Week 3

Question 1

What does a sensitivity analysis do? What is it mathematically?

Answer 1

A sensitivity analysis asks how sensitive your outpout is to the changes in an input of the model.

mathematically is is the percentage change in output divided by the percentage change in input.

Question 2

What are the steps in sensitivity analysis?

Answer 2

1. Determine the factor around which the sensitivity analysis will be built. Typically, focus on one, two, or (at most) three critical factors/inputs in the model.
2. The second component is determining the number of variations to analyze for each factor/input used in the sensitivity analysis.
3. The third component is the estimation of the output of the model for each possible variation in the critical factors/inputs.
4. The final component is the assignment of probabilities to each possible outputs generated from the variations in the critical factors/inputs.

Question 3

What is scenario analysis?

Answer 3

In scenario analysis we change a bunch of inputs to simulate a scenario, we than analyze the output of each of these scenarios.

Question 4

What are the steps in scenario analysis?

Answer 4

1. Identify how many scenarios to analyze
2. For each scenario, identify the critical inputs/factors to vary to generate the scenario based output.
3. Do sensitivity analysis by varying the critical inputs/factors for a given scenario and generate the output from the model.
4. The final component is the assignment of probabilities to each possible outputs generated from the pre-defined scenarios.

Question 5

What are some of the difficulties of Sensitivity and scenario analysis?
What can we use to solve this?

Answer 5

Sensitivity and scenario analysis onle allows for simple graphical representations if there is one one piece of uncertain input data, if there are more than one uncertain inputs it is not possible to visualize the uncertainty graphically.
This makes it difficult to get an idea of how output changes if you have many inputs to play with.

To solve this we can use a Monte Carlo Simulation.

Question 6

What is a Monte Carlo Simulation? How is it better than sensitivity and scenario analysis for multiple changing inputs?

Answer 6

A Monte Carlo Simulation is an automated what-if analysis that takes probabilities into account.

It allows for simple graphical representation (e.g histograms) even if there are multiple uncertain inputs, unlike sensitivity and scenario analysis.

Question 7

Why should we use Monte Carlo Simulations in investment analysis?

Answer 7

When we deal with uncertainty then a decision criteria based ona single number is not good, e.g a single NPV or IRR. Monte Carlo Simulation allows us to generate the whole distribution of potential NPV values, thater than only one.

Question 8

How does a Monte Carlo Simulation work?

Answer 8

1. Start from a logically correct spreadsheet model(filling some cells with uncertain numbers).
2. Determine sensible distributions for the uncertain numbers (based on historic data or subjective judgement).
3. Ask your computer to sample lots of scenarios randomly from these distributions.
4. Record the value of the baseline (e.g NPV) for each generated scenario.
5. Display the distribution of our baseline (over all samples)
6. Monte Carlo Simulation helps to avoid the flaw of averages.

Question 9

What are the critical inputs in a Monte Carlo Simulation model?

Answer 9

A logically correct model (e.g profit calculation).

A set of uncertain variables in the model e.g cash flows.

An approximate description of the distribution of the uncertainties (Very critical).

Question 10

How do we take statistical dependence into account with Monte Carlo Simulations?

Answer 10

Statistical dependence can be taken into account by building a model of the uncertainties (e.g making a value in one year equal to the previous year + a random effect, rather than just a value + a random effect.).