Pareto‐archived evolutionary wavelet network for financial constrained portfolio optimization

The multi‐objective portfolio optimization problem is too complex to find direct solutions by traditional methods when constraints reflecting investor's preferences and/or market frictions are included in the mathematical model and hence heuristic approaches are sought for their solution. In this paper we propose the solution of a multi‐criterion (bi‐objective) portfolio optimization problem of minimizing risk and maximizing expected return of the portfolio which includes basic, bounding, cardinality, class and short sales constraints using a Pareto‐archived evolutionary wavelet network (PEWN) solution strategy. Initially, the empirical covariance matrix is denoised by employing a wavelet shrinkage denoising technique. Second, the cardinality constraint is eliminated by the application of k‐means cluster analysis. Finally, a PEWN heuristic strategy with weight standardization procedures is employed to obtain Pareto‐optimal solutions satisfying all the constraints. The closeness and diversity of Pareto‐optimal solutions obtained using PEWN is evaluated using different measures and the results are compared with existing only solution strategies (evolution‐based wavelet Hopfield neural network and evolution‐based Hopfield neural network) to prove its dominance. Eventually, data envelopment analysis is also used to test the efficiency of the non‐dominated solutions obtained using PEWN. Experimental results are demonstrated on the Bombay Stock Exchange, India (BSE200 index: period July 2001–July 2006), and the Tokyo Stock Exchange, Japan (Nikkei225 index: period March 2002–March 2007), data sets. Copyright © 2010 John Wiley & Sons, Ltd.     

AN EVALUATION OF THE PERFORMANCE OF PORTFOLIOS SELECTED FROM VALUE LINE RANK ONE STOCKS: 1976–1982

In this study, the performance of portfolios selected from among Value Line rank one stocks is compared with portfolios consisting of randomly selected New York Stock Exchange and American Stock Exchange stocks. Results indicate that before considering transactions costs, active traders who invest in Value Line rank one stocks can earn positive excess returns. However, after considering transaction costs, neither active traders nor passive investors in rank one stocks can earn returns that are statistically greater than returns achieved by portfolios of randomly selected stocks. These results are not sensitive to variations in portfolio size.     

A smooth non-parametric estimation framework for safety-first portfolio optimization

In this paper, we adopt a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using China National Social Security Fund strategic stocks and Shanghai Stock Exchange 50 Index components.     

Seasonal variations in the U.S. Stock Market returns: 1927–1984

When the seasonal components of the monthly returns as opposed to the returns themselves, are examined over the 1927–1984 period, the Standard & Poor's 500 Composite Index (S&P 500) and the Center for Research in Security Prices (CRSP) value-weighted portfolio exhibit significant seasonality. Their seasonal behavior is quite similar to that of the smallest quintile of New York Stock Exchange (NYSE) stocks and the CRSP equally weighted portfolio during March through October. While January is strong for the two latter portfolios, December, November, and January appear to be consistently strong for the two former portfolios. The seasonal pattern has, however, changed substantially over time. While June and July returns experienced a significant drop in seasonal strength, March and April returns gained seasonal strength for all four portfolios from 1927–1958 to 1959–1984. These changes coincide in an inverse fashion with the shifts in interest rate seasonality.     

Multiobjective portfolio optimization with non-convex policy constraints: Evidence from the Eurostoxx 50

Our purpose in this paper is to depart from the intrinsic pathology of the typical mean–variance formalism, due to both the restriction of its assumptions and difficulty of implementation. We manage to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc., within the frame of complex scenarios, which demand for simultaneous optimization of multiple investment objectives. In such a case, the portfolio selection process reflects a mixed-integer multiobjective portfolio optimization problem. On this basis, we meticulously develop all the corresponding modeling procedures and then solve the underlying problem by use of a new, fast and very effective algorithm. The value of the suggested framework is integrated with the introduction of two novel concepts in the field of multiobjective portfolio optimization, i.e. the security impact plane and the barycentric portfolio. The first represents a measure of each security's impact in the efficient surface of Pareto optimal portfolios. The second serves as the vehicle for implementing a balanced strategy of iterative portfolio tuning. Moreover, a couple of some very informative graphs provide thorough visualization of all empirical testing results. The validity of the attempt is verified through an illustrative application on the Eurostoxx 50. The results obtained are characterized as very encouraging, since a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.     

