Big Short: Collateralized debt obligations (CDOs)
• Simple in concept: Portfolio of many assets plus cash waterfall changes risk profile
• Complex in structure: Rules in cash waterfall; over-collateralization and interest-
• Simple risk ratings: Diversity score (binomial expansion) or Gaussian copula plus
“shading” based on a committee
• Complex market structure: Borrowers, appraisers, mortgage brokers, commercial banks,
mortgage servicers, investment bankers, fund managers, rating agencies, institutional
investors, regulators (Fed, NAIC, SEC) lawyers and many consultants
• Simplicity in incentives: Money for nothing– or-- at the least-- mis-representation of
actual risk relative to fees and spreads
Communication regarding CDO risk to senior executives at financial institutions was
mostly not cognitively compelling.
“Real risk was not volatility; real risk was stupid investment decisions.” Lewis (2010)
Failure of a simple CDO model
• Materially underestimated risk of mezzanine and senior tranches
• Often over-simplified waterfall rules– e.g., equity prioritized
• Unrealistic assumptions with respect to default rates
• Herd mentality on CDO ratings
• Correlation dynamics not well represented– i.e., correlation went toward 1 in crisis.
Portfolio Simulation: A more complex, but better model
Sampling across the Latent Factors to simulation various risk conditions
K latent factors
Factor realizationsFactor Betas
K = 30 factors
N ≈ 10k ~ 500k positions/idiosyncratic draws
J ≈ 1m ~ 10m iterations
How much computing power needed?
Repeat J times
Repeat N times
Source: State Street Global Exchange℠
Figure provided for illustrative purposes only.
Multi-asset-class portfolio-risk modeling
Use-objective focuses on incorporating risk strategy into portfolio management
Start of TailExpected
• Model guides executives as to whether allocation is prudent from a risk perspective
• Model assists in evaluating how well components of portfolio contribute to overall risk/return
• Model provide input into strategic discussions on portfolio construction/management
Figure provided for illustrative purposes.
Interpreting simulated scenarios
Reverse Stress Testing
Values at horizon Search through
What factor realizations
generate a portfolio value
in the specified confidence
interval of portfolio
Source: State Street Global Exchange℠
Figure provided for illustrative purposes.
• Epistemic: Hard to understand conceptually
• Computational: Algorithm hard to understand and/or implement
• Dynamic: System changes over time– sometimes as a function of itself or its users
• Human minds are memory and predicting mechanisms: Does the complexity arise
from quantity of “insight chunks” that need to be remembered or from the quantity of
steps/inter-relationships in the predictive model?
• Simple heuristics may arise from highly complex models/systems. Complexity may arise
from incorporating nuances into interpretations/decisions based on a given heuristic.
Consilience: A frequent driver
A "jumping together” of knowledge by the
linking of facts and fact-based theory across
disciplines to create a common groundwork of
Wilson (1999) p. 8
What makes decision-support analytics complex?
• Multi-variate optimization problem– often with controls and results playing out over
different time horizons.
• Uncertainty– “risk” defined by known distributions and “Knightian uncertainty” defined by
unknown models/data-generating processes
• Interconnectedness– both explicit and implicit.
• Hierarchies of relationships and relevant assumptions
• Separation of point predictions/estimates and distribution estimates
Drivers of model complexity
– Macro-economic regime changes
– Firms changing leverage
– Governments changing regulation
• Heterogeneous return distributions by asset class
– Fat tails
• Capturing obscure, but material risks
– Correlated exposure to a latent factor (e.g., US housing market)
– Sectorally diversified investment-grade bond portfolio may constitute material
– Wrong-way, counterparty risk to an over-hedged energy company
• Human reaction to changing
- Bank management reaction to stress environment by changing underwriting standards
- Not selling in a down market and distressed-selling in an up market not recognized
- Inability or unwillingness to understand a model and its implications may lead to value-
- Traders gaming particularly sensitive aspects of a risk model
Shift in risk modeling favors more model complexity
Linear estimation is
Focus on 2nd moment Linear Regressions
Bias toward tractable
Focus on Skewness
and Tail, generated by
Need to recognize
with recognition of
Source: State Street Global Exchange℠
Albert Einstein displayed the
following aphorism in his office:
“Things that are difficult to do are
being done from the wrong centers
and are not worth doing.”
