
5
6
Moments of asset class returns
Statistical approach
Source: State Street Global Markets
Correlations of asset class returns
Statistical approach
Pre-crisis correlations for full sample (left) and turbulent sample (right)
Source: State Street Global Markets
Standard deviation of asset class returns
Statistical approach to modeling returns
Standard deviation of returns estimated on pre-crisis data (Jan 91 to Aug 08?)
Staasdasdasd
Source: State Street Global Markets