Historical VaR for Two Commodity Assets

1 What is Historical VaR for Two Assets?

Value at Risk (VaR) answers: “Over a given horizon, what is the maximum loss we might expect at a given confidence level?” For two commodity assets (e.g. Gas and Power), we use historical price data to estimate volatility and correlation, then combine them into a single portfolio VaR. Energy and commodity trading firms use VaR to set position limits, allocate capital, and report risk to regulators and management.

Two common approaches:

• Historical simulation:
  • Use past returns directly; sort them and take the percentile (e.g. 1st percentile for 99% VaR).
  • No assumption about the shape of the distribution—what happened in the past is replayed as possible outcomes.
  • Traders and risk teams use this when they want to capture fat tails and real market moves (e.g. spikes in power or gas) without assuming normality.
• Variance-covariance (parametric):
  • Assume returns are normally distributed; estimate daily volatilities and correlation from history, build a variance-covariance matrix, then compute portfolio VaR from the portfolio standard deviation and a Z-score.
  • Fast and easy to aggregate across books.
  • Energy companies often use it for daily limit monitoring and for portfolios where diversification (e.g. gas vs power) reduces risk.

In practice, commodity firms combine both: historical simulation for stress views and regulatory capital, and variance-covariance for quick daily VaR and limit checks. Correlation between commodities (e.g. gas and power) is estimated from data and drives how much diversification benefit the portfolio gets.

Distribution assumptions and energy markets

Variance-covariance VaR assumes returns are normally distributed. Energy and commodity price returns often behave differently: they exhibit heavy tails (more extreme moves than the normal distribution implies), skewness (asymmetric upside vs downside, e.g. power spikes vs gradual declines), and jumps (sudden large moves on supply shocks or demand spikes).

That means normal-based VaR can understate tail risk. Extreme events — such as the 2021 Texas freeze (power and gas price spikes) and the 2022 European gas crisis (supply disruption and record volatility) — fall far outside what a Gaussian model would predict.

For that reason, firms pair VaR with stress testing and scenario analysis (e.g. “what if gas triples?” or “pipeline outage”) to capture these tail events; see the section on alternative risk measures below.

Important Formulas

2 Calculation Steps

Historical price data feeds log returns; from these we derive daily volatilities and correlation. Those feed the variance-covariance matrix and portfolio VaR (individual and diversified).

3 VaR Calculator — Visual Summary

Edit the inputs below; calculated fields update automatically. Volatility and correlation are from price data (see sample table below).

4 VaR and confidence interval

Distribution of portfolio P&L (€). The shaded tail is the probability of loss exceeding VaR; the vertical line shows VaR at your chosen confidence level.

5 VaR in practice: purpose, flow & limits

The core purpose is straightforward: VaR gives traders and risk managers a single number that answers "what's the worst we could lose on a normal day?" It's the common language between the front office, risk desk, and board level.

How it flows through an energy trading firm

At the desk level, each trading desk — power, gas, oil, LNG, emissions — has a VaR limit set by the risk committee. A gas trader with a €5M VaR limit knows they can't build positions that push their 1-day 95% or 99% VaR above that threshold. When they're approaching the limit, they either reduce positions or need explicit approval to exceed it.

The calculator you just built mirrors exactly this: changing position sizes and seeing VaR react in real time is what risk systems like Allegro or Endur do on an intraday basis.

At the portfolio level, the firm aggregates desk-level VaR into an enterprise VaR. This is where correlation and diversification benefit become critical. A firm that's long gas and short power in a correlated market gets a lower portfolio VaR than the sum of individual VaRs.

Risk managers spend significant time debating whether historical correlations will hold — they often break down precisely when you need them most (2021 Texas freeze, 2022 European gas crisis).

Practical applications include:

• Setting and monitoring trading limits
• Calculating capital reserves and margin requirements
• Regulatory reporting under MiFID II and EMIR
• Credit exposure management with counterparties
• Board-level risk appetite communication

Where VaR falls short in energy is important to teach:

• Energy prices have fat tails and jumps (e.g. gas price spikes, negative power prices) that violate the normal distribution assumption.
• Firms supplement VaR with stress testing, CVaR/Expected Shortfall, and scenario analysis—see “Alternative risk measures” below.

Alternative risk measures

Beyond VaR, energy trading firms rely on complementary metrics and exercises:

• CVaR (Conditional VaR) / Expected Shortfall — the average loss given that the loss exceeds VaR. It captures the severity of the tail and is coherent (subadditive); regulators increasingly reference it for capital and risk limits.
• Stress testing — apply severe but plausible shocks (e.g. gas +200%, power spike, correlation breakdown) to the portfolio and measure P&L and liquidity impact.
• Scenario analysis — narrative-driven scenarios (pipeline outage, LNG diversion, extreme weather) to assess how the book would behave in specific crises.

These sit alongside VaR in limit frameworks and capital discussions. For a broader view of market, credit, and operational risk in energy and commodity trading, see Risks in energy & commodity trading. For how hedging and risk management interact, see Hedging explained.

Regulatory angle

Regulatory frameworks require firms to report and manage market risk; VaR is typically the backbone of the risk framework and feeds into capital requirements and position/margin rules.

• EMIR (EU): Clearing and margining for OTC derivatives; initial margin models (e.g. SPAN, PRISMA at ECC) are VaR-based. Firms must demonstrate adequate risk management and, where applicable, hold capital against non-cleared exposure.
• MiFID II (EU): Position limits and risk controls; VaR and related metrics support position reporting and concentration limits. ESMA publishes guidelines and technical standards—see ESMA regulation & policy for current requirements.
• CFTC (US): Swap dealers and major swap participants face capital and risk reporting rules; risk measurement and VaR-like metrics feed into capital adequacy. See CFTC regulations and capital requirements for swap dealers for details.