Presenting DRM Results:
Helping Executives Make Sense of DRM
Aleksey S. Popelyukhin, Ph.D.
Foreword ......
Anatomy of a Presentation ......
Skeleton (Text) ......
Muscles (Charts) ......
Uncertainty ......
Ranking ......
Development & Trends ......
Simulations ......
Allocations ......
Charts as Selection Tools! ......
Conventions, Expectations ......
Skin (Animation) ......
Brains (Logic Flow) ......
Not To Do List ......
Ockham’s Razor ......
Too Much Info ......
Not Enough Info ......
Dull Graphics ......
Other Sources of Inspiration ......
Websites ......
Charting software ......
Magazines ......
Conclusion ......
Acknowledgements ......
Appendix 1 ......
Appendix 2 ......
Appendix 3 ......
Bibliography ......
This paper has been written as a part of the “2003 CAS Working Party on Executive Level Decision Making using Dynamic Risk Modeling” research project (see Acknowledgements).
Foreword
Information… the most crucial ingredient of decision making.
Professionals are using more and more sophisticated tools to extract information from the data at hand. Unfortunately, those who are skilled in leadership, management and decision making – the senior management of a company – are not necessarily trained in advanced mathematics and statistics. Forgivably, the senior management team could quite possibly be unfamiliar with the concepts, terminology and notation used in modern financial analysis. Thus, it is up to actuaries – the most proficient DRM practitioners – to present results of their studies to the management in the most accessible and accurate way. Alas, it is easier said than done.
Presenting results of Dynamic Risk Modeling requires filigree techniques, deep knowledge of the subject and even some artistic skills in order to achieve that delicate balance of science and advertisement, which constitutes successful presentation. (Thinking of a presentation as a form of advertising may be new to actuaries, but an ability to sell the results of a study is quickly becoming a necessary skill). It’s a very narrow path indeed. One wrong choice in level of details or chart type or even color and the audience is lost. On the other hand, modern presenting tools are so rich and flexible that, with careful use of those tools, it is possible to express any thought, any notion, and any concept.
The following text is an attempt to create a guide for aspiring DRM presenters.
Anatomy of a Presentation
Skeleton (Text)
Any presentation is an attempt to express thoughts and deliver a message. And while visuals (charts, graphs and animations) on the slide help enormously, they are nevertheless just an aid. The text still remains the best tool for the job. For the high quality presentation, though, not any text suffices: the language of a presentation has to be precise, concise and help to emphasize.
Precise. Every statement in a presentation slide has to be correct:a presenter can not sacrifice accuracy for simplicity sake. It is not an easy task to formulate precise phrases for the audience that may not even be familiar with the terminology, but it has to be done. Perhaps, the best solution in this situation is to use analogies. However, analogies ought to be sophisticated enough and – sorry for the repetition – precise.
Concise. The text on the slides has to be laconic and succinct: it is practically impossible to get enough attention from the audience of multi-tasking, super-busy, patience-lacking, fast-reacting management types. The time invested in shortening every bullet in the presentation will pay back handsomely: food for thoughts is better digested when bits are concise.
Emphasize. Every presentation is an advertisement: the main message has to be emphatically accentuated. Indeed, a presenter is selling his point of view, conclusions of the study or recommendation for particular decision – there is nothing wrong with some emphasis.
Every presenter has three major time-tested presentation techniques at his disposal: analogy, humor and illustrations.
Analogy. Good analogy – like a flashlight – helps to highlight major points and focus on major features leaving out unnecessary details. Rarely used, but as effective is undeservingly forgotten negative analogy.
Humor. A smart, tasteful and appropriate joke can do wonders in capturing or restoring audience attention. And even if it doesn’t work, as a consolation, one may still contribute it to and warn others.
Illustrations. Items such as charts, drawings, animations, diagrams are always very useful. The presenter’s skill, however, lies not only in using illustrations per se, but in not using too many of them. Careful selection of only the most meaningful ones will be greatly appreciated by the audience. The following chapters may help in designing such a selection.
Muscles (Charts)
There exists innumerable diversity of chart types. Not every chart design is suitable for every purpose, though. Presentation of DRM study results poses additional difficulties. DRM operates with some specific notions that are not considered commonplace by charting software designers. Therefore, the chart types needed to illustrate these DRM concepts are not readily available in commercial software packages (e.g., Excel and PowerPoint). Particularly challenging are three of them: uncertainty, development and ranking. Let’s look at some examples of the charts we designed to illustrate these and other DRM notions. We intentionally limited ourselves with Excel Chart engine as the most ubiquitous charting tool available practically to everyone[1]:
Uncertainty
Uncertainty is a tricky notion: hard to explain – harder to illustrate. We present several approaches that attempt to do it.
One approach, the most obvious one, is to chart the chances. It could be a bar chart (a histogram) or a line chart. Excel allows displaying a probability density function (pdf) or a cumulative density function (cdf) or both on the same chart.
