Sensitivity Analysis in Investment Project Evaluation

This paper discusses the sensitivity analysis of valuation equations used in investment decisions. Since financial decision are commonly supported via a point value of some criterion of economic relevance (net present value, economic value added, internal rate of return, etc.), we focus on local sensitivity analysis. In particular, we present the differential importance measure (DIM) and discuss its relation to elasticity and other local sensitivity analysis techniques in the context of discounted cash flow valuation models. We present general results of the net present value and internal rate of return sensitivity on changes in the cash flows. Specific results are obtained for a valuation model of projects under severe survival risk used in the industry sector of power generation

Sensitivity Analysis in Decision Making: a Consistent Approach

Several recent works show that sensitivity analysis (SA) of decision-support models shares distinctive features with respect to the SA of generic simulation models. Purpose of this work is, then, to define the mathematical framework for the formulation of SA questions consistent with the theory underlying the decision-making model at hand. We define and compare the SA problem faced by a von Neumann-Morgenstern (vNM) decision maker to the problem that arises for a Bayesian decision maker. The SA problem for a VNM decision maker can be properly solved by making use of local SA methods. However, models containing non-binary events turn the problem into a constrained one, whose the solution requires the utilization of constrained derivatives. We then formulate the SA questions for a Bayesian decision maker. We show that to perform SA in the light of the state of belief one ought to utilize an approach based on the distance beteween distributions. We employ a recently introduced SA method that, while drawing form the Bayesian literature, shares the distinctive feature of avoiding to presuppose a change in the prior/posterior distributions. Investigation and comparison of the information and insights decision makers derive from the approaches conclude the work

Financial management in inventory problems: Risk averse vs risk neutral policies

In this work, we discuss the effect of risk measure selection in the determination of inventory policies. We consider an inventory system characterized by the loss function of Luciano et al. [2003. VaR as a risk measure for multi-period static inventory models. International Journal of Production Economics 81-82, 375-384]. We derive the optimization problems faced by risk neutral, quadratic utility, mean-absolute and CVaR decision makers. Results show that while the global nature of the optimal policy is assured for risk coherent and risk neutral decision makers, the convexity of the quadratic utility problem depends on the stochastic properties of demand. We investigate the economic and stochastic determinants of the different policies. This allows us to establish the conditions under which each type of decision maker is indifferent to imprecision in the distribution families. Finally, we discuss the numerical impact of the choice of the risk measure by means of a multi-item inventory. The introduction of an approach based on Savage Scores allows us to offer a quantitative measurement of the similarity/discrepancy of policies reflecting different risk attitudes.Inventory management Coherent risk measures Optimization with coherent risk measures Random demand modeling

On the Quantification and Decomposition of Uncertainty

In this work we deal with the quantitative assessment and decomposition of uncertainty. The decision making process is often accompanied by an uncertainty propagation exercise in the practice. We first analyze the meaning of uncertainty propagation from a subjective decision-making point of view. We show that, in order to quantify uncertainty, one has to resort to the distribution of the expected utility (U) originated from parameter uncertainty. We undertake the analytical determination of the moments U. We show that, if one considers the uncertain parameter space as subdivided in alternative preference regions delimited by indifference hypersurfaces, the moments of U are the sum of the moments of the expected utility of alternatives in the regions alternatives are preferred. As a consequence, if an alternative is never preferable, it does not contribute to uncertainty. In order to decompose uncertainty, we focus on the variance of U. By stating of Sobol' variance decomposition theorem in the Decision-Theory framework, we show that the variance of U can be expressed as sum of the variances brought by uncertain parameters individually and/or in groups. We then determine and discuss the meaning of global importance of parameters. Since parameters associated with the highest value of the global importance are the most effective in reducing uncertainty, gathering information on these parameters would reduce uncertainty in the most effective way. We illustrate the moment calculation and variance decomposition procedures by means of an analytical example. The application to the uncertainty analysis of an industrial investment decision-making problem concludes the paper

What drives value creation in investment projects? An application of sensitivity analysis to project finance transactions

Evaluating the economic attractiveness of large projects often requires the development of large and complex financial models. Model complexity can prevent management from obtaining crucial information, with the risk of a suboptimal exploitation of the modelling efforts. We propose a methodology based on the so-called "differential importance measure (D)" to enhance the managerial insights obtained from financial models. We illustrate our methodology by applying it to a project finance case study. We show that the additivity property of D grants analysts and managers full flexibility in combining parameters into any group and at the desired aggregation level. We analyze investment criteria related to both the investors's and lenders' perspectives. Results indicate that exogenous factors affect investors (sponsors and lenders) in different ways, whether exogenous variables are considered individually or by groups.Risk analysis Finance: investment analysis Sensitivity analysis