Risk Analytics and Stress Testing

BusinessMath Quarterly Series

11 min read

Part 8 of 12-Week BusinessMath Series

What You’ll Learn

The Problem

Risk management requires quantifying uncertainty. What’s the worst loss we might face? How would a recession affect our portfolio? Are we properly diversified?

Traditional risk analysis involves complex calculations:

Implementing these correctly requires statistical knowledge, careful handling of distributions, and proper correlation modeling. You need production-ready risk analytics without reinventing the math.

The Solution

BusinessMath provides comprehensive risk analytics including stress testing, VaR calculation, and multi-portfolio risk aggregation.

Stress Testing

Evaluate how portfolios perform under adverse scenarios:

import BusinessMath

// Pre-defined stress scenarios
var allScenarios = [
    StressScenario
            
              .recession, // Moderate economic downturn StressScenario
              
                .crisis, // Severe financial crisis StressScenario
                
                  .supplyShock // Supply chain disruption ] // Examine scenario parameters for scenario in scenarios { print("\(scenario.name):") print(" Description: \(scenario.description)") print(" Shocks:") for (driver, shock) in scenario.shocks { let pct = shock * 100 print(" \(driver): \(pct > 0 ? "+" : "")\(pct)%") } }

Output:

Recession:
  Description: Economic recession scenario
  Shocks:
    Revenue: -15.0%
    COGS: +5.0%
    InterestRate: +2.0%

Financial Crisis:
  Description: Severe financial crisis (2008-style)
  Shocks:
    Revenue: -30.0%
    InterestRate: +5.0%
    CustomerChurn: +20.0%
    COGS: +10.0%

Supply Chain Shock:
  Description: Major supply chain disruption
  Shocks:
    InventoryLevel: -30.0%
    DeliveryTime: +50.0%
    COGS: +25.0%

Custom Stress Scenarios

Create scenarios specific to your business:

// Pandemic scenario
let pandemic = StressScenario(
    name: "Global Pandemic",
    description: "Extended lockdowns and remote work transition",
    shocks: [
        "Revenue": -0.35,           // -35% revenue
        "RemoteWorkCosts": 0.20,    // +20% IT/remote costs
        "TravelExpenses": -0.80,    // -80% travel
        "RealEstateCosts": -0.15    // -15% office costs
    ]
)

allScenarios.append(pandemic)

// Regulatory change scenario
let regulation = StressScenario(
    name: "New Regulation",
    description: "Stricter compliance requirements",
    shocks: [
        "ComplianceCosts": 0.50,    // +50% compliance
        "Revenue": -0.05,            // -5% from restrictions
        "OperatingMargin": -0.03     // -3% margin compression
    ]
)
allScenarios.append(regulation)

Running Stress Tests

Apply scenarios to your financial model:

let stressTest = StressTest(scenarios: allScenarios)

struct FinancialMetrics {
    var revenue: Double
    var costs: Double
    var npv: Double
}

let baseline = FinancialMetrics(
    revenue: 10_000_000,
    costs: 7_000_000,
    npv: 5_000_000
)

for scenario in stressTest.scenarios {
    // Apply shocks
    var stressed = baseline

    if let revenueShock = scenario.shocks["Revenue"] {
        stressed.revenue *= (1 + revenueShock)
    }

    if let cogsShock = scenario.shocks["COGS"] {
        stressed.costs *= (1 + cogsShock)
    }

    let stressedNPV = stressed.revenue - stressed.costs
    let impact = stressedNPV - baseline.npv
    let impactPct = (impact / baseline.npv)

    print("\n\(scenario.name):")
    print("  Baseline NPV: \(baseline.npv.currency())")
    print("  Stressed NPV: \(stressedNPV.currency())")
    print("  Impact: \(impact.currency()) (\(impactPct.percent()))")
}

Value at Risk (VaR)

VaR measures the maximum loss expected over a time horizon at a given confidence level.

