Unobserved Market Research Articles

Equilibrium multi-period investment strategy for a DC pension plan with incomplete information: Hidden Markov model

In the financial market with both observable and unobservable market states, this article explores the equilibrium investment strategy for a DC pension plan with the mean-variance criterion in a discrete-time setting. The dynamics of the partially observed market state are described by a discrete-time finite-state hidden Markov chain. There is a riskless asset and a risky asset in the financial market, where the return rate of the risky asset depends both on the observable and unobservable market states. Meanwhile, the stochastic salary process is also modulated by the observable and unobservable market states. Under the framework of non cooperative game, we first define the equilibrium investment strategy for the multi-period mean-variance DC pension plan. By adopting the sufficient statistics method, the investment problem for the mean-variance DC pension plan with incomplete information is transformed into the one with complete information. The closed-form equilibrium investment strategy is derived by solving the extended Bellman equation. Finally, numerical results show that the incomplete information has significant impacts on the equilibrium investment strategy and the equilibrium efficient frontier. Neglecting the reality of incomplete information in the financial market will reduce the investment benefit of the DC pension plan. The longer the investment horizon, the greater the investment benefit loss for the DC pension plan.

Observable and Unobservable Investment Information in Multiple Markets

<p class="MsoNormal" style="margin-top: 12pt; text-align: justify;"><span lang="EN-US" style="font-family: 'times new roman', times, serif; font-size: 14pt;">This study considers the effects of disclosure conditions on firms' investment decisions when facing an identical competitor in multiple markets. Assuming that there are congestion costs between multiple investments to reduce marginal cost for each market, this study focuses on the cases where the disclosure conditions may differ by market. Like previous studies on single Cournot competition, these results show that firms invest more in the observable investment markets than in the unobservable markets under symmetric disclosure conditions. However, firms invest more in the unobservable market if there are asymmetric disclosure conditions.</span></p>

Strategic Complements or Substitutes? The Case of Adopting Health Information Technology by U.S. Hospitals

Abstract This paper explores the adoption choice of electronic medical records by U.S. hospitals, which could exhibit strategic complements or substitutes. I find complementarities in adoption through a reduced-form analysis with instruments for unobserved market characteristics. I further develop a dynamic oligopoly model to allow for strategic timing incentives that are missing in the static model. Adopting a dominant local vendor could increase per period profits from adoption by 9.2% over choosing a marginal vendor. A counterfactual analysis suggests that an incentive program rewarding coordination, not just adoption, is more effective in achieving interoperability, especially before the widespread adoption of the technology.

Inference in an incomplete information entry game with an incumbent and with beliefs conditioned on unobservable market characteristics

We consider a static entry game played between an incumbent and a collection of potential entrants. Entry decisions are made with incomplete information and beliefs are conditioned, at least partially, on a market characteristic that is unobserved by the econometrician. We describe conditions under which, even though the unobserved market characteristic cannot be identified, a subset of parameters of the model can still be identified, including all the strategic-interaction effects. We also characterize testable implications for strategic behavior by the incumbent when this player is able to shift the unobserved market characteristic to deter entry. We present results under Bayesian Nash equilibrium (BNE) and under the weaker behavioral model of iterated elimination of nonrationalizable strategies. Our empirical example analyzes geographic entry decisions in the Mexican internet service provider (ISP) industry. This industry has an incumbent, América Móvil (AMX), which established a widespread geographic presence as a monopolist following the privatization of Telmex in 1990. Our results show significant strategic interaction effects between AMX and its competitors, as well as evidence of strategic behavior by AMX to deter entry and maximize its market share.

Credit Spreads, Leverage and Volatility: A Cointegration Approach

This work documents the existence of a cointegration relationship between credit spreads, leverage and equity volatility for a large set of US companies. It is shown that accounting for the long-run equilibrium dynamic between these variables is essential to correctly explain credit spread changes. Using a novel structural model in which equity is modeled as a compound option on the firm’s assets, a new methodology for estimating the unobservable market value of the firm’s assets and volatility is developed. The proposed model allows to significantly reduce the pricing errors in predicting credit spreads when compared with several structural models. In terms of correlation analysis, it is shown that not accounting for the long-run equilibrium equation embedded in an error correction mechanism (ECM) results into a misspecification problem when regressing a set of explanatory variables onto the spread changes. Once credit spreads, leverage and volatility are correctly modeled, thus allowing for a long-run equilibrium, the fit of the regressions sensibly increases if compared to the results of previous research. It is further shown that most of the cross-sectional variation of the spreads appears to be more driven by firm-specific characteristics rather than systematic factors.

