Which probabilistic approach should we pick to assess risk? It depends on how we plan to use the output and what types of risk we face.

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 risks

Correct 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 risks

Correct 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. simulations

Correct 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 simulations

Correct 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 rate

Correct 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 rate

Correct Answer: A

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