FRM Part 1 - Book 4 - Valuation and Risk Models (Part 1/2)

After completing this reading you should be able to:

• Describe the mean-variance framework and the efficient frontier.

• Explain the limitations of the mean-variance framework with respect to assumptions about return distributions.

• Define the VaR measure of risk, describe assumptions about return distributions and holding period, and explain the limitations of VaR.

• Define the properties of a coherent risk measure and explain the meaning of each property.

• Explain why VaR is not a coherent risk measure.

• Explain and calculate Expected Shortfall (ES), and compare and contrast VaR and ES.

• Describe spectral risk measures, and explain how VaR and ES are special cases of spectral risk measures.

• Describe how the results of scenario analysis can be interpreted as coherent risk measures.

After completing this reading you should be able to:

• Explain and give examples of linear and non-linear derivatives.

• Describe and calculate VaR for linear derivatives.

• Describe the delta-normal approach for calculating VaR for non-linear derivatives.

• Describe the limitations of the delta-normal method.

• Explain the full revaluation method for computing VaR.

• Compare delta-normal and full revaluation approaches for computing VaR.

• Explain structured Monte Carlo, stress testing, and scenario analysis methods for computing VaR, and identify strengths and weaknesses of each approach.

• Describe the implications of correlation breakdown for scenario analysis.

• Describe Worst-Case Scenario (WCS) analysis and compare WCS to VaR.

After completing this reading you should be able to:

• Explain how asset return distributions tend to deviate from the normal distribution.

• Explain reasons for fat tails in a return distribution and describe their implications.

• Distinguish between conditional and unconditional distributions.

• Describe the implications of regime switching on quantifying volatility.

• Evaluate the various approaches for estimating VaR.

• Compare and contrast different parametric and non-parametric approaches for estimating conditional volatility.

• Calculate conditional volatility using parametric and non-parametric approaches.

• Explain the process of return aggregation in the context of volatility forecasting methods.

• Evaluate implied volatility as a predictor of future volatility and its shortcomings.

• Explain long horizon volatility/VaR and the process of mean reversion according to an AR(1) model.

• Calculate conditional volatility with and without mean reversion.

• Describe the impact of mean reversion on long-horizon conditional volatility estimation.

After completing this reading you should be able to:

• Describe external rating scales, the rating process, and the link between ratings and default.

• Describe the impact of time horizon, economic cycle, industry, and geography on external ratings.

• Define and use the hazard rate to calculate unconditional default probability of a credit asset.

• Define recovery rate and calculate the expected loss from a loan.

• Explain and compare the through-the-cycle and at-the-point internal ratings approaches.

• Describe alternative methods to credit ratings produced by rating agencies.

• Compare external and internal ratings approaches.

• Describe a ratings transition matrix and explain its uses.

• Explain the potential impact of ratings changes on bond and stock prices.

• Explain historical failures and potential challenges to the use of credit ratings in making investment decisions.

After completing this reading you should be able to:

• Identify sources of country risk.

• Explain how a country’s position in the economic growth life cycle, political risk, legal risk, and economic structure affect its risk exposure.

• Evaluate composite measures of risk that incorporate all types of country risk and explain limitations of the risk services.

• Compare instances of sovereign default in both foreign currency debt and local currency debt, and explain common causes of sovereign defaults.

• Describe the consequences of sovereign default.

• Describe factors that influence the level of sovereign default risk; explain and assess how rating agencies measure sovereign default risks.

• Describe characteristics of sovereign credit spreads and sovereign credit default swap (CDS) and compare the use of sovereign spreads to credit ratings.

After completing this reading, you should be able to:

• Evaluate a bank’s economic capital relative to its level of credit risk.

• Explain the distinctions between economic capital and regulatory capital, and describe how economic capital is derived. Identify and describe important factors used to calculate economic capital for credit risk: the probability of default, exposure, and loss rate.

• Define and calculate the expected loss (EL).

• Define and explain unexpected loss (UL).

• Estimate the mean and standard deviation of credit losses assuming a binomial distribution.

• Describe the Gaussian copula model and its application.

• Describe and apply the Vasicek model to estimate default rate and credit risk capital for a bank.

• Describe the CreditMetrics model and explain how it is applied in estimating economic capital.

• Describe and use the Euler’s theorem to determine the contribution of a loan to the overall risk of a portfolio.

• Explain why it is more difficult to calculate credit risk capital for derivatives than for loans.

• Describe challenges to quantifying credit risk.

After completing this reading, you should be able to:

• Describe the different categories of operational risk and explain how each type of risk can arise.

• Compare the basic indicator approach, the standardized approach, and the advanced measurement approach for calculating operational risk regulatory capital.

• Describe the standardized measurement approach and explain the reasons for its introduction by the Basel committee.

• Explain how a loss distribution is derived from an appropriate loss frequency distribution and loss severity distribution using Monte Carlo simulations.

• Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency and severity distributions.

• Describe how to use scenario analysis in instances when data is scarce.

• Describe how to identify causal relationships and how to use Risk and Control Self-Assessment (RCSA) and Key Risk Indicators (KRIs) to measure and manage operational risks.

• Describe the allocation of operational risk capital to business units.

• Explain how to use the power-law to measure operational risk.

• Explain the risks of moral hazard and adverse selection when using insurance to mitigate operational risks.

After completing this reading, you should be able to:

• Describe the rationale for the use of stress testing as a risk management tool.

• Identify key aspects of stress testing governance, including choice of scenarios, regulatory specifications, model building, stress-testing coverage, capital, and liquidity stress testing, and reverse stress testing.

• Describe the relationship between stress testing and other risk measures, particularly in enterprise-wide stress testing.

• Explain the importance of stressed inputs and their importance in stressed VaR and stressed ES.

• Identify the advantages and disadvantages of stressed risk metrics.

• Describe the key elements of effective governance over stress testing.

• Describe the responsibilities of the Board of directors and senior management in stress testing activities.

• Identify elements of clear and comprehensive policies, procedures, and documentation for stress testing.

• Identify areas of validation and independent review for stress tests that require attention from a governance perspective.

• Describe the important role of the internal audit in stress testing governance and control.

• Describe the Basel stress testing principles for banks regarding the implementation of stress testing.