Naive Diversification Strategies Research Articles

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.

On robust portfolio and naïve diversification: mixing ambiguous and unambiguous assets

Effect of the availability of a riskless asset on the performance of naive diversification strategies has been a controversial issue. Defining an investment environment containing both ambiguous and unambiguous assets, we investigate the performance of naive diversification over ambiguous assets. For the ambiguous assets, returns follow a multivariate distribution involving distributional uncertainty. A nominal distribution estimate is assumed to exist, and the actual distribution is considered to be within a ball around this nominal distribution. Complete information is assumed for the return distribution of unambiguous assets. As the radius of uncertainty increases, the optimal choice on ambiguous assets is shown to converge to the uniform portfolio with equal weights on each asset. The tendency of the investor to avoid ambiguous assets in response to increasing uncertainty is proven, with a shift towards unambiguous assets. With an application on the $$\textit{CVaR}$$ risk measure, we derive rules for optimally combining uniform ambiguous portfolio with the unambiguous assets.

Naive versus optimal diversification: Tail risk and performance

It is well documented in portfolio optimization that naive diversification outperforms optimal mean–variance diversification because the latter is subject to severe estimation error. Our study provides an alternative explanation for the outperformance of naive diversification by examining the tail risk of naive diversification relative to optimal mean–variance diversification. We utilize a rolling-sample approach and compare the out-of-sample performance and tail risk of various optimal strategies to that of the naive diversification strategy. Using portfolios consisting of individual stocks, we show that for portfolios containing relatively small number of stocks, naive diversification outperforms optimal mean–variance diversification and is less exposed to tail risk. However, for relatively large number of stocks in the portfolio, naive diversification maintains its superior performance but increases tail risk and results in more concave portfolio returns. These results imply that the outperformance of naive diversification acts as compensation for the increase in tail risk and concavity.

K-fold cross validation performance comparisons of six naive portfolio selection rules: how naive can you be and still have successful out-of-sample portfolio performance?

Recent research reports that optimal portfolio selection models often perform worse than equal-weight naive diversification in out-of-sample testing. This paper extends this line of inquiry by comparing the out-of-sample performance of the equal-weight naive strategy to the out-of-sample performance of five alternative naive strategies, each of which derives from a simple heuristic that does not require any optimization. Out-of-sample portfolio performance is assessed by mean, standard deviation, skewness, and Sharpe ratio; k-fold cross validation is used as the out-of-sample testing mechanism. The results indicate that the proposed naive heuristic rules exhibit strong out-of-sample performance, in most cases superior to the equal-weight naive strategy. These findings are consequential for at least two reasons: first, if these simple heuristic-based rules outperform the equal-weight naive strategy, then by transitivity they can outperform the mean–variance- and shortfall-optimal portfolio rules that have been shown in the literature to be inferior to the equal-weight naive rule, which further emphasizes the out-of-sample fragility of “optimal” methods; and second, among naive diversification strategies, some appear more robust in out-of-sample testing than others, hence the proposed methods may be useful when forming mixed portfolio selection models wherein a naive strategy is combined with an optimal strategy to improve performance.

Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

DeMiguel, Garlappi, and Uppal (DGU, 2009) evaluate 14 models of optimal asset allocation and find that none can consistently outperform the 1/N naive diversification strategy, which highlights estimation-risk concerns. Building from Stevens (1998), we provide a useful dichotomous classification of asset-allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal-only vs. full-matrix. In DGU (2009), the competing active strategies all belong to the full-matrix class. We argue that parsimonious diagonal-only strategies, that use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited data information while mitigating estimation risk. Using five different data sets of disaggregate portfolio returns over the 1926-2012 period, we find that 1/N is generally not optimal when compared with these simple diagonal strategies.

Real-Time Prediction and Post-Mortem Analysis of the Shanghai 2015 Stock Market Bubble and Crash

We construct mean-variance portfolios using a factor model approach. We show the importance of portfolio allocation for large unbalanced equity data sets using the full CRSP database. We compare the performance of our portfolio construction methodology to the 1/N naive diversification strategy, standard shrinkage procedures, and alternative factor model estimation. We document significant out-of-sample performance improvement in terms of Sharpe ratios, turnover and certainty equivalent. We show that it is due to improved expected returns estimation coming from the 2-pass regression approach.