The recipe: Excel’s standard dual-axes chart with all series but one displayed as bars and one series displayed as a line.
Suitable for: Distribution charts.
In some situations the graph presented above may contain more precision than the audience finds useful. Another way to represent information on the range of probable results is to display vanishing probabilities through the creative use of colors, or more precisely, shades of the same color fading into background.
The recipe: Excel’s standard bar chart with gradient fills (from any foreground color to the background color) and without borders.
Suitable for: Range of outcomes, expected values, spread.
One may expect that the audience’s eyes will subconsciously be drawn to the areas of higher color density, thus, focusing audience’s attention on the area of more probable outcomes (while still maintaining impression of the size of the whole range).
With the help of 3-D rotations it is possible to explain the relationship between the previous two illustration techniques. The series of charts below demonstrates how to associate shades of color with the likelihood levels.
The recipe: Start with a 3-D line chart colored with gradient fills and steadily changing its 3-D view parameters to convert it into 2-D bar chart.
Suitable for: Explanatory, illustrative or convention setting charts.
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Once the shading convention is established and understood it makes sense to use it for displaying random values and even random processes:
The recipe: One of the series on Excel’s gradientfilled bar chart is converted to a Line.
Suitable for: Cash flows, reserves, payouts, uncertain values over time.
In some situations charting detailed probability distributions may not be necessary or even possible: a chart of probable ranges of outcomes may suffice. Usually it happens when there is a need for a higher level analysis or final conclusion (like the choice between possible scenarios or options) and/or when minute details are not really needed and could even be distracting.
The simplest way to add information about the size of outcome ranges is to use error bars. Luckily, Excel supports error bars for both X and Y axes.
The recipe: Excel’s standard XY (scatter) plot with oversized (12 or more pts) markers. Specify additional series of numbers for minimum and maximum values of X and Y axes Error Bars
Suitable for: Functions of twouncertain variables.
For a less precise, but (arguably) more impressive illustration of 2-D range of possible outcomes one may use Bubble chart. Excel supports only “spherical” rather than “elliptical” bubbles: there is no control over top and bottom or left and right radii of the bubble. Thus, asymmetric distributions are getting displayed incorrectly. Still, bubbles better represent uncertainty than dots
The recipe: Excel’s standard Bubble chart with area’s “3-D effect” option enabled. Use the “width of bubbles” option if a bubbles’ size is defined by standard deviation, and use the “area of bubbles” option if their size is defined by variance. To display the bubbles’ centers add an additional series with the small constant bubble size.
Suitable for: Functions of twouncertain variables.
Ranking
Culturally, we have become accustomed only to extremes. Only “the largest”, “the fastest”, “the strongest” can attract our attention. No wonder, any decision maker would like to rank his options to choose “the best” one. This is not an easy task. Dynamic Risk Modeling output usually consists of simulated distributions. And, no matter how detailed and precise these distributions are, it is often not clear which one is “better”. In other words, we can easily compare points on the line (fixed values), but it is not evident how to compare curves (random values).
Even more complicated is the task of comparing values in two dimensions. One scenario may be more profitable, but risky; another one less risky, but less profitable.
The recipe: Excel’s bubble chart can be used with a picture as a fill effect.
Suitablefor: Illustration of indecisiveness.
To compare scenarios with two or more important qualities, criteria must be selected. Selecting such criteria (which allows ranking scenarios while taking into account multiple aspects) is a special skill. However, once a criterion or scoring system or measurement is chosen, the DRM presenter may help visualize it.
Generally speaking, ranking criteria may be defined through several variables by quite sophisticated formulae: we leave this case to proprietary software specialized in visualization. However, frequently enough, a criterion could be expressed rather simply through the relationship of two variables and, thus, can be visualized through color-coding and/or additional grids.
Many criteria consist of just comparing one variable to another. This comparison could be in the form of division of one variable by another (“return” / “std. deviation”, “ROE”/ “Relative Capital Consumption”, etc) thus, generating a family of lines (Y/X=C) where the criterion score remains constant. These lines are nothing other than rays originating in the corner with ever increasing slope and can be visualized with the simple Plot AreaFillEffect.
The recipe: In the Format Plot Area/Fill Effects dialog box choose Two colors gradient with the Diagonal up shading style. A darker color should represent higher values of the criterion and a lighter color – lower values.
Suitablefor: Functions of twouncertain variables.
In the cases where the gradient fill is too subtle or too imprecise (chart corner is not (0,0) or a criterion is more complicated than the value of Y/X) the next logical step would be to paint areas of “indifference” – areas where criterion scores are acceptably close.
Our example is again for Y/X=C family of lines, but this method works for any expression.
The recipe: Excel’s standard Stacked Area chart where series are painted with the darkening shades of the same color.
Suitablefor: Risk-reward charts.
A less intrusive and more flexible way to display areas of similar criterion scores is to chart one-parametric family of level curves. If the criterion is minimization of Y/X, draw lines Y/X=C for several values of C; if the criterion is expressed as Y2/X, draw a few parabolas Y2/X=C, etc…
The recipe: Within Excel use smoothedcustom line pattern without markers for the one-parametric family of lines.
