Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.     

Risk optimizations on basis portfolios: The role of sorting

This paper investigates the mean–variance and diversification properties of risk-based strategies executed on style or basis portfolios. We show that the performance of these risk strategies is highly sensitive to the sorting procedure used to form the basis assets. Whereas the extant literature provides mixed support for the outperformance of smart beta strategies based on scientific diversification, our designed strategies outperform both the market model and multifactor model. Our testing framework is based on bootstrapped mean–variance spanning tests and shows valid conclusions when controlling for multiple testing, transaction costs, and luck from random basis portfolio construction rules. Economically, our results are supported by diversification-based properties.     

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.     

Dynamic spillovers between energy and stock markets and their implications in the context of COVID-19

This study combined time-varying parameter vector autoregression (TVP-VAR) and a spillover index model to analyze the static, total, and net spillover effects of energy and stock markets before and after the COVID-19 outbreak. A network method was also used to depict structural changes more intuitively. Furthermore, we calculated and compared changes in the hedge ratio, optimal portfolio weights, and hedge effectiveness to guide investors to adjust portfolio strategies during COVID-19. The main findings were as follows: First, COVID-19 had a significant impact on spillover effects, and the average value of total spillover index increased by 19.94% compared with that before the epidemic. Second, the energy market was an important risk recipient of the stock market before COVID-19, and the extent of risk acceptance increased after the COVID-19 outbreak. Third, the hedging ratio, optimal portfolio weights, and hedge effectiveness showed huge changes after the COVID-19 outbreak, requiring investors to adjust their portfolio strategies.     

Forecasting market turbulence using regime-switching models

We propose an early warning system to timely forecast turbulence in the US stock market. In a first step, a Markov-switching model with two regimes (a calm market and a turbulent market) is developed. Based on the time series of the monthly returns of the S&P 500 price index, the corresponding filtered probabilities are successively estimated. In a second step, the turbulent phase of the model is further specified to distinguish between bullish and bearish trends. For comparison only, a Markov-switching model with three states (a calm market, a turbulent bullish market, and a turbulent bearish market) is examined as well. In a third step, logistic regression models are employed to forecast the filtered probabilities provided by the Markov-switching models. A major advantage of the presented modeling framework is the timely identification of the factors driving the different phases of the capital market. In a fourth step, the early warning system is applied to an asset management case study. The results show that explicit consideration of the models’ signals yields better portfolio performance and lower portfolio risk compared to standard buy-and-hold and constant proportion portfolio insurance strategies.     

Optimal portfolio choice of gold assets in the differential market and differential game structures

Portfolio choices of gold-related assets for market investors and dealers may not only depend on price differences and the inflation rate, but may also react to the market participants’ strategic behavior and risk attitude. This study develops a two-agent stochastic differential game model to solve the portfolio choice problem of the asset allocations of gold spot, futures, and cash for market participators who are exposed to inflation risks. The equilibrium prices of spot and futures driven by the volatility rate and co-variances that reflect various risk sources are also determined. Specifically, regarding the choice of hedging tools, market participators may prefer gold spot to futures for the purpose of hedging inflation risk. By capturing the stylistic facts of differential market and multiple agent structures, the article can develop a more reasonable and practical model to usefully explain the gold portfolio choices and pricing in the gold markets.     

Performance of Moving Average Trading Rules in a Volatile Stock Market: The Russian Evidence

This article examines the profitability of dual moving average crossover (DMAC) trading strategies in the Russian stock market over the 2003–12 period. It contributes to the existing technical analysis (TA) literature by testing, for the first time, the applicability of ordered weighted moving averages (OWMA) as an alternative calculation basis for determining DMACs. In addition, this article provides the first comprehensive performance comparison of DMAC trading rules in the stock market that is known as one of the most volatile markets in the world. The results show that the best trading strategies of the in-sample period can also outperform their benchmark portfolio during the subsequent out-of-sample period. Moreover, the outperformance of the best DMAC strategies is mostly attributable to their superior performance during bearish periods and, particularly, during stock market crashes.     

Equilibrium in risk-sharing games

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. In this paper, we propose a game where agents’ strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow–Debreu sharing rules. First, it is shown that agents’ best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation, and it is proved to exist for an arbitrary number of agents and to be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk-tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium than compared to the Arrow–Debreu one.     

Home bias in portfolio choices: social learning among partially informed agents

Using an ‘incomplete information’ model, we explore the role of social learning in the global portfolio choices of stock market investors. When partially informed followers attempt to estimate true domestic (home) mean returns, they likely acquire private domestic signals from partially informed leaders. However, the calibration results indicate the existence of home bias when partially informed agents have poor quality information. Partially informed agents are prone to a learning bias; they overreact to new domestic information due to overconfidence in their domestic private signals, but they demonstrate a conservative response to new information in foreign markets. Links between the private signals of partially informed agents may lead to correlated foreign investment strategies among such agents through social learning. We suggest the acquisition of private signals, along with the dissemination of information, affect international portfolio decision rules and are determinants of the phenomenon of home bias.     

