medium · FRM Part 1 Valuation and Risk Models
A risk manager computes a one-day 99% Value-at-Risk (VaR) of $2 million for a portfolio. However, the manager notes that the volatility is mean-reverting toward a lower long-run level.
If the manager scales the VaR to a 10-day horizon using the square-root-of-time rule, what is the likely bias in the result?
- The VaR will be over-estimated because the confidence level must be reduced when extending the time horizon.
- The result will be unbiased because the square-root rule is a mathematical identity that holds regardless of volatility dynamics.
- The 10-day VaR will be under-estimated because mean reversion ignores the potential for extreme tail events.
- The 10-day VaR will be over-estimated because the rule assumes volatility stays constant at its current high level.
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