Suitablefor: Functions of twouncertain variables.
Interestingly enough, while DRM models effortlessly churn out hard-to-compare probability distributions for different scenarios, they usually do not produce distributions of the differences. Clearly, for the purpose of comparison, it would be extremely useful to the “net effect” of the change in strategy (i.e., buying reinsurance or changing investment mix or reallocating capital). Indeed, it is enormously hard to compare random values after their distributions were generated, while it is only a marginal effort to calculate their difference inside every simulation path. And it makes more sense, because this way one measures the differences of outcomes in the same situations represented by the same step of a simulation. Adding the differences to each stream of random numbers to produce the “net effect” evaluation would be both practical and useful for the comparison between the options.
Surely, any type of chart discussed in this chapter will be as useful for illustrating the “net effects” of selecting one option instead of another.
Development & Trends
There exist several techniques to emphasize development, that is, change over time. Unfortunately, the easiest one – an arrow pointing in the proper direction – is not part of the Excel Chart engine and has to be employed with the help of other software.
A gradual change in color and/or line width may serve as some kind of arrow substitution as illustrated below. Ideally, the viewer’s eyes will move from “unpleasant” reddish tones to the “calm” yellowish shades – exactly in the direction we want them to.
Sometimes it is necessary to illustrate development of an uncertain value. In order to emphasize development as opposed to the full ranges of possibilities, it makes sense to use an established statistical convention: displaying probability distributions as fixed percentile boxes.
The recipe: Excel’s standard Stock Chart with 25th, 100th, 0 and 75th percentiles instead of Open-High-Low-Close prices. One can fill Up-Bars with the horizontal color preset.
Suitablefor: Development of uncertain values over time, random processes.
Unfortunately, Excel’s Stock Charts are too inflexible to show multiple percentiles and they don’t allow additional information (like positions of the mean and median) to be displayed. An elegant workaround allows displaying points and lines that help to illustrate trends and development.
The recipe: Excel’s standard Area Chart allows displaying YError Bars with a Custom Error Amount: just enable them for the 50th percentile series.
Suitablefor: Development of uncertain values over time, random processes.
Another way to emphasize development and make the viewer’s eyes to move in the proper direction is a gradual change of color in the background.
The recipe: Use a verticalgradient to fill the Chart Area. Employ different line patterns to display different percentiles while not distracting the viewer from the main development display.
Suitablefor: Development of uncertain values over time, random processes.
Using the same convention for displaying development of the random value one may compare two or more options. Beware of the viewer’s confusion – i.e., options displayed need to be distinctive.
The recipe: Use colors similar to background and low weights for benchmark scenario linesas opposed to brightcolors and higher width lines for the alternative scenario.
Suitablefor: Development of multiple uncertain values over time, options comparison.
While on the topic of comparison: instead of scenarios one may compare assets to liabilities. The technique described above will suffice, but there are other options.
The recipe: Excel’s standard Bubble chart with two series: one for assets and one for liabilities.
Suitablefor: Comparison of development of two uncertain values.
Surely, the notion of development immediately leads to the related notion of trends and forecasts. Excel provides a capability to add trend-lines to the chart. While not fully flexible (the user can’t create customized trend function and/or exclude data points from the trend calculation), it’s automatic and easily accessible.
The recipe: Excel’s standard Bubble chart with trend-lines and 2 points forecast for each series.
Suitablefor: Comparison of development of two uncertain values.
Those not satisfied with Excel’s built-in trend-line options may build their own trend-lines
The recipe: While it looks like an elaborate line chart, it is actually a gradient filledArea Chart with the Drop Lines option enabled.
Suitablefor: Emphasis on extrapolation of the trend.
Simulations
Displaying the raw simulation results rather than various statistics is complicated and rarely needed. The sheer volume of data from the DRM model’s simulation results will test the limits of Excel’s Chart Engine as well as the audience’s comprehension abilities. Nevertheless, a display of simulation outcomes can sometimes be quite impressive and may, at the very least, establish a reference point for the slides to follow.
The results of every single simulation are usually displayed as a point on a Scatter Chart. More often than not it is beneficial to color-code these data points according to some useful criteria. To assign different colors to different points one either should separate data into several series (which may pose some challenges) or write a simple VBA macro to do the job.
The recipe:Scatter Chart enhanced by VBA color assignment macro.
Suitablefor: Illustration of density areas of simulated results.
Allocations
A concept every manager is intimately familiar with is allocation:a set of positive values that add up to 100%. The only reason we will briefly discuss it here is the dynamic aspect of allocations. That is to say how an allocation of resources or assets will change depending on the options available to management and under review through the DRM study.
There are many ways to display an allocation: from a pie chart to a stack-up bar chart, but what is the best way to illustrate changes in allocation? We present a few types of charts. The choice is (as always) up to the user.