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Commodity Portfolio VaRの包括的な教育ガイドを準備中です。ステップバイステップの解説、数式、実例、専門家のヒントをお届けしますので、もうしばらくお待ちください。
Value at Risk (VaR) is a statistical measure of the maximum expected loss on a portfolio over a specified time horizon and at a given confidence level. Commodity Portfolio VaR quantifies the potential dollar loss from adverse price movements in a commodity positions book — covering energy, metals, agricultural, and other commodity exposures simultaneously. For example, a 1-day 99% VaR of $5 million means there is only a 1% probability of losing more than $5 million in a single trading day under normal market conditions. VaR is the cornerstone of market risk management at commodity trading firms, investment banks, hedge funds, and energy companies. The Basel III banking framework requires banks to maintain capital against trading book VaR, and commodity firms regulated under EMIR in Europe and Dodd-Frank in the US use VaR for margin and collateral purposes. Commodity portfolios present unique VaR challenges compared to equity or fixed income portfolios: commodity price distributions exhibit fat tails and skewness, correlations between commodities shift dramatically across market regimes, physical versus financial positions have different risk profiles, and term structure risk (basis between contract months) is as important as outright price risk. Three main VaR methodologies are used: parametric (variance-covariance) VaR assumes normally distributed returns and uses correlation matrices; historical simulation VaR replays actual historical price changes against the current portfolio without distributional assumptions; and Monte Carlo VaR generates thousands of simulated scenarios using estimated price processes, capturing non-linear risks from options. Commodity firms typically supplement VaR with stress testing against specific extreme scenarios (e.g., repeat of 2020 COVID price crash, 2008 commodity supercycle reversal) because VaR systematically underestimates tail risk during market dislocations.
See calculator interface for applicable formulas and inputs. This formula calculates commodity var calc by relating the input variables through their mathematical relationship. Each component represents a measurable quantity that can be independently verified.
- 1Identify all commodity positions in the portfolio with their mark-to-market values and price sensitivities (delta for linear positions, delta + gamma for options).
- 2Collect historical daily price returns for each commodity over a representative historical period (typically 1-3 years).
- 3Construct the variance-covariance matrix of commodity returns or collect the full historical return scenarios.
- 4For parametric VaR: compute portfolio variance using weights and the correlation matrix; σ_p = sqrt(w' Σ w).
- 5Apply the z-score: VaR = z × σ_p × Portfolio_Value × sqrt(holding_period_days).
- 6For historical simulation: apply each historical daily return vector to the current portfolio and sort the losses.
- 7Read off the 99th percentile loss as the 1-day 99% VaR; calculate CVaR as the average loss in the worst 1% of scenarios.
Negative correlation provides modest diversification benefit
The WTI position dominates the portfolio risk at $10M × 2.5% = $250,000 daily standard deviation. The gold position adds $45,000 standard deviation but the -0.10 correlation reduces the combined portfolio risk slightly below the simple sum. The 1-day 99% VaR of $580,691 means there is a 1% probability of losing more than this amount in a single trading day under normal market conditions.
Historical simulation captures non-normal distributions and fat tails better than parametric
Applying 500 historical daily return vectors to the current portfolio generates 500 hypothetical P&L outcomes. Sorting these from worst to best, the worst 5 scenarios (1% of 500) represent the tail loss distribution. The 5th worst outcome of $2.1M is the historical simulation 99% VaR. Note this is higher than parametric VaR might suggest if commodity price distributions are fat-tailed (which they typically are), because historical simulation captures the actual distribution including extreme events.
Historical stress loss of $16.55M far exceeds 1D VaR — illustrates VaR limitations
The COVID crash scenario applied to the current portfolio generates a loss of $16.55 million (33.1% of portfolio value). This scenario loss vastly exceeds a typical daily VaR figure of perhaps $1-2M, illustrating why commodity risk managers supplement VaR with stress testing. VaR is calibrated to normal market conditions; the COVID crash was a tail event that VaR systematically underestimated. Stress tests ensure capital and liquidity reserves are adequate for extreme but plausible scenarios.
CVaR of $1.86M preferred over VaR for regulatory capital purposes under Basel III SA-CCR
Conditional VaR (Expected Shortfall) averages the losses in the worst 1% of scenarios, giving $1.86M versus the VaR threshold of $1.2M. The CVaR/VaR ratio of 1.55 indicates significant tail risk beyond the VaR threshold — typical for fat-tailed commodity distributions. Basel III's Fundamental Review of the Trading Book (FRTB) moved from VaR to Expected Shortfall as the primary regulatory risk metric precisely because CVaR better captures the shape of the loss tail.