-- Diaconis (2003)
Albert Einstein may have said
something like “[Theories],
[Education] or [Things] should be as
simple as possible, but no simpler.”
Simplicity may not always be the primary or best criterion
• Also attributed to Einstein: "Any intelligent fool can make things bigger, more complex, and more
violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction.”
• Simplicity should be one goal, not a hard criterion.
• Usefulness should also be a goal and should be a hard criterion: Thus, simple enough, but no
simpler. This thought can lead to…
• Occam’s Razor: “Among competing hypotheses, the one with the fewest assumptions should be
– William of Ockham’s actual quote (I think): “Numquam ponenda est pluralitas sine
necessitate [Plurality must never be posited without necessity]”
– Bertrand Russell’s version: "Whenever possible, substitute constructions out of known
entities for inferences to unknown entities.”
• Simplicity in concept may belie complexity in reality– e.g., biological evolution, construct a
portfolio that finds highest return/risk
• Not likely to be a global principle– important that model “suitably” explains/predicts data
– “Suitably” implies matching model with use objective
– Over time, more complex models may explain data better and open new vistas e.g., atomic
theory, plate tectonics, Black-Scholes, light theory (Newton’s “simpler” particle’s versus
Huygen’s waves)– bottom-up, factor-based portfolio simulations?
Hume’s problem: When will a model perform?
• When is it reasonable to think the future will be like the past?
• Rephrase– what part of a model’s/system’s/algorithm’s structure will operate in the future
in the same way it has in the past?
– Means are difficult to estimate and historical observation may be a poor guide
– Volatility may be easier (than means) to estimate, but still may change so much that
historical observation is likely to be a poor guide.
– Underlying correlation structure may change-- but not as much as volatility
How much can/should non-linear-process-inducing feedback loops and tipping points be
included in a model and can historical observation help?
How does model complexification affect strategies for communicating to quantitatively-
informed business executives?
How do we know a portfolio-risk system/model works?
“Science is no inexorable march to truth, mediated by the collection of
objective information and the destruction of ancient superstition.
Scientists, as ordinary human beings, unconsciously reflect in their
theories the social and political constraints of their times.”
-- Stephen Jay Gould
Karl Popper’s process applied to portfolio-risk analysis:
• Problem situation: “Risk-appetite consistent allocation”
• Tentative theories: “Hypothesize scenarios”
• Error elimination: “Stress the stress test i.e., simulate”
However, falsifying every scenario is not possible; further, Gould argues to
beware theory-laden analyses.
Complex models perform better: Evolution
• Darwin (1859): Natural selection is a key mechanism of evolution based on the
differential survival and reproduction of individuals due to phenotype differences.
• Romanes (1895): Neo-darwinism refers to germ-plasm theory advocated by Wallace and
• Huxley (1942): Modern synthesis drew together multiple fields of biology marrying
natural selection, genetics, natural population analysis, systematics, etc.
• Today’s models of evolution are much more complex:
– Genetic networks composed of tens to hundreds of genes interact
– “Regulatory” genes behave conditional on the environment
– Some hereditary variations are nonrandom in origin
– Some acquired information is inherited (epigenetic inheritance)
– Evolutionary change can result from instruction as well as selection
Jablonka and Lamb (2014)
Complex models perform better: Risk analytics
• Capital-asset pricing model
• Markowitzian portfolio theory
• Continuous-time finance
• Value at risk
• Monte-Carlo simulation
• Expected-tail loss
Are these “advances” i.e., model complexification worth the investment?
Criteria for deciding degree of model complexity
• Model performance
• Ease of communicating actionable model output to quantitatively-informed executives
• Ignores extraneous information
• Balances model uncertainty and credibility of priors
• Minimizes over-fitting risk: Sample size relative to number of parameters
• Resistant to manipulation as a consequence of incentives
“Because complexity generates uncertainty, not risk, it requires a regulatory response
grounded in simplicity, not complexity.” (Haldane, 2005, p. 19)
What does this mean in practice?
