Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.     

Optimal liquidation in dark pools

We consider a large trader liquidating a portfolio using a transparent trading venue with price impact and a dark pool with execution uncertainty. The optimal execution strategy uses both venues continuously, with dark pool orders over-/underrepresenting the portfolio size depending on return correlations; trading at the traditional venue is delayed depending on dark liquidity. Pushing up prices at the traditional venue while selling in the dark pool might generate profits. If future returns depend on historical dark pool liquidity, then sending orders to the dark pool can be worthwhile simply to gather information.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

Optimal liquidation strategies regularize portfolio selection

We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under expected shortfall (ES) in the case of linear market impact. We show that, once market impact is taken into account, a regularized version of the usual optimization problem naturally emerges. We characterize the typical behavior of the optimal liquidation strategies, in the limit of large portfolio sizes, and show how the market impact removes the instability of ES in this context.     

Dynamic liquidation under market impact

The optimal liquidation problem with transaction costs, which includes a positive fixed cost, and market impact costs, is studied in this paper as a constrained stochastic optimal control problem. We assume that trading is instantaneous and the dynamics of the stock to be liquidated follows a geometric Brownian motion. The solution to the impulse control problem is computed at each time step by solving a linear partial differential equation and a maximization problem. In contrast to results obtained from the static formulation of Almgren and Chriss [J. Risk, 2000 Almgren, R and Chriss, N. 2000. Optimal execution of portfolio transactions. J. Risk, 3: 5–39. [Crossref] , [Google Scholar], 3, 5–39], when risk is not considered, the optimal liquidation strategy from our stochastic control formulation depends on temporary market impact cost and permanent market impact cost parameters. In addition, our computational results indicate the following properties of the optimal execution strategy from the stochastic control formulation. Due to the existence of a no-transaction region, it may not be optimal for some individuals to sell their assets on some trading dates. As the value of the permanent market impact parameter increases, the expected optimal amount liquidated at the terminal time increases. As the value of the quadratic temporary impact cost parameter increases, the expected optimal amount liquidated at trading times tends to be uniform, and the no-transaction region shrinks. In the presence of quadratic temporary market impact costs, in contrast to optimal strategies that result from fixed and/or proportional transaction costs alone, portfolios in the selling region are neither re-balanced into the no-transaction region nor into the sell and no-transaction interface.     

Discrete-time option pricing with stochastic liquidity

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500.     

Optimal pricing of intraday liquidity

This paper presents a general equilibrium model where intraday liquidity is needed because the timing of payments is uncertain. A necessary and sufficient condition for an equilibrium to be efficient is that the nominal intraday interest rate be zero, even when the overnight rate is strictly positive. Because a market for liquidity may not achieve efficiency, this creates a role for the central bank. I allow for the possibility of moral hazard and study policies commonly used by central banks to reduce their exposure to risk. I show collateralized lending achieves the efficient allocation, while, for certain parameters, caps cannot prevent moral hazard.     

Partial liquidation under reference-dependent preferences

We propose a multiple optimal stopping model where an investor can sell a divisible asset position at times of her choosing. Investors have $S$-shaped reference-dependent preferences, whereby utility is defined over gains and losses relative to a reference level and is concave over gains and convex over losses. For a price process following a time-homogeneous diffusion, we employ the constructive potential-theoretic solution method developed by Dayanik and Karatzas (Stoch. Process. Appl. 107:173–212, 2003). As an example, we revisit the single optimal stopping model of Kyle et al. (J. Econ. Theory 129:273–288, 2006) to allow partial liquidation. In contrast to the extant literature, we find that the investor may partially liquidate the asset at distinct price thresholds above the reference level. Under other parameter combinations, the investor sells the asset in a block, either at or above the reference level.     

Optimal portfolio liquidation in target zone models and catalytic superprocesses

We study optimal buying and selling strategies in target zone models. In these models, the price is modelled by a diffusion process which is reflected at one or more barriers. Such models arise, for example, when a currency exchange rate is kept above a certain threshold due to central bank interventions. We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem is formulated as the minimization of a cost–risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting, the catalyst is given by the barriers of the price process. For the cases in which the unaffected price process is a reflected arithmetic or geometric Brownian motion with drift, we moreover give a detailed financial justification of our cost functional by means of an approximation with discrete-time models.     

