Historical Simulation VaR for Crypto Portfolios and Hedges

Summary

The document introduces value at risk as an estimate of portfolio loss over a chosen horizon at a specified confidence level. It outlines parametric, historical simulation, and Monte Carlo approaches, then focuses on historical simulation: calculate portfolio returns from past price changes, sort them, and use the lower-tail percentile to estimate loss at the selected confidence level. The examples use daily crypto prices and illustrate applying the method to a BTC position and to a BTC–ETH long-short portfolio.

For multi-asset portfolios, the method uses aligned portfolio returns, which incorporate the assets' historical co-movement. The example reports lower VaR for the combined hedge than for the individual positions, attributed to BTC–ETH correlation. VaR remains a limited measure: it does not describe how severe losses can be beyond its threshold, and historical samples may not represent future regimes. The article also notes that normal-return assumptions can understate crypto risks such as jumps and volatility clustering.

Key ideas

• VaR estimates a loss threshold over a defined horizon and confidence level.
• Historical simulation estimates that threshold from the lower tail of observed portfolio returns without assuming a return distribution.
• Using portfolio-level historical returns incorporates the assets' observed correlation into the estimate.
• A BTC–ETH long-short example shows how historical co-movement can reduce estimated portfolio VaR.
• VaR does not quantify losses beyond its threshold, and past data may miss future extremes or changing market regimes.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.