Questioning the entire modeling enterprise
• Preproducibility is a prerequisite for attempting to reproduce a result: it involves providing
an adequate description of an experiment or analysis for the work to be re-undertaken. It
requires documentation, openness, and communication.
• Quantifauxcation is to assign a meaningless number, then pretend that since it’s
quantitative, it’s meaningful. Usually involves some combination of data, pure invention, ad-
hoc models, inappropriate statistics, and logical lacunae.
• Cost of most policy cost-benefit analyses is high: lost rationality
• Rates vs. probabilities
– Randomness created by taking a random sample, assigning subjects at random, etc.
– Probability model invented (assumed) for data that world generates– inferences are
only as good as the assumptions
– Aleatory: Coin toss, die roll, under some circumstances, behave “as if” random
– Epistemic: Stuff we don’t know
– Trials are random, have same chance of success and have known dependence– can
quantify estimate uncertainty.
– Ignorance does not equal randomness
– Tendency to treat haphazard as random
– Probability as metaphor
(From Stark 2015)
• Mis-specify data-generating process: Fail to estimate the “true” distribution due to the
fact that the underlying process differs materially from the model’s process assumptions.
– Second-order assessment of misspecification also important.
– What is range of wrong estimates?
– Are out-of-sample tests showing under-estimates in times of stress?
• Mis-estimate parameters: While the assumed data-generating process may be
reasonable, still fail to estimate “true” distribution based on parameterization problems.
– Are there enough data points to credibly estimate parameters?
– Can model structure be used to infer tail events without requisite data?
Risk versus uncertainty
• Frank Knight (Knight, 1921): "Uncertainty must be taken in a sense radically distinct from
the familiar notion of risk, from which it has never been properly separated.... The
essential fact is that 'risk' means in some cases a quantity susceptible of measurement,
while at other times it is something distinctly not of this character; and there are far-
reaching and crucial differences in the bearings of the phenomena depending on which
of the two is really present and operating.... It will appear that a measurable uncertainty,
or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one
that it is not in effect an uncertainty at all.”
• Risk is known unknowns i.e., data generating process, inter-relationships arising from
model structure, parameters imply known distributions
• Knightian uncertainty is unknown unknowns i.e., data generating process, model
structure and parameters are unknown
Types of ignorance
Hansen and Sargent (2015)
≡ Observable state variable at time t
≡ Control variable
≡ Random shock to process
1. “Bayesian decision maker” does not know β, but trusts prior prob. distribution
2. “Robust Bayesian decision maker” does not trust prior distribution for response
coefficient β; but uses operators to twist prior distributions to generate conservative est.
3. “Robust decision maker” uses a multiplier or constraint preferences to express doubt
regarding probability distribution of W conditional on X and U.
4. “Robust decision maker” asserts ignorance as in 3 by adjusting an entropy penalty to
Make model robust to particular alternative probability models.
“The trouble with most folks isn’t so much their ignorance, as knowing so
many things that ain’t so.” Josh Billings related by Friedman (1965)
Evaluating the adequacy of a theory/model
1. Accuracy [out-of-sample confirmation of estimated probability distribution and
contributions of underlying components to that distribution]
2. Consistency (both internal and external) [multi-asset-class, assets & liabilities]
3. Broadness in scope [granularity and comprehensiveness]
4. Simplicity [complex enough to capture dynamics, but simple enough to be diagnosed
and communicated to a quantitatively-informed business head]
5. Fruitfulness [output substantively contributes to impactful decisions]
Depending on the theory under evaluation, criteria may contradict each other so a relative
weighting may be needed i.e., given a particular circumstance, some criteria are more
important than others. Kuhn (1977)
In portfolio risk analysis, we typically add Timeliness to the evaluation process– a
successful theory/model/system that cannot provide timely output is useless.
