Equilibrium Portfolio Research Articles

Necessary and sufficient conditions for open-loop equilibrium portfolio for a DC pension plan with piecewise linear state-dependent risk tolerance

Wang, Chen, and Yang (2023) investigated the equilibrium behavioral strategy for a defined contribution (DC) pension plan during the accumulation phase and obtained the explicit expressions for the suboptimal equilibrium behavioral strategy. However, the authors failed to obtain the optimal solution and did not completely solve the pension investment problem with piecewise linear state-dependent risk tolerance. The primary objective of this article is to solve an improved version of the above DC pension plan problem thoroughly. We investigate the open-loop equilibrium portfolio for a DC pension plan and derive necessary and sufficient conditions for the open-loop equilibrium portfolio through coupled forward-backward stochastic differential equations (FBSDEs). The uniqueness of an equilibrium portfolio is obtained by decoupling FBSDEs. Finally, the economic significance and implications of the obtained open-loop equilibrium portfolio are illustrated from the theoretical perspective.

Equilibrium Portfolio Selection for Smooth Ambiguity Preferences

This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous-time market. The investor is uncertain about the risky asset’s drift term and updates the subjective belief according to the Bayesian rule. A verification theorem is established, and an equilibrium strategy can be decomposed into a myopic demand and two hedging demands. When the prior is Gaussian, we provide an equilibrium solution in closed form. Moreover, a puzzle in the numerical results is interpreted via an alternative representation of the smooth ambiguity preferences. Funding: This work was supported by the National Key R&D Program of China [Grant 2020YFA0712700], the National Natural Science Foundation of China [Grants 11871036, 11901574, 12071146, 12271290, and 12371477], and the MOE Project of Key Research Institute of Humanities and Social Sciences [Grant 22JJD910003].

A MODEL OF GROSS CAPITAL FLOWS: RISK SHARING AND FINANCIAL FRICTIONS

AbstractThis article builds a two‐country model of gross capital flows where agents share tradable output risk using two bonds, subject to stochastic collateral constraints. Equilibrium portfolios are short in domestic bonds and long in foreign bonds because the endogenous movements of the real exchange rate provide a hedge against domestic output shocks. Under negative domestic shocks, these external positions transfer wealth from home to abroad. During the Great Recession, the model shows that such wealth transfer from the United States mitigated the consumption drop abroad. Quantitatively, financial frictions account for about half of the collapse in U.S. gross flows in 2008.

Impulse balancing versus equilibrium learning an experimental study of competitive portfolio selection

The experiment lets investors interact in portfolio choices involving different risky assets, one for each state of the world. Probabilities of random states are commonly known. All assets pay the same dividend when their state is realized and becomes worthless otherwise. Whereas evolutionary stability and equilibrium behavior predict equal expected profits across assets, impulse balancing (Selten and Buchta, Games and human behavior: essays in the Honor of Amnon Rapoport, 1999) equalizes the expected regret. Thus, impulse balancing seems to capture tendencies of cyclical direction learning. In addition to analyzing whether and when behavior converges to impulse balancing or to equilibrium portfolios, we categorize portfolio adaptation by path dependence and sensitivity to state-specific probabilities. We show that portfolio choices are driven mainly by probability matching, but the effect becomes weaker over time. Furthermore, most portfolio adjustments are not compatible with directional learning.

Exchange Rate Transaction of International Trade Goods Based on Fuzzy Granulation and Deep Learning

The change of international trade goods exchange rate transaction has an impact on economic operations and economic stability. Therefore, an international trade goods exchange rate transaction based on fuzzy granulation and in-depth learning is proposed. Based on fuzzy information granulation and BP neural network, this paper analyzes the interest rate evaluation theory. For the future expectation of currency exchange rate, portfolio equilibrium determines the proportional relationship of each component in the portfolio and analyzes the impact of asset price and exchange rate change according to this relationship. Then, it points out the risk evaluation index system, calculates the risk degree of exchange rate transaction of international trade goods, and then evaluates the risk of exchange rate transaction of international trade goods. It completes the research on exchange rate transactions of international trade goods based on fuzzy granulation and in-depth learning. The experimental results show that excessive exchange rate fluctuation will bring the same proportion fluctuation to the asset price in the financial market, and the coordination between exchange rates and the coordination of exchange rate and asset price can promote the steady growth of national economy.