Post‐Retirement Financial Strategies: Forecasts and Valuation

This paper uses a discrete‐time, discrete‐state Monte Carlo simulation model to evaluate representative strategies for investing and spending a fixed sum designed to fund consumption during the period after retirement. Two assets are considered – one providing a riskless real return, the other a market portfolio of bonds and stocks. A stochastic process for the returns from the market portfolio is proposed. Then a set of Arrow‐Debreu state prices is obtained on the assumption that the market portfolio is an efficient investment strategy. The model is used to forecast ranges of consumption and ranges of the ratios of year‐to‐year consumption, and also to estimate the values of components of future consumption.     

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.     

TACTICAL ASSET ALLOCATION: CAN IT WORK?

Market events of the past ten years have sparked an interest in tactical asset allocation. In the current study we develop and test a model that incorporates currently available information into the tactical asset allocation process. The model provides an estimate of the probabilities that the upcoming market period will be bullish or bearish. Logit analysis is employed to determine which of the various timely and readily available data significantly affect these probabilities. These estimated probabilities are used to suggest the optimal allocations of funds over time between the risk-free asset and the market portfolio. Then, several timing strategies are compared with a buy-and-hold portfolio. An asset allocation strategy based on the probabilities assigned by the logit model appears to achieve greater terminal wealth with less variability of returns. Similar results are obtained for both an initial sample (1962–76 in our model) and a holdout sample (1977–88).     

An application of the Black–Litterman model with EGARCH-M-derived views for international portfolio management

This paper provides an application of the Black–Litterman methodology to portfolio management in a global setting. The novel feature of this paper relative to the extant literature on Black–Litterman methodology is that we use GARCH-derived views as an input into the Black–Litterman model. The returns on our portfolio surpass those of portfolios that rely on market equilibrium weights or Markowitz-optimal allocations. We thereby illustrate how the Black–Litterman model can be put to work in designing global investment strategies.      

Data-driven robust mean-CVaR portfolio selection under distribution ambiguity

In this paper, we present a computationally tractable optimization method for a robust mean-CVaR portfolio selection model under the condition of distribution ambiguity. We develop an extension that allows the model to capture a zero net adjustment via a linear constraint in the mean return, which can be cast as a tractable conic programme. Also, we adopt a nonparametric bootstrap approach to calibrate the levels of ambiguity and show that the portfolio strategies are relatively immune to variations in input values. Finally, we show that the resulting robust portfolio is very well diversified and superior to its non-robust counterpart in terms of portfolio stability, expected returns and turnover. The results of numerical experiments with simulated and real market data shed light on the established behaviour of our distributionally robust optimization model.     

机构投资对我国资本市场资产价格影响的实证研究

本文以1999年3月到2011年3月的沪深主板上市公司月收益率为样本,通过定义机构投资者的投资策略,对加入机构投资者影响后的CAPM扩展模型进行实证研究,发现扩展模型消除了经典CAPM中存在的异方差性,且不存在一阶自相关性;资产组合的收益率同市场组合收益率呈反比关系,与基准投资组合收益率呈正比关系;模型拟合度有了很大的改善。机构投资对我国资本市场资产价格产生了积极的影响。因此,我国资本市场应该大力发展机构投资者,机构投资者本身也应该朝着健康的方向发展。     

A simulation analysis of the microstructure of an order driven financial market with multiple securities and portfolio choices

In this paper we propose an artificial market where multiple risky assets are exchanged. Agents are constrained by the availability of resources and trade to adjust their portfolio according to an exogenously given target portfolio. We model the trading mechanism as a continuous auction order-driven market. Agents are heterogeneous in terms of desired target portfolio allocations, but they are homogeneous in terms of trading strategies. We investigate the role played by the trading mechanism in affecting the dynamics of prices, trading volume and volatility. We show that the institutional setting of a double auction market is sufficient to generate a non-normal distribution of price changes and temporal patterns that resemble those observed in real markets. Moreover, we highlight the role played by the interaction between individual wealth constraints and the market frictions associated with a double auction system to determine the negative asymmetry of the stock returns distribution.     

Timing and diversification: A state-dependent asset allocation approach

Abstract

The influence of changing economic environment leads the distribution of stock market returns to be time-varying. A conditionally optimal investment hence requires a dynamic adjustment of asset allocation. In this context, this paper examines the improvement in portfolio performance by simulating portfolio strategies that are conditioned on the Markov regime switching behaviour of stock market returns. Including a memory effect eliminates the empirical shortcoming of discrete state models, namely that they produce a standard and an extreme state in stock returns. So far, this has prevented the regimes from being used as a valuable conditioning variable. Based on a discrete state indicator variable, is presented evidence of considerable performance improvement relative to the static model due to optimal shifting between aggressive and well diversified portfolio structures.