Naive Diversification Research Articles

The equally weighted portfolio still remains a challenging benchmark

This research replicates the paper “Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?”, DeMiguel et al. (2009b). Similar to the referring paper, working in the mean–variance context, we compare the out-of-sample performance of the same investment strategies on the basis of standard metrics (Sharpe ratio, certainty equivalent and turnover). We consider proportional transaction costs and estimation rolling windows of limited length. Our study updates the original paper for many interesting aspects. First, to exclude that the empirical evidence of DeMiguel et al. (2009b), whose data stopped in 2004, could depend on very specific market behavior, we use an updated version of the original databases that contains the returns of the last 20 years. Recent data are characterized by a few severe systemic events, the 2008 global financial crisis and the shock related to the pandemic, and a generally higher level of price volatility than the previous periods. In our opinion, this variation in the market’s conditions makes the replication very interesting. Second, we introduce the Equally Risk Contribution (ERC) portfolio within the allocation strategies under comparison. This allocation rule is strictly related to the mean–variance approach when the variance is used as the referring risk measure and it constitutes a very interesting alternative investment benchmark. Moreover, using real data, we study whether a variation of the holding period or the length of the estimation window can modify the performance of all the strategies under comparison. Our findings confirm the results of DeMiguel et al. (2009b), i.e. that the equally weighted portfolio still remains a challenging benchmark to beat. Nevertheless, we find a few significant differences: the number of strategies that outperform naive diversification is larger due to the increased market volatility; limiting the impact of transaction costs by investing in a portfolio with a stable allocation as the ERC, or modifying the lengths of the estimation window and the holding period, is not sufficient to beat naive diversification systematically.

International Portfolio Diversification Benefits: An Empirical Investigation of the 28 European Stock Markets During the Period 2014–2024

Abstract This study investigates the benefits of international diversification in the stock markets of the 28 European countries (the EU and the UK) over two five-year periods: a stable period from 2014 to 2019 and a turbulent period from 2019 to 2024. The analysis draws on the Markowitz mean-variance, Sharpe reward-to-variability, and naive diversification models, based on which different investment strategies were developed and implemented. We find that actively managed portfolios perform significantly better than naively diversified portfolios. The analyzed markets exhibit positive short-term associations, with an average correlation coefficient of 0.29 in the first period and 0.46 in the second period. However, these markets do not show long-term cointegration. Recent crises have reduced diversification benefits, yet significant opportunities for diversification remain. Diversification benefits are almost halved in the second period: average single-market standard deviation can be reduced by 60.5% with investments in 20-indices portfolios in the stable period, and only by 33.7% with the same portfolio size in the turbulent period.

Portfolio Optimization Using ANNs and Mean-Semi Variance Markowitz Model: A Comparative Study of South Asian Economies

This study uses many portfolio approaches to optimize mean semi-variance portfolios using artificial neural networks for South Asian investors. These methods include the mean-semi variance strategy, minimal variance approach, limited portfolios with transaction costs and turnover constraints, constrained portfolios with risk and return diversification limits, and the equally weighted approach. These portfolio strategies are analysed using the excess Sharpe ratio and the Information Ratio for financial efficiency and diversity, respectively, and validated using the 130/30 portfolio strategy. The Pakistan Stock Exchange (PSX), Bombay Stock Exchange (BSE), Dhaka Stock Exchange (DSE), Columbo Stock Exchange (CSE), and Nepal Stock Exchange (NEPSE) supply daily data for empirical research. We use a large data collection from 2017 to 2021. The study found that ANN-generated estimators using a mean semi-variance optimization strategy outperformed alternative portfolio optimization methods in South Asian markets. The research reveals that ANN-based returns outperform correlation statistics, descriptive analysis, and mean square prediction error (MPSE). The study suggests utilizing naive diversification as a benchmark for other portfolio optimization methodologies.

Why Naive Diversification Is Not So Naive, and How to Beat It?