S&P Returns Data

Calculating VaR from Returns

// Portfolio returns (historical daily returns)
let spReturns: [Double] = [0.0088, 0.0079, -0.0116…] //(See file for data)

let periods = (0...(spReturns.count - 1)).map {
    Period.day(Date().addingTimeInterval(Double($0) * 86400))
}
let timeSeries = TimeSeries(periods: periods, values: spReturns)

let riskMetrics = ComprehensiveRiskMetrics(
    returns: timeSeries,
    riskFreeRate: 0.02 / 250  // 2% annual = 0.008% daily
)

print("Value at Risk:")
print("  95% VaR: \(riskMetrics.var95.percent())")
print("  99% VaR: \(riskMetrics.var99.percent())")

// Interpret: "95% confidence we won't lose more than X% in a day"
let portfolioValue = 1_000_000.0
let var95Loss = abs(riskMetrics.var95) * portfolioValue

print("\nFor \(portfolioValue.currency(0)) portfolio:")
print("  95% 1-day VaR: \(var95Loss.currency())")
print("  Meaning: 95% confident daily loss won't exceed \(var95Loss.currency())")

Conditional VaR (CVaR / Expected Shortfall)

CVaR measures the average loss in the worst cases (beyond VaR):

print("\nConditional VaR (Expected Shortfall):")
print("  CVaR (95%): \(riskMetrics.cvar95.percent())")
print("  Tail Risk Ratio: \(riskMetrics.tailRisk.number())")

// CVaR is the expected loss if we're in the worst 5%
let cvarLoss = abs(riskMetrics.cvar95) * portfolioValue
print("  If in worst 5% of days, expect to lose: \(cvarLoss.currency())")

CVaR is better than VaR because it captures tail risk—the average loss when things go really bad, not just the threshold.

Comprehensive Risk Metrics

Get a complete risk profile:

print("\nComprehensive Risk Profile:")
print(riskMetrics.description)

Output:

Comprehensive Risk Profile:
Comprehensive Risk Metrics:
  VaR (95%): -1.66%
  VaR (99%): -4.84%
  CVaR (95%): -2.76%
  Max Drawdown: 18.91%
  Sharpe Ratio: 0.05
  Sortino Ratio: 0.05
  Tail Risk: 1.66
  Skewness: 1.05
  Kurtosis: 18.53

Maximum Drawdown

Maximum drawdown measures the largest peak-to-trough decline:

let drawdown = riskMetrics.maxDrawdown

print("\nDrawdown Analysis:")
print("  Maximum drawdown: \(drawdown.percent())")

if drawdown < 0.10 {
    print("  Risk level: Low")
} else if drawdown < 0.20 {
    print("  Risk level: Moderate")
} else {
    print("  Risk level: High")
}

Sharpe and Sortino Ratios

Risk-adjusted return measures:

print("\nRisk-Adjusted Returns:")
print("  Sharpe Ratio: \(riskMetrics.sharpeRatio.number(3))")
print("    (return per unit of total volatility)")

print("  Sortino Ratio: \(riskMetrics.sortinoRatio.number(3))")
print("    (return per unit of downside volatility)")

// Sortino > Sharpe indicates asymmetric returns (positive skew)
if riskMetrics.sortinoRatio > riskMetrics.sharpeRatio {
    print("  Portfolio has limited downside with upside potential")
}

Sharpe Ratio penalizes all volatility (up and down). Sortino Ratio only penalizes downside volatility—better for assessing asymmetric strategies.

Tail Statistics

Skewness and kurtosis describe return distribution shape:

print("\nTail Statistics:")
print("  Skewness: \(riskMetrics.skewness)")

if riskMetrics.skewness < -0.5 {
    print("    Negative skew: More frequent small gains, rare large losses")
    print("    Risk: Fat left tail")
} else if riskMetrics.skewness > 0.5 {
    print("    Positive skew: More frequent small losses, rare large gains")
    print("    Risk: Fat right tail")
} else {
    print("    Roughly symmetric distribution")
}

print("  Excess Kurtosis: \(riskMetrics.kurtosis)")

if riskMetrics.kurtosis > 1.0 {
    print("    Fat tails: More extreme events than normal distribution")
    print("    Risk: Higher probability of large moves")
}

Aggregating Risk Across Portfolios

Combine VaR across multiple portfolios accounting for correlations:

// Three portfolios with individual VaRs
let portfolioVaRs = [100_000.0, 150_000.0, 200_000.0]

// Correlation matrix
let correlations = [
    [1.0, 0.6, 0.4],
    [0.6, 1.0, 0.5],
    [0.4, 0.5, 1.0]
]

// Aggregate VaR using variance-covariance method
let aggregatedVaR = RiskAggregator
            
              .aggregateVaR( individualVaRs: portfolioVaRs, correlations: correlations ) let simpleSum = portfolioVaRs.reduce(0, +) let diversificationBenefit = simpleSum - aggregatedVaR print("VaR Aggregation:") print(" Portfolio A VaR: \(portfolioVaRs[0].currency())") print(" Portfolio B VaR: \(portfolioVaRs[1].currency())") print(" Portfolio C VaR: \(portfolioVaRs[2].currency())") print(" Simple sum: \(simpleSum.currency())") print(" Aggregated VaR: \(aggregatedVaR.currency())") print(" Diversification benefit: \(diversificationBenefit.currency())")

Diversification benefit shows how much risk is reduced by not being perfectly correlated.

