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Managing water utility financial risks through third-party index insurance contracts
Harrison B. Zeff,
Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
Corresponding author: H. B. Zeff, Department of Environmental Sciences and Engineering, Rosenau Hall CB#7431, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7431, USA. (firstname.lastname@example.org)
 As developing new supply capacity has become increasingly expensive and difficult to permit (i.e., regulatory approval), utilities have become more reliant on temporary demand management programs, such as outdoor water use restrictions, for ensuring reliability during drought. However, a significant fraction of water utility income is often derived from the volumetric sale of water, and such restrictions can lead to substantial revenue losses. Given that many utilities set prices at levels commensurate with recovering costs, these revenue losses can leave them financially vulnerable to budgetary shortfalls. This work explores approaches for mitigating drought-related revenue losses through the use of third-party financial insurance contracts based on streamflow indices. Two different types of contracts are developed, and their efficacy is compared against two more traditional forms of financial hedging used by water utilities: Drought surcharges and contingency funds (i.e., self-insurance). Strategies involving each of these approaches, as well as their use in combination, are applied under conditions facing the water utility serving Durham, North Carolina. A multireservoir model provides information on the scale and timing of droughts, and the financial effects of these events are simulated using detailed data derived from utility billing records. Results suggest that third-party index insurance contracts, either independently or in combination with more traditional hedging tools, can provide an effective means of reducing a utility's financial vulnerability to drought.
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 Attractive sites for new water supply projects are becoming more scarce [Postel, 2000] and, even when available, are subject to increasing costs and challenging regulatory approval processes [Scudder, 2005]. As a result, water utilities increasingly rely on conservation strategies, both permanent and temporary, to improve the reliability and resilience of stressed water supplies [Renwick and Green, 2000]. While these strategies often offer cost-effective tools for managing water supply reliability, they can also have financial consequences.
 Water supply risk has traditionally been managed by designing sources that are sufficiently large to maintain reliability even under extremely dry conditions, leading to situations in which a significant portion of supply capacity is used only during the most severe droughts [Falkenmark et al., 1989]. Temporary conservation measures, such as restrictions on specific types of water use (e.g., lawn watering, car washing) are often implemented during these periods to reduce consumption, allowing utilities to reduce the capacity required to meet their reliability objectives. These measures can delay, or even eliminate, the need for costly infrastructure investments, but decreased water use poses a problem for water utilities given that a significant portion of their revenue often comes from the volumetric sale of water. Intermittent revenue reductions can be a particular challenge for water utilities because their costs are often dominated by invariant debt service payments, and costs, therefore, remain mostly constant despite changes in water production. Given that many utilities follow a “cost-recovery” budgetary model [Tiger, 2000], in which prices are set with the goal of returning revenues roughly in line with costs, reductions in water sales can leave them financially vulnerable during droughts. The threat of financial instability often contributes to making utilities hesitant to impose water use restrictions (and other temporary conservation measures), thereby limiting the use of an important class of demand management tools. Consequently, there may be a useful role for financial instruments that can mitigate the effects of large intermittent revenue losses through the provision of drought-related compensatory payments. This would allow utilities to make greater use of demand management approaches without compromising financial stability.
 Financial instruments are a common tool for mitigating weather-based financial risk in agriculture, mainly revolving around precipitation-based indices [Khalil et al., 2007; Barnett and Mahul, 2007; Martin et al., 2001]. When a given financial exposure to weather-based phenomena is known, contracts based on associated indices like temperature or precipitation are straightforward to implement [Stoppa and Hess, 2003; Chantarat et al., 2007] and can be adapted to cover a wide range of potential risks [Turvey, 2001; Skees and Barnett, 1999]. However, financial exposure does not always exhibit a strong correlation with weather indices, and thus payouts from many index-based contracts do not always effectively hedge the underlying financial risk [Woodard and Garcia, 2008]. More complicated contract structures have been designed to reduce “basis risk,” which occurs when payouts are needed but none are received (and vice versa). In the case of the Ontario ice-wine harvest, losses are a path-dependent function of the timing of winter temperatures, requiring contracts that adjust payouts through the winter based on the cumulative harvest [Turvey et al., 2006]. Basis risk has also been shown to be reduced for farmers in Germany when additional index parameters are included to build indices based on water capacity in the soil instead of simply precipitation [Kellner and Musshoff, 2011].
 There is a substantial body of research that describes more sophisticated contracts for physically delivering water to utilities during drought periods [Sankarasubramanian et al., 2009; Palmer and Characklis, 2009; Characklis et al., 2006; Gomez Ramos and Garrido, 2004; Lund and Israel, 1995; Michelsen and Young, 1993], but much less work has been done in the area of compensating utilities for drought-related financial losses. Drought-related losses for water utilities do not tend to be strongly correlated with precipitation or short term measures of streamflow, as the storage capacity available to the utility is often a confounding factor. Seasonal inflows to a reservoir have also been used to develop index insurance that compensates a utility for the increased costs associated with acquiring transferred water during dry periods [Brown and Carriquiry, 2007].
 While little work has been done to explore the financial risks and mitigation tools associated with reduced water consumption, there is a substantial literature on a similar phenomenon in the power sector. Financial insurance in the energy sector revolves primarily around demand-side factors [Bjorgan et al., 2009], using deviations from a standard temperature (measured as heating or cooling degree days) as a basis for compensating generators for lower than expected energy consumption/revenues [Zeng, 2000]. In the case of water, natural deviations from typical demand patterns are not often large enough to give rise to significant revenue losses, instead, it is the imposition of water use restrictions that can lead to substantial and immediate reductions in a utility's revenue stream. Furthermore, storage capacity, usually not a factor in power management, can have a significant influence on the timing and duration of water use restrictions.
