Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.     

Portfolio revision under mean-variance and mean-CVaR with transaction costs

The portfolio revision process usually begins with a portfolio of assets rather than cash. As a result, some assets must be liquidated to permit investment in other assets, incurring transaction costs that should be directly integrated into the portfolio optimization problem. This paper discusses and analyzes the impact of transaction costs on the optimal portfolio under mean-variance and mean-conditional value-at-risk strategies. In addition, we present some analytical solutions and empirical evidence for some special situations to understand the impact of transaction costs on the portfolio revision process.     

Life-cycle portfolio choice with liquid and illiquid financial assets

Traditionally, quantitative models that have studied households׳ portfolio choices have focused exclusively on the different risk properties of alternative financial assets. We introduce differences in liquidity across assets in the standard life-cycle model of portfolio choice. More precisely, in our model, stocks are subject to transaction costs, as considered in recent macroliterature. We show that when these costs are calibrated to match the observed infrequency of households׳ trading, the model is able to generate patterns of portfolio stock allocation over age and wealth that are constant or moderately increasing, thus more in line with the existing empirical evidence.     

模糊厌恶下股指期货风险对冲策略设计及实证分析

投资者对股指期货与现货有着不同的模糊厌恶,本文首先将此假设条件引入带交易成本的Garleanu and Pederson (2013)投资模型中,并以指数基金对冲策略为例,构建了一个股指期货动态对冲的理论模型。与非对冲策略相比,基于上述模型设计的对冲策略投资绩效更好,动态最优成交额占目标交易额的比例更小,目标成交额对收益率预测因子的敏感性更大。借助上述模型,本文选取2010年4月至2021年6月的中国ETF指数基金和股指期货数据,并以2015年9月股指期货管理措施实施为界进行区间划分,实证研究发现:(1)中国A股市场的ETF投资组合进行股指期货对冲显著提升了投资绩效,但股指期货管理会削弱该作用;(2)投资绩效改善主要来源于交易成本的下降与目标成交额因子敏感性的提升,该机制受到股指期货管理的约束;(3)与Garleanu and Pederson (2013)、Zhang et al. (2017)相比,本文对冲策略保留“抗跌”特点的同时增加了“易涨”特性。本文研究结果表明,在当前大力发展机构投资者的背景下应不断丰富股指期货、股指期权产品谱系,降低股指期货交易成本并完善持仓约束。     

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.     

Stock returns forecasting with metals: sentiment vs. fundamentals

Using six prominent metal commodities, we provide evidence on the out-of-sample forecasting of stock returns for the market indices of the G7 countries, for which there is little prior evidence in this context. We find precious metals (gold and silver) can improve forecast accuracy relative to the benchmark and performs well compared to forecast combinations. From an economic gains perspective, forecasting returns provides certainty equivalent gains in a market timing strategy for the G7 countries. These certainty equivalent gains are large enough to make active portfolio management attractive, even for individual investors. Gains remain after considering reasonable transaction costs.     

Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

Transaction costs, trading volume, and the liquidity premium

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. The results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.     

Deep hedging

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show in Section 4 that the set of constrained trading strategies used by our algorithm is large enough to ε-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available. We illustrate our approach by an experiment on the S&P500 index and by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard ‘complete-market’ solution.     

Focusing on the worst state for robust investing

Despite its shortcomings, the Markowitz model remains the norm for asset allocation and portfolio construction. A major issue involves sensitivity of the model's solution to its input parameters. The prevailing approach employed by practitioners to overcome this problem is to use worst-case optimization. Generally, these methods have been adopted without incorporating equity market behavior and we believe that an analysis is necessary. Therefore, in this paper, we present the importance of market information during the worst state for achieving robust performance. We focus on the equity market and find that the optimal portfolio in a market with multiple states is the portfolio with robust returns and observe that focusing on the worst market state provides robust returns. Furthermore, we propose alternative robust approaches that emphasize returns during market downside periods without solving worst-case optimization problems. Through our analyses, we demonstrate the value of focusing on the worst market state and as a result find support for the value of worst-case optimization for achieving portfolio robustness.     

Momentum profits in the Australian equity market: A matched firm approach

This paper examines momentum trading strategies within the Australian equity market over the period 1990 to 2007, inclusive. We analyse excess returns employing both Jegadeesh and Titman's (Jegadeesh, N., Titman, S., 1993. “Returns to buying winners and selling losers: implications for stock market efficiency”. The Journal of Finance, 48:65–91) zero cost investment portfolio approach and a matched control firm approach. We also allow for short sale restrictions, liquidity constraints and transaction costs in the form of bid-ask spreads. Testing reveals that both the Jegadeesh and Titman (Jegadeesh, N., and Titman, S. (1993). “Returns to buying winners and selling losers: implications for stock market efficiency”. The Journal of Finance, 48:65–91.) zero cost investment portfolio approach and the matched control firm approach yield excess profits. While the implementation of short sale restraints increases momentum profitability, the subsequent inclusion of bid-ask spreads results in a reduction in these gains. Further, we find that executing a momentum strategy in Australia results in statistically significant dollar profits.     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

Adverse selection in cryptocurrency markets

In this article we investigate the influence that information asymmetry may have on future volatility, liquidity, market toxicity, and returns within cryptocurrency markets. We use the adverse-selection component of the effective spread as a proxy for overall information asymmetry. Using order and trade data from the Bitfinex exchange, we first document statistically significant adverse-selection costs for major cryptocurrencies. Also, our results suggest that adverse-selection costs, on average, correspond to 10% of the estimated effective spread, indicating an economically significant impact of adverse-selection risk on transaction costs in cryptocurrency markets. Finally, we document that adverse-selection costs are important predictors of intraday volatility, liquidity, market toxicity, and returns.     

