Intuitive Understanding of Statistics in SAS Risk Engine

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Introduction

SAS Risk Engine supports a broad, comprehensive, and well-structured set of risk statistics that are systematically organized into logical groups. This structured design ensures that the same underlying measures can be applied consistently across a wide range of use cases, including market risk, portfolio risk, and credit risk, as well as regulatory and supervisory reporting requirements. These measures span global regulatory frameworks such as Basel, internal risk management and limit monitoring, stress testing, capital adequacy assessment, and senior management reporting. By providing a common and consistent statistical framework, SAS Risk Engine enables organizations to compare risk measures across portfolios, risk types, and methodologies while maintaining transparency, governance, and auditability.

This article introduces the fundamental nature of these statistics and explains them using a simple, intuitive and summarized approach to help readers build a clear conceptual understanding. The article is primarily targeted at beginners in risk analytics, as well as consultants and practitioners who are new to the domain and looking to develop an initial foundation in enterprise risk measurement. By the end of the article, readers should be able to recognize the key groups of risk statistics supported by SAS Risk Engine and understand the basic nature of several metrics in each of the groups.

Grouping of Available Statistics

For detailed information on the SAS Risk Engine, risk-related action sets, and

guidance on interpreting outputs,

please refer to the following:

Using the SAS Risk Engine Interface

Programming with SAS Risk Engine

The various statistics supported by SAS Risk Engine are grouped based on logic and functionality. Each group represents a distinct aspect of risk measurement, such as distribution characteristics, quantile-based measures, core risk metrics, tail risk analysis, contribution and incremental analysis, or exposure profiling. This grouping helps users quickly understand the purpose of each statistic, apply them consistently across different risk methodologies and portfolios, and select the appropriate measures for specific risk management, regulatory, or reporting use cases.

The following table provides an overview of the groups and corresponding statistics.

Group	Statistics	Group Explanation	What it Answers / Typical Purpose
MOMENTS	MEAN, STD, SKEWNESS, KURTOSIS	Descriptive statistics that summarize the central tendency, dispersion, and shape of the loss or exposure distribution.	What does the loss distribution look like?
QUANTILES	MIN, MAX, MEDIAN, Q1, Q3	Statistics that describe the distribution using ordered values and percentiles.	Where do losses sit when ordered?
VARSTATS	VAR, VAR_L, VAR_U, VAR_PCT, VARPCT_L, VARPCT_U, ES	Core risk measures used to quantify portfolio loss at a given confidence level and tail risk.	How bad can losses get at a confidence level?
EVSTATS	TAILINDEX, VAREVT, CONDEL	Extreme value theory–based measures used to model and quantify tail and extreme loss behavior.	How severe are extreme, crisis-level losses?
WITHOUT	VARWO, INCVAR, ESWO, INCES	Measures that assess the impact on portfolio risk when a position or sub-portfolio is removed or added.	How does a position change portfolio risk?
CONTRIB	CONTVAR, CONTES	Statistics that attribute total portfolio risk to individual positions or sub-portfolios.	Who is consuming the portfolio’s risk?
EXPOSURE	CURREXP, PEAKEXP, EXPEXP, EEE, EPE, EEPE	Exposure-based measures used to quantify current, expected, and effective exposure profiles over time.	How does exposure evolve over time?

Understanding the Statistics

In SAS Risk Engine, a range of key statistics is typically calculated on loss or exposure distributions for various risk types like market or credit risks, using historical and current (instrument- or counterparty-level) data, as well as simulated or projected future data from Monte Carlo simulations, scenario analyses, or other relevant methods. These analyses can cover multiple future time horizons using suitable models and scenario projections. For example, IFRS 9 forward-looking credit loss models estimate expected credit losses (ECLs) over the lifetime of financial assets—not just at default—by integrating historical data, current conditions, and forward-looking macroeconomic forecasts to provide a forward-looking assessment of potential losses.

While popular risk measures such as VaR and Expected Shortfall often get the spotlight, the basic statistical moments—Mean, Standard Deviation, Skewness, and Kurtosis—form the foundation of sound risk interpretation. Additionally measures based on extreme value theory, contribution-based measures and so on provide deeper insights.

