Estimating Portfolio Value at Risk with Historical Simulation
Summary
The document introduces Value at Risk (VaR) as an estimate of portfolio loss over a chosen horizon and confidence level. It contrasts parametric, historical simulation, and Monte Carlo approaches, then walks through historical simulation: calculate portfolio returns from past price changes, sort them, select the relevant lower-tail percentile, and scale the loss by position value. It also explains that using portfolio returns directly incorporates historical co-movement among assets.
Examples use cryptocurrency positions, including a long Bitcoin and short Ether combination, to illustrate how diversification or hedging can reduce estimated portfolio VaR relative to separate positions. These examples demonstrate the calculation rather than establish future risk or strategy performance. The document notes that VaR does not describe the severity of losses beyond its threshold, can depend on distribution assumptions in parametric versions, and relies on historical observations that may not represent changed or extreme market conditions. Historical simulation avoids a normality assumption but remains backward-looking and sensitive to its sample.
Key ideas
- VaR summarizes a loss threshold for a specified horizon and confidence level.
- Historical simulation estimates VaR by sorting observed portfolio returns and selecting a lower-tail percentile.
- Portfolio-level returns preserve the historical correlation between assets.
- A long-short combination may have lower estimated VaR when its positions offset each other.
- VaR does not measure how severe losses can be beyond its threshold and depends on relevant historical data.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.