A new computational tool for analysing dynamic hedging under transaction costs

This paper highlights a framework for analysing dynamic hedging strategies under transaction costs. First, self-financing portfolio dynamics under transaction costs are modelled as being portfolio affine. An algorithm for computing the moments of the hedging error on a lattice under portfolio affine dynamics is then presented. In a number of circumstances, this provides an efficient approach to analysing the performance of hedging strategies under transaction costs through moments. As an example, this approach is applied to the hedging of a European call option with a Black–Scholes delta hedge and Leland's adjustment for transaction costs. Results are presented that demonstrate the range of analysis possible within the presented framework.     

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.     

Trading strategies based on past returns: evidence from Germany

Among the various strategies studied in this paper, only momentum investing appears to earn persistently nonzero returns: From 1965 to 2014, the classical momentum strategy based on performance over the previous 2–12 months earned an average return of 1.57% per month (excluding microcap stocks and value-weighted returns). In the most recent 10-year period, this return was even larger—2.27%—which is much larger than in the USA. However, profitability net of transaction costs is weak because the strategy involves trading in disproportionately small stocks with high transaction costs, something that is particularly true for the loser portfolio. A strategy that concentrates only on the winner portfolio and thus avoids potential problems associated with (short) selling the costly loser portfolio appears to earn strong and persistently abnormal profits, even after transaction costs.     

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。     

A Stability Approach to Mean‐Variance Optimization

I jointly treat two critical issues in the application of mean‐variance portfolios, that is, estimation risk and portfolio instability. I find that theory‐based portfolio strategies, which are known to outperform naive diversification () in the absence of transaction costs, heavily underperform it under transaction costs. This is because they are highly unstable over time. I propose a generic method to stabilize any given portfolio strategy while maintaining or improving its efficiency. My empirical analysis confirms that the new method leads to stable and efficient portfolios that offer equal or lower turnover than and larger Sharpe ratio, even under high transaction costs.     

Market liquidity,closeout procedures and initial margin for CCPs*

ABSTRACT

Closeout procedures enable central counterparties (CCPs) to respond to events that challenge the continuity of their normal operations, most frequently triggered by the default of one or more clearing members. The procedures typically entail three main phases: splitting, hedging, and liquidation. Together, these ensure the regularity of the settlement process through the prudent and orderly liquidation of the defaulters’ portfolios. Traditional approaches to CCPs’ margin requirements typically assume a simple closeout profile, not accounting for the ‘real life’ constraints embedded in the management of a default. The paper proposes an approach to assess how distinct closeout strategies may expose a CCP to different sets of risks and costs taking into account real-life frictions. The proposed approach enables the evaluation of a full spectrum of hedging strategies and the assessment of the trade-offs between the risk-reducing benefits of hedging and the transaction costs associated with it. Using an unexplored set of transactional level data, the proposed framework is evaluated assuming the hypothetical default of a real CCP clearing member. We consider the worst-case loss of a large interest rate swap portfolio observed over the past 10 years (i.e. 2005–2015) and show that an efficient hedging strategy which minimises risk may not be optimal when transaction costs are taken into account. The empirical analysis suggests that transaction costs are a significant factor and should be accounted for when designing a hedging strategy. Specifically, it is shown that the risk-reducing benefits arising from more tailored hedging strategies may introduce higher transaction costs, and therefore may change the effectiveness of the strategies.     

The intra-day performance of market timing strategies and trading systems based on Japanese candlesticks

Abstract

We develop market timing strategies and trading systems to test the intra-day predictive power of Japanese candlesticks at the 5-minute interval on the 30 constituents of the DJIA index. Around a third of the candlestick rules outperform the buy-and-hold strategy at the conservative Bonferroni level. After adjusting for trading costs, however, just a few rules remain profitable. When we correct for data snooping by applying the SSPA test on double-or-out market timing strategies, no single candlestick rule beats the buy-and-hold strategy after transaction costs. We also design fully automated trading systems by combining the best-performing candlestick rules. No evidence of out-performance is found after transaction costs. Although Japanese candlesticks can somewhat predict intra-day returns on large US caps, we show that such predictive power is too limited for active portfolio management to outperform the buy-and-hold strategy when luck, risk, and trading costs are correctly measured.     

Portfolio optimisation with strictly positive transaction costs and impulse control

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a nontrivial asymptotically optimal solution for the problem of exponential utility maximisation.     

Implications of Transaction Costs for the Post–Earnings Announcement Drift

This paper examines the effect of transaction costs on the post–earnings announcement drift (PEAD). Using standard market microstructure features we show that transaction costs constrain the informed trades that are necessary to incorporate earnings information into price. This implies weaker return responses at the time of the earnings announcement and higher subsequent returns drift for firms with higher transaction costs. Consistent with this prediction, we find that earnings response coefficients are lower for firms with higher transaction costs. Using portfolio analyses, we find that the profits of implementing the PEAD trading strategy are significantly reduced by transaction costs. In addition, we show, using a combination of portfolio and regression analyses, that firms with higher transaction costs are the ones that provide the higher abnormal returns for the PEAD strategy. Our results indicate that transaction costs can provide an explanation not only for the persistence but also for the existence of PEAD.     

