Mean-variance Portfolio Research Articles

Revisit the Use of Index Returns as the Proxy of Market Return in CAPM

This study compares the performance of the capital asset pricing model (CAPM), which uses a mean-variance optimal portfolio, and the Jakarta Composite Index (JCI) as the market return proxy. The data samples are monthly stock returns of Kompas 100, LQ45, and IDX30 index from September 2012-August 2022. The expected returns of assets are calculated using the CAPM with rolling regression methodology based on each index's 2-5 years period. The mean-squared errors for each sample group are calculated to determine the CAPM performance. Although the market indexes have a sub-optimal risk and return profile according to their position on the efficient frontier diagram, this study finds that the JCI as the market proxy results in better CAPM performance than the optimal portfolio. However, the beta results from using JCI as the market proxy are also consistently higher than those using an optimal portfolio, leading to the overestimation bias of the asset risk. Since most studies in CAPM testing use the market index as the market return proxy, particularly JCI in Indonesia, this study provides new insight into the challenges of using the optimal portfolio as the market return proxy.

Portfolio selection model using teaching learning-based optimization approach

<p>Portfolio selection is among the most challenging processes that have recently increased the interest of professionals in the area. The goal of mean-variance portfolio selection is to maximize expected return with minimizing risk. The Markowitz model was employed to solve the linear portfolio selection problem. However, due to numerous constraints and complexities, the problem is so critical that traditional models are insufficient to provide efficient solutions. Teaching learning-based optimization (TLBO) is a powerful population-based nature-inspired approach to solve optimization problems. This article presents a portfolio selection model using the TLBO approach to maximize the portfolio's Sharpe Ratio. The Sharpe ratio combines both expected return and risk. This algorithm model the natural teaching process of the classroom with two main phases, viz., teaching and learning. Performance analysis has been undertaken to investigate the suitability of TLBO based solution approach by comparing it with genetic algorithm (GA) and particle swarm optimization (PSO) on the real datasets, Deutscher Aktienindex (DAX) 100, Hang Seng 31, Standard and Poor’s (S&P) 100, financial times stock exchange (FTSE) 100, and Nikkei 225. The empirical results verify the superiority of the TLBO over GA and PSO.</p>

Futuristic portfolio optimization problem: wavelet based long short-term memory

PurposeThis paper aims to propose an improved version of portfolio optimization model through the prediction of the future behavior of stock returns using a combined wavelet-based long short-term memory (LSTM).Design/methodology/approachFirst, data are gathered and divided into two parts, namely, “past data” and “real data.” In the second stage, the wavelet transform is proposed to decompose the stock closing price time series into a set of coefficients. The derived coefficients are taken as an input to the LSTM model to predict the stock closing price time series and the “future data” is created. In the third stage, the mean-variance portfolio optimization problem (MVPOP) has iteratively been run using the “past,” “future” and “real” data sets. The epsilon-constraint method is adapted to generate the Pareto front for all three runes of MVPOP.FindingsThe real daily stock closing price time series of six stocks from the FTSE 100 between January 1, 2000, and December 30, 2020, is used to check the applicability and efficacy of the proposed approach. The comparisons of “future,” “past” and “real” Pareto fronts showed that the “future” Pareto front is closer to the “real” Pareto front. This demonstrates the efficacy and applicability of proposed approach.Originality/valueMost of the classic Markowitz-based portfolio optimization models used past information to estimate the associated parameters of the stocks. This study revealed that the prediction of the future behavior of stock returns using a combined wavelet-based LSTM improved the performance of the portfolio.

Volatility linkages and value gains from diversifying with Islamic assets

Islamic assets, assets compliant with ethical and religious norms as codified in Sharia law, broaden the investor base. Do such investments contribute to mean-variance efficiency, and if so, how? Using daily data on stock, bond, and money market indices from nine Islamic countries and 37 non-Islamic ones from May 2007 to June 2010, we show that adding Islamic assets to an existing portfolio of conventional (non-Islamic) assets can expand the mean-variance frontier and thereby create additional value through diversification. The “specialness” of Islamic assets comes from a smaller set of common information and a lower degree of cross-market hedging between Islamic and conventional markets. This reduces volatility linkages between Islamic and conventional assets relative to volatility linkages between two conventional assets. Including one Islamic asset lowers volatility linkages by up to 3.16 percentage points after controlling for country-level fixed effects and time-varying characteristics. Low volatility linkages are key to increasing diversification benefits that arise from improvements in the global mean-variance portfolio. Our research contributes to the international business literature by highlighting the potential benefits of bridging religious, ethical, and cultural differences to add new markets to an incomplete international market structure and in so doing increase diversification benefits.

