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Kelvinstott riskanduncertainty-120312205323-phpapp02
- 2. ©KelvinStott2012
Risk & uncertainty are closely related, but slightly
different concepts
Both 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 potential
Subjective: they both depend on who knows what
Differences
Unlike 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…
- 3. ©KelvinStott2012
Known knowns (no risk/uncertainty)
Facts, outcomes or scenarios that we know with absolute
certainty, based on deterministic processes
Unknown knowns
Certain facts that others know but we don’t
Based on information asymmetry or poor communication
Known unknowns
Potential facts, outcomes, scenarios that we are aware of,
but don’t yet know with any certainty
Based on stochastic processes and known probability laws
Unknown unknowns
Potential facts, outcomes or scenarios that we are not yet
aware of, have not even considered
Often rare and extreme events or outliers (“black swans”),
not considered due to lack of experience/imagination
- 4. ©KelvinStott2012
Discrete
Based on uncertainty in discrete variables
No intermediate outcomes or scenarios
E.g., succeed/fail, true/false, event/no event, etc.
Defined by discrete probabilities
Continuous
Based on uncertainty in continuous variables
Intermediate scenarios/outcomes are possible
E.g., sales, costs, time, market share, etc.
Defined by continuous probability distributions
Complex
Combination of discrete & continuous uncertainty
Most real-life cases fall into this category
- 6. ©KelvinStott2012
PDF: Probability Density Function
Probability density vs value
Area under curve = CDF (see below)
CDF: Cumulative Distribution Function
Cumulative probability vs value
Gradient = PDF (see above)
Area = probability x difference in value
Inverted PDF
Value vs probability density
Inverted CDF
Value vs cumulative probability
- 8. ©KelvinStott2012
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
- 9. ©KelvinStott2012
Expected Value (EV) is the probability-weighted average
value of a given variable across all potential scenarios
Uncertainty is the mean absolute deviation (MAD) from
the Expected Value
Includes upside and downside uncertainty
Upside = downside: they always balance!
Risk is the mean absolute deviation (MAD) from a given
target, objective, or threshold
Includes upside and downside risk
Upside 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 Impact
Impact is a deviation (difference) in value
- 22. ©KelvinStott2012
Risk = Uncertainty when EV = target/threshold
Unlike uncertainty, risk cannot exist without a
target, objective, or threshold
Risk can exist without uncertainty (but we don’t
call it risk), when EV ≠ target/threshold
Downside risk always exists when EV < target
Upside risk always exists when EV > target
Without uncertainty, risk = expected loss/gain
If EV = target: upside risk = downside risk = 0
If EV < target: upside risk = 0; downside = target - EV
If EV > target: upside risk = EV - target; downside = 0
- 23. ©KelvinStott2012
Standard deviation (SD)
Root mean square deviation from Expected Value
Measures overall (upside + downside) uncertainty vs EV
Non-linear, places more weight on outliers (tails)
Variance
Mean square deviation from Expected Value
Non-linear measure of uncertainty, equal to SD squared
Expected downside uncertainty
Probability-weighted average negative deviation from EV
Linear measure of downside uncertainty only
Equal to 0.5 x mean absolute deviation (MAD) vs EV
Expected upside uncertainty
Probability-weighted average positive deviation from EV
Linear measure of upside uncertainty only
Equal to 0.5 x mean absolute deviation (MAD) vs EV
- 24. ©KelvinStott2012
MAD vs EV / EV
Mean absolute deviation from EV, as % of EV
Linear measure of overall (upside + downside) uncertainty vs EV
SD / EV
Non-linear measure of overall uncertainty, as % of EV
Also called the Coefficient of Variation (CV)
Variance / EV
Non-linear measure of overall uncertainty vs EV; not a % ratio
Also called Dispersion Index or Variance-to-Mean Ratio (VMR)
Expected downside uncertainty / EV
Probability-weighted negative deviation from EV, as % of EV
Linear measure of downside UC, equal to 0.5 x MAD vs EV / EV
Expected upside uncertainty / EV
Probability-weighted positive deviation from EV, as % of EV
Linear measure of upside UC, equal to 0.5 x MAD vs EV / EV
- 25. ©KelvinStott2012
Value at Risk (VaR)
Maximum negative deviation from target/threshold at X% probability
Does not consider upside, or potential impact of worst case scenarios
Expected Shortfall (ES)
Probability-weighted average deviation from target in X% worst cases
Measures downside risk across worst case scenarios only
Also called Expected Tail Loss (ETL) or Conditional Value at Risk (CVaR)
Probability of success or failure to reach target/threshold
Commonly used, but does not measure actual risk!
Does not consider potential impact of success or failure
Expected downside risk
Probability-weighted average negative deviation from target/threshold
Linear measure of downside risk (probability x negative impact)
Expected upside risk
Probability-weighted average positive deviation from target/threshold
Linear measure of upside risk (probability x positive impact)
- 27. ©KelvinStott2012
MAD vs target / target
Mean absolute deviation from target, as % of target
Linear measure of overall risk vs target/threshold
VaR / target
Value at Risk at X% probability, as % of target
Like VaR, does not consider worst case scenarios
ES / target
Expected Shortfall in X% worst cases, as % of target
Linear measure of extreme downside risk vs target
Expected downside risk / target
Probability-weighted negative deviation, as % of target
Expected upside risk / target
Probability-weighted positive deviation, as % of target
- 28. ©KelvinStott2012
Risk and uncertainty are based on lack of certainty
in a potential fact, event, outcome, or scenario
They include both upside & downside components
and are described by probability distributions
Uncertainty is measured relative to expected value
Risk 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
- 29. ©KelvinStott2012
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