Invariant Probabilistic Sensitivity Analysis

In evaluating opportunities, investors wish to identify key sources of uncertainty. We propose a new way to measure how sensitive model outputs are to each probabilistic input (e.g., revenues, growth, idiosyncratic risk parameters). We base our approach on measuring the distance between cumulative distributions (risk profiles) using a metric that is invariant to monotonic transformations. Thus, the sensitivity measure will not vary by alternative specifications of the utility function over the output. To measure separation, we propose using either Kuiper's metric or Kolmogorov-Smirnov's metric. We illustrate the advantages of our proposed sensitivity measure by comparing it with others, most notably, the contribution-to-variance measures. Our measure can be obtained as a by-product of a Monte Carlo simulation. We illustrate our approach in several examples, focusing on investment analysis situations.