Water Resources Management

, Volume 27, Issue 9, pp 3209–3225 | Cite as

Optimising Reliability: Portfolio Modeling of Contract Types for Retail Water Providers

  • Renée Kidson
  • Brent Haddad
  • Hui Zheng
  • Steven Kasower
  • Robert Raucher
Article

Abstract

This paper considers the retail water provider’s purchasing decision of a portfolio of permanent contracts from wholesalers with multiple volatile water sources. We consider the reliability of two contract types: (1) fixed annual quantities, and (2) an inflow harvest function with storage. Our four-reservoir case in Sydney (Australia) has cross-correlated inflow data. To accommodate multi-reservoir cross-correlation we adapt Portfolio Theory from finance to lognormal reservoir inflows, re-framing traditional storage theory from the wholesaler’s optimal operating policy to the retailer’s optimal purchasing policy. We find that Reliability improves with access to a source pool (cf. fixed quantities from separate sources), demonstrating the ‘insurance effect’, and the portfolio that minimises lognormal variance also minimises harvest (and thus environmental impact). Reform direction in Australian (and other international) water markets is towards multi-provider vertical disintegration, which may reduce pool opportunities and negate the insurance effect. We consider diminishing reliability returns as reservoir harvesting increases, and conclude a retail portfolio of permanent contracts from reservoirs, plus short-term contracts from alternative sources (either independently or negatively cross-correlated) efficiently secures high reliability. The challenge in incomplete water markets remains in encouraging and sustaining supply diversification that may only be needed aperiodically during extreme droughts.

Keywords

Reliability Retail water provider Contract Hydrological volatility Water supply system Portfolio theory Optimisation Storage Cross-correlation 