A Simple Example

Let’s consider an example where you invest in five stocks (or track the same stock with varying prices over the past 5 days or projected for the next 5 days; in simpler terms you have five numbers). Suppose the returns for these five stocks are 5%, 7%, 6%, 8%, and 50%. We will use this example as a reference throughout the article to illustrate several statistical measures. Note that the article assumes the values for certain metrics for illustrative purposes and do not provide the exact mathematical formula (or calculation details) for the sake of simplicity.

MOMENTS Group

Moments summarize the overall behavior of the loss distribution generated by simulations or scenarios for a given point of time or over different time horizons depending on the objective.

Mean (Average Return):

The mean is the average return across all investments and gives a simple snapshot of performance. For example, if five stocks return 5%, 7%, 6%, 8%, and 50%, the mean return is 15.2%. This tells you that, on average, these equities deliver about 15% return. However, the 50% outlier can make the average appear higher than what most stocks actually deliver. Note that all the other stocks are giving a single digit return only. Hence mean might be misleading in the presence of extreme (very low or very high) values for a large portion of your portfolio.

Standard Deviation (Volatility):

Standard deviation measures how much returns vary from the mean. In the same example, most stocks return 5–8%, but one stock jumps to 50%, creating high volatility. A high standard deviation signals unpredictable returns, while a low one indicates more stable performance across the equities.

Skewness (Asymmetry of Returns):

Skewness shows whether the returns are tilted toward extreme outcomes. Here, the 50% return pulls the mean ( or distribution) to the right, resulting in positive skewness. Most stocks deliver moderate returns, but occasionally, there’s a big gain. Positive skewness means rare big wins (like + 50%); negative skewness would indicate rare big losses (like – 50%). Skewness is largely about the direction of rare outcomes, not their exact intensity. The skewness can have 0, negative or positive values.

Kurtosis (Tail Risk / Extreme Returns):

Kurtosis provides an idea of likelihood/magnitude/frequency of extreme outcomes irrespective of the direction or simply heaviness of tails or extremes. If all equities were clustered very tightly around 9% (e.g., 8.5, 9, 9.5, 9, 8), kurtosis would be negative, indicating almost flat distribution, that is, no rare events. High kurtosis is an indicator of occasional and high magnitude outliers. In SAS, kurtosis can have 0, negative or positive values.

For more mathematical details refer to the following link: Details of skewness and kurtosis

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation / Risk Note
Mean – Expected Loss	Average loss across all simulated scenarios; simplest summary of the distribution.	Simulated 1-year credit losses: Mean = USD 10 million	“On average, I expect to lose USD 10 million over the year.”	Central to pricing, provisioning, budgeting, and baseline ECL calculations under IFRS 9	Does not show how bad losses can get; portfolios with same mean may have very different risk profiles
Standard Deviation – Volatility / Uncertainty	Measures how much losses fluctuate around the mean; captures outcome uncertainty.	Mean = USD 10 million, STD = USD 12 million	Low STD → stable, predictable; High STD → uncertain, volatile	Reflects riskiness beyond mean; high STD may require higher capital	Only measures volatility, not tail behavior; doesn’t show direction of extreme losses
Skewness – Asymmetry of Losses	Shows whether the distribution is symmetric or skewed toward extreme outcomes.	Most scenarios small losses (~USD 5–7M), rare large defaults (~USD 50M) → positive skew	Near 0 → symmetric; Positive → tail risk on loss side; Negative → tail risk on gains	Highlights the direction of tail risk; identifies portfolios vulnerable to sudden stress	Extreme outcomes may be rare but possible; skewness alone doesn’t quantify magnitude of tail losses
Kurtosis – Tail Thickness / Extreme Loss Risk	Measures how heavy the tails are; indicates likelihood of extreme losses beyond normal assumptions.	Most scenarios small losses, crisis scenario ~USD 80M → high kurtosis	Low → predictable stable losses; High → fat or heavy tails tails, crisis-prone	Important for stress testing, economic capital, and identifying VaR underestimation	Focuses on tail severity but not on mean or typical scenarios

QUANTILES Group

Quantiles describe the distribution using ordered outcomes, rather than averages.

Continuing with our example of five stocks returns to be 5%, 7%, 6%, 8%, and 50%

MIN – Worst Outcome: The minimum return among your five stocks is 5%, which represents the worst-performing stock in your portfolio. This metric shows the lowest outcome you could experience and helps set expectations for downside performance, highlighting the least favorable scenario without being skewed by the other stocks.

