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Estimate VaR by Monte Carlo simulation, by historical simulation, and by the parametric method, and explain what each result means

CFA® Level II · Portfolio Construction · Measuring and Managing Market Risk · L2.PM.5.c

The idea

Parametric VaR as a return is the expected return minus z times the standard deviation, where z is 1.65 at 5%, 1.96 at 2.5% and 2.33 at 1%; multiply by portfolio value and express as a loss. Portfolio standard deviation comes from weights, volatilities and correlations. To move from annual to daily figures, divide the mean by the number of trading days, often 250, and the volatility by its square root. For historical simulation, rank the revalued outcomes and take the one at the chosen percentile, for example the 25th worst of 500 for a 5% VaR under a common convention. The trap is scaling volatility by the number of days rather than its square root.

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