Understanding Value at Risk (VaR) in Commodity Risk and Trading

To calculate parametric VaR, you typically need:

• The expected (mean) return of the portfolio.
• The standard deviation of the portfolio's returns.
• A z-score, which represents the number of standard deviations away from the mean, corresponding to a chosen confidence level (e.g., 95% or 99%).

The basic formula for parametric VaR is:

*VaR = Portfolio Value × (Mean Return - (z-Score × Standard Deviation))*

The z-score is derived from the standard normal distribution based on the desired confidence level. For instance, a 99% confidence level corresponds to a z-score of approximately 2.33.

Example:

Imagine a portfolio of agricultural commodities worth $10 million. You want to calculate the 1-day VaR at a 99% confidence level. If the portfolio's expected daily return is 0.05% and the daily standard deviation is 1%, the z-score for 99% confidence is 2.33.

The VaR would be calculated based on these figures to estimate the maximum expected loss over one day with 99% confidence.

To implement the parametric VaR method, you'll primarily require:

• Historical price data for the commodities or assets in your portfolio. This data is used to calculate the mean returns and standard deviation.
• Time horizon: The period over which you want to estimate the risk (e.g., 1-day, 10-day).
• Confidence level: The probability level for the VaR estimate (e.g., 95%, 99%).
• Correlation data: If your portfolio has multiple assets, you'll need to understand how their prices move in relation to each other (correlation) to accurately assess portfolio-level risk. </aside>

You will specify the start and end dates for the historical data used in calculations. Some models also allow for a decay factor, which gives more weight to recent observations.

While relatively simple to implement, parametric VaR has several important limitations, especially relevant in the often-volatile agricultural commodity markets:

• Normality Assumption: The most significant limitation is its reliance on the assumption that asset returns are normally distributed. In reality, financial markets, including commodities, often experience "fat tails" – meaning extreme price swings (both gains and losses) occur more frequently than a normal distribution would predict. This means parametric VaR can underestimate the risk of large, unexpected losses, such as those seen during major market disruptions.
• Ignores Volatility Clustering: Parametric VaR often assumes that volatility (standard deviation) is constant over time. However, financial markets typically show "volatility clustering," where periods of high price swings are followed by more high swings, and periods of calm are followed by more calm. Standard parametric VaR may not adapt quickly enough to these changing volatility environments, potentially understating risk during turbulent times.
• Challenges with Non-Linear Portfolios: This method works best for assets whose value changes linearly with changes in risk factors (e.g., prices). It is less accurate for portfolios containing options or other non-linear derivatives, where the relationship between the asset's price and its value can be complex.
• Assumption of Stable Correlations: Parametric VaR calculations often use historical correlations between different assets. However, during periods of market stress, these correlations can change dramatically; assets that were previously uncorrelated might suddenly move in tandem. This can lead to an underestimation of portfolio risk when diversification benefits unexpectedly evaporate.
• Sensitivity to Historical Data: The accuracy of parametric VaR heavily depends on the historical data used. If the chosen historical period doesn't reflect potential future market conditions (e.g., using data from a period of unusually low volatility), the VaR estimate can be misleadingly low.
• Lack of Standardized Inputs: There isn't a universal agreement on precisely which statistical inputs or look-back periods to use, which can lead to inconsistencies in VaR figures across different calculations or systems.

Despite these limitations, parametric VaR can be a useful starting point for risk assessment, especially when its assumptions are understood and it is used in conjunction with other risk management tools and methodologies. 

RadarRadar transforms enterprise-wide commodity raw data into trusted application data for commodity risk management, performance and margin optimization and compliance reporting. Should you want more information on RadarRadar's Risk applications and Value at Risk (VaR) solutions, don't hesitate to book a demo.