FRM Part 2 - Book 1 - Market Risk (Part 1/2)

After completing this reading you should be able to:

• Estimate VaR using a historical simulation approach.

• Estimate VaR using a parametric approach for both normal and lognormal return distributions.

• Estimate the expected shortfall given P/L or return data.

• Define coherent risk measures.

• Estimate risk measures by estimating quantiles.

• Evaluate estimators of risk measures by estimating their standard errors.

• Interpret QQ plots to identify the characteristics of a distribution.

After completing this reading you should be able to:

• Apply the bootstrap historical simulation approach to estimate coherent risk measures.

• Describe historical simulation using non-parametric density estimation.

• Compare and contrast the age-weighted, the volatility-weighted, the correlation-weighted, and the filtered historical simulation approaches.

• Identify advantages and disadvantages of non-parametric estimation methods.

After completing this reading, you should be able to:

• Explain the importance and challenges of extreme values in risk management.

• Describe extreme value theory (EVT) and its use in risk management.

• Describe the peaks-over-threshold (POT) approach.

• Compare and contrast generalized extreme value and POT.

• Evaluate the tradeoffs involved in setting the threshold level when applying the generalized Pareto (GP) distribution.

• Explain the importance of multivariate EVT for risk management

After completing this reading you should be able to:

• Define backtesting and exceptions and explain the importance of backtestingVaR models.

• Explain the significant difficulties in backtesting a VaR model.

• Verify a model based on exceptions or failure rates.

• Define and identify Type I and Type II errors.

• Explain the need to consider conditional coverage in the backtesting framework.

• Describe the Basel rules for backtesting.

After completing this reading you should be able to:

• Explain the principles underlying VaR mapping, and describe the mapping process.

• Explain how the mapping process captures general and specific risks.

• Differentiate among the three methods of mapping portfolios of fixed income securities.

• Summarize how to map a fixed income portfolio into positions of standard instruments.

• Describe how mapping of risk factors can support stress testing.

• Explain how VaR can be used as a performance benchmark.

• Describe the method of mapping forwards, forward rate agreements, interest rate swaps, and options.

After completing this reading you should be able to:

• Explain the following lessons on VaR implementation: time horizon over which VaR is estimated, the recognition of time varying volatility in VaR risk factors, and VaR backtesting.

• Describe exogenous and endogenous liquidity risk and explain how they might be integrated into VaR models.

• Compare VaR, expected shortfall, and other relevant risk measures.

• Compare unified and compartmentalized risk measurement.

• Compare the results of research on “top-down” and “bottom-up” risk aggregation methods.

• Describe the relationship between leverage, market value of asset, and VaR within an active balance sheet management framework.

After completing this reading you should be able to:

• Describe financial correlation risk and the areas in which it appears in finance.

• Explain how correlation contributed to the global financial crisis of 2007 to 2009.

• Describe the structure, uses, and payoffs of a correlation swap.

• Estimate the impact of different correlations between assets in the trading book on the VaR capital charge.

• Explain the role of correlation risk in market risk and credit risk.

• Relate correlation risk to systemic and concentration risk.

After completing this reading you should be able to:

• Describe how equity correlations and correlation volatilities behave throughout various economic states.

• Calculate a mean reversion rate using standard regression and calculate the corresponding autocorrelation.

• Identify the best-fit distribution for equity, bond, and default correlations.

After completing this reading you should be able to:

• Explain the purpose of copula functions and the translation of the copula equation.

• Describe the Gaussian copula and explain how to use it to derive the joint probability of default of two assets.

• Summarize the process of finding the default time of an asset correlated to all other assets in a portfolio using the Gaussian copula.