Price impact, strategic interaction and portfolio choice

This paper studies the portfolio choice of two large investors who act strategically because their trading affects interest rates. Each investor chooses her optimal portfolio conditional on the portfolio of the opponent. Equilibrium portfolios and their performance depend on the investor’s characteristics (risk aversion and return impact) and on the characteristics of the opponent (risk aversion and return impact). Depending on the interplay among these characteristics, strategic interaction can (i) increase or decrease risk taking incentives, as compared to the Merton-style portfolio, (ii) induce the more risk-averse investor to invest relatively more in the risky asset and (iii) change the role of inflation-linked bonds from hedging instrument to borrowing opportunity.

Optimal portfolio financing selection in a capital-constrained supply chain with risk-averse members

ABSTRACT We first consider a supplier-retailer supply chain in which only the capital-constrained retailer is risk-averse while the supplier and the bank both are risk-neutral. The newsvendor-like retailer may fund its business by two portfolio financing schemes to satisfy uncertain market demand: (1) bank loans and the supplier’s equity investment (BCF-SI) and (2) bank loans and the supplier’s credit guarantee (BCF-SG). Using CVaR criterion, we model the behaviour of the risk-averse retailer to analytically derive the portfolio financing equilibrium in a Stackelberg supplier-led game separately for two portfolio financing schemes. We characterize the conditions under which the supplier and the retailer reach Pareto improvement under two portfolio financing schemes compared with the non-financing benchmark. Moreover, we extend the model to the case in that the supplier and retailer both are risk-averse while only the bank is risk-neutral to further investigate the impact of risk aversion on the optimal financing scheme selection. The numerical examples verify our theoretical results.

Nonunitary Parties, Government Formation, and Gamson’s Law

Following the coalition literature highlighting intraparty politics (e.g., Giannetti and Benoit 2009; Laver 1999; Strøm 2003), I address the well-known “portfolio allocation paradox” (Warwick and Druckman 2006) by introducing a new model of government formation based on two main assumptions. First, no actor has a structural advantage in the negotiations leading to government formation. Second, all actors who can deprive the coalition of a majority (or other critical threshold size) must be included in the negotiations—not just parties. Whereas standard bargaining models are inconsistent with Gamson’s Law, the model proposed here implies that equilibrium portfolio allocations should be mostly Gamsonian but with a small-party bias, as the empirical literature has long found. Empirically, I show that my model outperforms the literature’s standard specification (due to Browne and Franklin 1973). Moreover, one of the model’s new predictions—that candidate-centered electoral rules should promote more Gamsonian portfolio allocations—is supported.

Explaining equity home bias using hedging motives against real exchange rate and wage risks

This paper derives an optimal portfolio equilibrium using a two-country DSGE model with non-separable utility and two assets (home and foreign equities). We solve the model using a second-order approximation method, which enables us to derive a closed-form solution for optimal equity holdings. When the elasticity of substitution between home and foreign goods is below around 1.2, the covariance between wage and equity return becomes negative and the covariance between price and equity return becomes positive. In this case, home equity provides hedging against wage and real exchange rate risks and optimal portfolio equilibrium shows a home bias. In addition, we show that equity holding bias (either home or foreign) is amplified under separable utility case, implying that previous studies with separable utility may have overestimated equity holding bias.

Why are countries’ asset portfolios exposed to nominal exchange rates?

