9.1 Probabilistic Approaches

Question 1

What are the four steps in creating simulations?

Answer 1

V-P-C-R (very pretty chicks run)

1. Determine key input variables for simulation.
2. Define probability distributions of key variables.
3. Check for correlations across variables.
4. Run the simulation.

Question 2

Among the four steps in creating simulations, which step is the most difficult?

Answer 2

Determining the key input variables for simulation.

Question 3

What are the three options when performing the first step in creating simulations (determining the key input variables for simulation)?

Answer 3

1. Historical
2. Cross-Sectional (e.g., comparable companies’ data)
3. Pick a statistical distribution and estimate the parameters (e.g., assume normally-distributed growth with estimated mean and variance).

Question 4

What are your two choices when dealing with two variables that are highly correlated, such as interest rates and inflation?

Answer 4

Either:

1. Choose only one variable to vary (e.g., one with the largest impact on valuation), OR
2. Build correlations (different relationships between the two variables) explicitly into the simulation (resulting in greater detail but requiring more sophisticated simulation software).

Question 5

What are the two advantages of using simulations?

Answer 5

1. You have better input estimation because you are required to do more upfront brainstorming about the variability of your inputs.
2. You are using a distribution (of possible values) rather than a point estimate. By definition risky assets will have an uncertain value.

Question 6

What are the three types of constraints that the analyst must consider when preparing a simulation, since the downside of violating those constraints could lead to large costs or bankruptcy?

Answer 6

1. Book value of equity = There may be requirements to maintain minimum regulatory capital (e.g., banks and insurance companies). In some European companies, if your equity turns negative you cannot continue operations until you raise more capital.
2. Reduce risk to your company’s earnings and cash flows. Stay within debt covenants.
3. Market value = if the market value of the company falls below the value of the debt, then the company is in financial distress.

Question 7

What are the four potential problems with simulations?

Answer 7

1. GIGO
2. Real data may not fit your distributions you used in your model, e.g., you model is using a normal distribution of data, but the real-world data is non-normally distributed.
3. Non-Stationarity = The world is a dynamic place and what worked yesterday may not work tomorrow.
4. Dynamic correlations = When you build correlations in your model, you are assuming that these correlations are static … and they are not.

Question 8

What are the three types of simulations?

Answer 8

1. Scenario Analysis
2. Decision Trees
3. Monte Carlo simulations

Question 9

What are the three types of scenarios in Scenario Analysis?
What does Scenario Analysis ignore?

Answer 9

1. Base Case (the status quo … what you expect to happen under normal conditions).
2. Best Case
3. Worst case
   Scenario analysis ignores all other possibilities apart from these three.

Question 10

What is the sum of probabilities in Scenario Analysis and why?

Answer 10

Less than 100% because of all other possibilities you are ignoring apart from Base Case, Best Case, and Worst Case.

Question 11

What type of outcomes is Scenario Analysis best suited for?

Answer 11

Scenario Analysis is best suited for (1) DISCRETE outcomes (because you are only testing for three possible outcomes), and (2) For RISK THAT OCCUR CONCURRENTLY (i.e., risks that occur at the same time).

Question 12

Does Scenario Analysis accommodate correlated variables?

Answer 12

Yes, you can build in to each scenario that, for example, interest rates will go up and inflation will go up, as well as the relationships among any other correlated variables.

Question 13

Decision Trees are best suited for ________ and ______ risks. Why? What is different about this from Scenario Analysis?

Answer 13

sequential (e.g., if a pharmaceutical company is trying to get approval for a new drug, there is a first phase of testing, a second phase, and so on).
discrete
In contrast, Scenario Analysis should be used for concurrent risks.

Question 14

How easy is it to handle correlated risks with Decision Trees?

Answer 14

Correlated risks are difficult to model with decision trees.

Question 15

Decision Trees are best suited when ______ data is available because probabilities have to be estimated at each node.

Answer 15

historical;

Question 16

Monte Carlo Simulations consider ___ possible outcomes.

Answer 16

all;

the scenarios could be in the thousands.

Question 17

The probabilities for Monte Carlo simulations add up to a probability of what? Why?

Answer 17

1 … because all possible scenarios are considered.

Question 18

Monte Carlo Simulations are better suited for __________ risks, which can be either sequential or concurrent.

Answer 18

continuous;

Question 19

Can you model correlations within a Monte Carlo Simulation?

Answer 19

Yes.