Ali Lazrak

We study the effect of responsible consumption on asset prices. We introduce a preference bias in favor of ``green'' goods and  good-specific habits in a consumption-based dynamic asset pricing model with a variety of goods and show that when goods' demand elasticity is high, green assets are riskier while brown assets hedge consumption risk. As a result, the ``green minus brown'' asset return spread (the green premium) increases in goods' demand elasticity. Using change in product prices as a proxy for goods' demand elasticity and ESG scores as a measure of a firm's ``greenness,'' we find that in the cross section of US stocks over the 2012--2022 period, the annual green premium is 11.9\% for firms with high demand elasticity, while it is negligible and insignificant for firms with low demand elasticity. Moreover, consistent with our model, we find that the outperformance of green vs. brown stocks in the recent decade  is concentrated among firms facing high-demand elasticity in product markets. In contrast, green firms underperform brown in low-demand elasticity markets. Our model highlights that accounting for goods' demand elasticity is crucial for understanding the impact of the rising trend of responsible consumption on asset prices.

Abstract: We model stakeholder-driven institutional divestiture that promotes harmful-asset stranding through both an economic exposure channel and financial prices. We introduce two novel mechanisms. First, institutional divestiture weakens stakeholders' asset exposures, improving political conditions for stranding. Second, institutional divestiture credibly communicates information about citizen preferences, environmental harm, and economic benefits to financial markets and political participants. These channels drive harmful-asset divestiture, which reduces the asset price and raises its strand probability. Support for divestiture increases under supermajority strand requirements, and when stakeholders internalize aggregate harm. We detail the equilibrium interactions between information, divestiture, prices, and stranding in a dynamic, rational-expectations game.

We examine pre-vote interactions in a committee that enacts a welfare-improving reform through voting in the presence of heterogeneous utilities. Committee members make decentralized, irrevocable promises of non-negative transfers contingent on the vote outcome to influence others’ voting behavior. Equilibrium transfers ensure that no coalition can deviate in a coordinated manner that benefits all members while minimizing total transfers. We show that equilibria exist, are indeterminate, efficient, and involve transfers from high- to low-utility members. These transfers prevent reform opponents from persuading less enthusiastic supporters to vote against the reform.

Robust experimental evidence of expected utility violations establishes that individuals overweight utility from low probability gains and losses. These findings motivated development of rank dependent utility (RDU). We characterize optimal RDU portfolios for investors facing dynamic, binomial returns. Our calibration shows optimal terminal wealth has significant downside protection, upside exposure, and a lottery component. Optimal dynamic trades require higher risky share after good returns and, possibly, nonparticipation when returns are poor. RDU portfolios counterfactually exhibit excessive elasticity of risky share to wealth and momentum rebalancing. Our results suggest a puzzling inconsistency between behavior inside and outside the laboratory. 

This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is reminescent of the classical Hamilton-Jacobi-Bellman equation of optimal control, but with a non-local term. We give a local existence result, and several examples in the consumption saving problem. The analysis is then applied to suggest that non constant discount rates generate an indeterminacy of the steady state in the Ramsey growth model. Despite its indeterminacy, the steady state level is robust to small deviations from constant discount rates. 

We investigate a linear–quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind farm. Players are time-inconsistent because they discount the utility with a non-constant rate. Our objective is to identify a consistent planning equilibrium in which the players are aware of their inconsistency and cannot commit to a lobbDying policy. We analyse equilibrium behaviour in both single-player and two-player cases and compare the behaviours of the game under constant and variable discount rates. The equilibrium behaviour is provided in closed-loop form, either analytically or via numerical approximation. Our numerical analysis of the equilibrium reveals that strategic behaviour leads to more intense lobbying without resulting in overshooting. 

We study a standard real-option problem in which sequential decisions are made through voting by a group of members with heterogeneous beliefs. We show that, when facing both investment and abandonment timing decisions, the group behavior cannot be replicated by that of a representative “median” member. As a result, members’ disagreement generates inertia—the group delays investment relative to a single-agent case—and underinvestment—the group rejects projects that are supported by a majority of members, acting in autarky. These coordination frictions hold in groups of any size, for general voting protocols, and are exacerbated by belief polarization. 

We study a dynamic corporate investment problem where decisions have to be made collectively by a group of agents holding heterogeneous beliefs and adhering to a “utilitarian” governance mechanism in which each agent has a given influence in the decision. In this setting we show that: (i) group decisions are typically dynamically inconsistent, (ii) dynamic inconsistency leads to inefficient underinvestment, and (iii) the ability to trade securities among insiders or with outsiders may restore efficient investment decisions but it may, in some cases, lead to inefficient overinvestment. Our theory can help explain the empirical evidence on the effect of diversity of groups, such as corporate boards, on firms’ outcomes and, more generally, on the difference between group and individual behavior. 