Abstract We show theoretically that the usual estimated investment strategies will not achieve the optimal Sharpe ratio when the dimensionality is high relative to sample size, and the $ 1/N $ rule is optimal in a 1-factor model with diversifiable risks as dimensionality increases, which explains why it is difficult to beat the $ 1/N $ rule in practice. We also explore conditions under which it can be beaten, and find that we can outperform it by combining it with the estimated rules when $ N $ is small, and by combining it with anomalies or machine learning portfolios, conditional on the profitability of the latter, when $ N $ is large.

Empirical Evidence of Cognitive Biases among Chinese Investors

The convoluted world of finance is filled with a number of irrationalities that the science of behavioral finance seeks to explain by bringing cognitive biases. Cognitive bias is a systematic pattern of deviation from rationality and is caused by limited cognitive capacities. By specifically analyzing Chinese investors, the paper aims to identify common cognitive biases exercised by high net-worth Chinese investors that lead to insufficient diversification and naive diversification in portfolio construction and to explain the following scenarios that are not commensurate with classic financial theories: the reason why investors prefer rule of thumbs instead of complete diversification; or when they do diversify, they simply takes N instruments and consider it done; the fact that people stick with a chosen stock or fund even when their prospects are not favored and other opportunity has arisen; and that investors from the same social background as a whole might have experienced certain preferences. And finally, when the cognitive biases are exercised by large enough of a population, stock market might suffer abnormal variances from it. The answers to these questions are studied by qualitative research methodology in this paper, narrative inquiry and inductive approach, to generalize and conclude to observed examples.

Peranan Emas Dan Crypto Hedge Fund Dalam Meningkatkan Kinerja Indeks Portofolio Indeks Saham LQ45, JII, High Dividend, Dan Sri-Kehati

This research was conducted to determine the role of gold and crypto hedge funds in improving the performance of stock index portfolios. The stock index portfolio used consists of the LQ45, JII, High Dividend, and SRI-KEHATI indices. The purpose of this study is to analyze the role of gold and crypto hedge funds in improving the performance of stock index portfolios for the 2019-2021 period rather than investing in portfolios made up of stock indexes only. This study uses the Naive method and measures portfolio performance based on the Sharpe Index, Treynor Index, Jensen Index, Sortino Ratio, and Omega Ratio. This study concludes that the formation of a portfolio with the role of gold and crypto hedge funds can improve the performance of stock indexes using the calculation results of the Naive Diversification model in the period January 1 2019 to December 30 2021. In general it is found that portfolios formed with gold and crypto hedge funds as value better hedged than a portfolio formed without a hedge

Second-order uncertainty and naive diversification

This paper introduces a new model for decision making under ambiguity called second-order uncertainty. The decision maker considers all probability distributions associated with the given options, and chooses the allocation that minimizes the variability of outcome across all probabilities. Optimal allocation under second-order uncertainty is the equal weighted allocation, also called naive diversification.

An Empirical Analysis of the Benefits of Corporate Bond Portfolio Optimization in the Presence of Duration Constraints

This article analyzes the out-of-sample performance of portfolio optimization models in the US corporate bond universe. In our empirical study, we measure the benefits of naive diversification and find that it eventually reaches a limit as the number of bonds increases. Also, we observe substantial improvements in the risk-adjusted performance of scientific portfolio constructions when compared to simple barbell strategies for the same given duration. When duration constraints are relaxed, we find that both naively and scientifically diversified portfolios outperform cap-weighted benchmarks in terms of Sharpe ratio.

Second-Order Uncertainty and Naive Diversification

Second-Order Uncertainty and Naive Diversification

Portfolio Optimization with a Mean-Absolute Deviation-Entropy Multi-Objective Model.

Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.

Optimal and naive diversification in an emerging market: Evidence from China's A‐shares market

AbstractThis paper empirically investigates the out‐of‐sample performance of the 1/N naive rule and the Markowitz mean–variance strategies in the largest emerging market (i.e., China's A‐shares market) and provides three new findings. First, we show that some mean–variance optimization strategies can outperform the 1/N rule in China's A‐shares market, while minimum‐variance strategies cannot. Using certainty equivalent return (CER) instead of Sharpe ratios does not change our results qualitatively. Second, we find an obvious advantage of mean–variance optimization when N is large. Third, when transaction costs are taken into account, the profitability of the unconstrained mean–variance optimizations almost vanishes, while the profitability of the mean–variance optimizations with the short‐sale constraint remains. Our results are robust to using a shorter estimation window of about 60 months. These results provide support for the use of optimal diversification strategies in emerging markets.