Research on dynamic mean-variance portfolio selection

The covariance matrix of portfolio returns constructed by static mean-variance model will change with time, so the optimal portfolio with fixed weights may not be optimal. Based on the static mean-variance model, this paper introduces two new parameters of the length of dynamic historical period and holding period to construct a dynamic mean-variance model. Numerical analysis shows that the proposed dynamic portfolio strategy can achieve good returns.

Nonconvex multi-period mean-variance portfolio optimization

AbstractIn this paper, we address the problem of long-term investment by exploring optimal strategies for allocating wealth among a finite number of assets over multiple periods. Based on the classical Markowitz mean-variance philosophy, we develop a new portfolio optimization framework which can produce sparse portfolios. The sparsity of the portfolio at each and across periods is characterized by the possibly nonconvex penalties. For the constructed nonconvex and nonsmooth constrained model, we propose a generalized alternating direction method of multipliers and its global convergence to a stationary point can be guaranteed theoretically. Moreover, some numerical experiments are conducted on several datasets generated from practical applications to illustrate the effectiveness and advantage of the proposed model and solving method.

A Wavelet-Decomposed WD-ARMA-GARCH-EVT Model Approach to Comparing the Riskiness of the BitCoin and South African Rand Exchange Rates

In this paper, a hybrid of a Wavelet Decomposition–Generalised Auto-Regressive Conditional Heteroscedasticity–Extreme Value Theory (WD-ARMA-GARCH-EVT) model is applied to estimate the Value at Risk (VaR) of BitCoin (BTC/USD) and the South African Rand (ZAR/USD). The aim is to measure and compare the riskiness of the two currencies. New and improved estimation techniques for VaR have been suggested in the last decade in the aftermath of the global financial crisis of 2008. This paper aims to provide an improved alternative to the already existing statistical tools in estimating a currency VaR empirically. Maximal Overlap Discrete Wavelet Transform (MODWT) and two mother wavelet filters on the returns series are considered in this paper, viz., the Haar and Daubechies (d4). The findings show that BitCoin/USD is riskier than ZAR/USD since it has a higher VaR per unit invested in each currency. At the 99% significance level, BitCoin/USD has average values of VaR of 2.71% and 4.98% for the WD-ARMA-GARCH-GPD and WD-ARMA-GARCH-GEVD models, respectively; and this is slightly higher than the respective 2.69% and 3.59% for the ZAR/USD. The average BitCoin/USD returns of 0.001990 are higher than ZAR/USD returns of −0.000125. These findings are consistent with the mean-variance portfolio theory, which suggests a higher yield for riskier assets. Based on the p-values of the Kupiec likelihood ratio test, the hybrid model adequacy is largely accepted, as p-values are greater than 0.05, except for the WD-ARMA-GARCH-GEVD models at a 99% significance level for both currencies. The findings are helpful to financial risk practitioners and forex traders in formulating their diversification and hedging strategies and ascertaining the risk-adjusted capital requirement to be set aside as a cushion in the event of the occurrence of an actual loss.

Mean–variance portfolio selection under no-shorting rules: A BSDE approach

This paper revisits the mean–variance portfolio selection problem in continuous-time within the framework of short-selling of stocks is prohibited via backward stochastic differential equation approach. To relax the strong condition in Li et al. (Li et al. 2002), the above issue is formulated as a stochastic recursive optimal linear–quadratic control problem. Due to no-shorting rules (namely, the portfolio taking non-negative values), the well-known “completion of squares” no longer applies directly. To overcome this difficulty, we study the corresponding Hamilton–Jacobi–Bellman (HJB, for short) equation inherently and derive the two groups of Riccati equations. On one hand, the value function constructed via Riccati equations is shown to be a viscosity solution of the HJB equation mentioned before; On the other hand, by means of these Riccati equations and backward semigroup, we are able to get explicitly the efficient frontier and efficient investment strategies for the recursive utility mean–variance portfolio optimization problem.