Managing liquidity: Optimal degree of centralization

Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches. We translate this question into a facility location problem under uncertainty. We show that volatility is the key driver behind (de-)centralization. We provide an analytical solution for the 2-branch model and show that a liquidity center can be interpreted as an option on immediate liquidity. Therefore, its value can be interpreted as the price of information, i.e., the price of knowing the exact demand. Furthermore, we derive the threshold above which it is advantageous to open a liquidity center and show that it is a function of the volatility and the characteristic of the bank network. Finally, we discuss the n-branch model for real-world banking groups (10-60 branches) and show that it can be solved with high granularity (100 scenarios) within less than 30 s.     

Conic quantization: stochastic volatility and market implied liquidity

Market implied liquidity links the pricing of European options under stochastic volatility with the Conic Finance theory of two prices     

Risk allocation under liquidity constraints

Risk allocation games are cooperative games that are used to attribute the risk of a financial entity to its divisions. In this paper, we extend the literature on risk allocation games by incorporating liquidity considerations. A liquidity policy specifies state-dependent liquidity requirements that a portfolio should obey. To comply with the liquidity policy, a financial entity may have to liquidate part of its assets, which is costly.The definition of a risk allocation game under liquidity constraints is not straightforward, since the presence of a liquidity policy leads to externalities. We argue that the standard worst case approach should not be used here and present an alternative definition. We show that the resulting class of transferable utility games coincides with the class of totally balanced games. It follows from our results that also when taking liquidity considerations into account there is always a stable way to allocate risk.     

Payments and liquidity under adverse selection

Informational asymmetries regarding the future value of assets affect their role in exchange. I construct a random-matching economy composed of two assets: a risk-free bond and a Lucas tree whose terminal value is privately known to its holder. No restrictions are imposed on payment arrangements. The main finding supports a pecking-order theory of payments: Agents use their risk-free bonds first in order to finance their spending shocks, and they use their information-sensitive assets only if their holdings of bonds are depleted. The theory has implications for the optimal provision of risk-free bonds, the structure of asset returns, and liquidity.     

Stock liquidity premium with stochastic price impact and exogenous trading strategy

This paper provides a model which helps explain the variability of stock liquidity premium. Liquidity is modelled as a time-varying price impact and includes both permanent as well as temporary price impacts. Liquidity premium is defined as an additional expected return that stock should yield to compensate an investor for the potential loss of wealth utility caused by price impact costs. The numerical results presented show that liquidity premium varies with expected net stock return, return volatility and, to a lesser extent, with returns on risk-free bonds. Liquidity premium is a growing and convex function of liquidity costs, and temporary price impact has a more severe effect on liquidity premium than the permanent one.     

Currency hedging for multinationals under liquidity constraints

This paper examines the impact of liquidity risk on the behavior of a risk-averse multinational firm (MNF) under exchange rate uncertainty in a two-period dynamic setting. The MNF has operations domiciled in the home country and in a foreign country, each of which produces a single homogeneous good to be sold in the home and foreign markets. To hedge the exchange rate risk, the MNF has access to one-period currency futures and option contracts in each period. The MNF is liquidity constrained in that it is obliged to terminate its risk management program in the second period whenever the net loss due to its first-period hedge position exceeds a predetermined threshold level. We show that the MNF optimally sells less (more) and produces more (less) in the foreign (home) country in response to the imposition of the liquidity constraint. We show further that the liquidity constrained MNF optimally uses the currency option contracts in the first period for hedging purposes in general, and opts for a long option position if its utility function is quadratic in particular.     

Optimal execution with stochastic delay

Finance and Stochastics - We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs are liquidity-taking...     

Productivity and liquidity management under costly financing

We explore theoretically and empirically the relationship between firm productivity and liquidity management in the presence of financial frictions. We build a dynamic investment model and show that, counter to basic economic intuition, more productive firms could demand less capital assets and hold more liquid assets compared to less productive firms when financing costs are sufficiently high. We empirically test this prediction using a comprehensive dataset of Chinese manufacturers and find that more productive firms indeed hold less capital and more cash. We do not, however, observe this for US manufacturers. Our study suggests a larger capital misallocation problem in markets with significant financing frictions than previously documented.