The Mekong - applications of value at risk (VaR) and conditional value at risk (CVaR) simulation to the benefits costs and consequences of water resources development in a large river basin

Abstract

Conditional value at risk (CVaR) was developed as a coherent measure of expected loss given that actual loss exceeds some value at risk (VaR) threshold. To date the concept has been primarily used to support quantitative risk assessment for investment decisions and portfolio management, using stochastic financial models to minimise the risk of unacceptable monetary loss. Intriguingly, the models and concepts are potentially adaptable to water resources planning and operational problems. This paper explores the application of CVaR within the context of identifying the risk of macro-economic damage to the fishery resources of Tonle Sap given reduced volumes of flow on the mainstream Mekong during the flood season. Emphasis is placed on simulating the linkages between the seasonally available flows in the Mekong mainstream, Tonle Sap water levels, annual fish catch and its economic value. We present scenarios using real hydrological and fish catch data along with exploratory concepts of contingency fund costs in terms of national and international aid requirements. The objective is to estimate the potential economic loss at a prescribed level of probability and to illustrate how VaR and CVaR may be calculated in this context. We demonstrate the properties of these risk measures through their behaviour under continuous and discontinuous loss distributions. We show that CVaR has advantages over VaR even under a relatively simple modelling approach. In the case where a loss distribution has discontinuities, VaR is potentially a poor measure of risk as it can vary unacceptably with a small increase in probability level. CVaR is stable in these situations. Here we find that when the loss distribution is continuous the CVaR is only marginally higher than the VaR. However, for the more realistic model where the loss distribution is discontinuous, the CVaR is substantially greater. We demonstrate the potential use of these two risk measures on a simple set of models of the Tonle Sap fishery in Cambodia. The sustainability of this fishery is crucial to the country in order to avoid even further dependence on international donor aid. Estimating the financial risk to which the national government and potential aid donors might be exposed given any damage to the fishery is the essence of this exploratory study of VaR and CVaR. © 2006 Elsevier B.V. All rights reserved.