Understanding the decision maker: Elephant and the rider
• Elephant: Automatic processes
• Rider: Controlled processes
• Modeling decision making
– Humean model: Reason is a servant
– Platonic model: Reason could and should rule
– Jeffersonian model: Head and heart are co-emperors
• “Seeing that” vs. “Reasoning why”
• Rationalist delusion: Maintaining healthy skepticism of reason– smarter people
People who devote their lives to studying something often come to believe that the object
of their fascination is the key to understanding everything. Location 58
Conscious reasoning functions like a press secretary who automatically justifies any
position taken by the president. p. 106
And as reasoning is not the source, whence either disputant derives his tenets; it is in vain
to expect, that any logic, which speaks not to the affections, will ever engage him to
embrace sounder principles. – David Hume
How individuals make decisions
Agree on values Disagree on values
Agree on facts Computational decision Negotiate
Disagree on facts Experiment Paralysis or chaos
From Koomey (2001) figure 19.1 p. 88.
How to communicate in a cognitively compelling way?
• Research audience…
– Culture (values and biases)
– Education (general and specific to communicated analytics)
– Incentives (degree of departure from objectivity)
• Distill message...
– Empirical vs. rational/theoretical (where is the model in this iterative evolution?)
– Transparent assumptions
– Frank assessment of model uncertainty
– Link to audience’s narrative/values
• Use intuitive framing and strong visuals…
– Relevant metaphors
– Examples from different, but similar domains (e.g., health/medical)
– Design compelling graphs and figures
Working memory and compelling communication
• Working memory
– Operates over a few seconds
– Temporary storage
– Manipulates attention
– Focuses attention
– Resists distractions
– Guides decision-making
• Can only process 5 to 9 “chunks” of information within working memory at any given
moment in time (Miller, 1955)
• Deviating from expectations typically causes the listener to disengage
• Working memory dis-fluently “chunks” instead of always focusing on what matters
• Working memory “calls” long-term memory to assist in processing; if nothing is there,
cognitive flow is broken– result is likely disengagement
Education is essential to build up long-term memory
Building a narrative
1. Identify the [the set of] focal issue(s)
2. Determine the key micro or local forces impacting the focal issue(s)
3. Identify the key macro or global forces impacting the focal issue(s)
4. Rank by importance and uncertainty– distinguish parameterization of probability
distributions (known unknowns) from model uncertainty (unknown unknowns)
5. Select scenario logic in terms of the parameters (and maybe models) to adjust to show
range of possible outputs
6. Flesh out the scenarios of most importance and highest likelihood– drill into details of
micro/macro forces and nature of parameterized probabilities and uncertainty
7. Determine implications
8. Select leading indicators and signposts to monitor evolution of scenario in light of
From Koomey (2001)
• Explain signal and noise in specific terms
• Communicate how model disentangles signal and noise
• Identify and root out data biases
• Educate on error bars and confidence intervals
• Beware illusory precision– clarify how much precision is possible given data/model
Sampling error does not necessarily equal “uncertainty” in terms of implications of model
• False dichotomy: Presenting two choices such that it seems they are the only possibilities.
– Simple vs. complex model
– Use no models vs. use only one model
• Perfect as the enemy of the good (or good enough)
• Red herrings and missing forest for the trees
– Affect heuristic: Analyst or executive has “fallen in love with” a particular output so that
they minimize model problems and exaggerate model strengths.