THE CROSS-AUTOCORRELATION OF SIZE-BASED PORTFOLIO RETURNS IS NOT AN ARTIFACT OF PORTFOLIO AUTOCORRELATION

Prior studies find evidence of asymmetric size-based portfolio return cross-autocorrelations where lagged large firm returns lead current small firm returns. However, some studies question whether this economic relation is independent of the effect of portfolio return autocorrelation. We formally test for this independence using size-based portfolios of New York Stock Exchange and American Stock Exchange securities and, separately, portfolios of Nasdaq securities. Results from causality regressions indicate that, across all markets, lagged large firm returns predict current small firm returns, even after controlling for autocorrelation in small firm returns. These cross-autocorrelation patterns are stronger for Nasdaq securities.     

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.     

A Note on the Three–Portfolios Matching Problem

A typical problem arising in financial planning for private investors consists in the fact that the initial investor's portfolio, the one determined by the consulting process of the financial institution and the universe of instruments made available to the investor have to be matched/optimised when determining the relevant portfolio choice. We call this problem the three–portfolios matching problem. Clearly, the resulting portfolio selection should be as close as possible to the optimal asset allocation determined by the consulting process of the financial institution. However, the transition from the investor's initial portfolio to the final one is complicated by the presence of transaction costs and some further more specific constraints. Indeed, usually the portfolios under consideration are structured at different aggregation levels, making portfolios comparison and matching more difficult. Further, several investment restrictions have to be satisfied by the final portfolio choice. Finally, the arising portfolio selection process should be sufficiently transparent in order to incorporate the subjective investor's trade–off between the objectives 'optimal portfolio matching' and 'minimal portfolio transition costs'. In this paper, we solve the three–portfolios matching problem analytically for a simplified setting that illustrates the main features of the arising solutions and numerically for the more general situation.     

Should Venture Capitalists Put All Their Eggs in One Basket? Diversification versus Pure‐Play Strategies in Venture Capital

Managing the different companies in which they invest while at the same time performing portfolio optimization for themselves, venture capitalists position themselves as a pure-play or diversified conglomerate through their cumulative portfolios. I examine the effects of two investment strategies of venture capitalists:  1)  a specialist "pure-play" strategy that maximizes venture capital involvement and  2)  a more generalist strategy of diversification at the "firm" level that minimizes portfolio risk. I find that neither strategy optimizes both venture capital growth and time to entrepreneurial exit, which highlights a need for institutional investors to clarify fund objectives at the time a fund is established.     

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.     

Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman,mean-variance,and naïve diversification approaches

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N rule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.     

Cleaning house: Stock reassignments on the NYSE

A frequently occurring, yet unexplored, phenomenon of the New York Stock Exchange specialist system is that of reassignments of stocks by specialist firms on the floor of the Exchange. These events change the portfolios at the individual specialist level by reassigning one or more stocks from one individual specialist portfolio to another. We find that reassigned stocks have unusually wide spreads before reassignments and experience a decline in spreads to levels comparable to matched stocks after the reassignment. This improvement in liquidity is associated with a reduced cost of capital for the reassigned firms. We find that portfolio size, and industry and size concentration of the individual specialist portfolios are associated with the decision of specialist firms to reassign stocks.     

On the price of risk in a mean-risk optimization model

We investigate a mean-risk model for portfolio optimization where the risk quantifier is selected as a semi-deviation or as a standard deviation of the portfolio return. We analyse the existence of solutions to the problem under general assumptions. When the short positions are not constrained, we establish a lower bound on the cost of risk associated with optimizing the mean–standard deviation model and show that optimal solutions do not exist for any positive price of risk which is smaller than that bound. If the investment allocations are constrained, then we obtain a lower bound on the price of risk in terms of the shadow prices of said constraints and the data of the problem. A Value-at-Risk constraint in the model implies an upper bound on the price of risk for all feasible portfolios. Furthermore, we provide conditions under which using this upper bound as the cost of risk parameter in the model provides a non-dominated optimal portfolio with respect to the second-order stochastic dominance. Additionally, we study the relationship between minimizing the mean–standard deviation objective and maximizing the coefficient of variation and show that both problems are equivalent when the upper bound is used as the cost of risk. Additional relations between the Value-at-Risk constraint and the coefficient of variation are discussed as well. We illustrate the results numerically.     

TRADING OF NASDAQ STOCKS ON THE CHICAGO STOCK EXCHANGE

We use a linear programming model to form two portfolios with approximately equal levels of attributes such as financial leverage. One portfolio comprises stocks that trade exclusively on NASDAQ and the other, stocks that trade on both the Chicago Stock Exchange (CSE) and NASDAQ (CSE/NASDAQ). We find that spreads are lower for the CSE/NASDAQ portfolio, but so is the percentage of quotes at spreads of $0.125. In fact, the lower spreads observed for the CSE/NASDAQ portfolio arise from fewer quotes with spreads of more than $0.25.     