A free boundary problem arising from a multi-state regime-switching stock trading model

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.

Instrument-free identification and estimation of differentiated products models using cost data

We propose a new methodology for identifying and estimating demand in differentiated products models when demand and cost data are available. The method deals with the endogeneity of prices to demand shocks and the endogeneity of outputs to cost shocks by using cost data rather than instruments. Further, we allow for unobserved market size. Using Monte Carlo experiments, we show that our method works well in contexts where commonly used instruments are invalid. We also apply our method to the estimation of deposit demand in the US banking industry.

On the market price of risk

An important parameter describing the state of capital markets, investment opportunity sets, and asset pricing is the unobservable market risk price. The estimated risk price depends upon the selected asset set, the number of assets, the investment horizon, and the sample period. We document the large theoretical and empirical probability of an unacceptably negative sample estimate for the unbiased estimator of the squared risk price. We address admissibility and dominance under quadratic loss of alternative estimators, concluding that an optimized shrinkage estimator has the smallest expected quadratic loss compared with our alternative estimators. Using market data, we examine estimates for more inclusive investment opportunity sets and provide upper bounded estimates of the risk price and resultant unique Sharpe measure, to complement the existing literature’s Sharpe measure bounds and equity premium estimates. Finally, we examine time series properties, behavior in the business cycle, and relation to some recently advocated economic factors.

Effects of Market Structure on Broadband Quality in Local U.S. Residential Service Markets

This paper investigates the effects of changes in market structure on residential service quality in local U.S. broadband markets. Our analysis focuses on identifying causal effects on quality from entry (or exit) by firms using both legacy and non-legacy broadband network technologies. We analyze a very large and highly disaggregated census block-level data set we have constructed using Federal Communication Commission (FCC) data on residential broadband services deployment in populated U.S. census blocks between December 2014 and December 2018. We employ a difference-in-differences framework combined with both spatial fixed effects and spatial instrumental variables. The latter econometric tools are used to address unobserved market heterogeneity and concerns about significant error in measured ISP counts for fixed wireless ISPs. Our results suggest that entry by legacy technology (cable and DSL) service providers has large impacts on available service quality in local broadband markets, effects which diminish rapidly with continued entry. Contrary to expectations, entry by a single new fiber ISP seems to have no impact on available quality; entry by two fiber ISPs, by contrast, raises maximum available quality by a modest but statistically significant 90 Mbps. Entry by a fixed wireless ISP appears to have had a large, negative impact on maximum available download speeds offered by incumbent legacy ISPs. Economic explanations for these results are discussed and evaluated. We establish that (i) both fixed wireless and fiber ISPs compete in sets of speed tiers that are distinct from those offered by legacy ISPs, and speculate that (ii) price competition (as opposed to quality competition) may be more intense in markets with fixed wireless entry.

Demand Modeling in the Presence of Unobserved Lost Sales

We present an integrated optimization approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We employ a mixed-integer program (MIP) to jointly determine the prediction parameters associated with the customer arrival rate and their substitutive choices. This integrated approach enables us to recover proven, (near-) optimal parameter values with respect to the chosen loss-minimization (LM) objective function, thereby overcoming a limitation of prior multistart heuristic approaches that terminate without providing precise information on the solution quality. The imputations are done endogenously in the MIP by estimating optimal values for the probabilities of the unobserved choices being selected. Under mild assumptions, we prove that the approach is asymptotically consistent. For large LM instances, we derive a nonconvex-contvex alternating heuristic that can be used to obtain quick, near-optimal solutions. Partial information, user acceptance criteria, model selection, and regularization techniques can be incorporated to enhance practical efficacy. We test the LM model on simulated and real data and present results for a variety of demand-prediction scenarios: single-item, multi-item, time-varying arrival rate, large-scale instances, and a dual-layer estimation model extension that learns the unobserved market shares of competitors.This paper was accepted by Yinyu Ye, optimization.