MAX – Best Outcome: The maximum return is 50%, representing the best-performing stock. This shows the potential upside in your portfolio and indicates how extreme outcomes can significantly deviate from typical performance. It’s useful for understanding the potential for rare, high returns.

MEDIAN – Typical Outcome: The median return is 7%, which is the middle value when all stock returns are ordered. Half of the stocks perform above this level and half below. The median gives a more representative picture of your portfolio’s typical performance than the mean, which is skewed by the 50% outlier.

Q1 – Lower Quartile (25th percentile): Q1 is 5.5%, meaning 25% of your stocks have returns below this value. This metric highlights the lower end of performance and helps you understand how the weakest-performing stocks behave in your portfolio.

Q3 – Upper Quartile (75th percentile): Q3 is 8%, meaning 25% of your stocks perform better than this value. This provides insight into the better-performing segment of your portfolio and helps identify where the upside potential lies without being dominated by the extreme 50% return.

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Quantile Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation / Note
MIN – Best-Case Outcome	The minimum loss (or maximum gain) observed across all scenarios.	MIN = –USD 2 million	“In the best scenario, the portfolio gains USD 2 million.”	Identifies downside protection; helps understand hedging optionality	MIN may be driven by extreme or unlikely scenarios; don’t rely on it alone, it may understate risk
MAX – Worst-Case Outcome	The largest loss observed across all scenarios.	MAX = USD 50 million	“In the worst scenario, losses can reach USD 50 million.”	Highlights absolute downside exposure; useful for stress testing and senior management	MAX depends heavily on the scenario set; may overstate the risks
MEDIAN – Typical Outcome (50th percentile)	Half the scenarios are below, half above this value; robust central measure.	Median = USD 8 million, Mean = USD 10 million	“In more than half the scenarios, losses are below USD 8 million.”	Shows the typical or expected outcome; robust to extremes	Gap between median and mean signals skewness; median alone doesn’t show tail risk
Q1 – Lower Quartile (25th percentile)	Loss level below which 25% of scenarios fall.	Q1 = USD 5 million	“In the best 25% of scenarios, losses do not exceed USD 5 million.”	Defines favorable or normal conditions; useful for stable portfolio analysis	Only reflects benign scenarios, not extremes
Q3 – Upper Quartile (75th percentile)	Loss level below which 75% of scenarios fall (top 25% are worse).	Q3 = USD 15 million	“One-quarter of scenarios produce losses above USD 15 million.”	Acts as an early warning threshold; bridges typical vs. tail risk	Does not capture the absolute worst outcomes

VARSTATS Group

This group presents the core risk measures used to quantify portfolio loss at a given confidence level and tail or extreme risk. VaR (Value at Risk) measures potential losses and can be expressed in currency terms or as a percentage of the portfolio. It can be calculated over different time periods—days, months, or years—depending on trading frequency and over different confidence levels depending on regulatory and internal reporting requirements.

Value-at-Risk (VaR): VaR measures the maximum expected loss in your portfolio at a given confidence level. Since equities are traded daily and we have daily data for our five stocks, VaR can be based on days. For example, if the 95% 1-day VaR of your five-equity portfolio is assumed as USD 10,000, it means that under normal market conditions, you would not expect to lose more than USD 10,000 on 95 out of 100 trading days. VaR sets a threshold for potential losses, helping investors understand and prepare for routine market fluctuations. You might wonder what happens on the other 5 days, or if the loss exceeds USD 10,000 on specific day or days. This will be explained soon by another metric called Expected Shortfall (ES)

VAR_L and VAR_U: Confidence Bounds Around VaR: Because VaR is an estimate derived from simulations or historical data, it carries some uncertainty. VAR_L and VAR_U provide lower and upper bounds—say USD 9,000 and USD 12,000—indicating that the true VaR is likely to lie within this range. These bounds give investors a sense of reliability in the VaR estimate and prevent overconfidence in a single number.