– Saliency bias: Overly influence by analogous, past success
– Confirmation bias
– Availability bias
– Anchoring bias
– Halo effect: Impression of model author, analyst or even model influences interpretation
– Sunk-cost fallacy: A particular model output has driven strategy/investment
– Disaster neglect
– Loss aversion
Traps arising from logical fallacies and cognitive biases
Key points to remember for compelling communication
• Frame within a narrative
• Avoid “quantifauxcation”
• Contextualize (across time and across cohorts)
• Address biases: Highlight data selection concerns and explain assumptions & process
• Use transparency in model estimation process to spark questions and debate
• Compare output from multiple models (when possible)
• Visualize data– encourage interactive diagnostics and drill-down
• Emphasize actionable insight
– Explain key components of analytical process
– Teach how to understand confidence intervals (noise vs. signal)
Build on understanding: Descriptive, prescriptive and cognitive
Move from analysis (breaking into components) to synthesis (re-assembling with insight)
Principles of risk-data visualization
• Match output to use cases
– Concentration risk assessment
– Risk appetite assessment (stress testing)
– Position-level limits/allocation
• Prepare for multiple dimensions (e.g., region, sector, asset class, customer type, size)
• Incorporate drill-down capability
• Contextualize output (e.g., benchmarks, time series, scenario-based)
• Use robust statistics (e.g., median, inter-quartile, mean absolute deviation)
• Use techniques to address data difficulties (e.g., Winsorization, shrinkage)
• Target near-instantaneous rendering of decision-support output
Risk data tend to be defined by outliers
Data are all figurative for illustrative purposes
Multiple attributes represented in two dimensions
Expected Returns vs. Volatility by Exposure Size – Sharpe Ratio as Color
High Sharpe Ratios,
but small positions
OK Sharpe Ratios,
and larger position
Data are all figurative for illustrative purposes
So which is richer, from a data insight perspective?
Improve visualization independent of model complexity
• Google study (Tuch, et al., 2012) found for websites:
– Visually complex websites are less appealing
– Prototypical websites (for a given category) are more appealing
– Simpler design is rated higher
• What makes analytical output compelling and credible?
– Prototypicality: Basic mental image one’s brain creates to categorize everything with
which you interact.
– Cognitive fluency: One’s brain prefers output that is easier to process.
– Mere exposure effect: Familiarity arising from repeated exposure.
– Metric balancing: Too many metrics equals no understanding.
Be transparent as to epistemic nature of model output
• What the executive doesn’t know, but is knowable: Model output is available and useful
e.g., credible metrics identify risk (in the technical sense.)
• What the executive or the analyst don’t know yet, but is knowable: Proof-of-concept
model is available; however, more investment (e.g., data, analysts, systems, tools) is
• What is knowable with uncertainty: Model output is available and potentially useful;
however, questions remain as to whether the model itself is specified correctly e.g.,
metrics reflect Knightian uncertainty. (Bayesian methods may be helpful.)
• What is unknowable: Model output is not available.
• What one chooses not to know: Incentives overpower model output.
Contextualization: Describe regimes
• Business as usual (BAU) i.e., sustainable growth
• Cyclical (typical up and down growth– but same process and similar trend)
• Structural (move to a different growth path driven by a different process)
• Providing context is critical:
– Benchmark to competitors (cohorts)
– Benchmark to optimal, feasible outcome
– Show time series
– Drill into components on a consistent basis
Compelling communication requires multiple interactions
• Educate as to model’s usefulness as a function of complexity
• Frame key performance indicators (KPIs)
• Prototype, socialize, productionize
• Avoid big-bang projects– include executives in discovery/iteration process
Manage vagueness to communicate more compellingly
“Vagueness blurring and imprecision effectively provide a protective shell to guard [a]
statement against a charge of falsity.” (Rescher, p. 222)
• Distinguish overarching “truth claim” from (possibly inaccessible) “true details.”
• Avoid recommendation-rejection skepticism by…
– Combating cognitive myopia with context
– Clarifying certainty with respect to aspects of output
– Separating critical truth-claim components from color-commentary details
• Paradoxically, judicious omission of details (sometime unavoidable) may produce a
clearer, more compelling message. Finding the “goldilocks” balance is not always
– Truth claim: I grew up in San Francisco. This vague statement masks the true detail
that I grew up in Danville– loosely part of metropolitan San Francisco.
– Truth claim: Portfolio is likely to lose 10% or more of its value in the next structural
recession. This vague statement masks details that a simulation algorithm was used
to determine the frequency of losses beyond 10% and the modeler assumes a
structural recession occurs 3% (1-in-33 years) of the time, which marks the amount
of loss– in this case, 10% of starting portfolio value.
