Convergence Point

Introduction: Quantifying the Unquantifiable

You’re managing a portfolio worth €500M. Your CEO asks: “How much could we lose tomorrow?”

This isn’t a philosophical question—it’s the foundation of risk management. Without quantifying price risk, you’re flying blind. But measuring risk in energy markets is devilishly complex:

• Electricity trades 8,760 different products (every hour of the year)
• Prices are correlated but not perfectly (hour 13 ≠ hour 14)
• Historical volatility doesn’t predict future crashes
• Markets have “fat tails” (extreme events happen more than normal distributions predict)

Enter three critical tools: Stress Value, Value at Risk (VaR), and Pain at Risk (PaR). Let’s explore how traders quantify the seemingly unquantifiable—and why these models sometimes catastrophically fail.

Building the HPFC: 8,760 Prices from ~20 Data Points

Before measuring risk, you need a Hourly Price Forward Curve (HPFC)—a complete forecast of every hour’s price for the next 1-3 years.

The Challenge:

• Forward markets trade ~20 liquid products (month, quarter, year contracts)
• You need 8,760 hourly prices (or 35,040 for 15-minute intervals)
• How do you disaggregate aggregate contracts into hourly forecasts?

Step 1: Anchor with Liquid Products

Available Forward Prices (Example):

• Year 2026 Base: €85/MWh
• Year 2026 Peak: €105/MWh
• Q1-2026 Base: €95/MWh
• Q2-2026 Base: €78/MWh
• January 2026 Base: €100/MWh

These are volume-weighted average prices for their periods.

Step 2: Build Load Profile Shape

Use historical data to determine hourly shape:

Typical Patterns:

• Baseload hours (00:00-06:00): 70-80% of average
• Peak hours (08:00-20:00): 110-130% of average
• Super-peak (18:00-20:00): 140-160% of average
• Weekends: Lower peak, flatter curve

Example Historical Average (normalized to €100):

• Hour 01: €65
• Hour 02: €60
• Hour 03: €58
• …
• Hour 12: €115
• Hour 13: €120
• …
• Hour 19: €145

Step 3: Scale to Match Forward Prices

For January 2026:

• Forward Base contract: €100/MWh
• Historical shape suggests January average = €100
• Scale each hour:

Price(hour h) = Forward_Base × [Historical_Shape(h) / Historical_Average]

Example:

• Forward Base (Jan): €100/MWh
• Historical shape hour 19: €145
• Historical average: €100
• Price(hour 19) = €100 × (€145 / €100) = €145/MWh

Step 4: Integrate Peak Premiums

Peak contracts introduce constraints:

Peak Contract (08:00-20:00, Mon-Fri):

• Quoted at €105/MWh
• Our hourly model must average to €105 for peak hours
• Adjust peak hours proportionally

Iterative Process:

1. Build initial curve from baseload
2. Check: Do peak hours average to peak contract price?
3. If not, adjust peak hours up/down proportionally
4. Re-check base contract average (must still match)
5. Iterate until all constraints satisfied

Step 5: Add Seasonal and Weekly Patterns

Seasonal Adjustments:

• Winter: Higher morning/evening peaks (heating)
• Summer: Different peak (cooling, midday)

Weekly Patterns:

• Monday: Morning ramp-up (restart after weekend)
• Friday: Evening decline (weekend approaching)
• Weekend: Flatter, lower overall

Result: Complete HPFC

• 8,760 hourly prices for Year 2026
• Mathematically consistent with traded forward contracts
• Reflects realistic load/price patterns

Validation:

• Sum all 8,760 hours ÷ 8,760 = should equal Year Base forward
• Sum peak hours ÷ peak hour count = should equal Peak forward
• Visual inspection: Does curve “look right”?

Stress Value: Tomorrow’s Worst Case

Definition: The maximum potential loss if the worst plausible scenario occurs tomorrow.

