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 or idiosyncratic risk parameters). We base our approach on measuring 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 to use 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 contribution to variance. 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