We consider a continuous time principal-agent model where the principal/firm compensates an agent/manager who controls the output’s exposure to risk and its expected return. Both the firm and the manager have exponential utility and can trade in a frictionless market. When the firm observes the manager’s choice of effort and volatility, there is an optimal contract that induces the manager to not hedge. In a two factor specification of the model where an index and a bond are traded, the optimal contract is linear in output and the log return of the index. We also consider a manager who receives exogenous share or option compensation and illustrate how risk taking depends on the relative size of the systematic and firm-specific risk premia of the output and index. Whilst in most cases, options induce greater risk taking than shares, we find that there are also situations under which the hedging manager may take less risk than the non-hedging manager. 

We model the debt and asset risk choice of a manager with performance-insensitive pay (cash) and performance-sensitive pay (stock) to theoretically link compensation structure, leverage, and credit spreads. The model predicts that optimal leverage trades off the tax benefit of debt against the utility cost of ex-post asset substitution and that credit spreads are increasing in the ratio of cash-to-stock. Using a large cross-section of U.S.-based corporate credit default swaps (CDS) covering 2001 to 2006, we find a positive association between cash-to-stock and CDS rates, and between cash-to-stock and leverage ratios. 

We investigate the classical Ramsey problem of economic growth when the planner uses non-constant discounting. It is well-known that this leads to time inconsistency, so that optimal strategies are no longer implementable. We then define equilibrium strategies to be such that unilateral deviations occurring during a small time interval are penalized. Non-equilibrium strategies are not implementable, so only equilibrium strategies should be considered by a rational planner. We show that there exists such strategies which are (a) smooth, and (b) lead to stationary growth, as in the classical Ramsey model. Finally, we prove an existence and multiplicity result: for logarithmic utility and quasi-exponential discount, there is an interval I such that, for every k in I, there is an equilibrium strategy converging to k. We conclude by giving an example where the planner is led to non-constant discount rates by considerations of intergenerational equity. 

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic market. We demonstrate that the manager's focus on the short horizon is detrimental to the long-horizon investor. When the returns are iid, the performance loss is significant, even when horizons are not very different. When the returns are mean reverting, the performance loss is exacerbated. We show that the manager's strategy tends to increase (decrease) the risk in the latter part of the optimization period after a bad (good) performance in the earlier part of the period, in agreement with empirical observations.

We derive a closed-form solution for the optimal portfolio of a nonmyopic utility maximizer who has incomplete information about the alphas or abnormal returns of risky securities. We show that the hedging component induced by learning about the expected return can be a substantial part of the demand. Using our methodology, we perform an “ex ante” empirical exercise, which shows that the utility gains resulting from optimal allocation are substantial in general, especially for long horizons, and an “ex post” empirical exercise, which shows that analysts’ recommendations are not very useful.

This paper develops, in a Brownian information setting, an approach for analyzing the preference for information, a question that motivates the stochastic differential utility (SDU) due to Duffie and Epstein [Econometrica 60 (1992) 353–394]. For a class of backward stochastic differential equations (BSDEs) including the generalized SDU [Lazrak and Quenez Math. Oper. Res. 28 (2003) 154–180], we formulate the information neutrality property as an invariance principle when the filtration is coarser (or finer) and characterize it. We also provide concrete examples of heterogeneity in information that illustrate explicitly the nonneutrality property for some GSDUs. Our results suggest that, within the GSDUs class of intertemporal utilities, risk aversion or ambiguity aversion are inflexibly linked to the preference for information. 

This paper generalizes, in the setting of Brownian information, the Duffie–Epstein (1992) stochastic differential formulation of intertemporal recursive utility (SDU). We provide a utility functional of state-contingent consumption plans that exhibits a local dependency with respect to the utility intensity process (the integrand of the quadratic variation) and call it the generalized SDU. This mathematical generalization of the SDU permits, in fact, more flexibility in the separation between risk aversion and intertemporal substitution and allows to model asymmetry in risk aversion. We extensively use the backward stochastic differential equation theory to give sufficient conditions for comparative and absolute risk aversion behavior as well as aversion to specific directional risk. Additionally, we discuss whether our functional exhibits monotonicity to its information filtration argument. For purposes of illustration, we provide some applications to the consumption/portfolio strategy selection problem in a complete securities market.