Most countries hold large gross asset positions, lending in their domestic currency and borrowing in foreign currency. As a result, their balance sheets are exposed to nominal exchange rate movements. We argue that when asset markets are incomplete, this exposure provides partial insurance against shocks that move exchange rates. We demonstrate that this insurance motive can simultaneously generate realistic gross asset positions and resolve the Backus-Smith puzzle: that countries’ relative consumption and real exchange rates are negatively correlated. Local perturbation methods are inaccurate in this setting as they approximate around the wrong interest rate, even when they correctly characterize the average portfolio holdings. So to accurately solve the equilibrium portfolio problem, we extend Maliar and Maliar (2015)’s global projection method.

Dynamic Mean-Variance Efficient Fractional Kelly Portfolios in a Stochastic Volatility Model

Fractional Kelly portfolios are popular investment strategies in the market. In this paper, we improve the mean-variance efficiency of a fractional Kelly portfolio by minimizing the variance of the return of a portfolio subject to the constraint that the expected return rate of the portfolio is as high as that of the fractional Kelly portfolio. We consider so-called equilibrium portfolio strategies due to time inconsistency caused by the mean-variance criterion. We drive an equilibrium strategy in closed form and show that it reduces the variance of portfolio return compared to the fractional Kelly portfolio, although the reduction is quantitatively small.

An Extended McKean — Vlasov Dynamic Programming Approach to Robust Equilibrium Controls under Ambiguous Covariance Matrix

This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time-inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman's principle of optimality. Moreover, we model the state by a McKean — Vlasov dynamics under a set of non-dominated probability measures induced by the ambiguous covariance matrix of the noises. We apply a game-theoretic concept of subgame perfect Nash equilibrium to develop a robust equilibrium control approach, which can yield robust time-consistent decisions. We characterize the robust equilibrium control and equilibrium value function by an extended optimality principle and then we further deduce a system of Bellman — Isaacs equations to determine the equilibrium solution on the Wasserstein space of probability measures. The proposed analytical framework is illustrated with its applications to robust continuous-time mean-variance portfolio selection problems with risk aversion coefficient being constant or state-dependent, under the ambiguity stemming from ambiguous volatilities of multiple assets or ambiguous correlation between two risky assets. The explicit equilibrium portfolio solutions are represented in terms of the probability law.

ENVIRONMENTALISM, STIMULUS, AND INEQUALITY REDUCTION THROUGH INDUSTRIAL POLICY: DID CASH FOR CLUNKERS ACHIEVE THE TRIFECTA?

The 2009 American Cash for Clunkers program, which subsidized consumers who scrapped old vehicles and purchased new vehicles, was promoted by appealing to multiple constituencies. We evaluate the policy and alternatives according to its stated goals: emissions reductions, economic stimulus, and reducing inequality. We calibrate a dynamic partial equilibrium portfolio model to match consumer expenditure data from 1998 to 2011 focusing on heterogeneity across cars and trucks. We find the program generated $0.17 in environmental benefits, $0.28 in consumer surplus, and $0.31 in net discounted additional spending per subsidy dollar. Since subsidies largely went to middle‐income infra‐marginal consumers, the program exacerbated consumption inequality. We evaluate alternative policy designs and find no policy which simultaneously improves all outcomes. (JEL H23, L52, L92, D63)

International Financial Connection and Stock Return Comovement

This paper studies whether bilateral international financial connection data help predict bilateral stock return comovement. It is shown that, when the United States is chosen as the benchmark, a larger U.S. portfolio investment asset position on the destination economy predicts a stronger stock return comovement between them. For large economies such as the United States and Germany, the portfolio investment position is also the best predictor among other connection variables. The paper discusses with a simple general equilibrium portfolio model that the empirical pattern is consistent with the behavior of index investors who trade in response to risk-on/risk-off shocks.

Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets

In this paper, we aim to investigate the mean-variance portfolio selection in an economy with inflation risk. In the financial market, the inflation index can only be partially observed by a signal process. We transform the initial problem into an equivalent completely observed problem. The effect of the partially observed price index on the optimization problem is twofold. Firstly, the equivalent completely observed problem involves more estimation error. Secondly, the mean-variance criterion is distorted. Higher moment is assigned with a bigger weight. The optimization goal does not satisfy the assumption in the Bellman’s optimality condition and we derive the equilibrium strategy based on the extended HJB equation. Besides, we also show the results of the efficient frontier and strategy in the precommitment case. In the end of this paper, we present a sensitivity analysis to show the economic behaviors of the investor and compare the efficient strategies and frontiers in precommitment case and equilibrium case.

International Financial Connection and Stock Return Comovement

This paper studies whether bilateral international financial connection data help predict bilateral stock return comovement. It is shown that, when the United States is chosen as the benchmark, a larger U.S. portfolio investment asset position on the destination economy predicts a stronger stock return comovement between them. For large economies such as the United States and Germany, the portfolio investment position is also the best predictor among other connection variables. The paper discusses with a simple general equilibrium portfolio model that the empirical pattern is consistent with the behavior of index investors who trade in response to risk-on/risk-off shocks.

Investor sophistication and capital income inequality

Capital income inequality is large and growing fast, accounting for a significant portion of total income inequality. We study its growth in a general equilibrium portfolio choice model with endogenous information acquisition and heterogeneity across household sophistication and asset riskiness. The model implies capital income inequality that grows with aggregate information technology. Investors differentially adjust both the size and the composition of their portfolios, as unsophisticated investors retrench from trading risky securities and shift their portfolios to safer assets. Technological progress also reduces aggregate returns and increases the volume of transactions, features that are consistent with recent U.S. data.

Exploiting the low-risk anomaly using machine learning to enhance the Black–Litterman framework: Evidence from South Korea

Many studies have revealed that global financial markets are experiencing low-risk anomalies. In the Korean market, for example, even the portfolios of high-risk stocks recorded a loss of about 70% between 2000 and 2016. In this study, we construct a low-risk portfolio that responds to low-risk anomalies in the Korean market using the Black–Litterman framework. We use three machine-learning predictive and traditional time-series models to predict the volatility of assets listed in the Korean Stock Price Index 200 (KOSPI 200) and select the best-performing one. Then, we use the model to classify assets into high- and low-risk groups and create a Black–Litterman portfolio that reflects the investor's view where low-risk stocks outperform high-risk stocks. The experiment shows that reflecting the low-risk view in the market equilibrium portfolio improves profitability and that this view dominates the market portfolio.

Business Cycles in a Three-sector Growth Model with Portfolio Equilibrium between Land, Gold and Capital

This study generalises a growth model proposed by Zhang (2016) through allowing all the time-dependent variables to be time-dependent. Zhang’s model deals with dynamic interdependence between capital accumulation and environmental change, with portfolio equilibrium among land, gold and physical wealth in a multi-sector general equilibrium framework. The model explains the dynamics of prices, rents and distribution of land, gold, physical wealth and environmental change on the basis of micro-economic foundation. This article generalises the model to explain business cycles due to different exogenous shocks. We simulate the motion of the economy and conduct comparative dynamic analysis to demonstrate business cycles due to periodic oscillations in the propensity to use gold, the propensity to consume housing, the propensity to consume industrial goods, the propensity to consume agricultural goods, the propensity to save, and the tax rate on the consumption of industrial goods. JEL Classification: O41, D41, E32

On the theory of international currency portfolios

The paper develops a general equilibrium theory of the optimal currency composition of international bond portfolios. Like the partial equilibrium portfolio balance literature of the 1980s, the theory emphasizes the critical roles of government debt and government balance sheet operations in the determination of portfolios, prices and allocations. Consistent with empirical findings, optimal foreign currency positions are found to be small, with their size decreasing with exchange rate volatility, while optimal domestic currency positions are large and increasing with domestic interest rates. A large open market purchase of domestic currency bonds from private households lowers domestic interest rates.