VAR_PCT : VaR as a Percentage of Portfolio: VAR_PCT expresses VaR as a percentage of the portfolio rather than an absolute amount. For instance, if the 95% 1-day VaR of your five-equity portfolio is 2% (which is absolute terms is assumed to be USD 10,000 in our example), it means that under normal market conditions, you would not expect to lose more than 2% of your portfolio value on 95 out of 100 trading days This makes it easy to compare VaR across portfolios of different sizes and to relate it to other percentage or quantile-based metrics like Q1 and Q3. However, VAR_PCT alone doesn’t tell you the magnitude of extreme losses—that’s where the metric expected shortfall or ES comes in.

VARPCT_L and VARPCT_U: Bounds on VaR Percentage: These provide the lower and upper limits of the VAR_PCT estimate, for example 1.8% and 2.2%. They account for estimation uncertainty, ensuring that the VaR percentage is not treated as an exact figure. This is useful for risk governance and model validation.

Expected Shortfall (ES): ES measures the average loss if the VaR threshold is exceeded. Continuing the example, if the 95% VAR is USD 10000 (or 2 %), the ES might be USD 30000 (or 6%). This means that on the 5% of days when losses exceed 2% of the portfolio, the average loss is 30000 (or 6%). VaR gives a threshold for potential losses, while ES calculates the average loss beyond that threshold. ES captures extreme losses more effectively than VaR, providing a more realistic view of tail risk for your five-stock portfolio.

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation / Note
VaR – Value-at- Risk	Loss level not expected to be exceeded at a given confidence over a time horizon.	1-month VaR at 99% confidence = USD 50 million	“On 99 out of 100 times (months), losses will not exceed USD 50 million.”	Regulatory reporting, limit setting, risk comparison across portfolios	Does not indicate severity of losses beyond the threshold
VAR_L / VAR_U – Confidence Bounds on VaR	Lower (VAR_L) and upper (VAR_U) bounds of VaR to reflect estimation uncertainty.	VaR = USD 50M, VAR_L = USD 45M, VAR_U = USD 60M	“The true VaR likely lies between USD 45M and USD 60M.”	Prevents false precision; supports internal audit and model validation	Dependent on simulation/sample size; uncertainty may be large for limited data
VAR_PCT – VaR Percentile	Expresses VaR as a percentage of the portfolio rather than absolute amount.	VAR_PCT = 5	“There is a 1% chance that the portfolio will lose more than 5% in a month.	Aligns VaR with quantile-based thinking; easier to compare with Q1/Q3	Percentage alone doesn’t show magnitude of tail losses
VARPCT_L / VARPCT_U – Confidence Bounds on Percentage	Shows uncertainty bounds around the VaR percentage itself.	VAR_PCT = 5, VARPCT_L = 4.5, VARPCT_U = 5.5	“The true VaR percentage lies between 4.5 and 5.5.”	Validates model stability; important for governance	Only reflects percentage uncertainty, not loss magnitude
ES – Expected Shortfall / Conditional VaR	Average loss given that VaR is exceeded; captures tail severity.	99% VaR = USD 50M, ES = USD 85M	“If losses exceed USD 50M, the average loss is USD 85M.”	Measures extreme tail risk; more sensitive to fat tails; aligns with stress testing and Basel FRTB	Requires sufficient tail data; more sensitive to simulation variability

For more details on VaR , use the following link: Value at Risk

Extreme Value Theory or EVT Group

This group has measures based on Extreme Value Theory (EVT). EVT is a branch of statistics that focuses on modelling rare, extreme events—the tails of a distribution—rather than the typical, everyday outcomes. In risk management, EVT is used to estimate the probability and severity of extreme losses, helping to better capture tail risk beyond what VaR alone can show.

TAILINDEX: How Heavy Is the Tail?

TAILINDEX measures how likely extremely large losses are in your portfolio. For example, imagine your five equities usually fluctuate modestly, but occasionally one crashes dramatically during a market crisis. A TAILINDEX of 1.2 indicates a “fat tail,” meaning extreme losses decay slowly and very large losses are more probable than under normal assumptions. Conversely, a higher TAILINDEX (For example, 3) would indicate thinner tails, where extreme crashes are less likely. Investors use this to understand vulnerability to rare, catastrophic events that standard VaR might underestimate.

VAREVT:  Value-at-Risk Using Extreme Value Theory

VAREVT is a VaR measure that explicitly models the tail of the loss distribution using extreme value theory (EVT). It is a special theory refined to study portfolio behaviour in extreme conditions. For your five-equity portfolio, suppose the standard 99% 1-day VaR is USD 10,000, but the EVT-based VAREVT is USD 25,000. This tells you that if you account for the extreme tail behavior of the equities—like a sudden market crash—the potential loss could be much higher than standard VaR suggests. VAREVT gives a more conservative and realistic estimate of worst-case losses during crises.