References

  1. ABS: Australian Bureau of Statistics (2008) Publication 3222.0 - Population Projections, Australia, 2006 to 2101. http://www.abs.gov.au/Ausstats/abs@.nsf/mf/3222.0
  2. Aerts JCJH, Botzen W, van der Veen A, Krywkow J, Werners S (2008) Dealing with uncertainty in flood management through diversification. Ecol Soc 13(1):41, http://www.ecologyandsociety.org/vol13/iss1/art41/ Google Scholar
  3. Aitchison J, Brown JAC (1957) The lognormal distribution with special reference to its use in economics. Cambridge, UKGoogle Scholar
  4. Archibald TW, McKinnon KIM, Thomas LC (1997) An aggregate stochastic dynamic programming model of multireservoir systems. Water Resour Res 33(2):333–340CrossRefGoogle Scholar
  5. Awerbuch S (2006) Portfolio-based electricity generation planning: policy implications for renewables and energy security. Mitig Adapt Strateg Glob Chang 11(3):693–710CrossRefGoogle Scholar
  6. Becket L, Yeh WWG (1974a) Optimal timing, sequencing, and sizing of multiple reservoir surface water supply facilities. Water Resour Res 10(1):57–62CrossRefGoogle Scholar
  7. Becket L, Yeh WWG (1974b) Optimization of real time operation of a multiple-reservoir system. Water Resour Res 10(6):1107–1112CrossRefGoogle Scholar
  8. Bellman R (1953) An introduction to the theory of dynamic programming. The Rand Corporation, USA, 99 pp.Google Scholar
  9. Buytaert W, Beven K (2009) Regionalization as a learning process. Water Resour Res 45:W11419. doi:10.1029/2008WR007359 CrossRefGoogle Scholar
  10. Characklis GW, Griffin RC, Bedient PB (1999) Improving the ability of a water market to efficiently manage drought. Water Resour Res 35(3):823–832CrossRefGoogle Scholar
  11. Characklis GW, Kirsch BR, Ramsey J, Dillard KEM, Kelley CT (2006) Developing portfolios of water supply transfers. Water Resour Res 42:W05403. doi:10.1029/2005WR004424 CrossRefGoogle Scholar
  12. Chow VT (1954) The log-probability Law and its engineering application. Proc Am Soc Civ Eng 80(536):1–25Google Scholar
  13. Chow VT (1964) Handbook of applied hydrology. McGraw-Hill, New York, 1468 ppGoogle Scholar
  14. Cowan S (1997) Competition in the water industry. Oxford Rev Econ Policy 13(1):83–92CrossRefGoogle Scholar
  15. Dessai S, Browne A, Harou JJ (2013) Introduction to the special issue on “adaptation and resilience of water systems to an uncertain changing climate”. Water Resour Manag. doi:10.1007/s11269-012-0254-3
  16. Elton EJ, Gruber MJ (1974a) On the maximization of the geometric mean with lognormal return distribution. Manag Sci 21(4):483–488CrossRefGoogle Scholar
  17. Elton EJ, Gruber MJ (1974b) Portfolio theory when investment relatives are lognormally distributed. J Finance 29(4):1265–1273CrossRefGoogle Scholar
  18. Elton EJ, Gruber MJ, Brown SJ, Goetzmann WN (2007) Modern portfolio theory & investment analysis, 7th edn. Wiley, USA, 728 ppGoogle Scholar
  19. Fama E (1970) Efficient capital markets: a review of theory and empirical work. J Finance 25:383–417. doi:10.2307/2325486 CrossRefGoogle Scholar
  20. Figge F (2004) Bio-folio: applying portfolio theory to biodiversity. Biodivers Conserv 13:827–849CrossRefGoogle Scholar
  21. Frost AJ, Thyer MA, Srikanthan R, Kuczera G (2007) A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data. J Hydrol 340(3–4):129–148CrossRefGoogle Scholar
  22. Haddad BM (2000) Rivers of gold: Designing markets to allocate water in California. Island Press, USA, 196 pp.Google Scholar
  23. Hashimoto T, Stedinger JR, Loucks DP (1982) Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour Res 18:14–20CrossRefGoogle Scholar
  24. Hazen A (1914) Storage to be provided in impounding reservoirs for municipal water supply. Trans Am Soc Civ Eng 77:1539–1640Google Scholar
  25. Hukka JJ, Katko TS (2003) Refuting the paradigm of water services privatisation. Nat Resour Forum 27(2):142–155CrossRefGoogle Scholar
  26. Hurst HE (1951) Long term storage capacity for reservoirs. Trans Am Soc Civ Eng 116:770–799Google Scholar
  27. Jenkins MW, Lund JR (2000) Integrating yield and shortage management under multiple uncertainties. J Water Resour Plan Manag 126(5):288–297CrossRefGoogle Scholar
  28. Kidson RL, Haddad BM, Zheng H (2009a) Improving water supply reliability through portfolio management: Case study from Southern California. Proceedings, 4th WEAS International Conference in Water Resources, Hydrology and Hydraulics, University of Cambridge, 24–26 February 2009Google Scholar
  29. Kidson RL, Haddad BM, Zheng H (2009b) Risk profiles for water supplies with diversified sources. Proceedings, OzWater ‵09 Conference, Melbourne, Australia, 16–18 March 2009Google Scholar
  30. Kirsch BR, Characklis GW, Dillard KEM, Kelley CT (2009) More efficient optimization of long-term water supply portfolios. Water Resour Res 45:W03414. doi:10.1029/2008WR007018 CrossRefGoogle Scholar
  31. Klemes V (1987) One hundred years of applied storage reservoir theory. Water Resour Manag 1:159–175CrossRefGoogle Scholar
  32. Korteling B, Dessai S, Kapelan Z (2012) Using information-gap decision theory for water resources planning under severe uncertainty. Water Resour Manag. doi:10.1007/s11269-012-0164-4
  33. Kottegoda NT (1980) Stochastic water resources technology. Wiley, New York, 345 ppGoogle Scholar
  34. Little JDC (1955) The use of storage water in a hydroelectric system. J Oper Res Soc Am 3(2):187–197Google Scholar
  35. Lloyd EH, Odoom S (1964) Probability theory of reservoirs with seasonal input. J Hydrol 2(1):1–10CrossRefGoogle Scholar
  36. Lund JR, Israel M (1995) Optimization of transfers in urban water supply planning. J Water Resour Plan Manag 121(1):41–48CrossRefGoogle Scholar
  37. Marinoni O, Adkins P, Hajkowicz S (2011) Water planning in a changing climate: joint application of cost utility analysis and modern portfolio theory. Environ Model Softw 26(1):18–29CrossRefGoogle Scholar
  38. Markowitz HK (1952) Portfolio selection. J Finance 7:77–91Google Scholar
  39. Matalas NC (1967) Mathematical assessment of synthetic hydrology. Water Resour Res 3(4):937–945CrossRefGoogle Scholar
  40. McMahon TA, Pegram GGS, Vogel RM, Peel MC (2007) Revisiting reservoir storage–yield relationships using a global streamflow database. Adv Water Resour 30:1858–1872CrossRefGoogle Scholar
  41. Micevski T, Kuczera G (2009) Combining site and regional flood information using a Bayesian Monte Carlo approach. Water Resour Res 45:W04405. doi:10.1029/2008WR007173 CrossRefGoogle Scholar
  42. Moran PAP (1959) The theory of storage. Methuen, LondonGoogle Scholar
  43. Nandalal KDW, Bogardi JJ (2007) Dynamic programming based operation of reservoirs: applicability and limits. Cambridge University Press, 130 pp.Google Scholar
  44. NSW Government (2006) Metropolitan water plan. New South Wales Government, AustraliaGoogle Scholar
  45. Oudin L, Andréassian V, Perrin C, Michel C, Le Moine N (2008) Spatial proximity, physical similarity, regression and ungaged catchments: a comparison of regionalization approaches based on 913 French catchments. Water Resour Res 44:W03413. doi:10.1029/2007WR006240 CrossRefGoogle Scholar
  46. Perruso L, Weldon RN, Larkin SL (2005) Predicting optimal targeting strategies in multispecies fisheries: a portfolio approach. Mar Resour Econ 20:25–45Google Scholar
  47. Prattley DJ, Morris RS, Stevenson MA, Thornton R (2007) Application of portfolio theory to risk-based allocation of surveillance resources in animal populations. Prev Vet Med 81(1–3):56–69CrossRefGoogle Scholar
  48. Reichl JPC, Western AW, McIntyre NR, Chiew FHS (2009) Optimization of a similarity measure for estimating ungauged streamflow. Water Resour Res 45:W10423. doi:10.1029/2008WR007248 CrossRefGoogle Scholar
  49. Roy AD (1952) Safety first and the holding of assets. Econometrica 20(3):43–449Google Scholar
  50. SCA: Sydney Catchment Authority (2008) Supplementary submission: Sydney catchment authority pricing proposal 2008–09. Submitted to the Independent Pricing and Regulatory Tribunal (IPART), Nov 2008Google Scholar
  51. SCA: Sydney Catchment Authority (2010) Climate change impact assessment 2010. http://www.sca.nsw.gov.au/publications/publications/climate-change-impact-assessment-2010
  52. Stedinger JR, Vogel RM, Foufoula-Georgiou E (1993) Frequency analysis of extreme events. Ch 18. In: Maidment D (ed) Handbook of hydrology. McGraw-Hill, New YorkGoogle Scholar
  53. Tejada-Guibert JA, Johnson SA, Stedinger JR (1995) The value of hydrologic information in stochastic dynamic programming models of a multireservoir system. Water Resour Res 31(10):2571–2579CrossRefGoogle Scholar
  54. Troutman BM, Karlinger MR (2003) Regional flood probabilities. Water Resour Res 39:1095. doi:10.1029/2001WR001140 CrossRefGoogle Scholar
  55. Vogel RM, Bolognese RA (1995) Storage-reliability-resilience-yield relations for over-year water supply systems. Water Resour Res 31(3):645–654CrossRefGoogle Scholar
  56. Vogel RM, Sieber J, Archfield SA, Smith MP, Apse CD, Huber-Lee A (2007) Relations among storage, yield, and instream flow. Water Resour Res 43:W05403. doi:10.1029/2006WR005226 Google Scholar
  57. Wang QJ, Robertson DE, Chiew FHS (2009) A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites. Water Resour Res 45:W05407. doi:10.1029/2008WR007355 Google Scholar
  58. Warner R (2009) Secular regime shifts, global warming and sydney’s water supply. Geogr Res 47(3):227–241CrossRefGoogle Scholar
  59. Watkins DW, McKinney DC (1999) Screening water supply options for the Edwards Aquifer region in Central Texas. J Water Res Plan Manag 125(1):14–24CrossRefGoogle Scholar
  60. Willner J (1996) Privatisation of natural monopolies—comment. Rev Ind Organ 11(6):869–882CrossRefGoogle Scholar
  61. Yakowitz S (1982) Dynamic programming applications in water resources. Water Resour Res 18(4):673–696CrossRefGoogle Scholar
  62. Young RA (1986) Why are there so few transactions among water users? Am J Agric Econ 68(5):1143–1151CrossRefGoogle Scholar
  63. Zhang Y, Chiew FHS (2009) Relative merits of different methods for runoff predictions in ungauged catchments. Water Resour Res 45:W07412. doi:10.1029/2008WR007504 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Renée Kidson
    • 1
  • Brent Haddad
    • 2
  • Hui Zheng
    • 3
  • Steven Kasower
    • 4
  • Robert Raucher
    • 5
  1. 1.C/O Center for Integrated Water ResearchUniversity of California Santa CruzSanta CruzUSA
  2. 2.Engineering for Technology Management, Environmental Studies, Baskin School of EngineeringUniversity of California Santa CruzSanta CruzUSA
  3. 3.Economics and Business Building (H69)The University of Sydney Business School, The University of SydneySydneyAustralia
  4. 4.Digital Transportation CorporationStrategic Economic Applications Company (SEACO)SacramentoUSA
  5. 5.Stratus ConsultingBoulderUSA

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