Price Index Insurances in the Agriculture Markets

In this paper, we introduce price index insurances on agricultural goods. Seemingly similar to derivatives, there are significant differences between price index insurances and derivatives. First, unlike derivatives, there are no entrance barriers for purchasing insurances, making them the risk management tools that are accessible to almost all farmers. Second, since insurances are issued at a certain number for any individual farm, unlike futures, for example, they cannot be used for speculation and are used solely for hedging price risk. Third, unlike forwards, they are heavily regulated and do not default and cause counterparty risk. Besides all differences (or benefits), such products have just recently been introduced in the agricultural insurance market. In this paper, we investigate if there could have been a financially viable market where these products are traded. More precisely, we investigate if an insurance company can design a portfolio of optimal contracts that gives a higher Sharpe ratio than the financial market index prices (in our paper FTSE 100 and other three major indexes). To reach the paper's objective we take three steps, by considering theoretical, practical and corporation standpoints. In the first step, we will see how an optimal contract would look like from the demand side in a theoretical setup and we obtain the optimal contract from the farmers' standpoint. In the second step, by adopting a more practical approach, by meeting the Key Performance Indicators (KPI) requirements set by the market participants (both demand and supply side), we find the optimal policy specifications from the first step, in the market equilibrium. This step also helps to find some unobservable market parameters like volatility. Finally, by adopting a corporation standpoint we encounter our model to the UK farm index prices and find an optimal portfolio of the products on products from 10 commodities. We find out that investing in such a business is financially viable, as the optimal insurance portfolio produces a Sharpe ratio that outperforms FTSE 100 and other major market indexes.

Price Index Insurances in the Agriculture Markets

In this article, we introduce price index insurances on agricultural goods. Although these seem similar to derivatives, there are significant differences between price index insurances and derivatives. First, unlike derivatives, there are no entrance barriers for purchasing insurances, making them the risk management tools that are accessible to almost all farmers. Second, since insurances are issued in a certain number for any individual farm, unlike futures, for example, they cannot be used for speculation and are used solely for hedging price risk. Third, unlike forwards, they are heavily regulated and do not default and cause counterparty risk. In addition to all differences (or benefits), such products have just recently been introduced in the agricultural insurance market. In this article, we investigate if there could have been a financially viable market where these products are traded. More precisely, we investigate whether an insurance company can design a portfolio of optimal contracts that gives a higher Sharpe ratio than the financial market index prices (here, FTSE 100 and other three major indexes). To reach the article’s objective, we take three steps, in considering theoretical, practical, and corporation standpoints. In the first step, we show what an optimal contract would look like from the demand side in a theoretical setup and we obtain the optimal contract from the farmers' standpoint. In the second step, by adopting a more practical approach in meeting the Key Performance Indicators requirements set by the market participants (both demand and supply side), we find the optimal policies specifications from the first step, in the market equilibrium. This step also helps to determine some unobservable market parameters like volatility. Finally, by adopting a corporation standpoint we bring our model to the U.K. farm index prices and find an optimal portfolio of the products on products from 10 commodities. We demonstrate that investing in such a business is financially viable, as the optimal insurance portfolio produces a Sharpe ratio that outperforms the FTSE 100 and other major market indexes.

Testing unobserved market heterogeneity in financial markets: The case of Banco Popular

In this paper, we use a specification of the standardized duration to test unobserved heterogeneity in a nonlinear version based on a self-exciting threshold autoregressive conditional duration model. We illustrate the relevance of this procedure for identifying the presence of heterogeneous agents in the final days of trading of Banco Popular, the first bank rescued by the European Single Resolution Board.

Credit Spreads, Leverage and Volatility: a Cointegration Approach

This work documents the existence of a cointegration relationship between credit spreads, leverage and equity volatility for a large set of US companies. It is shown that accounting for the long-run equilibrium dynamic between these variables is essential to correctly explain credit spread changes. Using a novel structural model in which equity is modelled as a compound option on the firm's assets, a new methodology for estimating the unobservable market value of the firm's assets and volatility is developed. The proposed model allows to significantly reduce the pricing errors in predicting credit spreads when compared with several structural models. In terms of correlation analysis, it is shown that not accounting for the long-run equilibrium equation embedded in an Error Correction Mechanism (ECM) results into a misspesification problem when regressing a set of explanatory variables onto the spread changes. Once credit spreads, leverage and volatility are correctly modelled, thus allowing for a long-run equilibrium, the fit of the regressions sensibly increases if compared to the results of previous research. It is further shown that most of the cross-sectional variation of the spreads appears to be more driven by firm-specific characteristics rather than systematic factors.

Deep Reinforcement Learning in Agent Based Financial Market Simulation

Prediction of financial market data with deep learning models has achieved some level of recent success. However, historical financial data suffer from an unknowable state space, limited observations, and the inability to model the impact of your own actions on the market can often be prohibitive when trying to find investment strategies using deep reinforcement learning. One way to overcome these limitations is to augment real market data with agent based artificial market simulation. Artificial market simulations designed to reproduce realistic market features may be used to create unobserved market states, to model the impact of your own investment actions on the market itself, and train models with as much data as necessary. In this study we propose a framework for training deep reinforcement learning models in agent based artificial price-order-book simulations that yield non-trivial policies under diverse conditions with market impact. Our simulations confirm that the proposed deep reinforcement learning model with unique task-specific reward function was able to learn a robust investment strategy with an attractive risk-return profile.