Trading desk risk management at commodity trading firms and banks. This application is commonly used by professionals who need precise quantitative analysis to support decision-making, budgeting, and strategic planning in their respective fields
Basel III regulatory capital calculation for commodity trading books. Industry practitioners rely on this calculation to benchmark performance, compare alternatives, and ensure compliance with established standards and regulatory requirements, helping analysts produce accurate results that support strategic planning, resource allocation, and performance benchmarking across organizations
CME/ICE margin requirements using SPAN VaR methodology — Academic researchers and students use this computation to validate theoretical models, complete coursework assignments, and develop deeper understanding of the underlying mathematical principles
Commodity hedge fund risk reporting to investors and prime brokers. Financial analysts and planners incorporate this calculation into their workflow to produce accurate forecasts, evaluate risk scenarios, and present data-driven recommendations to stakeholders
Corporate treasury commodity risk quantification for board reporting. This application is commonly used by professionals who need precise quantitative analysis to support decision-making, budgeting, and strategic planning in their respective fields
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in commodity portfolio var calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in commodity portfolio var calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in commodity portfolio var calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
| Commodity | Annualized Vol | Daily Vol Approx. | 1D 99% VaR per $1M | Key Risk Driver |
|---|---|---|---|---|
| WTI Crude Oil | 35-45% | 2.2-2.8% | $51,000-65,000 | OPEC+ decisions, EIA data |
| Natural Gas (HH) | 60-100% | 3.8-6.3% | $88,000-147,000 | Weather, LNG exports |
| RBOB Gasoline | 35-50% | 2.2-3.1% | $51,000-72,000 | Crack spread, refinery ops |
| Gold | 12-18% | 0.75-1.1% | $17,500-26,000 | Fed policy, USD, risk sentiment |
| Silver | 25-40% | 1.6-2.5% | $37,000-58,000 | Gold correlation + industrial |
| LME Copper | 20-30% | 1.3-1.9% | $30,000-44,000 | China demand, supply |
What are the limitations of VaR for commodity portfolios?
VaR has several significant limitations in commodity applications: (1) it assumes normal (or near-normal) return distributions but commodity returns exhibit strong fat tails and skewness; (2) correlations used in parametric VaR are estimated from historical data and can change dramatically during market dislocations; (3) VaR does not capture liquidity risk — the cost of unwinding large positions in illiquid markets; (4) it ignores convexity (gamma risk) for options positions if only first-order delta sensitivities are used; and (5) it is backward-looking and may not capture new risk types (e.g., carbon price risk) not present in historical data.
What is the difference between VaR and Expected Shortfall?
VaR at the 99% confidence level tells you the maximum loss you would expect to see on 99% of trading days — it tells you nothing about how bad things get in the worst 1% of days. Expected Shortfall (CVaR) answers the question: given that you are in the worst 1% of outcomes, what is the average loss? For fat-tailed distributions like commodity returns, the ES is typically 1.5-2.5x the VaR, revealing the severity of tail losses that VaR ignores. The Basel III Fundamental Review of the Trading Book mandates ES rather than VaR for regulatory trading book capital.
How is VaR used for commodity margin requirements?
Exchange clearinghouses (CME Clearing, LME Clear) use variants of historical simulation VaR (SPAN — Standard Portfolio Analysis of Risk, developed by CME) to calculate initial margin requirements for futures positions. SPAN simulates portfolio gains and losses under a matrix of price and volatility scenarios, setting margin at a level covering expected losses under adverse but plausible conditions. Higher VaR = higher margin requirements = more capital tied up in the trading operation. Traders actively seek portfolio offsets (longs and shorts that reduce net VaR) to minimize margin requirements.
What is correlation risk in commodity portfolios?
Commodity correlations are highly unstable and regime-dependent. In normal markets, oil and copper may have a correlation of 0.4; during a demand shock they can reach 0.9 as all cyclical commodities fall together. Conversely, supply shocks often hit individual commodities, breaking typical correlations. Gold typically has a negative correlation with risk assets in crisis periods but can lose this property when financial stress forces liquidation of all assets. VaR models that use a fixed correlation matrix estimated from calm markets will systematically understate risk during crises.
How do commodity options affect VaR calculations?
Options create non-linear payoff profiles that simple delta-based VaR methods underestimate. A long call option on WTI crude has a positive delta (gains when oil rises) but also positive gamma (the delta accelerates as oil rises). Standard delta VaR calculates risk only from linear price sensitivity; delta-gamma VaR adds the second-order convexity correction. For large options books, full revaluation under each historical scenario (full-grid repricing) is necessary for accurate VaR, as analytical approximations are insufficient for deep in-the-money or near-expiry options.
What is backtesting and why is it required for VaR models?
Backtesting compares VaR model predictions to actual subsequent daily P&L outcomes to assess model accuracy. If a 99% 1-day VaR is correctly calibrated, you should see the actual loss exceed the VaR forecast approximately 1% of the time (about 2-3 times per year for daily data). Basel III's traffic light system categorizes VaR models by the number of backtesting exceptions per year: fewer than 5 exceptions = green zone (model acceptable); 5-9 = yellow zone (additional capital applied); 10+ = red zone (model rejected, mandatory recalibration). Regulators use backtesting results to assess the soundness of banks' internal VaR models.
How does term structure risk fit into commodity VaR?
A commodity portfolio is rarely a single spot exposure — it typically contains positions across multiple contract months (e.g., long June crude, short September crude) with exposures to both outright price movements and the spread between months. Term structure risk (also called curve risk or basis risk) requires including the correlation structure across the entire futures curve in the VaR calculation. A portfolio with offsetting near and far positions may have low outright price VaR but significant term structure VaR if the spread between months is volatile. Sophisticated commodity risk systems model the entire forward curve as a correlated risk factor.
プロのヒント
Complement your daily VaR report with a 'sensitivity P&L' attribution — breaking down how much of the portfolio VaR comes from each commodity and each risk factor (outright price, curve shape, volatility). This attribution identifies concentration risks that aggregate VaR masks and directs hedging attention to the largest marginal contributors to portfolio risk.
ご存知でしたか？
J.P. Morgan's 1994 introduction of RiskMetrics — the first standardized VaR framework — democratized market risk measurement and eventually led to VaR becoming the universal language of financial risk management worldwide. The original RiskMetrics technical document was published freely on the internet, an early example of open-source risk methodology that transformed the entire financial industry.