# Learning Objective 2: Risk Modeling and Aggregation of Risks

#1

Learning Objectives:
The candidate will understand the concepts of risk modeling and be able to evaluate and understand the importance of risk models.

Learning Outcomes:
The candidate will be able to:

a) Demonstrate how each of the financial and non-financial risks faced by an entity can be amenable to quantitative analysis including an explanation of the advantages and disadvantages of various techniques such as Value at Risk (VaR), stochastic analysis, and scenario analysis.

b) Evaluate how risks are correlated, and give examples of risks that are positively correlated and risks that are negatively correlated.

c) Analyze and evaluate risk aggregation techniques, including use of correlation, integrated risk distributions and copulas.

d) Apply and analyze scenario and stress testing in the risk measurement process.

e) Evaluate the theory and applications of extreme value theory in the measuring and modeling of risk.

f) Analyze the importance of tails of distributions, tail correlations, and low frequency / high severity events.

g) Analyze and evaluate model and parameter risk.

h) Construct approaches to modeling various risks and evaluate how an entity makes decisions about techniques to model, measure and aggregate risks including but not limited to stochastic processes.

*Updated for Spring 2018 Sitting

#2

I have a general question about VaR and the different ways to calculate it. Throughout Objective 2 we learn about what feels like 5000 different ways to calculate VaR. Can someone confirm if I am understanding the correct way to calculate each one?

1. Non-parametric VaR: Used when there is no distribution available, so you just take the 95th percentile of the sample of numbers available (ie. If you have 100 numbers, sort them from smallest to largest and take the 95th number)
2. Parametric VaR: Used when you can fit the data to a distribution (normal, exponential). To calculate, you can integrate from 0-95 or calculate std dev and scale by alpha.
3. Delta-Normal Method: Using the covariance matrix approach to calculate VaR, marginal VaR, incremental VaR, component VaR, etc. You use this if you are calculating the VaR of the portfolio (not sure about this one)?

Is there a preferred/easier way to calculate VaR? Does it just depend on the situation?? Am I missing any other ways to calculate VaR?

Thanks!