Linear Pricing Research Articles

Tackling nonlinear price impact with linear strategies

AbstractEmpirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, if the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.

Is Capital Structure Irrelevant with ESG Investors?

Abstract This paper examines whether capital structure is irrelevant for enterprise value and investment when investors care about environmental, social, and governance issues, which we refer to as “ESG-Modigliani-Miller” (ESG-MM). Theoretically, we show that ESG-MM holds with linear pricing and additive ESG. ESG-MM means that issuing low-yielding green bonds does not lower the overall cost of capital because it makes the issuer’s other securities browner. Hence, a firm’s incentive to make a green investment does not depend on its financing choice. We provide suggestive evidence of failure of ESG-MM, implying that firms and governments can exploit inconsistent ESG attribution or segmented markets. (JEL E22, G12, G32, G4, H23, Q56)

The relative importance of economic policy uncertainty and geopolitical risk on U.S. REITs returns

PurposeOur aim in this study is to investigate the relative importance of the economic policy uncertainty and of the geopolitical risk on U.S. REITs (Real Estate Investment Trusts) returns with a special focus on the different real estate sectors.Design/methodology/approachWe use an augmented Fama-French (1993)’s asset pricing model, including economic policy uncertainty indices (EPU), introduced by Baker et al. (2016), and geopolitical risk indices (GPR) recently developed by Caldara and Iacoviello (2022), to price the potential risk factors for U.S. Nareit indices returns. To obtain robust economic results, we correct for the problems of errors-in-variables in linear asset pricing models; we advocate the use of higher moments estimators as instruments in a generalized method of moments (GMM) framework.FindingsOur results report that economic policy uncertainty (EPU), and geopolitical risk (GPR) are priced for the different Nareit sectors for the last three decades. The GPR index stands as a relevant risk factor. The coefficient estimates are low compared to Fama-French risk factors. They are higher for Shopping Centers, Retail and Region Malls and lower for Health Care and Lodging/Resorts. EPU indices are also priced and less statistically significant. Health Care sector, followed by Shopping Centers and Retail are the most policy-sensitive sectors.Practical implicationsIn their “2023–2024 Top Ten Issues Affecting Real Estate” “political unrest and global economic health” is ranked 1 issue by the Counselors of Real Estate. Our results report that economic policy uncertainty and geopolitical risk are priced for the different Nareit sectors. They suggest implications for investors, insurers, bankers, policymakers and other stakeholders. The geopolitical risk index (GPR) stands as a relevant and significant risk factor for REITs returns.Originality/valueBased on parsimonious robust asset pricing models, the results shed a new light on the relative importance of geopolitical risk and economic policy uncertainty in the real estate sector, with a special focus on the different U.S. REITs sectors. They suggest possible implications for investors, insurers, bankers, policymakers and other stakeholders in a context marked by higher uncertainty shocks and geopolitical risks.

Demand Jump and Preemption under Irreversible Investment

Abstract This article shows that the possibility of preemption depends on the form of demand evolution and of the cost function. It characterizes the Markov perfect and open-loop equilibria of a two period game of capacity accumulation. When there is no demand evolution, there is no possibility of preemption under linear prices of investment. Preemption only appears when the demand shock between both periods is large enough.

Does cooperative intervention affect pricing decisions in the agricultural supply chain?

In global agricultural markets, farmers often face profit squeezes due to low bargaining power, which affects the sustainability of agriculture and the livelihoods of farmers. Cooperative intervention is seen as a key solution to improve bargaining power and optimize profit distribution in the agricultural supply chain. In this study, a two-stage dynamic game model is adopted to focus on bargaining power and compare the effects of linear pricing versus a double charging system under cooperative intervention. It is found that the cooperative is better when it has full bargaining power or when it faces downstream sellers with comparable bargaining power, and the dual-charging system is more favorable. When cooperatives bargain with sellers, the degree of differentiation of agricultural products affects the cooperatives’ profitability and cooperatives tend to maintain the two-part tariff when the bargaining power is less than a threshold condition containing the degree of differentiation of agricultural products; when discounts exceed the threshold, cooperatives shift to linear pricing to safeguard their profitability. Numerical analysis validates the theory and reveals the changing pattern of cooperative profits under market forces. This study not only provides theoretical support for the study of supply chain pricing strategies under the condition of considering the bargaining power of producers (farmers) but also provides management insights for the stability and sustainable development of agricultural supply chains. Its novel dynamic game framework is cross-culturally applicable to help farmers’ cooperatives cope with the challenge of profit distribution in a global context and emphasizes the importance of differentiation strategies to enhance bargaining power and promote fairness and efficiency in global agricultural supply chains.

