Question

analyze sensitivity, scenario, and simulation:

• Compare and contrast these methods.
• Identify the positive and negative of each method.
• Provide examples of companies that are using these methods.
  • What industries are they involved in?
  • Why do these companies/industries use these methods

Answer 1

1. SENSITIVITY ANALYSIS:

Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions. This technique is used within specific boundaries that depend on one or more input variables, such as the effect that changes in interest rates (independent variable) have on bond prices (dependent variable).

BREAKING DOWN Sensitivity Analysis

Sensitivity analysis is also referred to as "what-if" or simulation analysis and is a way to predict the outcome of a decision given a certain range of variables. By creating a given set of variables, an analyst can determine how changes in one variable affect the outcome.

Sensitivity Analysis Example

Assume Sue, a sales manager, wants to understand the impact of customer traffic on total sales. She determines that sales are a function of price and transaction volume. The price of a widget is $1,000, and Sue sold 100 last year for total sales of $100,000. Sue also determines that a 10% increase in customer traffic increases transaction volume by 5%, which allows her to build a financial model and sensitivity analysis around this equation based on what-if statements. It can tell her what happens to sales if customer traffic increases by 10%, 50% or 100%. Based on 100 transactions today, a 10%, 50% or 100% increase in customer traffic equates to an increase in transactions by 5%, 25% or 50%, respectively. The sensitivity analysis demonstrates that sales are highly sensitive to changes in customer traffic.

Sensitivity vs. Scenario Analysis

In finance, a sensitivity analysis is created to understand the impact a range of variables has on a given outcome. It is important to note that a sensitivity analysis is not the same as scenario analysis. As an example, assume an equity analyst wants to do a sensitivity analysis and a scenario analysis around the impact of earnings per share (EPS) on the company's relative valuation by using the price-to-earnings (P/E) multiple.

The sensitivity analysis is based on the variables affecting valuation, which a financial model can depict using the variables' price and EPS. The sensitivity analysis isolates these variables and then records the range of possible outcomes. In a scenario analysis, on the other hand, the analyst determines a certain scenario, such as a stock market crash or change in industry regulation. He then changes the variables within the model to align with that scenario. Put together, the analyst has a comprehensive picture. He now knows the full range of outcomes, given all extremes, and has an understanding of what the outcomes would be given a specific set of variables defined by real-life scenarios.

2. SCENARIO ANALYSIS:

Scenario analysis is a process of analyzing decisions by considering alternative possible outcomes.

• Scenario analysis is designed to see the consequences of an action under different sets of factors. For example, it shows how an investment ‘s NPV would differ under high and low inflation.
• Scenarios should be feasible enough to provide an accurate picture of the outcomes. A “good” scenario for an investor should not include winning the lottery because, though good, it is neither probable nor realistic for analyzing possible results.
• Many scenario analyses use 3 scenarios: base case, worst case and best case. However, the number and conditions of the scenarios in each analysis can vary.

Scenario analysis is a strategic process of analyzing decisions by considering alternative possible outcomes (sometimes called “alternative worlds”). It is not a predictive mechanism, but rather an analytic tool to manage uncertainty today..

For example, a firm might use scenario analysis to determine the net present value (NPV) of a potential investment under high and low inflation scenarios.

In another example, a bank might attempt to forecast several possible scenarios for the economy (e.g. rapid vs. moderate vs. slow growth) or it might try to forecast financial market returns (for bonds, stocks and cash) in each of those scenarios. Perhaps, it might also consider sub-sets of each of the possibilities. It might further seek to determine correlations and assign probabilities to the scenarios (and sub-sets if any). By analyzing these various scenarios, the bank will be in a better position to consider how best to allocate its assets.

Many scenario analyses use three different scenarios: base case, worst case and best case. The base case is the expected scenario: if all things proceed normally, this is what the expected outcome will be. The worst and best cases are obviously scenarios with less and more favorable conditions, but they are still confined by a sense of feasibility. For example, an investor creating the worst case scenario would not be well served to have it include a meteor strike that destroys the company. While clearly a bad scenario, it is not realistic enough to be helpful.

The purpose of scenario analysis is not to identify the exact conditions of each scenario; it just needs to approximate them to provide a plausible idea of what might happen.

3. MONTE CARLO SIMULATION:

Monte Carlo simulation uses statistical data to figure out the average outcome of a scenario based on multiple, complex factors.

• The statistical distribution is estimated for each input (eg. inflation rate, market risk ). Then, simulations are run to see how constantly changing inputs (based on their distribution) affect the output. The outputs are averaged to find the estimated output.
• Monte Carlo simulations are great for when there are multiple inputs that can all change and may be unrelated.
• Monte Carlo simulations can be applied in many areas of business, such as bond pricing, but are especially useful when estimating the “base case” is difficult to do by hand.

In order to account of complex, interconnected factors, all of which may affect financial outcomes, companies turn to statistical methods. The Monte Carlo method solves a problem by directly simulating the underlying process and then calculating the average result of the process. It simulates the various sources of uncertainty (eg. inflation, default risk, market changes, etc.) that affect the value of the instrument, portfolio, or investment in question, and calculates a representative value given these possible values of the underlying inputs. In essence, the Monte Carlo method is designed to find out what happens to the outcome on average when there are changes in the inputs.

Each potential factor is assigned a probability or statistical distribution. For example, the investor may estimate the probability of default on a bond as 20%. That means that 20% of the time, he will not earn back his principal. The investor may also estimate that the inflation rate is normally distributed around a mean of 3% and standard deviation of 0.5%.

The investor estimates the probability or distribution of every factor that could change the result of the investment. Then, he essentially uses the distributions to run many many simulations of all the inputs to see how they affect the output and then finds the average output.

For example, for bonds and bond options, under each possible evolution of interest rates the investor observes a different yield curve and a different resultant bond price. To determine the bond value, these bond prices are then averaged. To value the bond option, as for equity options, the corresponding exercise values are averaged and present valued. By determining the average, the investor can figure out what the expected value is.

The advantage of the Monte Carlo method is that it is able to handle multiple moving, and possible related, inputs. As the number of factors increases, it becomes harder to figure out the “base case. ” Statistical analysis through Monte Carlo simulations is great at handling problems with multiple, inter-related, and uncertain factors.