CONDEL: Conditional Extreme Loss (EVT-Based Expected Shortfall)

CONDEL measures the average severity of losses beyond the extreme threshold. (similar to ES but different in underlying theory). Continuing the example, if the EVT threshold is crossed, CONDEL might be USD 50,000. This means that once your portfolio enters a crisis-level scenario, the average loss could be USD 50,000, highlighting the true impact of rare, catastrophic events. Investors and risk teams rely on CONDEL to plan for stress scenarios, allocate economic capital, and prepare for extreme tail events that VaR alone cannot capture.

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation / Note
TAILINDEX – Tail Thickness	Measures how heavy the tail is—how quickly extreme losses decay.	TAILINDEX = 1.2	“Extreme losses decay slowly, so very large losses are more likely than under normal assumptions.”	Indicates crisis vulnerability; highlights if standard VaR assumptions underestimate tail risk	Sensitive to extreme observations; requires sufficient tail data
VAREVT – EVT-Based VaR	Value-at-Risk calculated using EVT tail modeling instead of full empirical distribution.	Standard 99% VaR = USD 50M, VAREVT = USD 80M	“When tail behavior is modeled explicitly, extreme losses are much larger than standard VaR suggests.”	Captures losses beyond historical data; provides conservative estimates during crises	Requires robust EVT modeling; sensitive to tail data quality
CONDEL – Conditional Excess Loss	Expected loss beyond an extreme threshold (EVT-based Expected Shortfall).	EVT threshold exceeded → CONDEL = USD 120M	“Once extreme losses occur, the average severity is catastrophic.”	Quantifies severity of extreme tail events; crucial for economic capital, reverse stress testing, recovery planning	Only applies to extreme events; ignores normal-range losses

WITHOUT Group

This group presents the measures that assess the impact on portfolio risk when a position or sub-portfolio is removed or added.

VARWO: Value-at-Risk Without a Position

VARWO measures how the portfolio’s VaR changes if a specific stock is removed. For instance, imagine your five-equity portfolio has a total 1-day VaR of USD 10,000. If you remove Stock E (the one with the most volatile returns), VARWO might drop to USD 7,500. This tells you that Stock E contributes significantly to potential losses in extreme scenarios. VARWO helps investors see which positions are driving risk and guides decisions on rebalancing or risk reduction.

INCVAR: Incremental Value-at-Risk

INCVAR quantifies the contribution of a single stock to the portfolio’s VaR. Using the same example, if the portfolio VaR is USD 10,000 and VARWO without Stock E is USD 7,500, then INCVAR = USD 2,500. This means Stock E alone increases potential portfolio loss by USD 2,500 under extreme conditions. Positive INCVAR indicates a position adds risk, while negative INCVAR would imply it reduces risk due to diversification.

ESWO: Expected Shortfall Without a Position

ESWO measures how the portfolio’s Expected Shortfall (average of worst losses) changes if a stock is removed. Suppose your portfolio ES is USD 15,000. Removing Stock E lowers ESWO to USD 11,000, showing that Stock E contributes heavily to tail risk. ESWO highlights positions that are particularly dangerous during market crises, beyond what VaR captures.

INCES: Incremental Expected Shortfall

INCES calculates how much a position adds to extreme tail losses. From the example above, INCES = USD 15,000 – USD 11,000 = USD 4,000 for Stock E. This shows that in a severe market downturn, Stock E could increase average extreme losses by USD 4,000. INCES is especially useful for identifying positions that may seem harmless under normal conditions but amplify losses in crises. 

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios. 