Access-based cost-benefit analysis

Current methods of cost-benefit analysis (CBA) for transport investments rely on travel-time savings for potential users. This approach presents a consistent and significant historical trend of forecast inaccuracy, and thus has been questioned and criticized. Access, or the ease of reaching valued destinations, can be used as an alternative. Access features a strong correlation with land value which can be measured through hedonic analysis, and subsequently, access gains offered by a transport initiative can be monetised via property uplift. We test this hypothesis and evaluate Sydney's South West Metro Link (SWML).We first develop linear and semi-log ordinary least square hedonic pricing models for house sales in the Sydney region. The models are set up with structural and neighbourhood attributes in addition to access measures, and result in a statistically significant fit.Next, we model changes to job access induced by the SWML. Benefits are then quantified by land value uplift and are estimated at $1.87 Billion in 2031 and between $1.53–$3.08 Billion in 2061, which reflect base and transit-oriented development (TOD) scenarios. The project is thus feasible should certain land use and economic conditions be met, including TOD to occur about station localities by 2061 and if project costs are minimal. Although limitations are noted, access-based CBA exhibits significant promise as an alternative approach to appraisal and has direct application in value capture strategy.

The welfare effects of input price discrimination revisited

This paper revisits the welfare effects of input price discrimination in the canonical model in which an upstream monopolist, under linear pricing, sells an intermediate good to downstream Cournot competitors with different marginal costs. By leveling the downstream players, input price discrimination may have a positive output effect, with the magnitude depending on the convexity of final market demand and its rate of change. When demand is linear, concave, or convex with limited and nonincreasing convexity, welfare is reduced compared with uniform pricing. Instead, when there is sufficient and nondecreasing convexity—often observed in constant elasticity demand—price discrimination increases total welfare.

Non-cooperative corporate social responsibility, bargaining, and double marginalization in bilateral monopoly

ABSTRACT This study incorporates CSR concerns in a general demand model focusing on the double marginalization problem in single-product successive monopolies. It assumes that the manufacturer or retailer non-cooperatively engages in CSR activities and bargains over the linear input price. The findings demonstrate that the ratio of retail and wholesale pass-through depends not only on the demand curvature and its derivative but also on the firm’s CSR weights and relative bargaining power. In a bilateral monopoly, including CSR considerations by either the manufacturer or the retailer may alleviate the double marginalization problem when bargaining over the linear wholesale price.

Optimal trading and competition with information in the price impact model

Information drives trading and hence affects price dynamics. We study how an informed trader optimally trades, how multiple traders compete with each other, and how their competition affects price dynamics as well as their inventories in the linear price impact model framework. We formulate the informed trading problem as a stochastic optimal control problem and a stochastic differential game in different cases. By virtue of different methods, problems are solved explicitly in all cases. In the case of a single trader, the risk-averse informed trader trades less in the beginning and then speeds up to reduce exposure to the volatility of dynamic information. In addition, the risk-averse trader reveals information more slowly and thus contributes less to price efficiency. When multiple risk-neutral traders compete with information, regardless of the competition structure, they tend to trade more rapidly in the early stage to fill orders at a good price. Competition and the presence of a leader help promote price efficiency, and competition also leads to the empirically observed mean-reverting behavior of price dynamics and order flows. Furthermore, among risk-averse informed traders, inventory management triggers predatory trading and active information leakage during informed trading, and the positions of traders with the same level of risk aversion tend to be identical and mean-reverting to zero under multiple rounds of competition.

