Value at Risk (VaR) is a statistical measure that quantifies the potential loss of a portfolio or strategy over a defined time period at a specified confidence level. It is one of the most widely used risk metrics in institutional finance and provides a single number that summarizes downside risk. A one-day 95% VaR of $50,000 means that on 95% of trading days, the portfolio is expected to lose no more than $50,000.
How VaR is calculated
There are three primary methods for calculating VaR. The parametric (variance-covariance) method assumes returns follow a normal distribution and calculates VaR directly from the portfolio's mean return and standard deviation. For a 95% confidence level, VaR equals the portfolio value multiplied by 1.65 standard deviations of daily returns. This method is computationally fast but relies on the normality assumption, which often understates tail risk.
The historical simulation method uses actual historical returns to estimate VaR. It sorts all historical daily returns and identifies the return at the chosen percentile. For 95% VaR with 1,000 days of data, VaR is the 50th worst day's loss. This method makes no distributional assumptions but is limited to the range of scenarios present in the historical data.
The Monte Carlo method generates thousands of simulated return paths based on the portfolio's risk characteristics and estimates VaR from the simulated distribution. This approach can incorporate non-normal distributions, correlations, and complex portfolio structures, but requires significant computational resources.
Interpreting VaR
VaR provides a threshold, not a maximum loss. A 95% VaR of $50,000 means that on 5% of days (about 13 trading days per year), the portfolio is expected to lose more than $50,000. VaR says nothing about how much more the loss could be on those days. This is the fundamental limitation of VaR: it describes the boundary of normal losses but is silent about extreme losses.
Conditional VaR (CVaR), also called Expected Shortfall, addresses this limitation by estimating the average loss on the days that exceed the VaR threshold. CVaR is a more conservative and arguably more useful risk measure for tail-risk-aware traders.
VaR in practice
Institutional investors and regulators use VaR extensively. Banks are required to hold capital reserves proportional to their trading book's VaR. Fund managers report VaR to investors as a measure of portfolio risk. Risk committees set VaR limits that traders cannot exceed.
For algorithmic traders, VaR helps calibrate position sizes and set risk budgets. If a strategy's VaR exceeds the trader's risk tolerance, positions need to be reduced. VaR can also be decomposed by position to identify which holdings contribute most to portfolio risk.
Practical example
A portfolio consists of $500,000 in equities with a daily standard deviation of 1.2%. The parametric 95% VaR is $500,000 * 1.65 * 1.2% = $9,900. This means the trader should expect to lose more than $9,900 on approximately one day out of 20. If this level of daily risk is unacceptable, the trader needs to reduce position sizes, hedge exposures, or diversify into uncorrelated assets.
How Tektii helps
Tektii calculates VaR and CVaR for backtested strategies using historical simulation, giving traders a clear view of their strategy's tail risk. The platform shows how VaR evolves over time and across different market regimes, helping traders understand whether their risk exposure remains within acceptable bounds. By integrating VaR into the standard analytics suite, Tektii brings institutional-grade risk measurement to individual algorithmic traders.