Risk-averse Agents Research Articles

Optimal Contracts with Privately Informed Agents and Active Principals

This paper considers an optimal contracting problem between an informed risk-averse agent and a principal, when the agent needs to perform multiple tasks, and the principal is active, i.e. she can influence some aspect of the agency relationship. It discusses the optimality of action restrictions in the equilibrium menus of linear contracts showing that private information considerations add new trade-offs to the optimal contracts in the multitask setting. The paper also has novel implications for the capital budgeting literature that studies informational problems. In particular the nature of the private information, e.g. whether it affects the marginal value of investment, the value of the agent's effort choice, or potential interactions between effort and investment, plays a crucial role in the optimal contracts. It is shown that several standard features of the optimal contracts are altered once the principal can affect the agency relationship through its capital budget, as well as through the compensation package.

Optimal contracts with privately informed agents and active principals

This paper considers an optimal contracting problem between an informed risk-averse agent and a principal, when the agent needs to perform multiple tasks, and the principal is active, namely she can influence some aspect of the agency relationship on top of the contract itself (i.e. capital budgets, task assignments). The paper shows how asymmetric information makes incentives and investment decisions substitutes for the principal. This result yields novel implications for contracting models with moral hazard and asymmetric information, i.e., capital budgeting or external capital raising games.

Equity portfolio insurance against a benchmark: Setting, replication and optimality

This paper undertakes the issue of portfolio insurance from the perspective of a risk-averse agent requiring his financial wealth to grow at a floored rate in excess of an equity benchmark. The suggested solution is a generalization of the CPPI approach within a two-equity asset framework. The paper examines some features of this extension related to its dynamic, its relative risk–reward profile and its static replication. It focuses more specifically on the optimal design of this portfolio strategy in the sense of consumption–investment decision making.

Pessimistic Optimal Choice for Risk-Averse Agents

We propose a general framework for the analysis of dynamic optimization with risk-averse agents, extending Whittle's (Whittle, 1990) formulation of risk-sensitive optimal control problems to accommodate time-discounting. We show how, within a Markovian set-up, optimal risk-averse behavior is identified via a pessimistic choice mechanism and described by simple recursive formulae. We apply this methodology to two distinct problems formulated respectively in discrete- and continuous-time. In the former, we extend Svensson's (Svensson, 1997) analysis of optimal monetary policy, showing that with a pessimistic central bank the inflation forecast is not longer an explicit intermediate target, the monetary authorities do not expect the inflation rate to mean revert to its target level and apply a more aggressive Taylor rule, while the inflation rate is less volatile. In the latter, we investigate the optimal production policy of a monopolistic entrepreneur which faces a demand schedule subject to stochastic shocks, once again showing that risk-aversion induces her to act more aggressively.

Tournaments with gaps

A standard tournament contract specifies only tournament prizes. If agents’ performance is measured on a cardinal scale, the principal can complement the tournament contract by a gap which defines the minimum distance by which the best performing agent must beat the second best to receive the winner prize. We analyze a tournament with two risk averse agents. Under unlimited liability, the principal strictly benefits from a gap by partially insuring the agents and thereby reducing labor costs. If the agents are protected by limited liability, the principal sticks to the standard tournament.

A Model of Monetary Policy and Risk Premia

We develop a dynamic asset pricing model in which monetary policy affects the risk premium component of the cost of capital. Risk-tolerant agents (banks) borrow from risk-averse agents (i.e. take deposits) to fund levered investments. Leverage exposes banks to funding risk, which they insure by holding liquidity buffers. By changing the nominal rate the central bank influences the liquidity premium in financial markets, and hence the cost of taking leverage. Lower nominal rates make liquidity cheaper and raise leverage, resulting in lower risk premia and higher asset prices, volatility, investment, and growth. We analyze forward guidance, a "Greenspan put'', and the yield curve.

