Understanding Risk & Uncertainty
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Transcript of Understanding Risk & Uncertainty
© Kelvin Stott 2012
Understanding Risk & Uncertainty
Kelvin Stott PhDPharma R&D Portfolio Strategy, Risk & Decision Consultant
March 2012
© Kelvin Stott 2012
Risk & uncertainty: Basic concepts
Risk & uncertainty are closely related, but slightly different conceptsBoth risk and uncertainty are:
Based on current lack of certainty in a potential fact, event, outcome, or scenario, etc.Defined by probabilities or probability distributions Include both upside and downside potentialSubjective: they both depend on who knows what
DifferencesUnlike uncertainty, risk involves exposure to impact: potential consequences that matter to a subject Hence, risk is even more subjective: depends on how much the potential consequences matter, to whom
Definitions will follow, after more background…
© Kelvin Stott 2012
3 basic sources of risk & uncertainty
Known knowns (no risk/uncertainty)Facts, outcomes or scenarios that we know with absolute certainty, based on deterministic processes
Unknown knownsCertain facts that others know but we don’tBased on information asymmetry or poor communication
Known unknownsPotential facts, outcomes, scenarios that we are aware of, but don’t yet know with any certaintyBased on stochastic processes and known probability laws
Unknown unknownsPotential facts, outcomes or scenarios that we are not yet aware of, have not even consideredOften rare and extreme events or outliers (“black swans”), not considered due to lack of experience/imagination
© Kelvin Stott 2012
3 basic forms of risk & uncertainty
DiscreteBased on uncertainty in discrete variablesNo intermediate outcomes or scenariosE.g., succeed/fail, true/false, event/no event, etc.Defined by discrete probabilities
ContinuousBased on uncertainty in continuous variablesIntermediate scenarios/outcomes are possibleE.g., sales, costs, time, market share, etc.Defined by continuous probability distributions
ComplexCombination of discrete & continuous uncertaintyMost real-life cases fall into this category
© Kelvin Stott 2012
Risk and uncertainty are often complex, based on discrete & continuous probability distributions
Discrete
Continuous
Complex
© Kelvin Stott 2012
Risk & uncertainty can be described by 4 types of probability distributions
PDF: Probability Density FunctionProbability density vs valueArea under curve = CDF (see below)
CDF: Cumulative Distribution FunctionCumulative probability vs valueGradient = PDF (see above)Area = probability x difference in value
Inverted PDFValue vs probability density
Inverted CDFValue vs cumulative probability
© Kelvin Stott 2012
Relationship between probability distributions
Inverted CDFValue
Cumulative probability
Value
Cum
ulati
vepr
obab
ility
CDF
Value
Prob
abili
ty
dens
ity
Invert
Invert
Integrate / Differentiate
Inverted PDFValue
Probabilitydensity
© Kelvin Stott 2012
Simple, continuous probability distributions can be described by 4 independent parameters
Mean Dispersion Skewness Kurtosis
Describes the location of the distribution
Describes the spread of the distribution
Describes the asymmetry of distribution
Describes the shape of the distribution
© Kelvin Stott 2012
Risk & uncertainty: Basic definitions
Expected Value (EV) is the probability-weighted average value of a given variable across all potential scenariosUncertainty is the mean absolute deviation (MAD) from the Expected Value
Includes upside and downside uncertaintyUpside = downside: they always balance!
Risk is the mean absolute deviation (MAD) from a given target, objective, or threshold
Includes upside and downside riskUpside risk ≠ downside risk: depends on EV vs target
Risk and uncertainty correspond to areas under CDF (or inverted CDF) value-probability curves
Areas correspond to Probability x ImpactImpact is a deviation (difference) in value
© Kelvin Stott 2012
High uncertainty; No set target/threshold=> Upside uncertainty = Downside uncertainty >> 0
Value
Cumulative probability →
Expected valueDownsid
e uncertain
ty
Upside uncertain
ty
© Kelvin Stott 2012
Some uncertainty; No set target/threshold=> Upside uncertainty = Downside uncertainty > 0
Value
Cumulative probability →
Expected valueDownsid
e uncertain
ty
Upside uncertain
ty
© Kelvin Stott 2012
No uncertainty; No set target/threshold=> Upside uncertainty = Downside uncertainty = 0
Value
Cumulative probability →
Expected value
No d’nside
uncertainty
No upside
uncertainty
© Kelvin Stott 2012
High uncertainty; Expected value = Target=> Upside risk = Downside risk >> 0
Value
Cumulative probability →
Expected value
Target or threshol
d
Downside risk
Upside risk
© Kelvin Stott 2012
Some uncertainty; Expected Value = Target=> Upside risk = Downside risk > 0
Value
Cumulative probability →
Expected value
Target or threshol
d
Downside risk
Upside risk
© Kelvin Stott 2012
No uncertainty; Expected Value = Target=> Upside risk = Downside risk = 0
Value
Cumulative probability →
Expected value
Target or threshol
d
No down-
side risk
No upside
risk
© Kelvin Stott 2012
High uncertainty; Expected Value < Target=> Upside risk < Downside risk
Value
Cumulative probability →
Expected value
Target or threshol
d
Downside risk
