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2020 Curriculum CFA Program Level II Quantitative Methods

Excerpt from "Probabilistic Approaches: Scenario Analysis, Decision Trees, and Simulations"

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Scenario analysis, which applies probabilities to a small number of possible outcomes, and decision trees, which use tree diagrams of possible outcomes, are techniques used to assess risk. Simulations are also used to assess risk.

Learning Outcomes

The member should be able to:

  • describe steps in running a simulation;
  • explain three ways to define the probability distributions for a simulation’s variables;

  • describe how to treat correlation across variables in a simulation;

  • describe advantages of using simulations in decision making;

  • describe some common constraints introduced into simulations;

  • describe issues in using simulations in risk assessment;

  • compare scenario analysis, decision trees, and simulations.


Estimating the risk-adjusted value for a risky asset or investment may seem like an exercise in futility. After all, the value is a function of the assumptions that we make about how the risk will unfold in the future. With probabilistic approaches to risk assessment, we estimate not only an expected value but also get a sense of the range of possible outcomes for value, across good and bad scenarios.

  • In the most extreme form of scenario analysis, you look at the value in the best case and worst case scenarios and contrast them with the expected value. In its more general form, you estimate the value under a small number of likely scenarios, ranging from optimistic to pessimistic.

  • Decision trees are designed for sequential and discrete risks, where the risk in an investment is considered into phases and the risk in each phase is captured in the possible outcomes and the probabilities that they will occur. A decision tree provides a complete assessment of risk and can be used to determine the optimal courses of action at each phase and an expected value for an asset today.

  • Simulations provide the most complete assessments of risk since they are based upon probability distributions for each input (rather than a single expected value or just discrete outcomes). The output from a simulation takes the form of an expected value across simulations and a distribution for the simulated values.

With all three approaches, the keys are to avoid double counting risk (by using a risk-adjusted discount rate and considering the variability in estimated value as a risk measure) or making decisions based upon the wrong types of risk.