## Scenario analysis

- Define your scenarios;
- best-worst-base
- There are a range of results!
- Check if risk makes a difference

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## Use distributions for the uncertainties to describe key risk drivers

Choose distribution based on historical data or expert opinion Distribution is important for the simulation; based on the given distribution, the simulator ill be more/less likely to pick numbers in specific ranges

- Uniform: same probability of all numbers in a given range
- Triangle: point within the range is much more likely than the other points
- Normal: you know the middle point but it could be off by X in either direction

- Run Risk
- Define distributions
- Define output cell fir which to simulate results
- Things to look out for
- Mean of objective variable (usually NAP)
- Compare results with scenario results
- Look at full range of outcomes
- Look at standard deviation and at confidence range
- Look at downside risk and upside potential.

- What is % of being above/below specific number?
- What is breakable probability?
- What is the distribution like?

Perform Monte-Carlo simulation to Evaluate different possible outcomes. Determine expected result, range of results, probability of results (e. G. Probability of break-even), downside risk, etc.

Advantages: avoid the Flaw of Averages, understand the risk, test your intuition

## Sensitivity analysis

### Purpose

- Examine sensitivity of results when model parameters are varied
- Observe change in results due to change in assumptions
- Identify main uncertainty drivers / key risk drivers

### Methodology

- What-if analysis (simple changing of numbers to see what happens)
- One-way & two-way sensitivity analysis
- Tornado diagrams
- One-way & two-way sensitivity analysis
- Use one-way sensitivity analysis (data table) to check how changes to a variable effect the output variable.
- Use Goal
- Seek to find breakable point of that variable.
- Use two-way sensitivity analysis (data table) to check for changes in two different variables at the same time
- Check for impact of each variable / parameter, sorted in order of magnitude
- Shows you on which variables you should focus most, where the most important risks lie!

## Example questions on risk analysis

- In what type of decision context could risk analysis be useful and why may it be dangerous to rely on single point forecasts?
- What techniques can you use to overcome the problems of such forecasts?
- How do you decide what technique is most appropriate to use?
- Every business decision entails risk dangerous!

A single point only ever tells us what the average Of two cases is, never what happens between the two cases!

Example answer for this part: These numbers are based on the average scenario which is not necessarily representative of the true value (argue why could over- or underestimate). Furthermore, they do not tell us anything about the risk.

## Technique: scenario analysis or simulation

- Explain in your own words how Monte Carlo Simulation could be useful to a decision maker
- Evaluate different possible outcomes
- Averages, understand the risk, test your intuition
- Explain how the simulation process works to produce results that are useful to a decision maker

Example answer: This is different from the E,250 that Carolina's predecessor estimated because the original estimate was made using only single-value estimates for each of the variables.

However, by using a Monte Carlo simulation that allows for a range of possible values (with a triangular distribution to account for the higher likelihood of the values Of 5% and 20% for economy and business, respectively). This means that, based on 1 ,OHO iterations of possible combinations for each of the variables as per the arranging definition of the potential values for each variable under each iteration, the mean of the cost is E 10,277.

A friend of yours has just learned about simulation methods and has asked you to conduct a complicated risk analysis to help her making a choice. She said she would be happy to let you solve the problem and then recommend what action she should take. Explain why she needs to be involved in the analysis and modeling process and what kind of information you need from her.

## Risk analysis requires information about the characteristics of a particular uncertainty

A simulation model has produced the following three risk profiles displayed below.

What advice would you give to the decision maker on the basis of this output?

Choice depends on risk attitude, personal wealth, importance of project success and cost of investment alternative. Alternative C has the highest associated payoff. However, range of possible payoffs is quite large. The steeper the shape of the probability distribution function, the smaller the range of possible expected payoffs (look at standard deviation of outcomes).

Consider 5% confidence interval of most likely payoffs. Alternative A has quite a big confidence interval with relatively flat slope at the edges. Look at intersection of B and C and argue which one is less risky.

Your boss has asked you to work up a simulation model to examine the uncertainty regarding the success or failure of five different investment projects. He provides probabilities for the success of each project individually (numbers given). Because the projects are run by people in different segments of their investment market, you both agree that it would be reasonable to believe that, given these probabilities, he outcomes of the projects are independent.

He points out, however, that he really is not fully confident in these probabilities and that they could be off by as much as 0. 05 in either direction on any given probability.

- How can you incorporate this uncertainty about the probabilities in the simulation model? Use normal distributions for each project with Sd= 0. 05
- Now suppose he changes probability to include ranges. How can you update your simulation model to take this additional information into account?

Update probability distributions - triangle, discrete, uniform, normal Example answer: He should use historical data and his expert judgment to estimate the distribution of inputs. He should apply a normal distribution if the different values are independent of each other.

Example for normal distribution argument: However, since the number of high quality applications is the sum of the individual decisions "whether or not to apply/' of a substantial amount of high caliber young professionals, and since this decision is taken by each potential applicant to a large extend independently of each other, the normal distribution with mean 630 seems reasonable. Moreover, given the potential range of high quality applications is between 51 0 and 750, a standard deviation of 60 seems reasonable; that is, the range of 240 students corresponds to 4 standard deviations. Since the proportion of offers accepted is again the sum of many individual decisions, the normal distribution with mean 58% and standard deviation of 2% might be reasonable.

- Interpret the following risk analysis result tables ask at: Minimum, expected, maximum, P(loss) = x % (downside risk), P(> X) = Y% (upside potential)

## Interpret sensitivity analysis

- Describe how output variable is sensitive to given assumptions/parameters.
- Describe how output variable minimizes and maximizes with the different scenarios; what is the upside potential and downside risk

Example answer: The total cost decreases by El ,800 for each 5% increase in the business class no-show rate from 15% to 20% (at which point it is minimized), but then increases by E,700 per percentage point increase from 20% to 30%. The rate Of increase is consistent regardless of the rate of economy no-show. The two-way sensitivity table and the accompanying chart show us that in the lower ranges of the possible no-show rates, the total cost is sensitive to both variables in fairly similar proportion, until the optimum combination is reached at 5% economy and 20% business. After this inflection point, the total cost becomes much more sensitive to changes in the business class no-show rate.

- Describe, compare and explain the shape of a distribution

Risk profile: probability of making a loss vs. a profit Minimum versus maximum Variance Size of 90% confidence interval around the mean. Include arguments why distributions might differ with different scenarios

- Make recommendation based on the results

Will usually be trade-off between high risk for higher return on average and lower risk for lower return on average Include risk profiles, probabilities, maximum and minimum numbers... Example answer: The policy that we have recommended is better than the others, because it has the lowest average total cost.

Furthermore, the 95% confidence interval has the narrowest range of possible values, as well as the lowest probability that costs will exceed El 7,000. However, even though our recommended policy is better overall, it is not necessarily going to be the best on each individual flight. However, this doses t matter since the average cost is the single most important criterion when choosing a policy because you have 365 * 4 flights per year. One additional insight you could generate is the simulated cost difference between the current and suggested policies. The new policy is worse than the original policy 6% of the times.

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