Historical Simulation VaR: Choosing the Tail Loss and Scaling Horizon

Summary

The document asks how to estimate a ten-day 99% value at risk for a hedge fund investment using 500 daily returns. It provides the worst 20 returns and raises a course rule to select the fifth-largest loss, then scale it by the square root of ten. The stated investment amount prompts a practical question: whether VaR should be reported as a percentage loss or a currency amount.

The material identifies key decisions in historical simulation: selecting the tail observation for the desired confidence level, converting returns into a portfolio loss, and extending a one-day estimate to a multi-day horizon. It does not provide an answer or validate the square-root-of-time scaling assumption. That scaling can be unsuitable when returns are not independent and identically distributed, so the prompt alone does not establish a reliable ten-day risk estimate.

Key ideas

• Historical simulation estimates VaR from observed past returns.
• The selected tail observation depends on the confidence level and sample size.
• A return-based VaR can be converted to a currency loss using the portfolio value.
• Square-root-of-time scaling relies on assumptions about return behavior and is not justified by the prompt alone.

Tags

# Calculate VaR using method of historical simulation


# Calculate VaR using method of historical simulation












A bank invests € $1.000.000$ in a hedge fund. The last 500 daily returns can be taken from a database. The worst 20 returns are

-4.58 -2.95 -2.95 -2.93 -2.17 -2.08 -2.06 -1.98 -1.94 -1.89 -1.83 -1.75 -1.73 -1.56 -1.54 -1.52 -1.45 -1.37 -1.17 -0.89

I want to determine the ten-day 99%-VaR using historical simulation.

According to my course material I need to determine the 5-highest loss and multiply it by $\sqrt {10}$.

Do I even need the € $1.000.000$ from the task?

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