The valuation of investments in business ventures, investments, mergers, and industrial projects is a complex decision-making exercise, which brings together several aspects from alternative disciplines. Firms ask opinions to consultants, and the decision process can last several months, with notable time and resource efforts. Best practices recommend decision-makers to support their decision based on a business plan (often called financial model). The model puts together all aspects of the investment project and obtains the relevant valuation criteria, upon which the decision is based. In several situations, investors realize that they are uncertain about several of the aspects of the transaction and wish to identify key sources of uncertainty. Then, best practices foresee that decision-makers assign probability distributions to the uncertain model inputs and obtain the investment risk profile.
Technically, the risk profile is the distribution of the Net Present Value (NPV). From the risk profile, a manager gains knowledge of the probability of negative NPV and of all relevant risk measures. However, this process does not give us information about what are the assumptions that drive results and uncertainty.
In their work Invariant Probabilistic Sensitivity Analysis (forthcoming in Management Science, doi: 10.1287/mnsc.2013.1719), Emanuele Borgonovo (Department of Decision Sciences) and Manel Baucells (RAND Corporation and Universitat Pompeu Fabra) propose new sensitivity methods for the analysis of business plans and investment evaluation.
The methods are based on computing the distance between conditional and unconditional risk profiles using the Kolmogorov-Smirnov and Kuiper metrics. This results in a set of sensitivity measures which are monotonic transformation invariant. Invariance is a property which has both theoretical and practical implications. The sensitivity measures are readily estimated from a given dataset, allowing the manager to obtain them straightforwardly from what is currently done, thus “at no additional” cost. By the measures, a manager gains insights on what are the sources of uncertainty and on the key-variables to monitor both in the due diligence and in the implementation phases. In a way, these methods allow one to make the best out of the resource consuming valuation efforts.