Long run water pricing strategy to optimize return and minimize affordability risk: Application of the Kelly Criterion to water utility revenues

Abstract:

Water service providers (hereafter “utilities”) in the U.S. have steadily implemented rate increases to offset rising material costs, declining demand, variable supply, and mounting regulatory pressures. As rates increase, customers and utilities face “affordability risk”: customer payments exceed affordability limits. While water utilities generally enjoy low delinquency and nonpayment levels, continued rate increases and unforeseen disruptions to local government services could increase delinquencies, potentially to the point of threatening overall utility revenue. We propose a new method to evaluate water utility pricing strategies, which have previously focused on consumption risk and time spans < 5 years, far less than the typical multi-decade duration of infrastructure. The method is a modified use of the Kelly Criterion, an optimal betting strategy derived from information theory, now increasingly used in portfolio management. The Kelly Criterion can dynamically address affordability risk over multiple periods. Key to our approach is conceptualizing water utilities as investors (who must constantly make allocation decisions), and different customer types (e.g., residential, commercial, industrial) as individual holdings in an investment portfolio. We apply our modified Kelly method to model the cumulative effects of non-payment on overall revenue growth in cities with a stable, increasing, and decreasing population. Through Monte Carlo simulations and Bayesian probabilistic methods, we determine the optimal price increase strategy for a utility (the “bet”) to implement annually. Preliminary results show differences in optimal pricing for shrinking versus growing cities, and importance in planning methods to account for “black swan” shock events (e.g. moratorium on shutoffs during Covid pandemic) in non-payment/delinquency levels. We show the cumulative gain from dynamic adjustments to pricing strategies with knowledge of changing affordability risk.