Stock market optimization amidst the COVID-19 pandemic: Technical analysis, K-means algorithm, and mean-variance model (TAKMV) approach

The Philippine stock market, just like most of its neighbors in the region, was seriously impacted by the global pandemic COVID-19. Investors remain hopeful while continuing to seek great ones in the damaged market. This paper developed a methodology for portfolio selection and optimization with the use of technical analysis, machine learning techniques, and portfolio optimization model. The combined methods of technical analysis, K-means clustering algorithm, and mean-variance portfolio optimization model will result in the development of the proposed TAKMV method. The study aims to integrate these three important analyses to identify portfolio investments. This paper uses the average annual risk and annual rate of return data for the years 2018 and 2020 to form the clusters and assessed the stocks that correspond to the investor's technical strategy such as Moving Average Convergence/Divergence (MACD) and Hybrid MACD with Arnaud Legoux Moving Average (ALMA). This paper solved the risk minimization problem on selected shares of the companies, based on the mean-variance portfolio optimization model. There are 230 and 239 companies for 2018 and 2020, respectively, listed in Philippine Stock Market, and all simulations were performed in MATLAB environment platform. Results showed that MACD strategy dominates the MACD-ALMA strategy in terms of the number of assets with a positive annual rate of return. The MACD works efficiently in the pre-COVID-19 condition while MACD-ALMA works efficiently during-COVID-19 condition, regardless of the number of assets with a positive annual rate of return. The results also show that the maximum expected portfolio return (RP) can be achieved using the MACD and MACD-ALMA in the pre-and during-COVID-19 conditions, respectively. The MACD-ALMA shows an advantage during high-risk market conditions and can also provide maximum RP. The performance of the TAKMV method was validated by applying its results and comparing it to the next year's historical price. The 2018 results were compared to 2019 data and the 2020 results were compared to 2021 data. For consistency, the comparison was applied to the same company per portfolio. Simulation results show that the MACD strategy is more effective compared to MACD-ALMA.

Factor-Targeted Asset Allocation: A Reverse Optimization Approach

We demonstrate that using a mean-variance portfolio to obtain implied factor risk premia can result in stable weights for a factor portfolio when assets’ expected returns follow a factor structure that is subject to pricing errors. We propose a methodology to construct asset portfolios based on these factor portfolio weights, taking into account the possibility of pricing errors. Our simulation shows that these “factor-targeted” portfolios have higher and more stable Sharpe ratios than traditional allocation methodologies in various scenarios involving expected return assumptions. Furthermore, while our factor-targeted portfolios exhibit similar Sharpe ratios to the mean-variance portfolio built using factors for high levels of pricing errors, the factor-targeted portfolios have more stable portfolio weights, which makes them more appealing in practice.

Prediction-based mean–variance portfolios with risk budgeting based on neural networks

The integration of return prediction and portfolio models has been widely investigated and proven effective. The derived prediction-based portfolios can be classified into five main categories. This paper comprehensively compares the out-of-sample performance of these categories based on the traditional mean–variance (MV) model for the first time, where different neural networks are used for return prediction. The MV model and equal-weighted portfolio are used as comparisons. Due to the high volatilities of these prediction-based portfolios, the risk budgeting method is applied to advance these portfolios, where stocks with higher predicted volatilities own higher proportions of portfolio risk contribution. The equal risk contribution is used as the benchmark. Further, the out-of-performance of these advanced portfolios is investigated after deducting transaction fees since their high turnovers can seriously affect the obtained profits in practical investments. Empirical tests are implemented with component stocks of the Shanghai Stock Exchange (SSE) 50 index, where daily data range from 2011 to 2021. Experimental results indicate that the prediction-based MV portfolio built with forecasted errors (MV-FE) is significantly superior to the others under different risk aversion levels, followed closely by the prediction-based MV portfolio built with forecasted returns (MV-FR). In particular, medium risk aversion is more suitable for these portfolios. Moreover, the risk budgeting method considerably reduces the volatilities of these portfolios and improves their risk-adjusted returns. The risk budgeting method is more efficient than the equal risk contribution method. After subtracting their transaction fees of turnovers, the MV-FR portfolio with risk budgeting, i.e., the MV-FR-RB portfolio, outperforms the others and still obtains satisfying performance. Also, there is little difference between the MV-FR and MV-FE portfolios with risk budgeting.

Automated stock picking using random forests

We derive a stock ranking by applying a technical features-based random forest model on an international dataset of liquid stocks. Rather than predicted return, our ranking is based on outperformance probability. By applying a decile split, we find that long–short portfolios achieve Sharpe ratios of up to 1.95 and a highly significant yearly six-factor alpha of up to 21.79%. Moreover, we show that outperformance probabilities serve as a superior measure of future returns in the context of portfolio optimization. Mean–variance portfolios using this measure are less volatile and more profitable than equally- or value-weighted portfolios. Our findings are robust to firm size, regional restrictions, and non-crisis periods and cannot be explained by limits to arbitrage.

Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation

The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New explicit expressions for optimal strategies are obtained, featuring the use of oblique projections that provide unified treatment of the case with and without a risk-free asset. The analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes. The main result advances our understanding of the efficient frontier formation in the most general case in which a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.