Optimal Beats Naive Diversification: Asset Allocation Using High-Frequency Data

This article evaluates the usefulness of high-frequency data in optimal portfolio choice. The authors use a comprehensive list of major stock indexes and different frequencies of observations. Furthermore, they consider the impact of economic cycles, microstructure noise, and seasonality on performance. Their results show the ability of high-frequency data–based strategies to beat both monthly and daily based strategies and the benchmark equally weighted portfolio, even in presence of transaction costs. The authors also find that the outperformance arises from the reduction in the estimation error of the covariance matrix, which offsets the increase in transaction costs. TOPICS:Performance measurement, portfolio construction, portfolio theory Key Findings • The authors evaluate the usefulness of high-frequency data in optimal portfolio choice. • They employ several stock indexes and different frequencies of observations. • The authors consider the impact of economic cycles, microstructure noise, and intraday seasonality on performance.

The Jury is Still Out On the Performance of Naive Diversification (1/N rule)

DeMiguel et. al. (2009b) made a compelling case that estimation error dwarfs diversification benefits resulting in naive diversification (1/N) dominating mean-variance portfolios. We illustrate the necessary and sufficient conditions for risk-based allocation rules to be optimal in a mean-variance framework. We show empirically that many common datasets satisfy such conditions, making these rules preferred to mean-variance in the presence of estimation error. Our out-of-sample tests show that these rules outperform both mean-variance and 1/N. Further, we show that clustering the data using machine learning enhances the diversification benefits of these rules by making the data closer to the required conditions for optimality.

Improving the naive diversification: An enhanced indexation approach

This paper employs enhanced indexation to derive an optimization model with an explicit objective to track and outperform the naive diversification (1/N) strategy. The proposed model is data-driven and can start from any number of historical return samples. Simulation shows that the number of samples needed for the new model to outperform the 1/N benchmark is much smaller than the number documented in existing literature for other models. Our out-of-sample tests show that the proposed enhanced indexation model with the 1/N strategy as benchmark can achieve higher expected returns and significantly higher Sharpe ratios in most of the test cases.

Practical Applications of Diversification Benefits, Where Art Thou?

<h3>Practical Applications Summary</h3> In <b>Diversification Benefits, Where Art Thou?</b>, in the Winter 2019 edition of <b><i>The Journal of Wealth Management</i></b>, authors <b>Sam Pittman</b>, <b>Amneet Singh</b>, and <b>Sangeetha Srinivasan</b>, all of <b>Russell Investments</b>, consider how diversification may improve risk-adjusted returns (RARs) and what asset sectors may deliver those benefits. The authors examine whether exposure to some asset classes neutralizes the benefits from holding other asset classes, and how the returns from naive diversification match up to those from other approaches. Prompted by increasing investor skepticism over the advantages of diversification, the authors construct optimal fixed-weight portfolios with volatilities equal to those of three US-centric benchmark portfolios. They consider the historical benefits from diversifying into international equities, real assets, and below-investment-grade bonds. The authors draw from 15 different asset classes, to discern the regularity and magnitude of RAR improvement from diversification over five-year holding periods. They find that certain asset classes deliver diversification benefits more reliably than others; that some asset classes’ diversification benefits are dampened by the presence of other asset classes; and that portfolio returns from diversified holdings are subject to cyclicality that has longer wavelengths than the US business cycle. History implies the benefits of diversification will return, the authors note. <b>TOPICS:</b>Wealth management, retirement, portfolio construction

Does sophistication of the weighting scheme enhance the performance of long-short commodity portfolios?

The commodity pricing literature advocates the design of long-short portfolios based on equal weights. Relaxing the assumption of naive diversification, this article studies the benefits of applying sophisticated weighting schemes to the construction of long-short momentum and term structure portfolios. Weighting schemes based on risk minimization and risk timing are found to dominate the naive allocation and the weighting schemes based on utility maximization. This conclusion is not challenged by concerns pertaining to transaction costs, illiquidity, data mining, sub-periods, and model parameters and robustly persists when we consider as sorting signals hedging pressure, speculative pressure and, to a lower extent, basis-momentum.

