Probability management in financial planning.

• Author: Savage, Sam L.
• Position: Cover story

"Give me a number," says the city manager anxiously. "I need to know when the new hotel complex will be shovel ready!" The director of planning, who has just explained that the amount of time needed to obtain each of the required permits is unpredictable, asks, "Would you settle for an average?" "If that's all you can give me," she responds. "The developers need to know when to schedule construction." "Well," says the planner, "there are ten permits being processed in parallel, and I estimate that each one will take six weeks on average, so that's my best guess--six weeks."

This example exhibits three key concepts about uncertainty that are important to public financial managers:

1. Uncertainties are endemic to planning for the future, whether long term or short term. Public finance activities--estimating project schedules, forecasting tax revenues, and planning reserves to cover natural disasters--are rife with uncertainties.

2. Most people, including city managers, are uncomfortable with uncertainty and prefer to picture the future in terms of average outcomes.

3. This leads to the "flaw of averages," a set of systematic errors that arises when uncertainties are represented by single numbers, and it explains why so many projects are behind schedule, beyond budget, and below projection. (1) In short, the flaw of averages states that plans based on average assumptions are, on average, wrong.

Exhibit 1 illustrates how the city manager and planner have just run afoul of this ubiquitous problem. The left-hand chart shows all the permits coming in at their average of six weeks. That looks good, right? However, the project can't start until all of the permits have been obtained. The right-hand chart shows that even if some permits come in at less than six weeks, it only takes one late permit to delay construction. All ten permits are about as likely to come in at six weeks or less as a flipped coin is likely to come up heads ten times in a row, which means that the estimate the planner provided has only one chance in a thousand of being achieved.

If any permit comes in later than six weeks, construction will be delayed. In the figure on the right, the model, which generates 1,000 sets of "time to issue" scenarios, displays the values that appear on the 77th scenario, which results in a start time of 8.8 weeks.

The discipline of probability management uses proven computer simulation techniques, which have only recently become available to a much wider audience, to eliminate errors caused by using averages (see the "Probability Management" sidebar). (2) This article outlines three simple example problems that apply probability management. The models used are all available for download from the "Models" page at ProbabilityManagement. org. You can download them and try out probability management techniques for yourself while reading this article.

(1) THE PROJECT PLANNING PROBLEM

The model is about to inform our city manager and planner that a flaw of averages in scheduling often leads to a flaw of averages in finances. Suppose the developer of the hotel complex has negotiated a deal requiring the city to forgive future tax revenues at the rate of $100,000 per week for any delay in construction beyond seven weeks.

Given the average assumptions, each permit is obtained in exactly six weeks, construction begins in exactly six weeks, and there is no penalty. However, the model that represents the case of the city manager and the planner (the Schedule. xlsx file at ProbabilityManagement.org) calculates average results over 1,000 scenarios, indicating that the expected time to start construction is 7.8 weeks, which means the city will likely face $86,000 in penalties (see Exhibit 2).

(2) THE PROBLEM OF FORECAST|NG UNCERTAIN TAX REVENUES

When forecasting future tax revenues, it is tempting to pick a single number as an educated guess, and then back off a bit just to be safe. What many people don't realize is that most forecasting techniques provide an explicit measure of the degree of uncertainty for the result. This measure of uncertainty is usually discarded, leading straight back to the flaw of averages.

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