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation / Note
VARWO – Value-at-Risk Without the Position	Portfolio VaR if a specific position/sub-portfolio is removed	Portfolio VaR = USD 100M, VARWO (without Segment A) = USD 85M	“Removing Segment A reduces portfolio VaR to USD 85M, showing it contributes to overall risk.”	Identifies key risk drivers; supports risk limits, rebalancing	Standalone risk doesn’t capture diversification effects
INCVAR – Incremental VaR	Change in VaR attributable to adding/removing a position	INCVAR = Portfolio VaR − VARWO = USD 100M − USD 85M = USD 15M	“Segment A adds USD 15M to portfolio VaR.” Positive → increases risk, Negative → reduces risk via diversification	Capital allocation, trade justification, risk-adjusted performance	Only captures a single quantile; doesn’t reflect tail beyond VaR
ESWO – Expected Shortfall Without the Position	Portfolio Expected Shortfall if a position is removed	Portfolio ES = USD 140M, ESWO (without Segment B) = USD 110M	“Removing Segment B reduces extreme losses from USD 140M to USD 110M.”	Identifies positions contributing to tail risk; useful in stress testing	Sensitive to tail simulation; assumes reliable ES estimation
INCES – Incremental Expected Shortfall	Change in ES due to a position	INCES = Portfolio ES − ESWO = USD 140M − USD 110M = USD 30M	“Segment B contributes USD 30M to extreme tail losses.” High INCES → amplifies crisis losses; Low/negative → mitigates tail risk	Highlights positions dangerous in crises; guides capital allocation for tail events	Requires accurate tail modeling; more variable than INCVAR

CONTRIB Group

Contribution measures allocate total risk to positions or sub portfolios.

CONTVAR: Contribution to Value-at-Risk

CONTVAR measures how much each stock contributes to the total portfolio VaR. For example, if your five-equity portfolio has a 1-day VaR of USD 10,000, CONTVAR might show that Stock A contributes USD 2,000, Stock B USD 1,500, Stock C USD 1,000, Stock D USD 3,000, and Stock E USD 2,500. This allocation tells you exactly which stocks are driving potential losses in extreme scenarios. CONTVAR helps investors identify the dominant risk sources and manage exposure at a position level, ensuring that risk is properly attributed across the portfolio.

CONTES: Contribution to Expected Shortfall

CONTES measures how much each stock contributes to the portfolio’s Expected Shortfall (ES), which captures the average of extreme losses. Using the same portfolio, if the portfolio ES is USD 15,000, CONTES may show Stock A = USD 3,000, Stock B = USD 2,000, Stock C = USD 1,500, Stock D = USD 5,000, and Stock E = USD 3,500. This reveals which stocks are responsible for extreme tail losses during crisis conditions. Unlike VaR, ES considers the severity of losses beyond the VaR threshold, so CONTES is particularly useful for understanding who is taking on risk in the worst-case scenarios.

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Limitation/Note
CONTVAR – Contribution to Value-at-Risk	How much a position/sub-portfolio contributes to total portfolio VaR	Total portfolio VaR = USD 100M, CONTVAR of Segment A = USD 18M	“Segment A accounts for USD 18M of total portfolio VaR.” Sum of all CONTVARs = total VaR	Capital allocation, desk-level risk limits, identifying dominant risk drivers	Shows today’s risk contribution; doesn’t require removing the position
CONTES – Contribution to Expected Shortfall	How much a position contributes to portfolio tail risk (ES)	Portfolio ES = USD 150M, CONTES of Segment B = USD 45M	“Segment B contributes 30% of extreme loss risk.”	Highlights positions that may appear quiet normally but dominate losses in stress events	Essential for stress testing, leverage-driven instruments, and correlated exposures

EXPOSURE Group

This group provides measures that describe current and future exposure profiles, where exposure represents the potential for present or future losses arising from specific events or business activities, helping organizations identify vulnerabilities and prioritize risk mitigation. Note that the notion of the exposure depends on the nature of business/investments/assets. In credit risk, exposure refers to the amount a lender may lose if a borrower defaults, typically measured as the outstanding loan balance and expected drawdowns, and is primarily downside-focused. In contrast, for equity investments, exposure represents the capital at risk due to market price movements, measured by the current or projected market value of the position, and reflects continuously changing, two-sided market risk.

CURREXP: Current Exposure

CURREXP measures the present exposure of the portfolio or a position at a given point in time. For example, if you hold five equities and today their combined mark-to-market exposure is USD 12,000, the CURREXP indicates that, at this moment, you are “at risk” of losing USD 12,000 if all positions were to be liquidated immediately. It’s a snapshot of current potential loss and helps investors monitor day-to-day risk.