An Experiment on Mutual Fund Fees in Retirement Investing

There is mounting evidence that retail investors make predictable, costly investment mistakes, including underinvestment, naive diversification, and payment of excessive fund fees. Over the past thirty-five years, however, participant-directed 401(k) plans have largely replaced professionally managed pension plans, requiring unsophisticated retail investors to navigate the financial markets themselves. Policy-makers have struggled with regulatory interventions designed to improve the quality of investment decisions without a clear understanding of the reasons for investor mistakes. Absent such an understanding, it is difficult to design effective regulatory responses. This article offers a first step in understanding the investor decision-making process. We use an internet-based experiment to disentangle possible explanations for inefficient investment decisions.The experiment employs a simplified construct of an employee’s allocation among the options in a retirement plan coupled with technology that enables us to collect data on the specific information that investors choose to view. In addition to collecting general information about the process by which investors choose among mutual fund options, we employ an experimental manipulation to test the effect of an instruction on the importance of mutual fund fees. Pairing this instruction with simplified fee disclosure allows us to distinguish between motivation-limits and cognition-limits as explanations for the widespread findings that investors ignore fees in their investment decisions.Our results offer partial but limited grounds for optimism. On the one hand, within our simplified experimental construct, our subjects allocated more money, on average, to higher value funds. Furthermore, subjects who received the fees instruction paid closer attentionto mutual fund fees and allocated their investments into funds with lower fees. On the other hand, the effects of even a blunt fees instruction were limited, and investors were unable to identify and avoid clearly inferior fund options. In addition, our results suggest that excessive, naive diversification strategies are driving many investment decisions. Although our findings are preliminary, they suggest valuable avenues for future research and important implications for regulation of retail investing.

Um índice de mínima variância de ações brasileiras

Este trabalho desenvolve um índice de carteiras de mínima variância global (MVP) para as ações mais líquidas do Brasil. Os resultados indicaram que a MVP sem limites sobre os pesos das ações não apresenta diferença significativa de desempenho em relação ao IBOVESPA. A imposição de um peso máximo de dez por cento em cada ação tornou possível superar o IBOVESPA. Contudo, os resultados desta estratégia são comparáveis aos de uma carteira igualmente ponderada e são superados por alguns fundos de gestão ativa em testes fora da amostra. Ainda assim, estas estratégias simples baseadas nestas restrições facilitam a replicação do MVP por investidores individuais e exchange traded funds e sustenta o poder de estratégias ingênuas de investimento.

Active Momentum Trading versus Passive '1/N Naive Diversification'

We consider a passive 1/N naive diversification strategy which is long in the equally weighted portfolio of stocks feasible for trading and short in the risk-free asset. We then examine the profi tability, exposures to risk factors, idiosyncratic variance as well as the relation between the momentum and the 1/N naive diversifi cation strategies. The set of sample stocks that we use to construct the equally weighted portfolio is the same as that for constructing the momentum strategies. We fi nd that both strategies generate an average pro t of 1% per month. The differences in raw and risk-adjusted pro ts between these two strategies are statistically and economically insignifi cant. These two strategies are independent of each other. The idiosyncratic variance of the momentum strategies is 20 times higher than that of the naive diversifi cation strategy. The findings are consistent over the period between 1926 and 2005 and various sub-sample periods including the periods examined in Jegadeesh and Titman (1993 and 2001) and in our simulations where we randomly select 10 years for 100 times. The results also hold when we conduct tests in sub-samples where we divide the sample, each month, into two groups of large and small size stocks.

Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/ N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/ N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/ N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

What's in Your 403(b)? Academic Retirement Plans and the Costs of Underdiversification

Sponsors of defined contribution retirement plans typically limit the investment choices of plan participants to a small number of investment managers and a limited number of investment vehicles. Such restrictions may limit excessive risk‐taking by participants but also may preclude opportunities for efficient diversification. Many college and university 403 (b) plans have restricted investment choices to the retirement annuities offered by TIAA‐CREF, the current manager of over half of all 403(b) contributions. Using 10 years of historical data, we study the efficiency of this TIAA‐CREF opportunity set relative to a larger set that includes several standard index funds. Extrapolations must be interpreted ‐with caution. Assuming optimal rebalancing, depending on loss aversion and diversification constraints, the historical sample of returns implies that over a 20‐year remaining work life, an employee ‐with an expanded menu that includes standard index funds could gain over 40% in terminal wealth compared to one who is restricted to TIAA‐CREF retirement annuities. Even when a naive diversification strategy of equally weighting (1/n) all available funds is used, the expandedmenu outperforms the restricted portfolio by more than 25% over20years. These differences generally are significant at conventional levels based on parametric and nonparametric testing and do not appear to result from idiosyncratic market performance durinz the sample period.