Welfare reducing vertical integration in a bilateral monopoly under Nash bargaining

AbstractWe consider a bilateral monopoly where a linear input price is determined by Nash bargaining. We show, with an increasing marginal cost of input production, that vertical integration reduces consumer surplus and welfare compared with bilateral monopoly if the bargaining power of the input supplier is low. This result is important for competition policies as it questions the common wisdom suggesting vertical integration increases welfare by eliminating the problem of double marginalization. Overproduction under bilateral monopoly compared with vertical integration is the reason for our result. Interestingly, consumer surplus and welfare can be higher under a linear input price compared with a two‐part tariff input price.

Oil Price Fluctuation and their Impact on the Macroeconomic Variables: The Case of Kuwait

The fluctuations in the international prices of crude oil have been a major concern for many economies who depend mainly on oil exports. Oil price shocks are a major disturbance for the economies of oil producing countries. This study investigates the impact of oil price shocks on selected macroeconomic variables in Kuwait using secondary data covering the period of 2001 to 2022. The study adopted the Vector autoregression (VAR) method to analyze the response of Kuwait macroeconomic variables to shocks in oil prices. Oil price in the study is considered in 2 categories: the linear oil price and the non-linear oil price (positive and negative changes in oil price). Based on the findings, it is observed that oil price shocks significantly impact macroeconomic variables in Kuwait. It is found that positive changes in oil prices have a more positive and significant impact on the macroeconomic variables compared to the negative changes in oil price. It is however concluded that there is a need for more policy developments to better harness periods of positive oil price experiences, and develop hedging risk framework for periods of negative changes in oil price in order to curb the impact of oil price shocks on Kuwait’s macroeconomy.

Combinable products, price discrimination, and collusion

We analyze the effect of different pricing schemes on the ability of horizontally differentiated firms to sustain collusion when customers are able to mix products to achieve a better match of their preferences. We compare the impacts on the likelihood of collusion and on consumer welfare from three pricing schemes: two-part tariffs, linear prices, and quantity-independent fixed fees. We find that a ban of either price component of the two-part tariff makes it more difficult to sustain collusion at profit-maximizing prices. We also find that whereas linear pricing is the most beneficial pricing schedule for customers in the absence of collusion, it is the most harmful pricing schedule for customers in the presence of collusion.

Enhancing Vegetable Price Forecasting Accuracy: A Hybrid SARIMA- DWT-GANN Approach

In the context of Malaysia's agricultural sector, the development of a robust vegetable price forecasting model holds paramount importance. The pricing dynamics of vegetables can significantly affect various stakeholders, including farmers, distributors, and consumers. The agricultural sector in Malaysia encounters persistent challenges such as supply-demand imbalances, seasonal variations, and market uncertainties, which can lead to income disparities for farmers and disruption in supply chains. Addressing these issues requires accurate and timely predictions of vegetable prices to enhance planning, resource allocation, and decision-making. This study introduces an innovative SARIMA-DWT-GANN hybrid model for vegetable price forecasting. By fusing the strengths of traditional time series modeling with the capabilities of neural networks, the proposed model offers a comprehensive solution to capture both linear and non-linear price patterns. The results demonstrate the superiority of the SARIMA-DWT-GANN model over the individual SARIMA model, as evident from correlation coefficients that closely approach unity and p-values confirming statistical significance. The model's ability to predict price changes has significant implications for making informed decisions throughout the agricultural supply chain. This research provides a robust forecasting tool that not only enhances market efficiency and profitability but also offers a promising solution to address the challenges in Malaysia's agricultural sector.

Machine Learning-Powered Combinatorial Clock Auction

We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, several papers have recently proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most important information from bidders. However, from a practical point of view, the main shortcoming of this prior work is that those designs elicit bidders' preferences via value queries (i.e., “What is your value for the bundle {A, B}?''). In most real-world ICA domains, value queries are considered impractical, since they impose an unrealistically high cognitive burden on bidders, which is why they are not used in practice. In this paper, we address this shortcoming by designing an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries (i.e., “At prices p, what is your most preferred bundle of items?''). We make two key technical contributions: First, we present a novel method for training an ML model on demand queries. Second, based on those trained ML models, we introduce an efficient method for determining the demand query with the highest clearing potential, for which we also provide a theoretical foundation. We experimentally evaluate our ML-based demand query mechanism in several spectrum auction domains and compare it against the most established real-world ICA: the combinatorial clock auction (CCA). Our mechanism significantly outperforms the CCA in terms of efficiency in all domains, it achieves higher efficiency in a significantly reduced number of rounds, and, using linear prices, it exhibits vastly higher clearing potential. Thus, with this paper we bridge the gap between research and practice and propose the first practical ML-powered ICA.

Socio-economic determinants of pricing water for domestic use: A comparison of blocks and linear tariffs

This article explores a model in which an agency can adopt different tariff schemes (block tariff or linear tariff) for selling water to a domestic buyer (a household), considering socio-economic factors like household size and income level. Through the formulation and examination of a static game involving a buyer and an agency, where the latter considers also the buyer’s welfare in its decisions, the socio-economic determinants significantly affect the optimal pricing within each of the two suggested tariff schemes. This analysis leads to the identification of conditions under which the agency deems a block tariff more advantageous compared to a linear tariff, as well as circumstances where adopting a linear pricing strategy emerges as the optimal approach. By introducing a (discrete-time) dynamic extension of the model, in which the agency is assumed to operate as a boundedly rational agent, we investigate the role of the altruism that the agency decides to adopt toward the buyer, observing that it ends up affecting the price dynamics (defined by a gradient-like mechanism). In addition, we apply the model to the real case of the Apulia region in Italy, comparing the unit price currently applied in the region with the results of applying the model in the Apulian territory.

Post-Shock Budgeting: A Methodological Framework

Traditional budgeting approaches have been criticised and called into question as not being able to adapt to management dynamics and context-specific planning needs. This is especially the case when major crises occur, with increased forecast uncertainty as a result. Adaptive techniques such as rolling and continuous budgeting have been developed to address such concerns, though trade-offs between the resulting optimisation of the planning, control and performance evaluation functions exist. A key, though not exclusive, effect of crises is the likely nonlinearity of effects of unit prices which will tend to revert to the mean, or in other words, rebound and gradually converge to pre-shock levels or to a steady state. Aiming to fill this research gap, this study presents a methodological framework, framed within a survival analysis paradigm, which can be used for post-shock budgeting. Following a description of the mathematical properties and steps required for application, the framework is illustrated using a stylised example of operational budget with results being compared between linear and nonlinear price rebound trajectories. The presented framework is a relatively simple and flexible solution to the issue of post-shock budgeting which can be readily developed and adapted, therefore lending itself to a widespread use.

Optimal liquidation with high risk aversion and small linear price impact

We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options in the case where the investor is required to liquidate her position. Our main result is establishing a non-trivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. We compute the limit of the corresponding utility indifference prices and find explicitly a family of portfolios which are asymptotically optimal.

Nash equilibria for relative investors with (non)linear price impact

We consider the strategic interaction of n investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is close to a critical parameter.

Mispricing in linear asset pricing models

ABSTRACT In the framework of a reduced-form asset pricing model featuring linear-in-instrument betas and time-varying risk premiums and allowing for missing factors, I propose a measure of mispricing that is largely free from the bias due to missing factors or missing instruments. Applying the model to U.S. equity data, I find evidence of mispricing in stock returns. A mispricing-based zero-dollar investment strategy intersecting momentum and contrarian horizons is highly profitable when applied to both firm- and portfolio-level returns, even after controlling for Fama-French factors, momentum and liquidity effects. Focusing on momentum, I find that the phenomenon is partially caused by the mispricing that does not vary with macro variables. Time-varying betas reduce the mispricing by 40% or better.

Optimal water tariffs for domestic, agricultural and industrial use

Consider a water supplier who determines sales rates with the goals of maximizing profits, protecting consumer welfare, and ensuring adequate future water supplies. Buyers are differentiated and can use the water for domestic, agricultural, and industrial purposes. We propose a leader-follower finite-horizon differential game. The leader (the water supplier) determines the selling price and the followers (consumers) react by requesting their optimal amount of water. We calculate a feedback Stackelberg equilibrium assuming that all user demand is satisfied (interior equilibrium). We compare two different tariff schemes: linear tariffs (the price paid is a multiple of the volume of water purchased), and increasing block tariffs (the unit price is lower for quantities of water that do not exceed a fixed threshold). We show that block pricing is never optimal and linear pricing is always preferred.