OPTIMAL LIQUIDATION AND ADVERSE SELECTION IN DARK POOLS

We consider an investor who has access both to a traditional venue and a dark pool for liquidating a position in a single asset. While trade execution is certain on the traditional exchange, she faces linear price impact costs. On the other hand, dark pool orders suffer from adverse selection and trade execution is uncertain. Adverse selection decreases order sizes in the dark pool while it speeds up trading at the exchange. For small orders, it is optimal to avoid the dark pool completely. Adverse selection can prevent profitable round‐trip trading strategies that otherwise would arise if permanent price impact were included in the model.     

Nonlinear price impact and portfolio choice

In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square‐root impact law and, as extreme cases, linear impact and proportional transaction costs.     

Optimal consumption and investment with liquid and illiquid assets

I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ordinary differential equation (ODE) with an integral constraint. I find an explicit characterization of model parameters for the well‐posedness of the problem, and show that the problem is well posed if and only if there exists a shadow price process. Finally, I describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.     

Should Stochastic Volatility Matter to the Cost-Constrained Investor?

Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969) . Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources. We examine the two-asset portfolio optimization problem when both elements are present. We show that a transaction cost framework can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.     

TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.     

INVESTING WITH LIQUID AND ILLIQUID ASSETS

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.     

A generalized theoretical modelling approach for the assessment of economic-capital under asset market liquidity risk constraints

This paper proposes a concrete theoretical foundation and a new modelling framework that attempts to tackle the issue of market/liquidity risk and economic-capital estimation at a portfolio level by combining two mutual asset market/liquidity risk models. In essence, this study extends research literature related to the assessment of the asset market/liquidity risk by providing a generalized theoretical modelling underpinning that handle, from the same perspective, market and liquidity risks jointly and integrate both risks into a portfolio setting without a commensurate increase of statistical postulations. As such, we argue that market and liquidity risk components are correlated in most cases and can be integrated into one single market/liquidity framework that consists of two interrelated sub-components. The first component is attributed to the impact of adverse price movements and is modelled based on the concept of liquidity-adjusted value-at-risk framework, while the second component focuses on the risk of variation in transactions costs due to the bid-ask spreads and it attempts to measure the likelihood that it will cost more than expected to liquidate the asset position. As such, the model comprises a new approach to contemplating the impact of time-varying volatility of the bid-ask spread and its upshot on the overall asset market/liquidity risk. The modelling framework can be constructive for financial service industries in emerging-economies and particularly in reinforcing rational economic-capital allocation in light of the aftermaths of the sub-prime financial crisis.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003     

Speculation and hedging in the currency futures markets: Are they informative to the spot exchange rates

This study presents an empirical analysis investigating the relationship between the futures trading activities of speculators and hedgers and the potential movements of major spot exchange rates. A set of trader position measures are employed as regression predictors, including the level and change of net positions, an investor sentiment index, extremely bullish/bearish sentiments, and the peak/trough indicators. We find that the peaks and troughs of net positions are generally useful predictors to the evolution of spot exchange rates, but other trader position measures are less correlated with future market movements. In addition, speculative position measures usually forecast price‐continuations in spot rates while hedging position measures forecast price‐reversals in these markets. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

DEFAULT AND SYSTEMIC RISK IN EQUILIBRIUM

We develop a finite horizon continuous time market model, where risk‐averse investors maximize utility from terminal wealth by dynamically investing in a risk‐free money market account, a stock, and a defaultable bond, whose prices are determined via equilibrium. We analyze the endogenous interaction arising between the stock and the defaultable bond via the interplay between equilibrium behavior of investors, risk preferences and cyclicality properties of the default intensity. We find that the equilibrium price of the stock experiences a jump at default, despite that the default event has no causal impact on the underlying economic fundamentals. We characterize the direction of the jump in terms of a relation between investor preferences and the cyclicality properties of the default intensity. We conduct a similar analysis for the market price of risk and for the investor wealth process, and determine how heterogeneity of preferences affects the exposure to default carried by different investors.     