 This work focuses on the development of financial hedging contracts for water utilities, with the objective of identifying highly correlated, independent indices linking hydrologic conditions with the implementation of water use restrictions and the attendant revenue losses. In order to make these contracts effective, the indices describing the timing and size of the payments must be transparent and beyond the ability of either counterparty to significantly influence (i.e., free of “moral hazard”). Correlations between the magnitude and timing of contract payouts and revenue losses (i.e., basis risk) are evaluated and compared against more traditional approaches for hedging a utility's financial risk, such as drought surcharges or self-insurance through the buildup of a contingency fund. Developing and evaluating these contracts require actuarial information related to the frequency and magnitude of drought, the conditions dictating water use restrictions, and the accompanying revenue shortfalls. Toward that end, hydrologic and financial data from the Department of Water Management in Durham, North Carolina are used within a model that quantifies the utility's financial risks under a set of defined demand management policies. The ability to mitigate the financial variability that accompanies these policies will be an important consideration in determining when, and to what degree, they will be implemented. The results should provide information valuable in making these choices, but also general insights that may be useful in the development of water resource planning strategies.
 Creating a predictive financial risk model requires knowledge of a utility's water supply profile and how it translates into relevant financial measures. To this end, Durham's current pricing structure, demand profile and billing information were integrated with a multireservoir model of its supply system developed in previous work [Palmer and Characklis, 2009]. Three different risk mitigation approaches are then used to hedge the financial risk arising from the imposition of outdoor water use restrictions, the method most commonly used by utilities (including Durham) to reduce water consumption during dry weather periods.
2.1. Financial Hedging
 The unpredictable nature of drought, and hence the imposition of water use restrictions, make the resulting revenue losses difficult for utilities to plan for and absorb. Nonetheless, increasing water demand, combined with the challenges of developing new water supplies, suggest that that the use of restrictions will become more common in the future. Consequently, revenue shortfalls are likely to grow in a manner that will leave utilities with larger and more frequent disruptions. Recognizing this, some utilities have already begun to employ measures such as drought surcharges and contingency funds as a means of ensuring financial stability. While these approaches can be effective, third-party financial insurance contracts and hybrid combinations involving more traditional approaches may provide new alternatives.
2.1.1. Drought Surcharges
 During periods when water use restrictions are in place, utilities can increase prices to compensate for lost revenue while also providing incentives for their customers to conserve. The combination of restrictions and higher prices, however, tends to be unpopular with consumers [Tiger, 2009], and utility managers often find the implementation of substantial drought surcharges to be politically challenging. The city of Durham currently employs a relatively progressive five-tier increasing block rate pricing structure, and consultations with utility personnel in Durham yielded several different surcharge schemes that they deemed to be acceptable, including either a 20%–30% surcharge on: (i) all customers; (ii) all commercial, industrial, and outdoor use (but not residential users); and (iii) customers in the highest usage tier (i.e., more than 11,000 gal/month). In addition, a fourth surcharge scheme was developed to explore how much prices would need to rise to compensate for nearly all of the conservation-related revenue losses (the standard here, used for contingency funds as well, is a scheme providing a 95% probability that losses will not exceed 1% of revenues). In all cases, the reduced consumption resulting from both usage restrictions and higher prices is considered.
2.1.2. Contingency Funds
 Through annual contributions to a contingency fund, a utility can accumulate resources during years without water use restrictions and use them to compensate for revenue losses during years in which restrictions are imposed. The constant payments to such a fund are attractive to utilities from a budgetary perspective, but the variability of drought still creates challenges. A contingency fund could theoretically provide protection against any potential revenue shortfall, but maintaining a fund large enough to compensate for the impacts of multiple droughts over a period of several years, or an extended multiyear drought, would require annual contributions far in excess of expected revenue losses. Another practical limitation is the challenge of preserving these funds for their intended use, particularly when they remain unused for lengthy periods (and have, therefore, grown relatively large), as they may be appropriated by cash-strapped municipal governments for other purposes. Other concerns involve rate-payer perception and bond covenants that limit the accumulation of funds for anything other than capital improvements.
 When determining the appropriate size for such a fund, utilities must balance contribution size, potential growth of the fund over time (including interest on unused funds, assumed to grow at 5% annually), and the degree of financial protection provided against revenue losses. Several contingency fund scenarios are explored and then compared on the basis of their effectiveness in limiting the probability of revenue losses greater than some specified percentage of total revenues.
2.1.3. Third-Party Financial Insurance Contracts
 Financial insurance contracts allow the buyer to transfer some of the financial risk of drought to the “writer” (i.e., seller) of the contract, presumably a third-party insurer with a sufficiently large and diversified asset base to absorb the costs of such events. From the utility's perspective, third-party contracts might be attractive as they involve both constant payments and the insurer absorbing the risks of high-cost, low-frequency events (e.g., multiple droughts over a few years or a long, multiyear drought) that would otherwise require the maintenance of large, infrequently used contingency funds. Assuming that a utility were interested in protecting itself against all drought/restriction-related losses (unlikely, but a useful example), expected losses evaluated over the long-term would serve as the initial basis for a third-party insurer's calculations of the price for this type of contract. Of course, the insurer would then add factors related to return on investment and a “risk premium” (the insurer's hedge against a range of unknown factors). In addition to paying the return/risk premium, the utility would also give up the benefit of returns on the unused portion of the payments made to their contingency fund. It is worth considering, however, that third-party contracts would allow a utility to transfer unknown risks to the insurer as well (hence the risk premium), which include hydrologic variability arising from changes in climate and/or land use, or even underestimates of drought frequency based on short-historic records.
 A significant challenge in developing third-party contracts is identifying independent indices that correlate well with water use restrictions (i.e., revenue losses). Third-party insurance contracts typically involve some level of basis risk, and the ideal contract would minimize basis risk using independently verifiable indices that would be difficult for either the insurer or the insured to manipulate. Low-precipitation levels are the underlying cause of drought and water use restrictions, but hydrologic and geographic factors often lead to correlations between rainfall and reservoir storage (the source for most large water utilities) being relatively weak. Reservoir inflow is a more obvious candidate, but water use restrictions are difficult to anticipate with short-term (e.g., weekly) inflows alone. Utilities typically have sufficient storage to prevent a dry month, or months, from motivating water use restrictions, thus it is necessary to use indices reflecting longer cumulative trends.
 Within the energy sector, the heating and cooling degree day indices (HDD/CDD) are the basis for hedging contracts. In this case, a baseline temperature is established (usually 65°F, the temperature at which little heating and/or cooling is used) and deviations between daily mean temperatures and the baseline accumulate at daily intervals. Aggregate values for HDDs or CDDs can then be compared with threshold HDD/CDD values reflective of historic temperature patterns. These differences generally correlate well with deviations from historic power demands for heating and cooling services, which tend to dominate overall power use. When the thresholds are crossed, contract payouts are specified to compensate the contract holder for the resulting revenue losses [Cao et al., 2003].
 These contracts provide a good framework for dealing with financial risks in the power sector, but storage represents a crucial difference between water and power utilities when trying to hedge against financial uncertainty. Water is easier and less expensive to store than electricity, allowing water utilities to meet demand even during periods when demand temporarily exceeds supply (e.g., reservoir inflow). Many utilities already use reservoir storage as a trigger for water use restrictions, so insurance contracts could include a threshold value related to storage, but there must also be some consideration of the rate at which storage is both increased through inflows and depleted through withdrawals and releases. Here contracts are evaluated based on their ability to minimize basis risk by returning payouts of the appropriate magnitude during the years in which revenue losses are experienced. Two contract types with different approaches to minimizing basis risk are explored.
2.1.4. Drawdown Contracts
 The first contract is relatively straightforward and uses an index that compares weekly reservoir inflows to a defined baseline of reservoir “withdrawals,” which include average historical demand from utility customers, evaporation, and any mandatory releases (e.g., environmental flows). A withdrawal baseline (WB) for each week of the year is developed that reflects seasonal changes in historical reservoir withdrawal patterns, such that
where i = week of the year, i = 1, 2, …52; WBi = withdrawal baseline for week i (million gallons, MG); Evi = average historical evaporation in week i (MG); Ri = mandatory releases in week i (MG); and Di = average utility demand in week i (MG).
 When inflows to a reservoir in a given week fall below this weekly withdrawal baseline (WB, the reservoir is likely to be drawn down. The deficit that accumulates over time is designated as “drawdown” flows (DF), which are tracked over the course of the contract period (Figure 1), which begins in week i = mStart and ends in week mEnd, of any given year, such that
where mstart= the first week in contract m; mend = the last week in contract m; and I = weekly inflow (MG).
 Presuming that the imposition of water use restrictions is linked to reservoir storage (as is typically the case for utilities using surface water), contracts can be written against the DF index to take advantage of the correlation between drawdown flows and the revenue losses resulting from water use restrictions. In this case, each drawdown flow contract is small, designed to provide $1 for every million gallons (MG) of cumulative drawdown flows that exceed the specified drawdown threshold (Figure 2), and therefore scalable to allow the utility to vary the number of contracts to a desired level of financial protection.
 Assuming a scenario in which a contract period begins with a full reservoir and a utility that wants their hedging contracts to begin paying out as soon as water use restrictions are implemented, the drawdown flow threshold (x) would be set to reflect the difference between reservoir capacity and the storage volume that would trigger restrictions. The drawdown threshold could also be set higher (i.e., for a lower reservoir level) such that payouts would only begin during more severe droughts when revenue losses became large. The degree of mitigation would depend on the number of contracts purchased. The contract price, assumed to be annual, is determined by estimating the expected number of drawdown flows that accumulate in excess of the threshold using the historical (or synthetic) streamflow record. A factor is also included to account for both return on investment and a risk premium (RR), such that
where Cm = contract price in period m ($/yr); j = index of years in historical/synthetic inflow record, j = 1, 2,…N; DFi,j = drawdown flows based on inflows in week i of year j in historical/synthetic record (MG); and xm = drawdown flow threshold specified in contract m (MG).
 If these contracts were to become common, the return/risk premium would be determined by a combination of market competition and the variability of the hydrologic system in question. However, the market for even the most commonly traded weather index-based insurance products is not very liquid, and calculations of the market rate of risk based on actual option prices can be highly erratic [Alaton et al., 2002]. Given the highly regional nature of drought, these types of contracts are also unlikely to be traded in any significant volumes. Insurers would, therefore, be likely to price the risk based the expected contract payout as well as some measure of the contract payout variability. To calculate the risk/return premium, RR, for the various contracts developed in this paper, market rate of risk is calculated such that,
where σ = standard deviation of annual contract payouts and λ = market rate of risk.
 Market rate of risk (λ) is assumed to be constant for all contracts, making the risk premium on contracts dependent on a measure of the “spread” of the potential contract payouts. Data from HDD/CDD option contracts [Cao and Wei, 2004], suggests that a risk premium of 12% is appropriate benchmark for the relatively simple “drawdown” contracts, described in equation (3). “Drawdown” contracts serve as a baseline to be used in RR calculations for the more complex contracts described in later sections. The implied λ from the initial case and the σ of a specific contract type's predicted payout distribution are used to determine the overall RR (Table 1).
Threshold altered to correspond to stage 2 (or higher) water use restrictions.
Replicates water use restriction triggers
Replicates water use restriction triggers
Probability of contract payouts
Average annual contract payouts
Contract risk premium (RR)
Probability of payouts greater than revenue losses
Average excess payout
Probability of payouts less than revenue losses
Average payout shortfall
 Reservoir storage at the time that the insurance contracts are purchased also has an impact on contract price. Low reservoir storage at the time of purchase will increase the likelihood of water use restrictions, so if contracts are to provide the same level of mitigation, the drawdown flow threshold must be decreased. As this lower threshold has a higher probability of being crossed, the price of the insurance contracts will increase. For the sake of comparative consistency, contracts described here are assumed to be purchased once per year at the beginning of the irrigation season (April), when Durham reservoir levels are typically full.
 It is important to note that the contract premium-payout schedule is not dependent on actual physical conditions (i.e., the reservoir storage at any point in time), but rather on the volume of drawdown flows which, given a reasonably accurate model, should be well correlated with reservoir storage. The accounting involved resembles a water balance model in which the only input not established at the time of contract signing is reservoir inflow (I). As inflows can generally be tracked independently and transparently, there is little opportunity for problems related to moral hazard. Note that even if a utility were to deliberately misrepresent its average weekly demand schedule (Di) it would be afforded no financial advantage. Any additional payouts arising from the misrepresentation would be reflected in the actuarial calculations determining the contract price paid by the utility. Of course, if contract payouts and losses are to be highly correlated, this water balance approach must be sufficiently accurate that an honest accounting of demand (and evaporation and mandatory releases) leads to accurate estimates of reservoir level. With respect to surface water applications, a water balance approach typically yields estimates that represent the state of the reservoir very well. It should be noted, however, that while there may be a temptation to assume that these hedging contracts could be easily translated to applications involving groundwater (i.e., underground “reservoirs”), difficulty in accurately characterizing subsurface processes would likely complicate matters.
184.108.40.206. “DUBSO” Contracts
 Although drawdown flows address some potential sources of basis risk, some aspects of water storage available to utilities remain which confound the relationship between streamflow and revenue losses related to water use restrictions. For example, water use restrictions can sometimes be avoided during an exceptionally dry period if a large storm rapidly refills reservoirs in the middle of such a period, even as a large volume of drawdown flows would be recorded. More detailed indices can lead to greater correspondence between revenue losses and a system's hydrologic behavior, forming the basis of more sophisticated index insurance contracts. In this case, a new index, “Filling flows” (FF) is defined, which accounts for flows that exceed typical WB withdrawals, such that
 A small correction is required to equation (4) in that filling flows that occur when the reservoir is full are released downstream as spillage and have no effect on reservoir storage. Spillage can be calculated using a water balance model that uses filling flows as the only inputs and draw down flows as the only outputs, such that
where Wi = spillage in week i (MG); RC = reservoir capacity (MG); RSo = initial reservoir storage (MG); t = prior week during contract period, t = 1, 2, …, i.
 Filling flows calculated in equation (4) must be modified to include spillage from equation (6) such that,
 With the updated measure of filling flows equation (7), current reservoir storage can be estimated in any week i, such that:
where S = estimated reservoir storage.
 This estimate of storage volume can be incorporated into a contract using both the filling and drawdown flow indices. Financial contracts are commonly written using the difference between two variables, referred to in the financial literature as “spread options” [Zhang, 1995], and the difference between drawdown and filling flows can be used to correlate contract payments with periods of use restrictions. If, in a given week, the estimated storage, Si, drops below the storage volume used by the utility to trigger use restrictions (zm), contracts can be designed to trigger a payout. No payouts occur during weeks in which storage is above this threshold. This type of all-or-nothing contract is often labeled as a “binary option.” Here the contracts are designed to payout $1 in each week when thresholds have been triggered, such that
where Pi = contract payouts in week i and zm = storage threshold specified in contract m (MG).
 The $1 payouts provided by these contracts allow for scalability to any desired level of financial protection. Payouts occur in each week in which thresholds have been triggered, so a utility desiring full mitigation could purchase a number of contracts equal to the expected revenue losses from 1 week of water use restrictions. The contract price (Cm) can be calculated using a historic (or synthetic) streamflow record of length “N” years to determine the expected value of potential payments calculated in equation (9), plus the return/risk factor, such that
 A contract with this basic structure is flexible enough to adapt to more complex rules that describe the timing of, and degree to which, water use restrictions are employed. More sophisticated contracts become attractive when it is considered that utilities often employ water use restrictions in multiple stages, mandating larger reductions in water consumption, and therefore larger revenue shortfalls, as reservoir levels fall. In such a case, more sophisticated contracts can be developed to increase payouts when reservoir storage thresholds for these higher restriction stages are crossed. Some utilities also change the reservoir levels that trigger use restrictions over the course of the year to better reflect the varying risk of shortages arising from changes in seasonal streamflow and demand patterns, patterns that can also be reflected in the threshold levels used in the contracts. Other utilities wait to lift restrictions until such time as the reservoirs rise to levels significantly higher than those used to trigger restrictions initially (a cautionary hedge against short-lived recoveries).
 All of these scenarios apply to the rules used to govern water use restrictions implemented by the City of Durham. While payouts from multiple stages of restrictions and seasonally variable restriction thresholds can be accommodated within the framework of equation (8), the contract structure needs to be modified to account for operation rules that employ both “down-and-in” thresholds, which trigger restrictions and contract payouts, and different (i.e., higher) “up-and-out” thresholds, which lift restrictions and signal an end to contract payouts. Each “down-and-in, up-and-out, binary spread option” (DUBSO) contract provides a $1 payout every week in which the storage value (Si) falls below the “down-and-in” threshold (zm), until it has risen above the higher “up-and-out” threshold (z*m). When using model simulations to assess contract performance in this scenario, DUBSO contract payouts in week i become dependent on payouts from the previous week. If Pi−1 = 0 (indicating that the initial threshold triggering payouts has not been crossed), Pi can be determined from equation (8), but if Pi−1 = 1 (indicating that the initial threshold has been crossed and payouts are being made), then a payout is made, such that
where z*m = “up-and-out” storage threshold used to lift water use restrictions (MG).
 Once new potential payouts have been calculated using historical (or synthetic) streamflows, the price of a “DUBSO” contract can be determined using equation (9).
 Expected revenue shortfalls from each restriction stage, combined with the level of mitigation the utility desires, can be used to evaluate the quantity of $1 contracts a utility purchases. Using this structure, payments can also be provided to mitigate the increasing revenue shortfalls that occur during higher restriction stages, as extra contracts can be purchased using thresholds corresponding to each restriction stage. As with the drawdown contracts, the payments of DUBSO contracts are dependent on only one real-time input, streamflow, thereby reducing concerns over moral hazard.
220.127.116.11. Hybrid Schemes
 Surcharges, contingency funds, and third-party contracts can also be combined to reduce the financial risk of water use restrictions. Two examples are described here in which third-party contracts designed to mitigate the impacts of more extreme events (by setting higher threshold values) are combined with surcharges or contingency funds designed to limit the effects of more frequent, but less severe, drought events.
2.2. Study Region
2.2.1. Reservoir Simulation Model
 The city of Durham's Department of Water Management operates two reservoirs with 6.35 billion gallons of capacity. A reservoir simulation model was used to determine the frequency and severity of revenue losses due to water use restrictions, based on estimations of inflows, withdrawals, releases, and evaporative data. Historical reservoir inflows were used to validate simulated reservoir storage levels against observed storage, as demonstrated in earlier work [Palmer and Characklis, 2009]. Validation included assessment of the Nash-Sutcliffe efficiency (0.95), percent bias (0.81%), and the root mean square error observations standard deviations ratio (0.22), all of which fall within the “very good” category of model evaluation performance ratings as outlined by Moriasi et al. .
 The reservoir simulation model was then expanded to include the use of synthetic reservoir inflow records to allow for the analysis of a broader range of hydrologic scenarios, and a more detailed set of actuarial estimates. In this case, synthetic streamflows are generated using a modified Fractional Gaussian Noise approach, labeled the “Autocorrelated Bootstrap” method [Kirsch et al., 2012] which reproduces standard statistical moments, as well as variations in the seasonal autocorrelation observed in the historic record. This approach is used to generate 50,000 unique 16 year synthetic streamflow records representing the period 2010–2025, which are then used in Monte Carlo simulations. It is important to note that revenue losses and contract payments are calculated using two reservoir simulations which are essentially water balance models running in two parallel, but slightly different forms. When estimating revenue losses, the model considers the inverse correlation between demand and streamflow [Mitchell et al., 2001], choosing demand values through use of monthly joint probability density functions (PDFs) derived from the historical demand record (corrected for annual growth) and the corresponding historical streamflow data. Two joint PDFs were used to account for changes in this correlation over the course of the year, one for the irrigation season, April through October, and another representing the wetter months of November through March. This water balance also accounts for reductions in water consumption during water use restrictions. When evaluating the performance of the third-party contracts, a parallel simulation uses the withdrawal baseline value estimated for each time step at the time of contract purchase instead of an “actual” consumption value, tracking drawdown and/or filling flows to assess the frequency and magnitude of contract payouts. Deviation between the withdrawal baseline and demand in any given week is not typically large, but does give rise to some degree of basis risk (i.e., mismatch between losses and payouts), more so for drawdown flow contracts, a topic that will be revisited.
2.2.2. Water Use Restrictions
 Like many utilities, Durham employs multiple stages of water use restrictions, with these applying to both residential irrigation and large consumers in the commercial and industrial sectors. Implementation is linked to reservoir storage thresholds, but due to seasonal changes in water use and streamflow patterns, these thresholds vary by time of year. From April to October, Stage 1 restrictions are implemented when total reservoir storage falls below 80% of storage capacity. During the nonirrigation (November–March) season, reservoirs are allowed to drop to 45% of the total storage volume before water use restrictions are put in place. Stages 2, 3, and 4 restrictions are implemented when reservoirs reach 60, 45, and 35% of storage capacity, respectively, during irrigation season and 40, 35, and 25% during nonirrigation season. Although Durham has not strictly adhered to these defined thresholds in the past, N. C. recently passed SL 2008-143, commonly known as the Drought Management Act, which, among other provisions, mandates that utilities enact restrictions at (or before) their planning thresholds.
 Data from earlier droughts demonstrate that reductions to outdoor water use and large commercial/industrial users progressively increase as water use restrictions become more severe. Overall, water use is expected to decrease by 15% in irrigation season and by 7% in nonirrigation season use during Stage 1 restrictions. In Stages 2 and 3, restrictions are expected to achieve reductions of 30 and 40%, respectively, during the irrigation season, and 12 and 17% during the nonirrigation season. Stage 4 restrictions are considered a water emergency, and reductions of 55% and 30% during the irrigation and nonirrigation season are expected. This difference between the expected (i.e., unrestricted) water demand and consumption levels under restrictions serves as a basis for estimating utility revenue losses.
2.2.3. Utility Revenues
 Two-part tariffs face an inherent tradeoff between the revenue stability provided by fixed fees and the conservation signals sent by volumetric rates [Mohayidin et al., 2009], yet appear to be reasonably efficient for natural monopolies such as water utilities [Brown et al., 1992; Griffin, 2001]. In reaction to two significant droughts during the past decade, Durham has increased the emphasis it places on conservation signals by altering its volumetric rates to include a five-tier increasing block structure. To avoid having to independently meter sewer use, utilities typically link volumetric sewer charges to water use, and this is also the case for Durham, which charges one volumetric rate for sewer services. The average volumetric revenue from water use is equal to the weighted average of water use within each rate tier, plus the additional volumetric sewer charge. Increased irrigation during the summer significantly changes the distribution of usage in each rate tier, causing seasonal variations in average water revenue. The average volumetric revenue from water use also changes when restrictions are implemented, because water conservation changes the distribution of water use by tier. The average monthly usage distributions among the tiers are calculated using billing data provided by Durham's Department of Water Management. Within the model, modifications are included to account for reductions in consumption resulting from drought surcharges, which involves using demand elasticities derived from a rate study done for a neighboring community [Burton and Associates, 2007]. The impacts of restrictions on each tier were assessed considering both tiered water rates and sewer rates. Revenues are evaluated at weekly intervals over 50,000 realizations reflecting conditions described by the reservoir simulation model over the period 2010–2025. Analysis suggests that significant revenue losses are likely as early as 2015, increasing further by 2025 (Figure 3), estimates that are consistent with extrapolations of Durham's recent experiences.
 With knowledge of the distribution of revenue losses, a utility can make informed decisions regarding the level of financial risk mitigation it would like to purchase via third-party contracts, including both the number of contracts and the desired threshold levels. With respect to drawdown contracts, a utility interested in trying to completely mitigate all revenue shortfalls could simply divide expected revenue losses by the expected volume of drawdown flows that exceed the threshold (set to reflect the reservoir level at which restrictions are imposed), and determine the number of $1 contracts required. The threshold and number of contracts could also be calibrated such that the utility is insured against only more severe droughts.
 Simulations are run over the period 2010–2025, during which the city of Durham does not expect to have any new water sources come online. Long-term demand predictions used in the model could be reduced, of course, through structural conservation-related activities (e.g., retrofits, building codes), lessening the city's vulnerability to revenue losses, but these are not considered as part of this work. Thus, the scenarios modeled here are considered to be reflective of current trends with the exception of the employment of the three mitigation instruments considered.
2.2.4. Limitations and Caveats
 This paper explores whether index insurance contracts have the potential to be useful to water utilities concerned with drought-related revenue variability. The development of a fully theoretical framework for the pricing of streamflow-based index insurance is outside the scope of this paper, and the pricing of risk will likely be left to the individual firms writing and purchasing contracts. Even the most commonly traded forms of weather derivatives, such as HDD/CDD contracts, have limited liquidity in the market and are subject to large bid/ask spreads. The contracts described in this paper are likely to require even greater customization subject to highly variable valuations of the “market price of risk,” with more sophisticated methods of valuation then are used here.
 With respect to hydrologic considerations, these contracts are applied to single-purpose reservoirs that generally refill each year, a situation that does not exist in all regions. Many reservoirs, particularly in the Western United States, are built to hold several years of water supply and do not refill every year. In this case, contracts would have to be written for a number of years at a time, not a single year as is the case for Durham. However, growth in water demand is fairly predictable in most places and predictions over a useful contract period (e.g., 5–10 years) are generally reliable. Multiuse reservoirs (e.g., hydropower, recreation) may also complicate matters as they tend to have more complex release schedules, which could make the development of a “‘withdrawal baseline” more complex. Basis risk for large, multiuse reservoirs may be greater than those observed in the Durham example used here, and further work would be needed to accurately describe contract performance for those systems.
 Results indicate a 32% chance of Durham implementing water use restrictions at some point during the year 2015, growing to 37% by 2025 (Figure 3). The average total volumetric revenue for the Durham Department of Water Management is predicted to be $84.7MM in 2015 and $95.4MM in 2025, but expected losses due to water use restrictions in 2015 projected to be $0.7 million (MM), growing to $1.2MM in 2025. However, there is a 5% chance of losses greater than $3.0 million in 2015, and a 1% chance they will grow to at least $5.3MM. By 2025, annual losses grow to at least $4.8MM in 5% of simulations and 1% of simulations reach $8.2MM, indicating a reasonable probability of unplanned revenue shortfalls between 4 and 8.5% of total annual volumetric revenue, a level that Durham personnel suggest would be quite disruptive.
3.1. Drought Surcharges
 Relative to a “no mitigation” scenario, significant reductions in revenue shortfalls are seen when surcharges are applied to all users (Figure 4), but are less effective when targeted at only commercial/industrial users or high-volume users (>11,000 gallons per month). Across all cases, the difference between a 20% and 30% surcharge were relatively small, so only the results from the 30% increase are shown. The groups targeted by the surcharges, high-volume water users in particular, have relatively high demand elasticity [Burton and Associates, 2007], leading to larger reductions in consumption as prices rise. Consequently, there is a somewhat counterintuitive result in that applying a 30% surcharge to the highest volumetric usage tier, expected revenue losses in 2015 increase from $0.72MM to $0.75MM. Surcharges on all commercial, irrigation, and industrial use leads to a more intuitive result in that they decrease expected shortfalls to $0.70MM. The effects of drought surcharges on the more extreme scenarios are smaller. In 2015, there is a 1% probability of revenue losses above $5.0MM when using a 30% drought surcharge on commercial, irrigation, and industrial use, a small decrease relative to the no mitigation scenario. Applying a 30% surcharge to all users is more effective, reducing expected revenue losses below $0.50MM and losses at the 1% level to around $2.7MM.
 While current utility thinking is that surcharges over 30% are unlikely to be implemented, an investigation of higher levels yielded interesting results. In this case, all customers were targeted with surcharges of 40% in excess of their normal tiered prices in each block, resulting in a risk profile in which the utility has a 95% probability of preventing losses greater than 1% of annual volumetric revenue (a comparative standard that will be used with contingency funds as well). It is common for utilities with increasing block rates to exempt the first rate block (in Durham's case, <3750 gallons per month) from drought surcharges to allow “essential” water uses to remain at a constant rate. In order to achieve the same level of mitigation (95% probability of preventing losses greater than 1% of annual volumetric revenue) without applying surcharges to the rate block, surcharges must be increased to 50% on all other customers.
 In general, this analysis also yielded evidence of drought surcharges being less effective at compensating for extreme events because larger revenue losses correspond to droughts that last longer and require greater reductions in consumption (as a result of increasing stages of drought measures). When reductions in consumption are larger, less revenue can be raised by assessing surcharges. Surcharges also disproportionally affect outdoor water use, and longer restrictions tend to extend into the nonirrigation season when less water is used outdoors, thereby limiting their ability to increase revenue.
3.2. Contingency Funds
 A tradeoff exists between the effectiveness of a contingency fund, the size of the annual contribution, and the expected amount of unused funds that accumulate over time. For comparative purposes, the funds described ensure that revenue losses remain below 1% (or 0.5%) of annual revenue in 95% or 97.5% of all simulations (Figure 5), even as losses in the remaining simulations can grow significantly larger. A fund meeting the 95% benchmark requires an annual utility payment to the fund of $0.8MM (i.e., mitigation costs), resulting in an expected accumulation of reserve funds on the order of $2.7MM by 2015. There is also a 13% chance that the contingency fund would remain unused in the six years from 2010 to 2015, resulting in a $5.2MM accumulation of reserve funds. If annual losses are limited to 0.5% of total volumetric revenue 95% of the time, the annual contribution to the fund increases to $0.9MM, raising the expected amount of the reserve fund to $3.0MM, with a 13% chance that it would not be drawn on and thus grow as large as $6.2MM. Increasing the confidence level associated with contingency fund protection to 97.5% requires somewhat larger annual contributions and a commensurate increase in the expected size of the accumulated reserve. Given the organizational relationship of Durham's Department of Water Management to the larger city government, department personnel have expressed doubts that a fund this large could be maintained over time without being appropriated for other purposes.
3.3. Third-Party Hedging Contracts
 Drawdown contracts have annual costs of $0.8MM in 2015, similar to the contribution to a contingency fund maintaining losses below 1% of annual revenue in 95% of simulations. The worst case revenue losses, at least $0.9MM in 5% of simulations and at least $2.1MM in 1% of simulations, are slightly higher and lower, respectively, than those indices for the same contingency fund. The DUBSO contracts provide for greater correlation between insurance payouts and revenue shortfalls, mitigating almost all the financial risk from water use restrictions, even during the worst case scenarios (Figure 6). However, DUBSO contracts have slightly higher annual costs ($1.2MM in 2015) because they provide utilities with payouts slightly higher than their expected revenue losses (Table 1).
 Drawdown and DUBSO contracts can also be written with increased thresholds, causing payouts to be less frequent, but to occur during more severe droughts with larger revenue losses. These contracts increase the expected basis risk, but also decrease the annual contract cost (Figure 6). In 2015, the costs of drawdown flow contracts with thresholds designed to trigger payments only after stage 2 restrictions have been implemented are only $0.2MM (down from $0.8MM with original thresholds), but expected revenue losses increase to $0.6MM. For DUBSO contracts, annual costs are reduced from $1.1MM to $0.4MM, but expected revenue losses are $0.4MM. These altered thresholds do, however, limit exposure to more severe revenue losses effectively. With higher (altered) thresholds, drawdown flow and DUBSO contracts allow only a 1% probability of revenue losses over $3.9MM and $3.0MM, respectively, down from $5.3MM with no mitigation.
 The combination of third-party contracts using altered thresholds (i.e., those that mitigate more severe losses), and contingency funds, which can be designed to reduce the impact of less severe events, can also be effective. Such a hybrid scheme compares favorably to either approach used independently, both in terms of annual cost to the utility and the resulting probability of revenue (Figure 7). When DUBSO contracts provide payments during extreme droughts (i.e., droughts which trigger at least stage 2 restrictions), the additional annual contribution required to maintain a 95% probability of revenue losses less than 1% of revenue drops to $0.4 MM. When this cost is combined with the $0.4MM annual cost of DUBSO contracts, the total annual payment is $0.8MM, roughly equivalent to a similar contingency fund (95% probability of revenue losses less than 1% of total revenue). However, this hybrid mitigation provides greater protection against extreme events (those at the 1% level or above), results in an accumulation of reserve funds that is substantially smaller ($1.8MM versus $2.7MM) and has expected revenue shortfalls ($0.2MM) that are only 65% of the shortfalls experienced when using the contingency fund alone.
 Drought surcharges can also be combined with DUBSO contracts. Surcharges alone have some effect in reducing expected revenue losses, concentrating their effects on the smaller, more frequent losses not covered by the insurance contracts. However, their effect is limited, as discussed previously. Combining one of the more realistic surcharge scenarios, a 30% price increase on all users, with DUBSO contracts using increased thresholds has only a small change in effect over what would have been seen using the altered DUBSO contracts alone (Figure 7). Protection against larger revenue losses is limited to less than $3.0MM at the 1% level, and expected losses are roughly half of what would occur with no mitigation.
3.4. Basis Risk
 All of the financial tools described in this paper involve some amount of basis risk, resulting in revenue losses which remain after mitigation has been applied. Basis risk occurs when utilities self-insure if the contingency fund is not adequate to cover all existing losses (Figure 8). When a contingency fund is large enough to ensure revenue losses remain below 1% of annual revenue in 95% of years, the Pearson's correlation between revenue losses and payouts from available funds is 0.88. Drawdown contracts are structured to provide payouts proportional to the volume of drawdown flows in a given contract periods, but the relationship between revenue losses and drawdown flows is not linear, resulting in significant basis risk during years with larger revenue losses. The more complex DUBSO contracts have less basis risk than simpler drawdown contracts, but a tendency to provide payouts that are slightly larger than revenue losses, particularly in years with high-revenue losses, increases basis risk and adds to the overall cost of the contract. The Pearson's correlation between DUBSO contract payouts and revenue losses is 0.96, compared to a correlation of 0.81 for drawdown contracts. When DUBSO contracts using increased thresholds are combined with small contingency funds, the basis risk in years with large revenue losses is significantly reduced. Although some basis risk remains (Pearson's correlation = 0.95), it is primarily limited to years with small revenue losses.
 It is worth noting that any lost revenue and/or mitigation costs is likely to eventually be passed along to utility customers in the form of increased prices. However, the price increases needed to cover these losses/costs will be relatively small. In 2015, the expected revenue losses due to water use restrictions are only 0.85% of the total annual revenue collected from volumetric water charges. In 2025, this value increases to 1.25% of total annual volumetric revenue. Additional costs accrued to utilities from mitigation measures, including such factors as return/risk premium payments to third parties, will increase this only slightly. Including the revenue losses which remain as a result of basis risk, a contingency fund with an annual contribution of $0.8MM only represents a total cost to the utility of 1.3% of annual volumetric revenue in 2015, and drawdown and DUBSO contracts cost the utility, respectively, 1.0% and 1.4% of annual volumetric revenue. As such, customer price increases required to accommodate these types of financial management strategies are likely to be minimal.
 Reconciling growing water demand with a slower pace of supply development will require water managers to take advantage of a variety of management strategies to maintain the reliability of their water sources. Conservation measures involving water use restrictions are likely to figure prominently in these plans, but the resulting revenue losses and financial instability present a disincentive to utilities considering their implementation. While more traditional approaches, such as drought surcharges and contingency funds, can limit the impact of revenue losses arising from these conservation measures, this investigation suggests that third-party contracts, even the simpler drawdown form, also have the potential to be effectively employed. Whether used independently, or in combination with surcharges or contingency funds, third-party contracts offer several advantages that may make them attractive to water utilities, even when accounting for the additional costs of including third-party returns and risk premium. The contracts allow water utilities to protect against large swings in revenue without the need for substantial price increases during drought or the maintenance of large contingency funds. They also allow the utility to transfer the financial risk of unlikely events, such as extended or successive droughts, to a third party. While such instruments are not currently available, there appears to be a reasonable case to be made that they could play a useful role in the future, as demand management strategies become a more prominent part of water resource planning.
 The authors would like to thank the Water Resources Research Institute of the University of North Carolina for its support of this work (project 70250). Thanks also to individuals at the Durham Department of Water Management (Vicki Westbrook), Orange Water and Sewer Authority (Ed Holland, Pat Davis) and Town of Cary (Leila Goodwin and Syd Miller) for their data and knowledge regarding their water supply systems. Concepts related to the third-party index insurance products described in this work are subject to a pending patent.