An analysis of risk-based asset allocation and portfolio insurance strategies

This paper compares traditional portfolio insurance strategies with modern risk-based dynamic asset allocation strategies within a currency portfolio context for reserve management. Given the objective of preserving reserve value, the evaluation of the hedging performances of various strategies focuses on four perspectives regarding, in particular, the return distribution of the hedged portfolio. In terms of the Sharpe Ratio, the constant proportional portfolio insurance is the best performer due to having the lowest volatility, while the Value at Risk strategy based upon the normal distribution is the worst due to its having the smallest return. From the perspective that the return distribution of the hedged portfolio is shifted to the right, the synthetic put performs the best, with the expected shortfall strategy the second best. In terms of the cumulative portfolio return across years, the expected shortfall strategy using the historical distribution ranks first, as a result of its participation in upward markets. Furthermore, the expected shortfall-based strategy results in a lower turnover within the investment horizon, thereby saving transaction costs.     

Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

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.     

Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz

Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the Extreme Risk Index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, our study seems to be the first application of extreme value techniques in portfolio management on a large scale. The primary aim of our investigation is the potential of ERI in practice. The performance of this strategy is benchmarked against the minimum variance portfolio and the equally weighted portfolio. These fundamental strategies are important benchmarks for large-scale applications. Our comparison includes annualized portfolio returns, maximal drawdowns, transaction costs, portfolio concentration, and asset diversity in the portfolio. In addition to that we study the impact of an alternative tail index estimator. Our results show that the ERI strategy significantly outperforms both the minimum-variance portfolio and the equally weighted portfolio on assets with heavy tails.     

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.     

Fundamental‐based Market Strategies

A significant body of literature has raised the possibility that portfolio outperformance based on a simple accounting‐based investment strategy can persist through time because markets may ignore and potentially misinterpret financial market signals. Employing a fundamental‐based strategy, we show that superior performance can be earned consistently through time by identifying and investing in firms with more favourable performance and credit signals. The strength of these portfolios are additionally characterised by the ability of the strategies to avoid firms with poor future prospects. These findings are robust across varying time periods after both transaction costs and related market constraints are considered.     

Transaction cost optimization for online portfolio selection

To improve existing online portfolio selection strategies in the case of non-zero transaction costs, we propose a novel framework named Transaction Cost Optimization (TCO). The TCO framework incorporates the L1 norm of the difference between two consecutive allocations together with the principles of maximizing expected log return. We further solve the formulation via convex optimization, and obtain two closed-form portfolio update formulas, which follow the same principle as Proportional Portfolio Rebalancing (PPR) in industry. We empirically evaluate the proposed framework using four commonly used data-sets. Although these data-sets do not consider delisted firms and are thus subject to survival bias, empirical evaluations show that the proposed TCO framework may effectively handle reasonable transaction costs and improve existing strategies in the case of non-zero transaction costs.     

Portfolio strategies and performance

The relative performance of several portfolio selection strategies is assessed empirically. These strategies vary in sophistication from a ‘naive’ strategy of maintaining equal dollar investments in each stock available to a strategy that periodically uses updated parameter estimates to calculate new optimal proportions of portfolio value to be invested in the stocks available. Although it is to be expected a priori that relatively sophisticated strategies will perform at least as well as the more naive strategies, implementation costs will clearly differ across strategies and across investor-specific parameters such as total portfolio value. Thus estimation of the various strategies' performance gross of these costs is a necessary consideration in rational strategy selection by any given investor.     

International equity portfolio allocations and transaction costs

In spite of the critical role of transaction cost, there are not many papers that explicitly examine its influence on international equity portfolio allocation decisions. Using bilateral cross-country equity portfolio investment data and three direct measures of transaction costs for 36 countries, we provide evidence that markets where transaction costs are lower attract greater equity portfolio investments. The results imply that future research on international equity portfolio diversification cannot afford to ignore the role of transaction costs, and policy makers, especially in emerging markets, will have to reduce transaction costs to attract higher levels of foreign equity portfolio investments.     

THE ECONOMIC GAINS OF TRADING STOCKS AROUND HOLIDAYS

I assess the economic gains of strategies that account for the effect of holiday calendar effects on the daily returns and volatility of the 30 stocks in the Dow Jones Industrial Average index. The dynamic strategies use forecasts from stochastic volatility models that distinguish between regular trading days and different types of holidays. More important, I assess the economic value of conditioning on holiday effects and find that a risk-averse investor will pay a high performance fee to switch from a dynamic portfolio strategy that does not account for the effect of holidays on daily conditional expected returns and volatility to a strategy that does. This result is robust to reasonable transaction costs.