Semyon Malamud

Information Percolation With Equilibrium Search Dynamics

We solve for the equilibrium dynamics of information sharing in a large population. Each agent is endowed with signals regarding the likely outcome of a random variable of common concern. Individuals choose the effort with which they search for others from whom they can gather additional information. When two agents meet, they share their information. The information gathered is further shared at subsequent meetings, and so on. Equilibria exist in which agents search maximally until they acquire sufficient information precision and then search minimally. A tax whose proceeds are used to subsidize the costs of search improves information sharing and can, in some cases, increase welfare. On the other hand, endowing agents with public signals reduces information sharing and can, in some cases, decrease welfare.

Information Percolation in Segmented Markets

We study equilibria of dynamic over-the-counter markets in which agents are distinguished by their preferences and information. Over time, agents are privately informed by bids and offers. Investors differ with respect to information quality, including initial information precision, and also in terms of market “connectivity,” the expected frequency of their bilateral trading opportunities. We characterize endogenous information acquisition and show how learning externalities affect information gathering incentives. More “liquid” markets lead to higher equilibrium information acquisition when the gains from trade and market duration are sufficiently large. On the other hand, for a small market duration, the opposite may occur if agents vary sufficiently in terms of their market connectivity.

Endogenous Completeness of Diffusion Driven Equilibrium Markets

We study the existence of dynamic equilibria with endogenously complete markets in continuous-time, heterogenous agents economies driven by diffusion processes. Our main results show that under appropriate conditions on the transition density of the state variables, market completeness can be deduced from the primitives of the economy. In particular, we prove that a sufficient condition for market completeness is that the volatility of dividends be invertible and provide higher order conditions that apply when this condition fails as is the case in the presence of fixed income securities. In contrast to previous research, our formulation does not require that securities pay terminal dividends, and thus allows for both finite and infinite horizon economies.

Relative Extinction of Heterogeneous Agents

In all the existing literature on survival in heterogeneous economies, the rate at which an agent vanishes in the long run relative to another agent can be characterized by the difference of the so-called survival indices, where each survival index only depends on the preferences of the corresponding agent and the properties of the aggregate endowment. In particular, one agent experiences extinction relative to another (that is, the wealth ratio of the two agents goes to zero) if and only if she has a smaller survival index. We consider a simple complete market model and show that the survival index is more complex if there are more than two agents in the economy. In fact, the following phenomenon may take place: even if agent one experiences extinction relative to agent two, adding a third agent to the economy may reverse the situation and force the agent two to experience extinction relative to agent one. We also calculate the rates of convergence.

Long run forward rates and long yields of bonds and options in heterogeneous equilibria

Abstract We prove that, in a heterogeneous economy with scale-invariant utilities, the yield of a long term bond is determined by the agent with maximal expected marginal utility. We also prove that the same result holds for the long term forward rates. Furthermore, we apply Cramér’s large deviations theorem to calculate the yield of a long term European call option. It turns out that there is a threshold risk aversion such that the option yield is independent of the risk aversion when the latter is above the threshold. Surprisingly, the long term option yield is always greater than or equal to the corresponding equity return. That is, in the long run, it is more profitable to buy a long maturity call option on equity than the equity itself.

Momentum and Risk Adjustment

Dudler and Gmür introduce a new class of momentum strategies: the risk-adjusted time-series momentum (RAMOM) strategies, which are based on averages of past futures returns that have been normalized by their volatility. They test these strategies on a universe of 64 liquid futures contracts and show that RAMOM strategies outperform the standard time-series momentum strategies. In addition, RAMOM trading signals have another useful and important feature: They are naturally less dependent on high volatility. Finally, dollar turnover of RAMOM strategies is about 40% lower than that of time series momentum (TSMOM), implying a drastic reduction in trading costs.

A Dynamic Equilibrium Model of ETFs

I develop a dynamic general equilibrium model of exchange traded funds (ETFs) that accounts for the two-tier ETF market structure with both a centralized exchange (secondary market) and a creation/redemption mechanism (primary market) operating through market-making firms known as Authorized Participants (APs). The model is tractable and allows for any number of ETFs and basket securities. I show that the creation/redemption mechanism serves as a shock propagation channel through which temporary demand shocks may have long-lasting impacts on future prices. In particular, they may lead to a momentum in asset returns and a persistent ETF pricing gap. Improving liquidity in the primary market stimulates creation/redemption and therefore strengthens the shock propagation channel. As a result, it may amplify the volatility of both the underlying assets and the ETF pricing gap. At the same time, introducing new ETFs may reduce both the volatility and co-movement in the returns and may improve the liquidity of the underlying securities.

Universal bounds for asset prices in heterogeneous economies

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artificial homogeneous economy populated solely by this agent, and calculate the “homogeneous” price of an asset in each of these economies. Dumas (Rev. Financ. Stud. 2, 157–188, [1989]) conjectured that the risk free rate in a heterogeneous economy must lie in the interval determined by the minimal and maximal of the “homogeneous” risk free rates. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one, and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.

Optimal Risk Sharing with Limited Liability

We solve the general problem of optimal risk sharing among a nite number of agents with limited liability. We show that the optimal allocation is characterized by endogenously determined ranks assigned to the participating agents and a hierarchical structure of risk sharing, where all agents take on risks only above the agent-speci fic thresholds determined by their ranks. When all agents have CARA utilities, linear risk sharing is optimal between two adjacent thresholds. We use our general characterization of optimal risk sharing with limited liability to solve the problem of optimal insurance design with multiple insurers. We show that the optimal thresholds, or deductibles, can be efficiently calculated through the fixed point of a contraction mapping. We then use this contraction mapping technique to derive a number of comparative statics results for optimal insurance design and its dependence on microeconomic characteristics.

Risk Adjusted Time Series Momentum

We introduce a new class of momentum strategies, the risk-adjusted time series momentum (RAMOM) strategies, which are based on averages of past futures returns, normalized by their volatility. We test these strategies on a universe of 64 liquid futures contracts and show that RAMOM strategies outperform the time series momentum (TSMOM) strategies of Ooi, Moskowitz, and Pedersen (2012) for almost all combinations of holding and look-back periods. This outperformance is driven by the following new striking stylized fact that we document: For almost all of the 64 futures contracts, independent of the asset class, realized futures volatility is contemporaneously negatively related to the Fama and French (1987) market (MKT), value (HML), and momentum (UMD) factors. As a result, RAMOM returns have a natural, built-in exposure to the MKT, HML, and UMD factors and outperform TSMOM returns precisely in times when (some of) the factors deliver good returns. In particular, RAMOM allows investors to gain significant exposure to Fama and French factors without actually trading the very large stock universe. Furthermore, dollar turnover of RAMOM strategies is about 40% lower than that of TSMOM, implying a drastic reduction in trading costs. We construct measures of momentum-specific volatility, both within and across asset classes, and show how these volatility measures can be used for risk management. We find that momentum risk management significantly increases Sharpe ratios, but at the same time may lead to more pronounced negative skewness and tail risk. Furthermore, momentum risk management leads to a much lower exposure to market, value, and momentum factors; as a result, risk-managed momentum returns offer much higher diversification benefits than those of standard momentum returns.