WATCH REPLAY: Benoit Ladouceur – Five distributions that will immediately improve your risk analysis

“It may sound like modelling is a nearly mythical experience where you need to have a firm grasp of arcane mathematics and hermetic financial models to do simulations, but that’s just not the case,” said Benoit Ladouceur, specialist director enterprise risk at VIA Rail Canada.

He was giving a practical presentation to an audience at Risk Awareness Week 2020 looking at some of the benefits that Monte Carlo simulation techniques can bring to business decision making, whilst also highlighting the many limitations of using risk heatmaps.

He asked the audience: “What’s our role as risk management specialists? First, keep the board and the auditors happy, but then what’s the other goal? It’s to help inform decisions that are considering risk. And you need to do some modelling or mathematics to be able to do that.”

He argued that modelling forces risk managers to challenge assumptions and put critical thinking into understanding the problems they face.

He said: “People that are pushing for single value deterministic models often forget that it’s easier to come up with a range rather than just coming up with specific point. You’ve got a lot more chances of getting it wrong if you’re just providing information for a certain point.”

For example, a simple model might look at revenue, operating costs and operating income. Of course, if you know those numbers, you can feed them into a single-value deterministic model, but to do that, you need to know precisely what will happen in the future.

In reality, you’ve usually got a wide possible range for revenues and another for operating costs. And as such, your operating income will vary substantially depending on where in those ranges the true numbers fall.

Ladouceur argued that it is critical that risk professionals adopt better stochastic methods to help with risk analysis and modelling. He laid out five possible distributions that can immediately improve the results from using a single value deterministic model.

Uniform distribution

In a Uniform distribution, all values between two points have the same likelihood of occurrence. To find out the two bounds the typical question to ask your experts is: “What are the minimum and maximum values this price can take?”. So, for instance, if you were looking at the cost of a manufacturing part, you might know that the price will fall between £150 – £300 per unit.

Triangular Distribution or PERT

This distribution is similar to the Uniform one with an upper or lower bound, but it also has a mode. Ladouceur says that you want to ask experts the same questions as before, but also to find out which outcome is most often represented.

LogNormal with alternative parameters

The third distribution recommended by Ladouceur is the LogNormal with alternative parameters. This is similar to the triangle distribution, but slightly more difficult to calculate.

Ladouceur says: “A log normal distribution with alternative parameters just requires someone to have some insight in the problem, but not necessarily mathematics.”

“This is a very useful distribution to model things that have got a long right tail like project cost overrun, for example, where there’s a centre of mass where most of the potential or the possibilities are, but it can reach much higher as well.”

To get a lognormal distribution you once again need to ask: “what’s the value we would expect most of the time for this price.” But you also need to find out the high and low value that expert would expect to see only once about every 20 times.

Beta distribution

Ladouceur’s fourth distribution is the Beta distribution, which he says is ideal for scenarios where risk professionals have limited data sets. However, the method can only be used for situations with one of two outcomes as it’s a continuous distribution of the probability of a given binary outcome.

The smaller the sample size, the more uncertainty you get within your model, but that means that as you get more data or carry out more tests your model will get more precise. This means that you can constantly refine and get better insights for decision making.

Poisson distribution

This distribution is useful to assess the likelihood of a specific event happening within a certain timeframe. For instance, to use Ladouceur’s example, what is the chance that security will patrol just as I am carrying out my heist on a jewellery shop.

The Poisson distribution allows you to answer these questions by modelling discrete events over a period of time. It’s a distribution that is defined by only one parameter (Lambda). To calculate lambda you need to see how many events happen over a period of time multiplied by the period of time you are interested in.

For instance, if there was one patrol every 480 minutes and you think your heist will take an hour, your Lambda would be 1/480*60 = 1.25.

Ladouceur says: “Here the assumptions are key because (they are not true) your test is basically garbage. So, the assumption for Poisson distribution is that the average rate of the event is constant…. the events are independent from each other and two events cannot occur exactly at the same time.

“This could be used for a for many problems. Once again, it is not a complicated distribution to get. You just need to understand how you calculate that Lambda and then you pick the right distribution for the model you’re running.”

Ladouceur concluded “Modelling forces you to think things through. And if you’re honest and you have the right people around the table and they answer truthfully, it will provide you with valuable insight about your business.”

“Even if you don’t have all the data, it will still be a more useful endeavour than a single point estimate if you’re doing a model, because basically what you’re using is ranges and theoretically it should be easier to come up with a range then coming up with a precise number.

“Of course, it looks much simpler to just go with one of the off the shelf solutions which put all the risk in big, colourful heatmaps, and that’s less thinking – but it’s not actually helping your business. So you might as well dive in and take the time to learn”

Ladouceur’s five key steps to begin modelling:

  • Understand your objectives – and always keep them in mind
  • Try to organise them as a hierarchy – By doing your simulation, you’ll get insights and may understand that some things are more important than others.
  • Break down the problem: and understand it step by step. This can be achieved in multiple ways. For instance, a budget or financial model can be broken down according to revenues, expense, tax amortization etc. Or you might want to borrow other risk management tools such as a layer of protection analysis methodology.
  • Facilitating the workshop
    1. Have a clear scope: what question are you trying to answer
    2. Get the right quorum: choose the right external and internal experts
    3. Gather data where possible
    4. Explain the nature of the simulation: make sure the people around the table understand the task and the expectations
    5. Inform people of psychological biases.
    6. Explain what Monte Carlo is and how it’s going to work
  • Check the assumptions within your models


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