IT Implementation Contract Design: Analytical and Experimental Investigation of IT Value, Learning, and Contract Structure

This article analytically and experimentally investigates how firms can best capture the business value of information technology (IT) investments through IT contract design. Using a small sample of outsourcing contracts for enterprise information technology (EIT) projects in several industries—coupled with reviews of contracts used by a major enterprise software maker—the authors determine the common provisions and structural characteristics of EIT contracts. The authors use these characteristics to develop an analytical model of optimal contract design with principal–agent techniques. The model captures a set of key characteristics of EIT contracts, including a staged, multiperiod project structure; learning; probabilistic binary outcomes; variable fee structures; possibly risk-averse agents; and implementation risks. The model characterizes conditions under which multistage contracts enable clients to create and capture greater project value than single-stage projects, and how project staging enables firms to reduce project risks, capture learning benefits, and increase development effort. Finally, the authors use controlled laboratory experiments to complement their analytical approaches and demonstrate robustness of their key findings.

Comparative Ross risk aversion in the presence of mean dependent risks

This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessarily mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross for mean independent risks. Our theoretical results are related to utility functions having the n-switch independence property.

The Supply Side of Jobless Recoveries

The fraction of unemployed households with revolving credit more than tripled between the late 1970s and the early 1990s, and new evidence suggests that close to 20% of unemployed households use revolving credit to replace lost income while as much as 40% default in response to job loss. Moreover, research by Chetty (2008) suggests that access to liquid assets is an important determinant of job finding. The natural question is, how has access to 'on-demand' credit changed the way labor markets respond to downturns? After exploring the interaction between job loss/credit markets in the data and describing the innate endogeneity associated with any reduced form answer, I build a new model that features risk averse agents who face both search frictions in the labor market (Menzio and Shi, 2011) and the credit market (Eaton and Gersovitz, 1981). The model mechanism is that easy credit conditions provide a safety net which incentivizes agents to search for better-paying but scarcer jobs. While this is welfare improving, the side effect is joblessness. Following a downturn, I find that an economy with easy credit access experiences a 10% larger drop in employment per capita compared to an economy in which credit is tight (e.g. a 2.2% drop in employment per capita with easy credit access versus a 2% drop with tight credit access). I argue that the model rationalizes a portion of jobless recoveries via supply side phenomenon.

Evolutionary justifications for non-Bayesian beliefs

This paper suggests that the evolutionarily optimal belief of an agent’s intrinsic reproductive ability is systematically different from the posterior belief obtained by the perfect Bayesian updating. In particular, the optimal belief depends on how risk-averse the agent is. Although the perfect Bayesian updating remains evolutionarily optimal for a risk-neutral agent, it is not for any other. Specifically, the belief is always positively biased for a risk-averse agent, and the more risk-averse an agent is, the more positively biased the optimally updated belief is. Such biased beliefs align with experimental findings and also offer an alternative explanation to the empirical puzzle that people across the population appear overconfident by consistently overestimating their personal hereditary traits.

Test Contract

In this paper I examine a T-period agency model with imperfect public monitoring between a risk-neutral principal and a risk-averse agent where signals can depend on the agent's past actions and exhibit serial correlation. In this general environment, I show that near-efficiency obtains when T is large if the monitoring technology satisfies two basic properties: concentration of measure and informativeness. The tension between these properties determines the boundary at which asymptotic efficiency obtains in agency models with frequent actions, unifies and extends various efficiency results in the agency literature, quantifies the value of knowing detailed features of signal processes and solves a large class of incentive problems with highly persistent monitoring technologies.

Possibilistic Risk Aversion and Coinsurance Problem

The coinsurance problem is an important topic in insurance decisions. A risk-averse agent should choose a coinsurance rate maximizing the expected final wealth. In this paper, we propose a possibilistic model of coinsurance problem. A decision problem whose solution is the optimal coinsurance is formulated. Some of its properties, the calculation modality and its behavior towards the changes of risk aversion are studied.

Exchange Rate Volatility in Nigeria: Evidence from a Parametric Measure

The study uses a parametric measure to discover the trend and possible causes of exchange rate volatility in Nigeria over the period 1986: 1-- 2009: 4. The study revealed that exchange rate has been volatile in Nigeria given the fact that the standard deviation of exchange rate has been unusually high and unusually low during the period under investigation. The parametric measure of exchange rate further confirmed a high degree of volatility which portrays higher risk to a risk-averse economic agent. The study therefore recommends that the government should always take a cognizance look at the frequent movement in the exchange rate with a view to regulating it because higher risks attached to high degree of volatility may scare off both domestic and foreign investors.