The Portfolio Optimization Performance during Malaysia’s 2018 General Election by Using Noncooperative and Cooperative Game Theory Approach

Game theory approach is used in this study that involves two types of games which are noncooperative and cooperative. Noncooperative game is used to get the equilibrium solutions from each payoff matrix. From the solutions, the values then be used as characteristic functions of Shapley value solution concept in cooperative game. In this paper, the sectors are divided into three groups where each sector will have three different stocks for the game. This study used the companies that listed in Bursa Malaysia and the prices of each stock listed in this research obtained from Datastream. The rate of return of stocks are considered as an input to get the payoff from each stock and its coalition sectors. The value of game for each sector is obtained using Shapley value solution concepts formula to find the optimal increase of the returns. The Shapley optimal portfolio, naive diversification portfolio and market portfolio performances have been calculated by using Sharpe ratio. The Shapley optimal portfolio outperformed the naive diversification portfolio and market portfolio in 6 months before and after the GE14.

The role of an option-implied distribution in improving an asset allocation model

The objective of this paper is to extend the information embedded in option-implied distribution to asset allocation model. This paper examines whether a parameter estimated from an option-implied distribution can improve a minimum-variance portfolio which consists of many risky assets. The option-implied distribution under a risk-neutral assumption is called risk-neutral density (RND) whereas a risk-world density (RWD) is calculated by incorporating a risk-premium. The computation of option-implied distributions is based on the Dow Jones Industrial Average (DJIA) index options and its constituents. The data covers the period from January 2009 until December 2015. Portfolio performance is evaluated based on portfolio volatility and Sharpe ratio. The performance of a portfolio based on an option-implied distribution is compared to a naive diversification portfolio. The empirical evidence shows that for a portfolio based on an option-implied distribution, the volatility of the portfolio is reduced and the Sharpe ratio is increased.

Choice Simplification: A Theory of Mental Budgeting and Naive Diversification*

Abstract We develop a theory of how an agent makes basic multiproduct consumption decisions in the presence of taste, consumption opportunity, and price shocks that are costly to attend to. We establish that the agent often simplifies her choices by restricting attention to a few important considerations, which depend on the decision at hand and affect her consumption patterns in specific ways. If the agent’s problem is to choose the consumption levels of many goods with different degrees of substitutability, then she may create mental budgets for more substitutable products (e.g., entertainment). In some situations, it is optimal to specify budgets in terms of consumption quantities, but when most products have an abundance of substitutes, specifying budgets in terms of nominal spending tends to be optimal. If the goods are complements, in contrast, then the agent may—consistent with naive diversification—choose a fixed, unconsidered mix of products. And if the agent’s problem is to choose one of multiple products to fulfill a given consumption need (e.g., for gasoline or a bed), then it is often optimal for her to allocate a fixed sum for the need.

Does the Inclusion of Exposure to Volatility into Diversified Portfolio Improve the Investment Results? Portfolio Construction from the Perspective of a Polish Inwestor

The main goal of this research is to analyse the investment benefits from an incorporation of the volatility exposure to the diversified portfolio from the perspective of a Polish investor. Volatility, treated as a new asset class, may improve the performance of the portfolio due to its negative correlation with most types of assets. This topic has been widely investigated for the United States and Europe whereas the Polish market appears to be not heavily researched and this study may fill this gap. The research covers the period from October 2010 to July 2018 and is performed on daily close prices. To construct the portfolios the analysis uses the mean-variance framework and the naive diversification approach. The comparison of risk-adjusted returns between investments with and without volatility exposure enables an answer to the research question about an improvement of the results by the addition of a non-standard asset to the diversified portfolios. The VXX is considered as the proxy for volatility as it is the most popular ETN which follows the volatility index derivatives with the given maturity. To test the robustness of the results the portfolios are constructed with a broad range of different parameters and assumptions imposed on the optimization procedure.