Decentralized investment management: an analysis of non-profit pension funds

We investigate delegated investment management in private pension accounts using data from Australian accumulation (superannuation) funds. In Australian non-profit pension funds, trustees choose investment managers on behalf of members. We find that funds with many delegated managers have higher risk-adjusted returns than those with few. However funds with 13 or less specialized managers show no improvement over funds with a single diversified manager. All do worse than a benchmark portfolio of asset-class indices. Further, by using random selection to mimic the choices of an uninformed individual choosing from the same menu of delegate managers as used by trustees, we show that returns from pension funds with large numbers of trustee-selected managers compare favorably with returns from randomly selected, equally weighted portfolios. However this improvement falls off quickly for funds with fewer trustee-selected managers, or when randomly selected portfolios are also diversified across asset classes. Results indicate that an uninformed individual following a naive diversification strategy would have done as well as most trustee boards in this sample.

Heuristics and Biases in Retirement Savings Behavior

Standard economic theories of saving implicitly assume that households have the cognitive ability to solve the relevant optimization problem and the willpower to execute the optimal plan. Both of the implicit assumptions are suspect. Even among economists, few spend much time calculating a personal optimal savings rate. Instead, most people cope by adopting simple heuristics, or rules of thumb. In this paper, we investigate both the heuristics and the biases that emerge in the area of retirement savings. We examine the decisions employees make about whether to join a savings plan, how much to contribute, and how to invest. Saving for retirement is a difficult problem, and most employees have little training upon which to draw in making the relevant decisions. Perhaps as a result, investors are relatively passive. They are slow to join advantageous plans; they make infrequent changes; and they adopt naive diversification strategies. In short, they need all the help they can get. We discuss the possible role of interventions aiming to improve retirement decision making. Fortunately, many effective ways to help participants are also the least costly interventions: namely, small changes in plan design, sensible default options, and opportunities to increase savings rates and rebalance portfolios automatically.

What's in Your 403(b)? Academic Retirement Plans and the Costs of Underdiversification

Many college and university 403(b) plans restrict investment choices to the funds offered by TIAA-CREF, the current manager of over half of all 403(b) contributions. In the face of 2006 Internal Revenue Code changes some sponsors are dropping alternatives to TIAA-CREF. Using historical data, we study the efficiency of the TIAA-CREF opportunity set relative to a larger set that includes several standard index funds. Assuming optimal rebalancing, depending on loss-aversion, financial sophistication, and diversification constraints, over a forty-year work-life, an employee who is restricted to TIAA-CREF could lose more than half of terminal wealth, compared to investing in the expanded menu. Even when a naive diversification strategy of equally weighting (1/n) all available funds is used, the expanded menu outperforms the restricted portfolio by about one-third over the employee's work-life.

Biases in Allocation Under Risk and Uncertainty: Partition Dependence, Unit Dependence, and Procedure Dependence

Previous studies of employee investment in retirement plans suggest that people typically naively diversify their investment funds, tending to allocate 1/n of the total to each of n available instruments (Benartzi & Thaler, 2001). In this paper we provide experimental evidence that this bias extends to allocation among simple chance prospects and demonstrate three new violations of rational choice theory implied by use of the naive diversification strategy. Study 1 demonstrates “partition dependence” in which participants' allocations among a fixed set of investments varies with the hierarchical structure of the option set (e.g., by vendor and instrument). Study 2 demonstrates “unit dependence” in which participants' preferred allocations vary with the metric in which the investment is reported (dollars versus number of shares). Study 3 demonstrates “procedure dependence” in which the bias toward even allocation disappears if participants are asked to choose from a menu of possible portfolios. We show that these results extend to sophisticated participants, simple well-specified gambles and incentivecompatible payoffs. We close with a discussion of theoretical and prescriptive implications.

A behavioral model for asset allocation

This paper describes a study, in which we examine the diversification behavior of financial advisors. Learning from BENARTZI and THALER (2000) about investors' naive diversification strategies, we find evidence that the advisor's asset allocation can be described by a new behavioral portfolio model. To verify these findings we distributed questionnaires among several investment consultants who gave us information about their market expectations and three asset allocation recommendations. Their recommendations indeed seem to be described by the behavioral portfolio model. Finally, we examine losses of efficiency for their recommendations.

Risk and Real Estate Investment: An International Perspective

The literature regarding portfolio analysis for institutional real estate investors has until now largely been concerned with benefits associated with naive diversification strategies. In this pape...

A STUDY OF POSSIBLE GAINS FROM INTERNATIONAL INVESTMENT AND THE STATIONARITY OF INTER‐COUNTRY CORRELATION COEFFICIENTS: A REPLY

Previous studies have demonstrated that substantial benefits (beyond those available from a naive diversification strategy) were available to the international investor who could perfectly predict future inter‐country correlation coefficients. The present author's second paper (Watson, 1980) tested the null hypothesis that the sample correlation coefficients were drawn from the same population. The fact that the null hypothesis was not rejected does not exclude the possibility, as Yallup correctly points out, that the data could be generated by another process.