Collusion Under Persistent Shocks

We study a repeated Cournot competition model where prices are determined not only by firms’ quantities but also unobservable market shocks (Green and Porter, 1984). Unlike Green and Porter (1984), market shocks are persistent and today’s market condition affects tomorrow’s market condition. With such persistence, a cheating firm can manipulate its rival’s belief about future market conditions. Such belief manipulation creates another channel for the firm to optimally cheat on the opponent. Despite this additional channel, we show that under certain conditions, firms can still collude. Moreover, persistence rather makes it easier to collude.

Firm’s Credit Risk in the Presence of Market Structural Breaks

The financial crises which occurred in the last several decades have demonstrated the significant impact of market structural breaks on firms’ credit behavior. To incorporate the impact of market structural break into the analysis of firms’ credit rating transitions and firms’ asset structure, we develop a continuous-time modulated Markov model for firms’ credit rating transitions with unobserved market structural breaks. The model takes a semi-parametric multiplicative regression form, in which the effects of firms’ observable covariates and macroeconomic variables are represented parametrically and nonparametrically, respectively, and the frailty effects of unobserved firm-specific and market-wide variables are incorporated via the integration form of the model assumption. We further develop a mixtured-estimating-equation approach to make inference on the effect of market variations, baseline intensities of all firms’ credit rating transitions, and rating transition intensities for each individual firm. We then use the developed model and inference procedure to analyze the monthly credit rating of U.S. firms from January 1986 to December 2012, and study the effect of market structural breaks on firms’ credit rating transitions.

Market earnings expectation, measurement error in analysts’ consensus forecasts and prediction of stock returns

PurposeIn capital markets research, analysts’ consensus forecasts are widely used as a proxy for unobservable market earnings expectation. However, they measure the market earnings expectation with error that may vary cross-sectionally, as the market does not consistently rely on analysts’ consensus forecasts to form earnings expectation (Walther, 1997). Based on this notion, this paper aims to relate the prediction of future stock returns to the cross-sectional variation of the error in measuring market earnings expectation embedded in analysts’ consensus forecasts.Design/methodology/approachThis study uses empirical analyses based on stock returns and annual analysts’ consensus forecasts.FindingsBased on the analytical work by Abarbanell et al. (1995), this study reports that when the measurement error in annual analysts’ consensus forecasts is the smallest, forward earnings-to-price ratio (constructed with annual analysts’ consensus forecasts) best explains future stock returns, and the forward earnings-to-price ratio-based investment strategy is the most profitable.Originality/valueFindings of this study are useful to capital markets research that relies on the market earnings expectation and to practitioners seeking more profitable investment strategies.

Optimal investment management for a defined contribution pension fund under imperfect information

This paper investigates an optimal multi-period investment management problem for a defined contribution pension fund under the mean–variance criterion with imperfect information, meaning that both observable and unobservable states exist in the financial market. The dynamics of the unobservable market state process are formulated by a discrete-time finite-state hidden Markov chain with time-varying transition probability matrices. Due to the long investment horizon of a defined contribution pension fund, our paper considers only risky assets whose returns depend on both the observable and unobservable market states. Meanwhile, the stochastic salary process is also modulated by the observable and unobservable market states. By adopting sufficient statistics, the portfolio optimization problem for the defined contribution pension fund with imperfect information is transformed into one with complete information. Then, the optimal investment strategy and the efficient frontier are explicitly derived using the dynamic programming approach and the Lagrange dual method. Finally, numerical results show that the imperfection of market state information may cause a loss of investment return.

Strategic Complements or Substitutes: The Case of Adopting Electronic Medical Records (EMRs) by U.S. Hospitals

This paper explores the adoption choice of electronic medical records by U.S. hospitals, which could exhibit strategic complements or substitutes. I find complementarities in adoption through a reduced-form analysis with instruments for unobserved market characteristics. I further develop a dynamic oligopoly model to allow for strategic timing incentives that are missing in the static model. Adopting a dominant local vendor could increase per-period profits from adoption by 9.2% over choosing a marginal vendor. A counterfactual analysis suggests an incentive program rewarding coordination, not just adoption, is more effective in achieving interoperability, especially before the widespread adoption of the technology.