The Markowitz’s Mean–Variance Interpretation under the efficient market hypothesis in the context of critical recession periods

The validity of the Efficient Market Hypothesis (EMH) as an assumption for portfolio optimization in the Mean–Variance (MV) framework under large scale financial crises is tested for two of the most prominent periods of global economic instability of the first quarter of the 21’st century. Despite that emergent large scale correlations are detected for the considered critical periods, EMH appears to hold from an expected profit standpoint. In concordance with well established results regarding risk assessment under stable economic periods, we find that the risk of the MV portfolios turns out to be however sub optimal during crises. A spatio-temporal covariance prediction model is proposed and it is shown that by the application of this predictive model to the MV framework, the portfolio’s risk assessment can to some extent be alleviated.

Rehabilitating Mean–Variance Portfolio Selection: Theory and Evidence

Recent research has proven that the application of mean–variance portfolio selection is justified if, and only if, asset returns follow a skew-elliptical generalized location and scale (SEGLS) distribution. This irrefutably corrects the widespread fallacy that mean–variance analysis can be used only for portfolios with normally or symmetrically distributed constituents. To make this important finding accessible to a wide range of academics and practitioners, the authors of this article present it in a nontechnical form and additionally highlight that, under the SEGLS distribution and some mild axiomatic requirements, mean–variance analysis and many alternative mean-risk approaches deliver the same optimal portfolios. In a numerical study, they illustrate the key features of the novel SEGLS distribution. In an empirical study, they emphasize its practical relevance by gathering existing and providing new evidence in its favor.

International Portfolio Choice with Frictions: Evidence from Mutual Funds

Abstract Using data on international equity portfolio allocations by U.S. mutual funds, we estimate a portfolio expression derived from a standard mean-variance portfolio model extended with portfolio frictions. The optimal portfolio depends on the previous month and the buy-and-hold portfolio shares, and a present discounted value of expected excess returns. We estimate expected return differentials and use them in the portfolio regressions. The estimates imply significant portfolio frictions and a modest rate of risk aversion. While mutual fund portfolios significantly respond to expected returns, portfolio frictions lead to a weaker and a more gradual portfolio response to changes in expected returns. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

Goals-Based Investing and JWM: Where They Have Been, Where They Are Headed

<i>The Journal of Wealth Management</i> has played a key role in supporting research that benefits individual investors. What began as concern over taxes, has grown into its own branch of portfolio theory, now known as goals-based investing. Though originally a behavioral adaptation to mean-variance portfolio theory, goals-based investing now boasts its own normative and axiomatic support, as well as making way for behavioral considerations. I review the story of these ideas over the last quarter-century and highlight the role <i>JWM</i> has played in supporting them.

An alternative stochastic model for linear portfolios

Stock market returns often tend to follow a non-normal probability distribution due to extreme losses in the tails. These cause fatter tails than normal and consequently heavy-tailed probability distributions are mostly used for modeling returns. In this work, we consider the generalized T (GT) distribution which can be heavy-tailed through its parameters and propose to use it in modeling the random stock returns. The GT distribution also contains the normal, Student t and generalized Laplace distributions as special or limiting cases of the shape parameters. The closed form expressions for the important risk measures are obtained. In case of a portfolio modeling, a multivariate extension of the distribution within the class of elliptical distributions is used. The tail mean-variance portfolio model based on the multivariate GT distribution is developed and optimal portfolio problem is solved. Risk measures for the random return of an asset whose density function is a mixture of the GT densities are obtained. The computability of all expressions derived is shown, and a real data application consisting of seven real stocks from the same sector is given.

Portfolio Construction Based on Optimization Model and Combination of Various Assets

Since the fifties of the last century, the concept of portfolio management is proposed to enrich the portfolio theory by Markowitz et al., as well as the improvement of portfolio theory by later generations, forming a modern portfolio management theory. This paper uses Markowitz's mean variance portfolio theory to perform a portfolio return maximization analysis on selected assets with assumptions that investors are risk-averse according to mean variance theory. Based on mean variance portfolio theory, as well as Python computational simulation modeling, Monte Carlo simulation is used to find the effective set and effective frontier of the portfolio, and the optimal solution of the portfolio is filtered according to the two constraints of maximum Sharpe ratio and minimum volatility. According to the analysis, the portfolio return of the maximum Sharpe ratio is relatively high, and the maximum Sharpe ratio combination is more worthwhile than the minimum volatility combination. Overall, these results provide enlightenment for further exploration and implementation of portfolio theory.