Marginal VaR

Understand how much each portfolio contributes to total risk:

for i in 0..
            
              .marginalVaR( entity: i, individualVaRs: portfolioVaRs, correlations: correlations ) print("\nPortfolio \(["A", "B", "C"][i]):") print(" Individual VaR: \(portfolioVaRs[i].currency())") print(" Marginal VaR: \(marginal.currency())") print(" Risk contribution: \((marginal / aggregatedVaR).percent())") }

Marginal VaR tells you: “If I added $1 more to this portfolio, how much would total VaR increase?”

Try It Yourself

S&P Returns Data (add to the /Sources file of your playground)

Click to expand full playground code 
import BusinessMath

// Pre-defined stress scenarios
var allScenarios = [
    StressScenario
              
                .recession, // Moderate economic downturn StressScenario
                
                  .crisis, // Severe financial crisis StressScenario
                  
                    .supplyShock // Supply chain disruption ] // Examine scenario parameters for scenario in allScenarios { print("\(scenario.name):") print(" Description: \(scenario.description)") print(" Shocks:") for (driver, shock) in scenario.shocks { let pct = shock * 100 print(" \(driver): \(pct > 0 ? "+" : "")\(pct)%") } } // Pandemic scenario let pandemic = StressScenario( name: "Global Pandemic", description: "Extended lockdowns and remote work transition", shocks: [ "Revenue": -0.35, // -35% revenue "RemoteWorkCosts": 0.20, // +20% IT/remote costs "TravelExpenses": -0.80, // -80% travel "RealEstateCosts": -0.15 // -15% office costs ] ) allScenarios.append(pandemic) // Regulatory change scenario let regulation = StressScenario( name: "New Regulation", description: "Stricter compliance requirements", shocks: [ "ComplianceCosts": 0.50, // +50% compliance "Revenue": -0.05, // -5% from restrictions "OperatingMargin": -0.03 // -3% margin compression ] ) allScenarios.append(regulation) let stressTest = StressTest(scenarios: allScenarios) struct FinancialMetrics { var revenue: Double var costs: Double var npv: Double } let baseline = FinancialMetrics( revenue: 10_000_000, costs: 7_000_000, npv: 5_000_000 ) for scenario in stressTest.scenarios { // Apply shocks var stressed = baseline if let revenueShock = scenario.shocks["Revenue"] { stressed.revenue *= (1 + revenueShock) } if let cogsShock = scenario.shocks["COGS"] { stressed.costs *= (1 + cogsShock) } let stressedNPV = stressed.revenue - stressed.costs let impact = stressedNPV - baseline.npv let impactPct = (impact / baseline.npv) print("\n\(scenario.name):") print(" Baseline NPV: \(baseline.npv.currency())") print(" Stressed NPV: \(stressedNPV.currency())") print(" Impact: \(impact.currency()) (\(impactPct.percent()))") } // Portfolio returns (historical daily returns) come from Sources: spReturns: [Double] let periods: [Period] = (0..
                    
