Tracking a rainfall index constrained by Conditional Value-at-Risk

Abstract

Portfolio replication is a well studied problem from finance, whereby a subset of instruments is selected to track the average movement of all such instruments. Using expected monetary value as the decision criterion for selection is a trade-off of over and under estimators. An alternate criterion developed in finance is Conditional Value-at-Risk, employed to measure and restrict excessive deviation either above or below the centre. That same objective may be useful in monitoring environmental variables where the exclusion or inclusion of extreme values may be critical to representing the features of interest of the variable. We demonstrate the application of the risk measure to meteorological data in Australia, selecting a weighted combination of stations to best track an index of average annual rainfall. References

• Howlett, P. G. and Piantadosi, J. (2007). A note on Conditional Value at Risk. Optimization, 56, 629--632. doi:10.1080/02331930701617080
• Rockafellar, R. T. and Uryasev, S. (2002). Conditional Value-at-Risk for General Loss Distributions. Journal of Banking and Finance, 26, 1443--1471. doi:10.1016/S0378-4266(02)00271-6
• Webby, R. B., Adamson, P. T., Boland, J., Howlett, P. G., Metcalfe, A. V. and Piantadosi, J. (2006). The Mekong---applications of Value-at-Risk and Conditional-Value-at-Risk simulation to the benefits, costs and consequences of water resources development in a large river basin. Ecological Modelling, 201, 89--96. doi:10.1016/j.ecolmodel.2006.07.033
• Yamout, G. M., Hatfield, K. and Romeijn, H. E. (2007) Comparison of new conditional value-at-risk management for optimal allocation of uncertain water supplies. Water Resources Research, 43, W07430. doi:10.1029/2006WR005210
• Yum, K.-K., Blackmore, J. and Anticev, J. (2009). Modelling and evaluating water allocation risks using Value-at-Risk. Proceedings of the 18th World IMACS/MODSIM Congress. http://www.mssanz.org.au/modsim09/G3/yum.pdf [20/04/2010].