(Almost) crystal ball: Monte Carlo simulation

Although net present value (NPV) rocks, it is hard to believe that any financial metric representing the future outcome of an investment correctly describes what will REALLY happen. After all, cash flows that are inputs into the NPV analysis are forecasts and forecasts are never accurate. In lieu of a good crystal ball, you can run some scenario analyses or go straight to Monte Carlo simulation.

Monte Carlo simulation is a sophisticated scenario analysis. It’s a technique where you can model thousands of scenarios in a matter of seconds. Unlike typical scenario or what-if analyses that allow you to analyze the impact of changing one input variable at a time, Monte Carlo simulation analyzes all possible combinations at once. In a typical scenario analysis, you manually calculate as many scenarios as you deem necessary. Monte Carlo simulation, on the other hand, calculates these scenarios automatically, based on your definition of simulation parameters. It allows you to run thousands of scenarios instead of the few in a typical what-if analysis.

Monte Carlo simulation was popularized by physicists in the 1950s at the dawn of the computer age and it got its name from the Monte Carlo Casino in Monaco. Games of chance played at a casino exhibit random behavior that is bound by the characteristics of the game. When rolling a die for example, you know that a number between 1 and 6 will come up, but you don’t know which one.

Similarly, in an investment project you may know the range of possible financial outcomes, but you don’t know exactly which one will materialize. Monte Carlo simulation allows you to model all potential scenarios driven by the uncertain inputs. As a result you will know not just whether an investment will be profitable, but how likely it is to be profitable and how profitable it is likely to be.

Although Monte Carlo simulation will not eliminate uncertainties in business decisions, it can help you to understand them in normal business circumstances. For example, if there is a chance of negative financial outcome in your business, Monte Carlo simulation allows you to assess what might go wrong and helps you to be proactive with the decisions you make. Similarly, if you’re allocating resources among several projects, Monte Carlo simulation helps you to determine which ones have the greatest chance of success.

Monte Carlo simulation can especially be helpful in financial projections for investments that are not based on repeated past experiences. These projections are most often badly flawed. Although Monte Carlo simulation will not help to predict all possible events, it will help to prepare for those events.

Monte Carlo simulation can only go so far, however. It is, like also standard scenario analyses, only accurate for scenarios not wildly different than typical business circumstances. There may be, however, extraordinary, though not absolutely unlikely events that are widely different. Events like these, referred to also as Black Swans, have a low likelihood of occurrence, but big impact. Since Black Swans are unexpected by definition, they are not modeled in financial analyses. But more on Black Swans at some other point in time.