Explain how value at risk (VaR) is applied to gauge the risk of a portfolio
The idea
Value at risk is a minimum loss that is expected to be exceeded with a given small probability over a given horizon, under normal market conditions. A one-day 5% VaR of 2 million means that losses of at least 2 million are expected on about one day in twenty; equivalently, with 95% confidence the loss will be smaller. It is used to set limits, allocate risk and report to boards and regulators. The probability and horizon must be stated: a 1% VaR exceeds a 5% VaR, and with independent returns and zero mean, VaR grows with the square root of the horizon. The trap is reading VaR as the maximum possible loss.
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- Contrast three ways to estimate VaR: Monte Carlo simulation, historical simulation, and the parametric (variance–covariance) method
- Estimate VaR by Monte Carlo simulation, by historical simulation, and by the parametric method, and explain what each result means
- 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