Should investors include Bitcoin in their portfolios? A portfolio theory approach

Many papers in recent years have examined the benefits of adding alternative assets to traditional portfolios containing stocks and bonds. Bitcoin has emerged as a new alternative investment for investors which has attracted much attention from the media and investors alike. However relatively little is known about the investment benefits of Bitcoin and therefore this paper examines the benefit of including Bitcoin in a traditional benchmark portfolio of stocks and bonds. Specially, we employ data up to June 2018 and analyse the potential out-of-sample portfolio benefits resulting from including Bitcoin in a stock-bond portfolio for a range of eight popular asset allocation strategies. The out-of-sample analysis shows that, across all different asset allocation strategies and risk aversions, the benefits of Bitcoin are quite considerable with substantially higher risk-adjusted returns. Our results are robust to rolling estimation windows, the incorporation of transaction costs, the inclusion of a commodity portfolio, alternative indices, short-selling as well as two additional optimization techniques including higher moments with (and without) variance-based constraints (VBCs). Therefore, our results suggest that investors should include Bitcoin in their portfolio as it generates substantial higher risk-adjusted returns.     

Bonds versus stocks: Investors’ age and risk taking

It has become increasingly popular to advise investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the well-known decision rules such as mean–variance or stochastic dominance rules are unable to explain this common practice. Almost stochastic dominance (ASD) and almost mean–variance (AMV) approaches are used to examine the dominance of stock and bond portfolios. ASD and AMV rules unambiguously support the popular practice of advising higher stock to bond ratio for long investment horizons. Hence, we provide an explanation to the practitioners’ recommendation within the expected utility paradigm.     

THE MEAN‐GINI EFFICIENT PORTFOLIO FRONTIER

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.     

Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market

The Markowitz portfolio optimization model, popularly known as the Mean-Variance model, assumes that stockreturns follow normal distribution. But when stock returns do not follow normal distribution, this model wouldbe inadequate as it would prescribe sub-optimal portfolios. Stock market literature often deliberates that stock returns are non-normal. In such context the Markowitz model would not be sufficient to estimate the portfolio risks. The purpose of this paper is to expand the original Markowitz portfolio theory (mean-variance) via adding the higher order moments like skewness (third moment about the mean) and kurtosis (fourth moment about the mean) in the return characteristics. The research paper investigates the impact of including higher moments using multi-objective programming model for portfolio stock selection and optimization. The empirical results indicate that the inclusion of higher moments had a considerable impact in estimating the returns behavior of portfolios. The portfolios optimized using all the four moments, generated higher returns for the given level of risk in comparison to the returns of the Markowitz model during the study period 2000–2011. The results of this study would be immensely useful to fund managers, portfolio managers and investors as it would help them in understanding the Indian stock market behavior better and also in selecting alternative portfolio selection models.     

Volume- and size-related lead-lag effects in stock returns and volatility: An empirical investigation of the Warsaw Stock Exchange

We analyze the autocorrelation structure of returns and volatility of stocks listed in the single auction system on the Warsaw Stock Exchange during the period January 1996 - October 2000. First, we find that size- and volume-related cross-autocorrelation in portfolio returns exists even after accounting for the portfolio's own-autocorrelation. Second, we find that size and volume leadership are independent from each other. Third, our results indicate slower adjustment of the small (low volume) portfolios to market-wide information that differs for up and down markets. We also find evidence for volatility spillovers between portfolio returns.     

Neural network copula portfolio optimization for exchange traded funds

This paper attempts to investigate if adopting accurate forecasts from Neural Network (NN) models can lead to statistical and economically significant benefits in portfolio management decisions. In order to achieve that, three NNs, namely the Multi-Layer Perceptron, Recurrent Neural Network and the Psi Sigma Network (PSN), are applied to the task of forecasting the daily returns of three Exchange Traded Funds (ETFs). The statistical and trading performance of the NNs is benchmarked with the traditional Autoregressive Moving Average models. Next, a novel dynamic asymmetric copula model (NNC) is introduced in order to capture the dependence structure across ETF returns. Based on the above, weekly re-balanced portfolios are obtained and compared using the traditional mean–variance and the mean–CVaR portfolio optimization approach. In terms of the results, PSN outperforms all models in statistical and trading terms. Additionally, the asymmetric skewed t copula statistically outperforms symmetric copulas when it comes to modelling ETF returns dependence. The proposed NNC model leads to significant improvements in the portfolio optimization process, while forecasting covariance accounting for asymmetric dependence between the ETFs also improves the performance of obtained portfolios.