Good analysis produces a substantial amount of raw data – but people need processed information to make decisions. The processing of data into information is what begins the transition from analysis to communication. All the fancy analysis in the world is useless if you can’t communicate your results in a clear, simple fashion. That means writing clearly, and boiling down results to good graphics. We are firm believers in telling the story with pictures. That doesn’t mean “dumbing it down:” But it does mean the careful consideration of the questions we’re trying to answer and the judicious use of more sophisticated graphics, or statistics.

# Answering the Question

How many times have you seen this graphic from Excel?

It’s got all the data, and zero information. Your decision is made around the differences between two options – so that’s what you want to see. But the analysis has to start with building those options, and the average analyst just shows those options. From this, option 2 looks better, maybe. So we can make our presentation *much *better just by showing Option 2 minus Option 1:

So now option 2 looks way better, but even that doesn’t show the whole picture. We can total the differences, and start getting real answers:

Now we can draw some real conclusions. If we’re sure the project will last the full period, Option 2 looks better, but if there is any real chance of early termination, we’re probably better off with Option 1, as 2 is no better until almost the end.

# Summarize

One of our favorite plot types is the “box plot”. a box plot replaces thousands of numbers with a simple box, with whiskers that represent the spread of the data. The simplest explanation is graphical:

The box represents the middle 50% of the data. The “whiskers” represent the middle 99.3% of all data. The red line is the median – where half of all data is above, or below. The plus is the average, or mean: an average different from a median implies the existence of an uneven distribution to one side or the other. Occasionally there will be marks to the top or bottom of the whiskers, representing extremly high or low values. A good example of the use of a box plot is our simulated future gas prices. If we look at 5000 simulated future price paths, it’s literally impossible to determine anything useful, and nearly impossible to draw any conclusions at all:

But a boxplot per month summarizes all of that data, and starts to give us information:

And now we can draw some real conclusions:

- It’s difficult to see gas prices above $6.
- For the most part, prices will never exceed $9.50 – and that’s
*very*unlikely. - Prices skew upward from the median. (to be expected on a price distribution, at these low prices)
- You are equally as likely to see $0.50 as $8 in 2018.

These are not fundamentally driven price forecasts – they are just paths that “look right” (in a mathematical sense) when seeded with the performance of prices in the past. We just used them as an example of how you can summarize large sets of data with a simple plot tool.

# Putting it all Together

This final example shows the decision-making power of good statistics and a simple graphic. In the finance world, they talk about an “efficient frontier” – if you have multiple opportunities, you should always choose the one with the highest return for a given level of risk (in most cases, the standard deviation of the expected results). Presuming a company has multiple opportunities available, you can combine them in various ways, depending on the company’s constraints. Graphically, if we plot the risk vs return of all of the possible combinations, some decisions make themselves very clear: Why invest in a lower return for the same risk?

In the world of simple valuation techniques, you can’t even have this discussion: there is no information on risk. Now, when you can decide your risk tolerance, your investment choices become clear.

Even better, you can decide on your risk measure: Is standard deviation too esoteric? Do you really worry about losing money on projects? We can substitute probability of losing money instead of standard deviation. You can also decide your return measure: Don’t like NPV? You can use capital efficiency (PNPV/investment), or just about any other measure.

We believe strongly in the power of the right analysis, with the right picture, to simplify the most complex of decisions. In our experience, if you can’t find the picture that makes the decision obvious, it’s more likely that no one has yet asked the right question.

Let us help you Make Risk Clear.