Upside risk
© Kelvin Stott 2012
Some uncertainty; Expected Value < Target=> Upside risk < Downside risk
Value
Cumulative probability →
Expected value
Target or threshol
d
Downside risk
Upside risk
© Kelvin Stott 2012
No uncertainty; Expected Value < Target=> Upside risk = 0 < Downside risk
Value
Cumulative probability →
Expected value
Target or threshol
d
No upside
risk
Downside risk
© Kelvin Stott 2012
High uncertainty; Expected Value > Target=> Upside risk > Downside risk
Value
Cumulative probability →
Target or threshol
d
Expected value
Downside risk
Upside risk
© Kelvin Stott 2012
Some uncertainty; Expected Value > Target=> Upside risk > Downside risk
Value
Cumulative probability →
Target or threshol
d
Expected value
Downside risk
Upside risk
© Kelvin Stott 2012
No uncertainty; Expected Value > Target=> Upside risk > Downside risk = 0
Value
Cumulative probability →
Target or threshol
d
Expected value Upside
risk
No down-
side risk
© Kelvin Stott 2012
Notes & observations
Risk = Uncertainty when EV = target/thresholdUnlike uncertainty, risk cannot exist without a target, objective, or thresholdRisk can exist without uncertainty (but we don’t call it risk), when EV ≠ target/threshold
Downside risk always exists when EV < targetUpside risk always exists when EV > target
Without uncertainty, risk = expected loss/gainIf EV = target: upside risk = downside risk = 0If EV < target: upside risk = 0; downside = target - EVIf EV > target: upside risk = EV - target; downside = 0
© Kelvin Stott 2012
Other absolute measures of uncertainty
Standard deviation (SD)Root mean square deviation from Expected ValueMeasures overall (upside + downside) uncertainty vs EVNon-linear, places more weight on outliers (tails)
VarianceMean square deviation from Expected ValueNon-linear measure of uncertainty, equal to SD squared
Expected downside uncertaintyProbability-weighted average negative deviation from EVLinear measure of downside uncertainty onlyEqual to 0.5 x mean absolute deviation (MAD) vs EV
Expected upside uncertaintyProbability-weighted average positive deviation from EVLinear measure of upside uncertainty onlyEqual to 0.5 x mean absolute deviation (MAD) vs EV
© Kelvin Stott 2012
Relative measures of uncertainty (noise-to-signal ratios)
MAD vs EV / EVMean absolute deviation from EV, as % of EVLinear measure of overall (upside + downside) uncertainty vs EV
SD / EVNon-linear measure of overall uncertainty, as % of EVAlso called the Coefficient of Variation (CV)
Variance / EVNon-linear measure of overall uncertainty vs EV; not a % ratioAlso called Dispersion Index or Variance-to-Mean Ratio (VMR)
Expected downside uncertainty / EVProbability-weighted negative deviation from EV, as % of EVLinear measure of downside UC, equal to 0.5 x MAD vs EV / EV
Expected upside uncertainty / EVProbability-weighted positive deviation from EV, as % of EVLinear measure of upside UC, equal to 0.5 x MAD vs EV / EV
© Kelvin Stott 2012
Other absolute measures of risk
Value at Risk (VaR)Maximum negative deviation from target/threshold at X% probabilityDoes not consider upside, or potential impact of worst case scenarios
Expected Shortfall (ES)Probability-weighted average deviation from target in X% worst casesMeasures downside risk across worst case scenarios onlyAlso called Expected Tail Loss (ETL) or Conditional Value at Risk (CVaR)
Probability of success or failure to reach target/thresholdCommonly used, but does not measure actual risk!Does not consider potential impact of success or failure
Expected downside riskProbability-weighted average negative deviation from target/thresholdLinear measure of downside risk (probability x negative impact)
Expected upside riskProbability-weighted average positive deviation from target/thresholdLinear measure of upside risk (probability x positive impact)
© Kelvin Stott 2012
Alternative measures of risk
Value
Downside riskValue at
Risk (VaR) at X
%
Probability of
success (or
failure)
Expected Shortfallbelow X% Cumulative probability →
Upsiderisk
Target or threshol
d
© Kelvin Stott 2012
Relative measures of risk (risk-target ratios)
MAD vs target / targetMean absolute deviation from target, as % of targetLinear measure of overall risk vs target/threshold
VaR / targetValue at Risk at X% probability, as % of targetLike VaR, does not consider worst case scenarios
ES / targetExpected Shortfall in X% worst cases, as % of targetLinear measure of extreme downside risk vs target
Expected downside risk / targetProbability-weighted negative deviation, as % of target
Expected upside risk / targetProbability-weighted positive deviation, as % of target
© Kelvin Stott 2012
Conclusion and key messages
Risk and uncertainty are based on lack of certainty in a potential fact, event, outcome, or scenarioThey include both upside & downside components and are described by probability distributionsUncertainty is measured relative to expected valueRisk is measured relative to a set target/threshold, with potential consequences that matter (impact)They can be measured in many ways, but the best measures are based on probability-weighted average deviation in value (probability x impact), corresponding to areas under a CDF curve
© Kelvin Stott 2012
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