Bubbles, crashes and risk

A restricted-perceptions equilibrium exists in which risk-averse agents believe stock prices follow a random walk with a conditional variance that is self-fulfilling. When agents estimate risk, bubbles and crashes arise. These effects are stronger when agents allow for ARCH in excess returns.

Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging

Proper Scoring Rules (PSRs) are popular incentivized mechanisms to elicit an agent's beliefs. This paper combines theory and experiment to characterize how PSRs bias reported beliefs when (i) the PSR payments are increased, (ii) the agent has a financial stake in the event she is predicting, and (iii) the agent can hedge her prediction by taking an additional action. In contrast with previous literature, the PSR biases are characterized for all PSRs and all risk averse agents. Our results reveal complex distortions of reported beliefs, thereby raising concerns about the ability of PSRs to recover truthful beliefs in general decision-making environments.

Change in Risk and Bargaining Game

This paper studies the comparative statics regarding changes in risk on Nash's solution to bargaining games with stochastic outcome and disagreement points. When absolute risk tolerance is linear with constant slope, the Nash's solution to bargaining with risky outcomes and risky disagreement points can be viewed as division of divisible certainty equivalent between two risk-averse agents. We show that whether a deterioration of a bargainer's risky prospect is advantageous to his opponent often depends on whether preference displays decreasing absolute risk aversion (DARA). Specifically, for perfectly correlated risky prospects, DARA a la Arrow-Pratt works to the concavity of the joint certainty equivalent with respect to a bargainer's initial wealth or size of risky exposure; for independent risky prospects, DARA a la Ross vulnerates his risk bearing under Rothschild-Stiglitz increase in risk taking the form of adding an independent noise, both leading to the bargainer's increased propensity for risk aversion as well as the joint size of the pie. These results illuminate how individual risky prospect as well as risk preference influence the cooperating partners' income shares and thus the market equilibrum of marriage formation. We also show that this result is robust under Rubinstein's non-cooperative bargaining game.

Jobless Recoveries and the Revolving Credit Revolution (Preliminary)

Access to revolving credit more than doubled between 1983 and 1992 among both employed and unemployed households, and new evidence suggests that close to 20% of unemployed households use revolving credit to replace lost income. Labor markets have also experienced sluggish recoveries following the 1991, 2001, and 2007 recessions. These two facts motivate the question posed in this study: how has access to 'on-demand' credit changed the way labor markets respond to downturns? To answer this question, I build a model with risk averse agents who face both search frictions in the labor market and search frictions in the credit market. In the model, easy credit conditions provide a safety net that incentivizes agents to search for better paying jobs. Following a downturn, I find that an economy with easy credit access experiences a 10% larger drop in employment per capita compared to an economy in which credit is tight (e.g. a 2.2% drop in employment per capita with easy credit access versus a 2% drop with tight credit access).

Liquid Assets, Illiquid Assets and Sunspots

In this paper, I first show that liquid assets make risk-averse agents better off by eliminating multiple equilibria and thus eliminating speculation based on nonfundamentals. I then show that illiquid assets make risk-averse agents worse off by enlarging the set of economies (or agent preferences) that give rise to sunspot equilibria. In addition, my results show that with illiquid assets, nonfundamental volatility results as follows: In order to smooth consumption, some agents endogenously create private claims backed by these illiquid capital assets. These claims have multiple price equilibria, and their fluctuating prices cause the prices of the illiquid capital assets to fluctuate as well. The excess volatility makes all risk-averse agents worse off (in a Pareto sense). My model also shows equilibrium idiosyncratic risk bearing in illiquid asset markets by certain segments of the population which should be of concern to regulators and policy makers. For example, in real estate markets, there is a role for government intervention and for government-supplied liquidity and for its active management.

In This Issue

In This Issue

Risk Aversion, Indivisible Timing Options, and Gambling

In this paper we model the behavior of a risk-averse agent who seeks to maximize expected utility and who has an indivisible asset and a timing option over when to sell this asset. Our main contribution is to show that, contrary to intuition, optimal behavior for such a risk-averse agent can include risk-increasing gambles. For example, a manager with a choice over when to disinvest from a project, a private homeowner with a property to sell, or an employee with a grant of American-style stock options may be better off taking positions in other assets with zero Sharpe ratio that are uncorrelated with the underlying project, house, or stock price risk. The results have wider implications for the modeling and interpretation of portfolio optimization problems involving American-style timing decisions.