Asymmetric Correlations in Predicting Portfolio Returns*

Rigorous statistical tests have been designed to detect the existence of asymmetric correlations. However, these tests can hardly further facilitate future investment or risk management because asymmetric correlations are time‐varying and difficult to predict. In this paper, we construct a unified state‐space model, which not only measures in‐sample asymmetric correlations, but also exploit out‐of‐sample asymmetric correlations in the context of predicting portfolio returns. First, we regard time‐varying correlation between market returns and portfolio returns as a state variable and model it as an AR(1) process. Then, we measure future asymmetric correlations based on correlation coefficients between two unpredictable components in market returns and correlation, respectively. Third, we clarify the intuition, calculate asymmetric correlations for two portfolio sets and estimate the economic value of applying our model in asset allocation. Finally, we try to search for potential variables that can explain future asymmetric correlations. The results show that market‐wide liquidity, variance, earning price ratio, and investor sentiment can partially explain the asymmetry correlation phenomenon.     

Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model

We consider a general semimartingale model of a currency market with transaction costs. Assuming that the price process is continuous and the solvency cone is proper we prove a hedging theorem describing the set of initial endowments that allows the investor to hedge a contingent claim in various currencies by a self‐financing portfolio.     

OPTIMAL INVESTMENT IN CREDIT DERIVATIVES PORTFOLIO UNDER CONTAGION RISK

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs) and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced‐form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice dependence structure between the Hamilton‐Jacobi‐Bellman equations associated with the default states of the portfolio. We show existence and uniqueness of a classical solution to each equation and characterize them in terms of solutions to inhomogeneous Bernoulli type ordinary differential equations. We provide a precise characterization for the directionality of the CDS investment strategy and perform a numerical analysis to assess the impact of default contagion. We find that the increased intensity triggered by default of a very risky entity strongly impacts size and directionality of the investor strategy. Such findings outline the key role played by default contagion when investing in portfolios subject to multiple sources of default risk.     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.     

OPTION PRICING AND HEDGING WITH SMALL TRANSACTION COSTS

An investor with constant absolute risk aversion trades a risky asset with general Itô‐dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading‐order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.     

Flight-to-liquidity: Evidence from China's stock market

In an order-driven and strictly regulated stock market, illiquidity risks' effects on asset pricing should be highlighted, particularly in such extreme market conditions as those in China. This paper utilizes panel data from China's stock market in an attempt to answer whether the illiquidity risk in various dimensions—including price impacts, the transaction speed, trading volume, transaction costs, and asymmetric information—can explain stock returns. We find that almost all dimensions of stock illiquidity are positively associated with excess stock returns. More importantly, smaller, less-liquid stocks suffer more liquidity costs, providing a strong evidence for “flight-to-liquidity.” Additionally, the transaction costs and asymmetric information, denoted by bid-ask spreads, robustly account for these illiquidity effects on stock pricing and differ from the findings in the U.S. market. We also find that the “flight-to-liquidity” can partially explain the idiosyncratic volatility puzzle, investors' gambling, and herding psychologies. This study provides substantial policy implications in regulation and portfolio management for emerging markets.     

RISK HORIZON AND REBALANCING HORIZON IN PORTFOLIO RISK MEASUREMENT

This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a 10‐day value‐at‐risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a 1‐year horizon. More importantly, whereas 10‐day VaR is ordinarily calculated with a portfolio’s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio’s profit and loss distribution over a risk‐measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics.     

Portfolio choice with small temporary and transient price impact

We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen. In the large‐liquidity limit where both frictions are small, we derive explicit formulas for the asymptotically optimal trading rate and the corresponding minimal leading‐order performance loss. We find that the losses are governed by the volatility of the frictionless target strategy, like in models with only temporary price impact. In contrast, the corresponding optimal portfolio not only tracks the frictionless optimizer, but also exploits the displacement of the market price from its unaffected level.     

The determinants of price discovery on bitcoin markets

This paper investigates whether market quality, uncertainty, investor sentiment and attention, and macroeconomic news affect bitcoin price discovery in spot and futures markets. Over the period December 2017–March 2019, we find significant time variation in the contribution to price discovery of the two markets. Increases in price discovery are mainly driven by relative trading costs and volume, and uncertainty to a lesser extent. Additionally, medium-sized trades contain most information in terms of price discovery. Finally, higher news-based bitcoin sentiment increases the informational role of the futures market, while attention and macroeconomic news have no impact on price discovery.