Moving from discovery to action
Persuade decision makers regarding…
Chronic model weaknesses
• No feedback loops
• No thresholds
• Inadequate spill-over effects
• Aikman, David, Piergiorgio Alessandri, Bruno Eklund, Prasanna Gai, Sujit Kapadia, Elizabeth
Martin, Nada Mora, Gabriel Sterne and Matthew Willison, 2009, “Funding liquidity risk in a
quantitative model of systemic stability,” Working Paper 372, Bank of England.
• Arrow, Kenneth J. and Gerard Debreu, 1954, "Existence of an equilibrium for a competitive
economy,” Econometrica 22 (3), pp. 265–290.
• Bohn, Jeffrey and Roger Stein 2009, Active Portfolio Management in Practice, Wiley.
• Diaconis, Persi, 2003, “The problem of thinking too much,” Bulletin American Academy of
Science, Spring, pp. 26-38.
• Fender, Ingo and John Kiff, 2004, “CDO rating methodology: Some thoughts on model risk and
its implications,” Monetary and Economic Department, BIS.
• Feynman, Richard P., 1974, “Cargo cult science,” Engineering and Science, June, pp. 10-13.
• Folinsbee, Kaila E; et al. 2007, "Quantitative approaches to phylogenetics; §5.2: Fount of
stability and confusion: A synopsis of parsimony in systematics,” In Winfried Henke, ed.
Handbook of Paleoanthropology: Primate evolution and human origins: Volume 2, Springer, p.
• Gordy, Michael B., 2003, “A risk-factor model foundation for ratings-based bank capital rules,”
Journal of Financial Intermediation, 12, pp. 199-232.
• Gray, Dale and Samuel Malone, 2008, Macrofinancial Risk Analysis, Wiley.
• Haidt, Jonathan, 2012, The righteous mind: Why good people are divided by politics and
religion, Pantheon Books, New York, NY.
• Haldane, Andrew G., 2012, “The dog and the frisbee,” Bank of England speech.
• Hamilton, James, 1994, Time Series Analysis, Princeton University Press.
• Hansen, Lars P. and Thomas J. Sargent, 2015, “Four types of ignorance,” Journal of Monetary
Economics, 69, pp. 97-113.
• Hansen, Lars P. and Thomas J. Sargent, 2007, “Recursive robust estimation and control
without commitment,” Journal of Economic Theory, 136, pp. 1-27.
• Jablonka, Eva and Marion J. Lamb, 2014, Evolution in four dimensions: genetic, epigenetic,
behavioral, and symbolic variation in the history of life, MIT Press, Cambridge, MA.
• Kalirai, Harvir and Martin Scheicher, 2002, “Macroeconomic Stress Testing: Preliminary Evidence for
Austria,” Financial Stability Report 3, Oesterreichische Nationalbank, 58-74.
• Knight, Frank H., 1921, Risk, Uncertainty, and Profit, Hart, Schaffner & Marx; Houghton Mifflin
Company: Boston, MA.
• Koomey, Jonathan, 2001, Turning numbers into knowledge: Mastering the art of problem solving,
Analytics Press, Oakland, CA.
• Kuhn, Thomas S., 1977, The essential tension: Selected studies in scientific tradition change,
University of Chicago Press, Chicago.
• Lewis, Michael, 2010, The big short: Inside the doomsday machine, W.W. Norton & Company: New
• Lucas, Robert, 1977, “Understanding business cycles,” in K. Brunner and A.H. Metzler, eds.,
Stabilization of the domestic and international economy, Carnegie-Rochester Conference Series on
Public Policy, 7729.
• Popper, Karl, 1972, Objective knowledge: An evolutionary approach, Clarendon Press, Oxford.
• Rescher, Nicholas, 2004, “Leibniz quantitative epistemology,” Studia Leibnitiana, 36(2), pp. 210-231.
• Simon, Herbert A., 1955, “A behavioral model of rational choice,” Quarterly Journal of Economics,
69(1), pp. 99-118.
• Stark, Philip B., 2015, “Pay no attention to the model behind the curtain,” Working paper, UC
• Vasicek, Oldrich A., 1997, “The distribution of loan portfolio value,” Working paper, KMV.
• Wilson, Edward O., 1999, “Consilience: The unity of knowledge,” First Vintage Books, New York, NY.
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