Strategic Asset Allocation in Money Management

This article analyzes the dynamic portfolio choice implications of strategic interaction among money managers. The strategic interaction emerges as the managers compete for money flows displaying empirically documented convexities. A manager gets money flows increasing with performance, and hence displays relative performance concerns, if her relative return is above a threshold; otherwise she receives no (or constant) flows and has no relative concerns. We provide a tractable formulation of such strategic interaction between two risk averse managers in a continuous-time setting, and solve for their equilibrium policies in closed-form. When the managers’ risk aversions are considerably different, we do not obtain a Nash equilibrium as the managers cannot agree on who loses (getting no flows) in some states. We obtain equilibria, but multiple, when the managers are similar since they now care only about the total number of losing states. We recover a unique equilibrium, however, when a sufficiently high threshold makes the competition for money flows less intense. The managers’ unique equilibrium policies are driven by chasing and contrarian behaviors when either manager substantially outperforms the opponent, and by gambling behavior when their performances are close to the threshold. Depending on the stock correlation, the direction of gambling for a given manager may differ across stocks, however the two managers always gamble strategically in the opposite direction from each other in each individual stock.Money Managers, Strategic Interaction, Portfolio Choice, Relative Performance, Incentives, Risk Shifting, Fund Flows, Tournaments

Difference in Interim Performance and Risk Taking with Short-sale Constraints

Absent much theory, empirical works often rely on the following informal reasoning when looking for evidence of a mutual fund tournament: If there is a tournament, interim winners have incentives to decrease their portfolio volatility as they attempt to protect their lead, while interim losers are expected to increase their volatility so as to catch up with winners. We consider a rational model of a mutual fund tournament in the presence of short-sale constraints and find the opposite – interim winners choose more volatile portfolios in equilibrium than interim losers. Several empirical works present evidence consistent with our model, however based on the above informal argument they appear to conclude against the tournament behavior. We argue that this conclusion is unwarranted. We also demonstrate that tournament incentives lead to differences in interim performance for otherwise identical managers, and that mid-year trading volume is inversely related to mid-year stock return.mutual fund tournament, risk-taking incentives, relative performance, portfolio choice, short-sale constraints

Equilibrium Mispricing in a Capital Market with Portfolio Constraints

This paper develops a general equilibrium, continuous time model where portfolio constraints generate mispricing between redundant securities. Constrained consumption-portfolio optimization techniques are adapted to incorporate redundant, possibly mispriced, securities. Under logarithmic preferences, we provide explicit conditions for mispricing and closed-form expressions for all economic quantities. Existence of an equilibrium where mispricing occurs with positive probability is verified in a specific case. In a more general setting, we demonstrate the necessity of mispricing for equilibrium when agents are heterogeneous enough. The construction of a representative agent with stochastic weights allows us to characterize prices and allocations, given mispricing occurs.

Monopoly Power and the Firm’s Valuation:

Recent anti-trust cases exacerbated the concerns of investors regarding the effects of a firm's monopoly power on its production choice, shareholder value, and the overall economy. We address this issue within a dynamic equilibrium model featuring a large monopolistic firm whose actions not only affect the price of its output, but also effectively influence the valuation of its stock. The latter renders time inconsistency to the firm's dynamic production choice. When the firm is required to pre-commit to its strategy, the ensuing equilibrium is largely in line with the predictions of the textbook monopoly model. When the firm behaves in a time-consistent manner, however, the predictions are strikingly at odds. The trade-off between current profits and the valuation of future profits induces the firm to increase production beyond the competitive benchmark and cut prices. This policy may result in destroying shareholder value, and does indeed fully wipe out the firm's profit in the limit of the decision-making interval shrinking to zero, in line with the Coase conjecture

A Model of Credit Risk, Optimal Policies, and Asset Prices

This paper studies the optimal policies of borrowers (firms or individuals) who may default subject to default costs, and analyzes the asset pricing implications. Borrowers defaulting under adverse economic conditions may, despite incurring default costs, emerge as wealthier than non-borrowers or those who can default costlessly. Under many economic scenarios, borrowers takes on less risk exposure than non-borrowers, and asset substitution is not pronounced. However, a larger risk exposure by borrowers may occur as well, depending on the structure of default costs and on how debt maturity relates to the planning horizon. In the latter case, borrowers’ default policies render binary options to be useful credit derivatives for lenders in hedging the credit-risk component of their assets. In our model, the asset-value dynamics are endogenously determined, and are shown to exhibit stochastic mean return and volatility in contrast to the exogenously assumed constant mean and volatility in many credit risk models. We consider a variety of extensions, including equilibrium, where a lower (higher) risk exposure by borrowers manifests itself in an attenuated (amplified) market volatility and risk premium, but the market value is always higher in economic downturns, and lower in upturns, compared to an economy without the presence of credit risk

Risk Management with Benchmarking

Portfolio theory must address the fact that in reality, portfolio managers are evaluated relative to a benchmark, and therefore adopt risk management practices to account for the benchmark performance. We capture this risk management consideration by allowing a prespecified shortfall from a target benchmark-linked return, consistent with growing interest in such practice. In a dynamic setting, we demonstrate how a risk averse portfolio manager optimally under- or overperforms a target benchmark under different economic conditions, depending on his attitude towards risk and choice of the benchmark. Investors can therefore achieve their desired gain/loss characteristics for funds under management through an appropriate combined choice of the benchmark and money manager

Multiplicity in General Financial Equilibrium with Portfolio Constraints, Second Version

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.Multiple equilibria, asset pricing, portfolio constraints, indeterminacy, financial equilibrium

Risk Management with Benchmarking

Portfolio theory must address the fact that, in reality, portfolio managers are evaluated relative to a benchmark, and therefore adopt risk management practices to account for the benchmark performance. We capture this risk management consideration by allowing a pre-specified shortfall from a target benchmark-linked return, consistent with growing interest in such practice. In a dynamic setting, we demonstrate how a risk averse portfolio manager optimally under- or over-performs a target benchmark under different economic conditions, depending on his attitude towards risk and choice of the benchmark. The analysis therefore illustrates how investors can achieve their desired gain/loss characteristics for funds under management through an appropriate combined choice of the benchmark and money manager. We consider a variety of extensions, and also highlight the ability of our setting to shed some light on documented return patterns across segments of the money management industry