                       = TimeSeries(periods: periods, values: spReturns) let riskMetrics = ComprehensiveRiskMetrics( returns: timeSeries, riskFreeRate: 0.02 / 250 // 2% annual = 0.008% daily ) print("Value at Risk:") print(" 95% VaR: \(riskMetrics.var95.percent())") print(" 99% VaR: \(riskMetrics.var99.percent())") // Interpret: "95% confidence we won't lose more than X% in a day" let portfolioValue = 1_000_000.0 let var95Loss = abs(riskMetrics.var95) * portfolioValue print("\nFor \(portfolioValue.currency(0)) portfolio:") print(" 95% 1-day VaR: \(var95Loss.currency())") print(" Meaning: 95% confident daily loss won't exceed \(var95Loss.currency())") print("\nConditional VaR (Expected Shortfall):") print(" CVaR (95%): \(riskMetrics.cvar95.percent())") print(" Tail Risk Ratio: \(riskMetrics.tailRisk.number())") // CVaR is the expected loss if we're in the worst 5% let cvarLoss = abs(riskMetrics.cvar95) * portfolioValue print(" If in worst 5% of days, expect to lose: \(cvarLoss.currency())") print("\nComprehensive Risk Profile:") print(riskMetrics.description) let drawdown = riskMetrics.maxDrawdown print("\nDrawdown Analysis:") print(" Maximum drawdown: \(drawdown.percent())") if drawdown < 0.10 { print(" Risk level: Low") } else if drawdown < 0.20 { print(" Risk level: Moderate") } else { print(" Risk level: High") } print("\nRisk-Adjusted Returns:") print(" Sharpe Ratio: \(riskMetrics.sharpeRatio.number(3))") print(" (return per unit of total volatility)") print(" Sortino Ratio: \(riskMetrics.sortinoRatio.number(3))") print(" (return per unit of downside volatility)") // Sortino > Sharpe indicates asymmetric returns (positive skew) if riskMetrics.sortinoRatio > riskMetrics.sharpeRatio { print(" Portfolio has limited downside with upside potential") } print("\nTail Statistics:") print(" Skewness: \(riskMetrics.skewness.number(2))") if riskMetrics.skewness < -0.5 { print(" Negative skew: More frequent small gains, rare large losses") print(" Risk: Fat left tail") } else if riskMetrics.skewness > 0.5 { print(" Positive skew: More frequent small losses, rare large gains") print(" Risk: Fat right tail") } else { print(" Roughly symmetric distribution") } print(" Excess Kurtosis: \(riskMetrics.kurtosis.number(2))") if riskMetrics.kurtosis > 1.0 { print(" Fat tails: More extreme events than normal distribution") print(" Risk: Higher probability of large moves") } // Three portfolios with individual VaRs let portfolioVaRs = [100_000.0, 150_000.0, 200_000.0] // Correlation matrix let correlations = [ [1.0, 0.6, 0.4], [0.6, 1.0, 0.5], [0.4, 0.5, 1.0] ] // Aggregate VaR using variance-covariance method let aggregatedVaR = RiskAggregator
                      
                        .aggregateVaR( individualVaRs: portfolioVaRs, correlations: correlations ) let simpleSum = portfolioVaRs.reduce(0, +) let diversificationBenefit = simpleSum - aggregatedVaR print("VaR Aggregation:") print(" Portfolio A VaR: \(portfolioVaRs[0].currency())") print(" Portfolio B VaR: \(portfolioVaRs[1].currency())") print(" Portfolio C VaR: \(portfolioVaRs[2].currency())") print(" Simple sum: \(simpleSum.currency())") print(" Aggregated VaR: \(aggregatedVaR.currency())") print(" Diversification benefit: \(diversificationBenefit.currency())") for i in 0..
                        
                          .marginalVaR( entity: i, individualVaRs: portfolioVaRs, correlations: correlations ) print("\nPortfolio \(["A", "B", "C"][i]):") print(" Individual VaR: \(portfolioVaRs[i].currency())") print(" Marginal VaR: \(marginal.currency())") print(" Risk contribution: \((marginal / aggregatedVaR).percent())") }

→ Full API Reference: BusinessMath Docs – 2.3 Risk Analytics

Modifications to try:

  1. Create custom stress scenarios for your industry
  2. Calculate VaR and CVaR for different confidence levels
  3. Compare Sharpe vs Sortino ratios for asymmetric strategies

Real-World Application

Risk managers use these tools daily:

BusinessMath makes these institutional-grade analytics accessible in 10-20 lines of Swift code.

★ Insight ─────────────────────────────────────

Why Both VaR and CVaR?

VaR answers: “What’s the threshold of the worst 5% of outcomes?” CVaR answers: “When you’re in that worst 5%, how bad does it actually get?”

Example: Portfolio with VaR₉₅ = -$100k, CVaR₉₅ = -$500k

CVaR captures tail risk—the thing that kills portfolios. VaR alone can be misleading for fat-tailed distributions.

This distinction matters for crypto, options, and leveraged strategies where tails are fat.

─────────────────────────────────────────────────

📝 Development Note

The hardest part of implementing VaR wasn’t the math—it was choosing which variant to implement. There are three common methods:

  1. Historical VaR: Use actual historical percentile
  2. Parametric VaR: Assume normal distribution
  3. Monte Carlo VaR: Simulate future scenarios

We chose Historical VaR as the default because:

But we documented this choice explicitly in both code and DocC, so users know what they’re getting.

The lesson: When multiple valid implementations exist, pick one, document it clearly, and make the choice transparent.

Related Methodology: When Tests Pass But Code Is Wrong (Week 9) - Validating statistical implementations

Next Steps

Coming up this week: Week 3 explores operational models—growth, depreciation, and revenue modeling.

Case Study: Week 3 Friday combines depreciation + TVM for capital equipment purchase decisions.

Series Progress:

Tagged with: risk-and-simulation, portfolio