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.

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 spreadsheet 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 (e.g. what if gas prices triple overnight?); CVaR / Expected Shortfall (average loss beyond VaR); and scenario analysis tied to specific events like pipeline outages or LNG cargo diversions.

Regulatory angle (EMIR and MiFID II):

• Firms must demonstrate adequate risk management frameworks; VaR is typically the backbone.
• Position limits under MiFID II are often expressed in VaR-equivalent terms.
• Margining under EMIR clearing obligations ties directly to VaR-based initial margin models (e.g. SPAN or PRISMA at ECC).