Estimate VaR by Monte Carlo simulation, by historical simulation, and by the parametric method, and explain what each result means
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.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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- Explain how value at risk (VaR) is applied to gauge the risk of a portfolio
- Contrast three ways to estimate VaR: Monte Carlo simulation, historical simulation, and the parametric (variance–covariance) method
- Set out the strengths and weaknesses of VaR
- Set out the ways VaR has been extended
- Explain sensitivity and scenario risk measures and weigh them against VaR
- Show how exposure measures for equities, fixed income, and options can help gauge and control market risk and volatility risk
- Set out how sensitivity and scenario risk measures are applied
- Set out the strengths and weaknesses of sensitivity and scenario risk measures
- Explain the limits used to control market risk, among them stop-loss limits, scenario limits, position limits, and risk budgeting
- Explain how risk measures can guide decisions on allocating capital
- Set out the risk measures relied on by insurers, pension funds, asset managers, and banks