## Saturday, March 2, 2013

### 3 in 1 risk chart

A question from a client today kind of goes like this: "Is it possible to plot three types of risk variables in one chart and if so, what kind of risk chart could we use to achieve this goal?"

This is an interesting query for sure and risk charting is an area of risk management which is fascinating but can be quite complex. There is certainly more than one answer to such a question but today we'll take a look at Polar Charts as a solution.

The question could also be written up diagrammatically as we have done in Figure 1:

Figure 1 : 3 in 1 Risk Chart Request | Causal Capital    [ Click image to enlarge ]

So we have some risk data, perhaps loss data that is showing the size of losses and which risk-causal categories these losses are occurring on. We are also capturing which departments are suffering these losses.  Three variables of risk are being shown for each loss record, they are; loss amount, category and department or class.

For example, we could have a loss of fraud in payroll for \$100 or a loss from IT disruption in logistics for \$1000 and so on.

So then, is it possible to pull all of this information into one view or chart of risk?

The type of chart we are going to use to achieve this view of risk is a Polar Plot and our example is based on a small set of loss data records across three sample risk categories.

Figure 2 : Chart and Source Code | Causal Capital    [ Click image to enlarge ]

To conceptualise the risk data into a Polar Plot or radar chart as this graph type is often named, actually consumed more time than the coding effort required to generate the output. Such is the life when planning risk framework development.

Figure 3 : Chart Enlarged | Causal Capital    [ Click image to enlarge ]

The entire program for this risk chart was built in R-Project using the ggplot2 graphics library and I am personally a bit of a fan of ggplot2, it supports a huge array of chart types that can be customised with 'relative' ease.

So there we have it, our 3 in 1 risk chart.

#### 1 comment:

1. I plot risk on a scatter plot graph with y-axis=probability and x-axis =impact \$m. The marker = 80th percentile of the distribution.

This is a common method of displaying risks in a graph. Risk is calculated as the product of probability (Bernoulli distribution) and impact (a continuous distribution). The y-axis is probability 0 to 1, x-axis for impact 0 to 50.

Obviously since the product of two distributions is a third continuous distribution and you cannot plot a number of risk distributions on a scatter plot. Companies are often interested in the 80th percentile so the scatter plot locates the marker of the basis of the P() v. P(80) impact.

This tells the reader nothing about the nature of the underlying distribution’s uncertainty in terms of standard deviation, min-max range, kurtosis, upper/lower quartile range.

This is the challenge to demonstrate the relative value of a set of risks by P(80) value and also their distribution uncertainty.

Do you have any suggestions?