- CFA Exams
- 2021 Level 2 > Study Session 3. Quantitative Methods (2) > Reading 9. Probabilistic Approaches: Scenario Analysis, Decision Trees, and Simulations
- 3. An overall assessment of probabilistic risk assessment approaches

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**Subject 3. An overall assessment of probabilistic risk assessment approaches**

Do we want to have a complete assessment of all possible outcomes? If yes, scenario analysis cannot be used.

Risk types:

- Scenario analysis: discrete risk, concurrent risk, correlated risk
- Decision trees: discrete risk, sequential risk, independent risk
- Simulations: continuous risk, either sequential or concurrent risk, either correlated or independent risk

Can a probabilistic approach be used as a complement to or substitute for risk-adjusted value? What rate should be used as the discount rate?

Scenario analysis cannot be used as a substitute for risk-adjusted value. When it is used as a complement, a risk-adjusted discount rate should be used.

Both decision trees and simulations can be used as either complements to or substitutes for risk-adjusted value, but the discount rates used are different.

#### Practice Question 1

Which statement is TRUE?A. Simulations always lead to better decisions because they provide distribution in the expected value.

B. In simulations, we should discount cash flows at a risk-adjusted rate, in most cases.

C. Well-planned and executed simulations always yield better estimates of expected value than conventional risk-adjusted value models.Correct Answer: B

A is false. It is common to make mistakes, such as double-counting risk or making decisions based upon the wrong types of risk.

B is true. In most cases we should use a risk-adjusted rate in simulations, but there is one exception. When we use the standard deviation in values from a simulation as a measure of investment risk, we should use the risk-free rate.

C is false. The expected values from simulations should be fairly close.

#### Practice Question 2

It is difficult to model ______ in decision trees.A. discrete risks

B. sequential risks

C. correlated risksCorrect Answer: C

Scenario analysis or simulations should be used instead to model correlated risks.

#### Practice Question 3

It is difficult to model ______ in scenario analysis.A. discrete risks

B. sequential risks

C. correlated risksCorrect Answer: B

Scenario analysis is better suited to assess concurrent risks.

#### Practice Question 4

Which approach cannot be used as a substitute for risk-adjusted value?A. scenario analysis

B. decision trees

C. simulationsCorrect Answer: A

Scenario analysis does not look at the full spectrum of possible outcomes.

#### Practice Question 5

Which approaches can be used as either complements to or substitute for risk-adjusted value?A. Decision trees and scenario analysis

B. Simulations and decision trees

C. Scenario analysis, decision trees and simulationsCorrect Answer: B

Scenario analysis does not look at the full spectrum of possible outcome, and therefore cannot be used as a substitute for risk-adjusted value.

#### Practice Question 6

If scenario analysis is used as a complement to risk-adjusted value, ______ should be used as the discount rate.A. the risk-free rate

B. a risk-adjusted discount rate

C. the market rateCorrect Answer: B

This approach uses expected cash flows, which should be discounted by a risk-adjusted discount rate.

#### Practice Question 7

If the approach of simulation is used as a substitute for risk-adjusted value, ______ should be used as the discount rate.A. the risk-free rate

B. a risk-adjusted discount rate

C. the market rateCorrect Answer: A

The cash flows should be discounted back at a risk-free rate to arrive at value.

### Study notes from a previous year's CFA exam:

3. An overall assessment of probabilistic risk assessment approaches