PEAKEXP: Peak Exposure

PEAKEXP captures the maximum exposure across all future time points and scenarios. Suppose over the next month, your five-equity portfolio could reach a worst-case exposure of USD 20,000 due to potential price swings. PEAKEXP shows this peak level, highlighting the maximum risk the portfolio could face before any mitigation or hedging. It’s particularly useful for setting conservative limits and stress testing.

EXPEXP: Expected Exposure

EXPEXP calculates the average expected exposure at a future time point across all scenarios. For instance, one month from now, the expected exposure of the portfolio might be USD 15,000. This gives a forward-looking view of typical exposure, not just extreme cases, allowing risk managers to plan for likely losses under normal market conditions.

EEE: Expected Exposure at Default

EEE measures the exposure you would face if a counterparty defaults at different points in time. In our equity example, if one of the positions depends on financing from a broker and default occurs, the EEE could be USD 18,000. This aligns risk with the likelihood of default and ensures realistic credit or counterparty loss estimates.

EPE: Expected Positive Exposure

EPE is the time-weighted average of expected exposure over the life of the positions. For the five equities, across the next month, the average exposure might be USD 16,000. This helps regulatory calculations and provides a smooth measure of portfolio risk over time rather than at a single point.

EEPE: Effective Expected Positive Exposure

EEPE is a conservative adjustment of EPE to prevent underestimation of exposure due to declining risk profiles. In the same example, while EPE is USD 16,000, EEPE might be USD 18,500 after applying regulatory constraints, ensuring you account for potential spikes in risk. EEPE is essential for Basel III compliance and prudent risk management.

The following table helps you understand these metrics and how they relate to risk analysis. The table assumes data from a retail loan portfolio across several simulated scenarios.

Statistic	What it Tells You	Example (Retail Loan Portfolio)	Intuitive Interpretation	Why Risk Teams Care	Key Note
CURREXP – Current Exposure	Current mark-to-market exposure assuming default today	Current MTM = USD 12M	“If the counterparty defaults today, I’m exposed to USD 12M.”	Day-to-day counterparty monitoring, limit breaches, collateral calls	Captures today’s exposure; no future scenarios considered
PEAKEXP – Peak Exposure	Maximum exposure across future scenarios	PEAKEXP = USD 45M	“At its worst, exposure could reach USD 45M.”	Highlights extreme counterparty risk, conservative credit limits	May be driven by extreme/rare scenarios; interpret cautiously
EXPEXP – Expected Exposure	Average exposure at a future time point	Year 2 EE = USD 18M	“On average, exposure in two years = USD 18M.”	Core input to CVA, reflects typical exposure	Focuses on mean, not extremes
EEE – Expected Exposure at Default	Exposure assuming counterparty defaults at a future time	EEE = USD 25M	“Expected exposure if default occurs = USD 25M.”	Aligns exposure with default likelihood, realistic credit loss estimation	Conditional on default timing
EPE – Expected Positive Exposure	Time-weighted average of expected exposure over the life of a transaction	EPE = USD 20M	“Across 5 years, average positive exposure = USD 20M.”	Regulatory CCR standard, Basel capital calculations	Captures exposure evolution over time
EEPE – Effective Expected Positive Exposure	Conservative version of EPE adjusted for declining profiles	EPE = USD 20M → EEPE = USD 26M	“Regulatory-adjusted effective exposure = USD 26M.”	Required under Basel III / SA-CCR, ensures conservative profiles	Adjusted to avoid understating exposure

Conclusion

In conclusion, the SAS Risk Engine organizes its risk metrics into a comprehensive grouping that converts raw simulation results into actionable insight. An intuitive understanding of these metrics is essential for beginning your journey into risk analytics using SAS Risk Engine. Throughout this article, each metric group has been explained using simple, layman-friendly, and intuitive examples to demystify statistical metrics and make them accessible to a broader audience. Moment-based statistics describe the shape, variability, and uncertainty of risk, while quantiles and Value at Risk (VaR) establish clear loss thresholds. Extreme Value Theory (EVT) metrics capture tail behavior and stress conditions during crisis scenarios. WITHOUT and contribution (CONTRIB) measures link risk directly to portfolios, positions, and decision-making. Finally, exposure metrics provide a forward-looking view of current and evolving risk profiles. Collectively, these metric groups enable risk managers to move beyond isolated numbers toward informed, defensible decisions—particularly when markets deviate from normal behavior.

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