Liquidity and Expected Returns: Lessons from Emerging Markets

Given the cross-sectional and temporal variation in their liquidity,emerging equity markets provide an ideal setting to examinethe impact of liquidity on expected returns. Our main liquiditymeasure is a transformation of the proportion of zero dailyfirm returns, averaged over the month. We find that it significantlypredicts future returns, whereas alternative measures such asturnover do not. Consistent with liquidity being a priced factor,unexpected liquidity shocks are positively correlated with contemporaneousreturn shocks and negatively correlated with shocks to the dividendyield. We consider a simple asset-pricing model with liquidityand the market portfolio as risk factors and transaction coststhat are proportional to liquidity. The model differentiatesbetween integrated and segmented countries and time periods.Our results suggest that local market liquidity is an importantdriver of expected returns in emerging markets, and that theliberalization process has not fully eliminated its impact.     

Transaction costs and crowding

We use industry data to determine whether crowding of the investment space is caused by portfolio construction processes typical to the investment community. In particular, this paper examines the extent that transaction cost models cause crowding of the investment space, even when the investment models are completely unrelated to one another. We find that as transaction costs become more significant in the portfolio creation process as portfolios increase in size from $500 million to $5 billion, crowding actually declines for long-only portfolios and mainly declines, but sometimes increases for market neutral portfolios. This research sheds more light on how crowding develops through actions by players within the financial system.     

Financial Transaction Taxes,Market Composition,and Liquidity

We use the introduction of a financial transaction tax (FTT) in France in 2012 to test competing theories on its impact. We find no support for the idea that an FTT improves market quality by affecting the composition of trading volume. Instead, our results are in line with the hypothesis that a lower trading volume reduces liquidity and in turn market quality. Consistent with theories of asset pricing under transaction costs, we document a shift in security holdings from short‐term to long‐term investors. Finally, we find that moderate aggregate effects on market quality can mask large adjustments made by individual agents.     

Liquidity Premia and Transaction Costs

Standard literature concludes that transaction costs only have a second‐order effect on liquidity premia. We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime‐switching model in which the investment opportunity set varies over time, we explicitly characterize the optimal consumption and investment strategy. In contrast to the standard literature, we find that transaction costs can have a first‐order effect on liquidity premia. However, with reasonably calibrated parameters, the presence of transaction costs still cannot fully explain the equity premium puzzle.     

Linear predictability vs. bull and bear market models in strategic asset allocation decisions: evidence from UK data

Most papers in the portfolio choice literature have examined linear predictability frameworks based on the idea that simple but flexible Vector Autoregressive (VAR) models can be expanded to produce portfolio allocations that hedge against the bull and bear dynamics typical of financial markets through careful selection of predictor variables that capture business cycles and market sentiment. Yet, a distinct literature exists that shows that non-linear econometric frameworks, such as Markov switching, are also natural tools to compute optimal portfolios arising from the existence of good and bad market states. This paper examines whether and how simple VARs can produce portfolio rules similar to those obtained under a simple Markov switching, by studying the effects of expanding both the order of the VAR and the number/selection of predictor variables included. In a typical stock-bond strategic asset allocation problem for UK data, we compute the out-of-sample certainty equivalent returns for a wide range of VARs and compare these measures of performance with those of non-linear models. We conclude that most VARs cannot produce portfolio rules, hedging demands or (net of transaction costs) out-of-sample performances that approximate those obtained from simple non-linear frameworks.     

In search of a theory of debt management

The complete market approach to government debt management argues that a portfolio of non-contingent bonds at different maturities should be chosen so that fluctuations in market value offset changes in expected future deficits. However, this approach recommends huge fluctuations in positions, enormous changes in portfolios for minor changes in maturities and no presumption it is always optimal to issue long and invest short term in a wide array of model specifications. These extreme, volatile and unstable features are undesirable for two reasons. Firstly fragility of portfolios to small changes in assumptions means that it is often better to follow a balanced budget rather than issue the optimal debt portfolio under some possibly misspecified model. Secondly for even miniscule transaction costs, governments prefer a balanced budget rather than the large positions complete markets recommends. The complete market recommendations conflict with a number of features we believe are integral to bond market incompleteness, e.g. transaction costs, liquidity effects, robustness, etc. and which need to be explicitly incorporated into the portfolio problem.     

Multivariate utility maximization with proportional transaction costs

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given terminal date. We prove the existence of an optimal portfolio process under the assumption of asymptotic satiability of the value function. Sufficient conditions for this include reasonable asymptotic elasticity of the utility function, or a growth condition on its dual function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer.