Mean-variance Strategy Research Articles

Modeling dynamic higher-order comoments for portfolio selection based on copula approach

This paper introduces a novel approach to estimating time-varying higher-order comoments from a theoretical standpoint. We present how to estimate the dynamic higher-order comoments of asset returns under the copula framework, which builds on the ARCD and copula-DCC models to capture the time variation in higher-order moments and correlations of asset returns. Additionally, the elements in the coskewness and cokurtosis matrices are calculated by the double, triple, and quadruple integrals associated with the joint density function of asset returns. The empirical application to five international market indexes shows that the portfolio with time-varying higher-order comoments estimated by the copula approach significantly outperforms equally weighted and mean–variance strategies in economic performance. The robustness analysis verifies the validity and robustness of the proposed estimation method. Our research offers fresh insights for portfolio analysis and risk management decision-making in practical scenarios.

The self-coordination mean-variance strategy in continuous time

The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the pre-committed strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the self-coordination strategy balances between the global investment interest and local investment interests of the investor. However, the self-coordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.

A novel online portfolio selection approach based on pattern matching and ESG factors

In modern finance, social investment portfolios have attracted the attention of researchers, investors, and practitioners. Regarding the long-term nature of this investment, the selection of the portfolios for a single period should be reconsidered as an online portfolio selection which focuses on the allocation of portfolios over multiple periods to maximize the expected growth rate of the portfolio. Besides common factors such as return on investment, many investors are willing to invest in assets complying with sustainability requirements. This study develops an online portfolio selection strategy that considers Environmental, Social, and Governance factors in addition to return and risk. Due to the diversity of constructed portfolios, different assets are first clustered based on their mutual information. The clustering model is selected through a comparison between four different clustering models. Then, a novel pattern-matching approach is implemented on the clustered assets that not only considers the amount of profitability of previous windows but also finds the optimal length and number of windows. After predicting the last groups of windows based on the pattern-matching, superior assets in terms of return and Sharpe ratio in each cluster are chosen, and the final portfolios are established regarding two scenarios; (i) a mean-variance strategy, and (ii) a developed mean-variance strategy which considers Environmental, Social, and Governance factors besides return and risk.The presented approaches are compared with several well-known benchmarks on four different datasets (i.e. 100 selective assets from S&P 500 index, S&P 500, Nikkei 225, and Dow Jones). The results indicate the superiority of the approach based on a simple mean-variance strategy over others in metrics such as Sharpe Ratio and Deflated Sharpe. Approaches containing Environmental, Social, and Governance factors also show not only profit and less volatility but the highest deflated Sharpe ratio, which can be considered as an excellent opportunity for investors to have responsible investing and have a better edge than the market.

Modelling and filtering for dynamic investment in the precious-metals market

ABSTRACT Taking financial positions on precious metals could serve as risk management mechanism against both inflation and economic downturn. The demand for precious metals depends on their consumption- and investment-asset role. We consider the accurate and efficient price modelling of gold, silver, platinum and palladium under a hidden Markov model (HMM) multivariate framework. The interplay of various computational implementation aspects is underscored. Recursive model parameter estimates are generated, which are then utilized to test several dynamic investment strategies. We consider the pure-switching, mixed-switching and mean-variance strategies. The pure switching strategy outperforms the other two strategies 61.76% of the time. Benchmarking against the asset-only strategy and within the 25-year data examined in our study, investing in palladium is found to be better than the above-mentioned strategies. A general mean-variance strategy for any number of assets is also presented in conjunction with a filtering-based parameter estimation for any number of HMM states.

The Interaction of Major Crypto-assets, Clean Energy, and Technology Indices in Diversified Portfolios

Cryptocurrencies have gained high interest from media, regulatory authorities, and both retailer and institutional investors especially in the COVID-19 pandemic followed by a tremendous academic interest. Classification of cryptos as an asset is one important issue while another crucial topic is the significantly high return and volatility fluctuations which does not make life easier for portfolio investors. High energy consumption to produce cryptos and carbon emission issues are also not developing the favor of cryptocurrencies. Moreover, in financial literature recent studies show that prices of renewable energy stocks have long-term cointegrating relationship with technology companies. In this context first we employ an asymmetric VAR-GARCH model to study spillover effects between major crypto-currencies, clean energy, and technology indices. Using daily data of the two major cryptocurrencies for the period of 1/1/2016 and 30/09/2021, we relate risk and return of different mean-variance portfolio strategies to Bitcoin (BTC), Etherium (ETH), S&P Global Clean Energy Index (SPGCE) and MSCI World Information Technology Index (MSCIWIT). Secondly, we apply the Markowitz mean-variance framework to assess risk-return benefits of cryptocurrency-portfolios. Our main goal is to offer optimal portfolio allocation approaches including cyptocurrencies with traditional financial assets. We will combine cryptocurrencies, clean energy, and technology indices to maximize return and Sharpe ratio. Furthermore, we will use our asymmetric VAR-GARCH models results to understand and cross check the Markowitz portfolio allocation results in details.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

Can volatility solve the naive portfolio puzzle?

We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of portfolios and econometric models across multiple datasets, most models achieve higher Sharpe ratios and lower portfolio volatility that are statistically and economically significant relative to the naive rule, even after controlling for turnover costs. Our results suggest benefits to employing more sophisticated econometric models than the sample covariance matrix, and that mean-variance strategies often outperform the naive portfolio across multiple datasets and assessment criteria.

An experimental study on diversification in portfolio optimization

New diversification strategies, along with other naive strategies as 1/N portfolios, have been proposed in the literature as a method for overcoming concentration limitations of the mean–variance model. However, it is not clear whether these strategies outperform the classical mean–variance model in all scenarios. Motivated by these points, this manuscript contributes an experimental study in which 11 diversification and mean–variance strategies are compiled and compared with a complete repository of 10 portfolio time series problems with three different estimation windows (composing a total of 30 datasets) and then evaluated using four performance metrics. Additionally, a novel purely data-driven method for determining the optimal value of the hyper-parameter associated with each approach is also proposed. Unlike results previously found in the literature, the empirical results obtained in this study show that equally weighed models obtain the worst ranking in all evaluation metrics except for the stability index, which is hypothetically due to the hyper-parameter optimization raising the transaction cost debate.

Learning Equilibrium Mean-Variance Strategy

We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time-inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium strategy. Under an incomplete market setting, we obtain a semi-analytical, exploratory, equilibrium mean-variance strategy that turns out to follow a Gaussian distribution. We then focus on a Gaussian mean return model and propose an algorithm to find the equilibrium strategy using the reinforcement learning technique. Thanks to a thoroughly designed policy iteration procedure in our algorithm, we can prove our algorithm's convergence under mild conditions, despite that dynamic programming principle and the usual policy improvement theorem fail to hold for an equilibrium solution. Numerical experiments are given to demonstrate our algorithm.

Confident Risk Premiums and Investments using Machine Learning Uncertainties

This paper derives ex-ante (co)variances of stock-level and portfolio-level risk premium predictions from neural networks (NNs). Considering precision, I provide improved investment strategies. The confident high-low strategies that take long-short positions exclusively on stocks with precise risk premiums deliver superior out-of-sample returns and Sharpe ratios than traditional high-low strategies because precise measurements have low squared forecast errors. Mean-variance strategies incorporating covariances of return predictions outperform existing strategies too. Risk premium variances reflect time-varying market uncertainty and spike after financial shocks. Cross-sectionally, the level and precision of risk premiums are correlated, thus NN-based investments deliver more gains in the long positions.

Evaluation of Multi-Asset Investment Strategies with Digital Assets

The drastic growth of the cryptocurrencies market capitalization boosts investigation of their diversification benefits in portfolio construction. In this paper with a set of classical and modern measurement tools, we assess the out-of-sample performance of eight portfolio allocation strategies relative to the naive 1=N rule applied to traditional and crypto-assets investment universe. Evaluated strategies include a range from classical Markowitz rule to the recently introduced LIBRO approach, Trimborn et al. (2019). Furthermore, we also compare three extensions for strategies with respect to input estimators applied. The results show that in the presence of alternative assets, such as cryptocurrencies, Mean-Variance strategies under-perform the benchmark portfolio. In contrast, CVaR optimization tends to outperform the benchmark as well as geometric optimization. Furthermore, we find evidence that liquidity-bounded strategies tend to perform very well. Thus, our findings underscore the non-normal distribution of returns as well as the necessity to control for liquidity constraints at alternative assets markets.

Can Volatility Solve the Naive Portfolio Puzzle?

We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of econometric and portfolio models across multiple datasets, most models achieve higher Sharpe ratios and lower portfolio volatility that are statistically and economically significant relative to the naive rule, even after controlling for turnover costs. Our results suggest benefits to employing more sophisticated econometric models than the sample covariance matrix, and that mean-variance strategies often outperform the naive portfolio across multiple datasets and assessment criteria.

High-Frequency Trading with Fractional Brownian Motion

In the high-frequency limit, conditional expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon, and making dynamic optimization problems tractable. We find an explicit formula for locally mean-variance optimal strategies and their performance for an asset price that follows fractional Brownian motion. Without trading costs, risk-adjusted profits are linear in the trading horizon and rise asymmetrically as the Hurst exponent departs from Brownian motion, remaining finite as the exponent reaches zero while diverging as it approaches one. Trading costs penalize numerous portfolio updates from short-lived signals, leading to a finite trading frequency, which can be chosen so that the effect of trading costs is arbitrarily small, depending on the required speed of convergence to the high-frequency limit.

Forecasting Commodity Futures Returns: An Economic Value Analysis of Macroeconomic vs. Specific Factors

We test whether three well-known commodity-specific variables (basis, hedging pressure, and momentum) may improve the predictive power for commodity futures returns of models otherwise based on macroeconomic factors. We compute recursive, out-of-sample forecasts for fifteen monthly commodity futures return series, when estimation is based on a stepwise model selection approach under a probability-weighted regime-switching regression that identifies different volatility regimes. Comparisons with an AR(1) benchmark show that the inclusion of commodity-specific factors does not improve the forecasting power. We perform a back-testing exercise of a mean-variance investment strategy that exploits any predictability of the conditional risk premium of commodities, stocks, and bond returns, also taking into account transaction costs caused by portfolio rebalancing. The risk-adjusted performance of this strategy does not allow us to conclude that any forecasting approach outperforms the others. However, there is evidence that investment strategies based on commodity-specific predictors outperform the remaining strategies in the high-volatility state.

Time-consistent mean-variance portfolio selection with only risky assets

Time consistency and optimal diversification criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytical solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio selection is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytical solution of the time-consistent mean-variance strategy with risky assets via the solution of an Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.

OPTIMAL INVESTMENT STRATEGY WITH DIVIDEND PAYING AND PROPORTIONAL TRANSACTION COSTS

A Markowitz’s mean-variance investment strategy is studied in a market with a stock, a bond, dividend payment and proportional transaction costs. Two control variables, portfolio strategy and dividend are considered in this paper. The control variables are inherent with a finite time horizon. This paper aims at minimizing the investment portfolio risk and maximizing the dividend process of the investment over time subject to portfolio allocation strategy, expected net wealth and investment costs over time. The method of Lagrangian multiplier was adopted. As a result, the optimal portfolio and optimal dividend payment are obtained. We found that the optimal portfolio process depends on the optimal dividend payment over time. Also, obtained in this paper, is the optimal portfolio with no dividend payment. We found that for the investment to achieve high target, more of the fund should be invested in stock and low dividend should be declared. The region of boundedness for stock purchase and stock sale are established. We found that for the investment to break-even, the quantum amount of stock sold must be greater than the quantum amount of stock purchase over time. The efficient frontier of the investment strategy was also obtained.

A Robust Decision Support Approach to Portfolio Risk Reduction Based on Credit Default Swap

We construct portfolios from the credit default swap (CDS) market by incorporating cardinality and solvency constraints into mean-variance and conditional value at risk (CVaR) models. Cardinality constraints are applied to limit the portfolio size and improve the allocation structure, while the solvency constraint is used to insulate the default risks of the portfolios under worst scenarios. CDS-based portfolios involve uncertainties that stem from spread changing and jump-to-default volatilities. We show that these uncertainties can be identified and managed using our developed systematic approach. Market data analysis from the CDS portfolios shows that using cardinality constraints reduces counterparty risks significantly. The proposed cardinality constrained CVaR model has robust performance in terms of the portfolio Sharpe ratio and one other metric, and also generally outperforms the associated mean-variance strategy. <b>TOPICS:</b>CLOs, CDOs, and other structured credit, portfolio management/multi-asset allocation, VAR and use of alternative risk measures of trading risk

Time-Consistent Investment Strategy with Only Risky Assets and Its Link with Myopic Strategy in High Dimensions

Time-consistency and optimal diversification (minimum-variance) criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytic solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytic solution of the time-consistent mean-variance strategy with risky assets via the solution of the Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.

Optimal Portfolio Strategy for Risk Management in Toll Road Forecasts and Investments

The study leveraged modern portfolio theory and stochastic time series models to develop a risk management strategy for future traffic projections along brownfield toll facilities. Uncertainty in future traffic forecasts may raise concerns about performance reliability and revenue potential. Historical time series traffic data from brownfield corridors were used for developing econometric forecast estimates, and Monte Carlo simulation was used to quantify a priori risks or variance to develop optimal forecasts by using mean-variance optimization strategies. Numerical analysis is presented with historical toll transactions along the Massachusetts Turnpike system. Suggested diversification strategies were found to achieve better long-term forecast efficiencies with improved trade-offs between anticipated risks and returns. Planner and agency forecast performance expectations and risk propensity are thus jointly captured.

Mean-variance versus naïve diversification: The role of mispricing

We compare the equal-weight naïve 1/N portfolio with mean-variance strategies from the perspective of mispricing (alpha) and provide three new findings. First, we analytically show that the 1/N rule approaches the ex ante mean-variance efficient portfolio in the absence of mispricing. With mispricings, mean-variance strategies can overcome the difficulty brought by the imprecise parameter estimates and outperform 1/N by exploiting the mispricing. Second, with mispricings the 1/N rule is unlikely to outperform mean-variance strategies even when N is large, since mean-variance strategies have more opportunities to exploit mispricings. Third, minimum-variance strategies do not exploit mispricings and underperform the 1/N rule.