Methodology:

Step 1: Identify Worst-Case Scenario

For a long position (you’ve bought energy):

• Worst case = prices fall (you lose on inventory)
• Scenario: Prices drop by historical maximum daily decline

Historical Analysis:

• Review last 10 years of daily price changes
• Identify worst single-day drop: -€15/MWh (example)
• This becomes your stress scenario

**For a short position (you’ve sold energy):

• Worst case = prices rise (you must buy back expensive)
• Scenario: Prices rise by historical maximum daily increase
• Historical max: +€25/MWh

Step 2: Apply Stress to Current Position

Example:

• Open position: Long 200 MW for Q1-2026
• Volume: 200 MW × 2,160 hours = 432,000 MWh
• Current Q1 price: €95/MWh
• Stress scenario: Price drops €15/MWh to €80/MWh

Stress Value Calculation:

Stress Value = Position × Price Change
            = 432,000 MWh × (-€15/MWh)
            = -€6,480,000

Interpretation: If tomorrow brings the worst daily price movement we’ve seen historically, we’ll lose €6.48M.

Management Response:

Traffic Light System:

Green: Stress Value < 10% of risk capital

• Current risk: Acceptable
• Action: Monitor, no changes needed

Yellow: Stress Value 10-25% of risk capital

• Current risk: Elevated
• Action: Consider partial hedge, increase monitoring frequency

Red: Stress Value > 25% of risk capital

• Current risk: Unacceptable
• Action: Mandatory risk reduction (sell half position, buy hedge, etc.)

Example:

• Risk capital: €30M
• Stress value: €6.48M
• Percentage: 6.48 / 30 = 21.6% → Yellow
• Action: Portfolio manager must justify position or reduce to below 10% threshold

Value at Risk (VaR): Statistical Probability

Definition: The maximum loss not expected to be exceeded at a given confidence level over a specified period.

Standard: 95% Daily VaR

• Translation: “We’re 95% confident we won’t lose more than €X tomorrow.”
• Inverse: “5% chance we’ll lose more than €X tomorrow.”

VaR Calculation: Historical Simulation Method

Step-by-Step Process:

Step 1: Collect Historical Price Data

• Last 500 trading days of forward contract prices
• Daily closing prices for relevant products

Example Dataset (Q1-2026 Forward):

Day 1: €92/MWh
Day 2: €93/MWh
Day 3: €91/MWh
...
Day 500: €95/MWh

Step 2: Calculate Daily Returns

Return(t) = [Price(t) - Price(t-1)] / Price(t-1)
Day 2: (€93 - €92) / €92 = +1.09%
Day 3: (€91 - €93) / €93 = -2.15%
...

Result: 499 daily returns (500 days – 1)

Step 3: Sort Returns from Worst to Best

Return 1: -8.2% (worst day)
Return 2: -6.5%
Return 3: -5.9%
...
Return 25: -2.1% ← 5th percentile (95% confidence)
...
Return 499: +7.3% (best day)

Step 4: Identify 95% Confidence Threshold

• Sort 499 returns
• 5th percentile = position 25 (0.05 × 499 ≈ 25)
• Return at position 25: -2.1%

This means: 95% of days had returns better than -2.1%

Step 5: Apply to Current Position

Current Position:

• Long 200 MW Q1-2026
• Volume: 432,000 MWh
• Current price: €95/MWh
• Position value: €41,040,000

VaR Calculation:

VaR (€) = Position Value × VaR (%)
        = €41,040,000 × 2.1%
        = €862,000

Interpretation:

• 95% confidence we won’t lose more than €862k tomorrow
• 5% chance we’ll lose more than €862k tomorrow
• Expected maximum loss on a “normal bad day”

VaR vs. Stress Value:

Same Position (Long 200 MW Q1-2026):

• Stress Value: €6,480,000 (worst historical day: -15€/MWh)
• 95% VaR: €862,000 (95% confidence threshold: -2.1%)

Different Questions:

• Stress: “What if the worst repeats?”
• VaR: “What’s the likely maximum on a normal bad day?”

Why Both Matter:

• VaR: Day-to-day risk management (most days)
• Stress: Extreme scenario planning (rare but devastating)

VaR Limitations: Black Swans and Fat Tails

VaR is powerful but deeply flawed. Let’s examine why:

Limitation 1: VaR Says Nothing About the Tail

VaR tells you the 95th percentile, not what happens beyond it.

Example:

• 95% VaR: €1M
• This means 5% of days exceed €1M loss
• But how bad are those 5% days?
  • Could average €1.2M (tolerable)
  • Could average €10M (catastrophic)

VaR doesn’t distinguish!

Real Example:

• Bank has 99% VaR of €10M (seems safe)
• But in the 1% tail:
  • 0.5% of days: €15M loss
  • 0.4% of days: €25M loss
  • 0.1% of days: €100M+ loss (wipeout)

Average tail loss: €35M (3.5x the VaR!)

Solution: Use Conditional VaR (CVaR) or Expected Shortfall

• CVaR = Average loss in the worst 5% of cases
• More informative than VaR alone

Limitation 2: Fat Tails (Extreme Events Are More Common Than Normal Distribution Predicts)

Normal Distribution Assumption:

• VaR often assumes returns follow a normal (Gaussian) bell curve
• Extreme events (>3 standard deviations) should be very rare

Energy Market Reality:

• Extreme events happen far more often than normal distribution predicts
• “Once in 100 year” events occur every few years

Example: 2022 European Gas Crisis

• Historical average gas price: €25/MWh
• Historical volatility (std dev): €8/MWh
• August 2022 price: €340/MWh

Under Normal Distribution:

• This is (€340 – €25) / €8 = 39 standard deviations
• Probability: 10^-330 (essentially impossible in universe’s lifetime)

Actual: It happened.

Fat Tails Mean:

• Standard VaR models underestimate extreme risk
• Models calibrated on “normal times” fail during crises

Risk Manager Dilemma:

• Use conservative models → Trade less, earn less, lose to competitors
• Use optimistic models → Trade more, earn more, but catastrophic when crisis hits

Limitation 3: VaR Is Backward-Looking

Historical VaR assumes the future resembles the past.

Breaks Down When:

• Structural market changes: Coal phase-outs altered price dynamics
• New regulations: Carbon pricing changed merit order
• Geopolitical shocks: Russian gas cut-off unprecedented
• Technology shifts: Solar/wind penetration changes volatility patterns

2010 VaR Model:

• Based on 2000-2010 data (stable markets)
• VaR: €500k
• Seemed accurate for years

2022 Reality:

• Same portfolio, 2022 crisis
• Actual loss: €15M (30x VaR)
• Model useless

What Changed:

• Pre-2022: Abundant Russian gas supply (baseline assumption)
• 2022: Supply shock no historical precedent for

Lesson: VaR works until it doesn’t. Always stress-test against scenarios not in historical data.

Limitation 4: Correlation Breakdowns

VaR often assumes stable correlations between assets.

Normal Times:

• German power ≈ French power (correlation: 0.85)
• VaR model: “Diversify across countries for lower risk”

Crisis Times (French Nuclear Outages):

• German power: €100/MWh
• French power: €250/MWh
• Correlation breaks down

Portfolio Impact:

• Expected (VaR model): Diversification reduces risk
• Actual: French positions lost €50M, German hedges only offset €10M
• Net loss: €40M (vs. VaR of €8M)

Lesson: Correlations converge to 1.0 during crises (everything moves together).

PaR: When Liquidity Disappears

Pain at Risk (PaR): The additional loss incurred from having to liquidate positions in illiquid markets.

The Concept:

Normal VaR assumes:

• You can trade at market prices
• Liquidity is always available

Reality:

• During crises, bid-ask spreads widen
• Large positions can’t be unwound without moving the market

Example:

Position:

• Long 500 MW Year-2026
• Mark-to-market value: €50M
• Normal bid-ask spread: €0.20/MWh

Crisis Scenario:

• News: Major nuclear plant offline for 2 years
• Market panics, you need to exit position
• Normal spread: €0.20/MWh
• Crisis spread: €8/MWh (40x wider!)

Liquidation Cost:

PaR = Position × (Crisis Spread - Normal Spread)
    = 500 MW × 8,760h × (€8 - €0.20)
    = 4,380,000 MWh × €7.80
    = €34,164,000

Total Loss:

• VaR: €2M (price movement)
• PaR: €34M (liquidation cost)
• Total: €36M

VaR completely missed the dominant risk!

When PaR Matters Most:

1. Large Positions Relative to Market Depth

• You hold 500 MW, daily market volume is 2,000 MW
• Unwinding would absorb 25% of daily volume
• You’ll move prices against yourself

2. Exotic Products

• Custom delivery terms
• Illiquid tenors (specific weeks)
• Few market participants

3. Crisis Periods

• Everyone wants to exit simultaneously
• Liquidity providers withdraw
• “Flight to safety” (only liquid products trade)

4. Forced Liquidation

• Margin calls demand immediate action
• Can’t wait for favorable liquidity
• Must take any price offered

Mitigation:

1. Position Sizing:

• Limit position to X% of average daily market volume
• Rule of thumb: < 5% of volume (can unwind in one day without major impact)

2. Liquidity Reserves:

• Maintain cash to avoid forced liquidation
• Can wait for better liquidity conditions

3. Gradual Unwinding:

• Don’t exit 500 MW in one trade
• Spread over days/weeks: 50 MW per day

4. Prefer Liquid Products:

• Standard base/peak contracts
• Avoid exotic structured products unless premium justifies illiquidity risk

The Traffic Light System: Operational Risk Limits

Risk metrics must drive actions, not just reports.

Daily Risk Dashboard (7:15 AM Report to Traders):

Position Summary:

• Open Position: Long 350 MW Q1-2026
• Current value: €33M

Risk Metrics:

Actions:

• 🟢 Green (< 70%): Monitor, no action required
• 🟡 Yellow (70-90%): Caution, consider reducing exposure
• 🔴 Red (> 90%): Mandatory action, must reduce within 24 hours

Example Decision:

• Stress Value at 75% (Yellow)
• Portfolio manager decision: Sell 100 MW to reduce stress to ~60% (Green)
• Execute: Sell 100 MW Q1-2026 at current market €95/MWh
• New position: Long 250 MW (reduced from 350 MW)
• New stress: €3.2M (down from €4.5M, now 53% of limit → Green)

Escalation Process:

Red Status Triggered:

• Automatic alert to risk committee
• Portfolio manager must submit risk reduction plan within 2 hours
• Execution deadline: 24 hours
• If not complied: Override trades executed by risk management

Example:

• VaR hits €1.1M (110% of limit → Red)
• Email sent: “VaR limit breached, immediate action required”
• Trader submits plan: “Will sell 150 MW by end of day”
• Execution: Sells in 3 tranches (50 MW each) throughout day
• End of day: VaR reduced to €850k (85% of limit → Yellow, acceptable)

Why Models Fail: The 2008 and 2022 Lessons

2008 Financial Crisis:

• VaR models assumed housing prices wouldn’t fall nationally
• Correlations underestimated (all banks exposed simultaneously)
• Tail risk ignored (rare events were actual events)
• Result: “25-sigma events” occurred (mathematically impossible, yet happened)

2022 Energy Crisis:

• VaR models based on pre-war supply assumptions
• Russian gas cut-off: No historical precedent
• Price spikes exceeded worst historical scenarios by 5-10x
• Result: VaR said “€2M max loss,” actual was “€50M+”

The Fundamental Problem:

Models assume:

• Markets are continuous (no gaps)
• Liquidity always exists
• Correlations are stable
• The future resembles the past

Reality:

• Markets gap overnight (Russian invasion)
• Liquidity vanishes in crises
• Correlations go to 1.0 (everything falls together)
• The future brings new regimes

What Professional Risk Managers Do:

1. Use Multiple Models:

• VaR (for normal times)
• Stress tests (for historical worst cases)
• Scenario analysis (for unprecedented events)

2. Add Judgment:

• Models inform decisions, don’t make them
• Human override when models seem wrong

3. Reverse Stress Testing:

• Question: “What scenario would bankrupt us?”
• Design hedges specifically for that scenario
• Even if low probability

4. Conservative Buffers:

• Use 99% VaR instead of 95% (stricter)
• Add 50% margin to stress values
• Assume worst liquidity conditions

5. Regular Back-Testing:

• Did yesterday’s actual loss exceed VaR?
• If yes, how often? (Should be ~5% of days for 95% VaR)
• If more often, model is wrong → recalibrate

Key Takeaways

✓ HPFC construction: Disaggregate ~20 liquid products into 8,760 hourly prices
✓ Stress Value: Worst historical daily loss applied to current position
✓ VaR (95%): Maximum expected loss on a “normal bad day” (95% confidence)
✓ VaR limitations: Says nothing about tail, assumes normal distributions (false), backward-looking
✓ Fat tails: Extreme events far more common than models predict (“25-sigma” events happen)
✓ PaR: Liquidity costs during forced liquidation (often larger than VaR)
✓ Traffic light system: Green/Yellow/Red status drives mandatory risk actions
✓ Models fail in crises: 2008 and 2022 proved VaR dangerously underestimates tail risk

Next in Series: Post 11: Risk Management Processes: From Theory to Corporate Governance