**Naive Diversification Isn’t So Naive After All**

__Mike Dickson Jr.__

Horizon Investments; University of North Carolina at Charlotte

May 18, 2016

**Abstract: **

I conduct a horse-race of 15 portfolio construction techniques over 8 empirical datasets comprised of individual stocks. I also conduct a robust Monte Carlo analysis that confirms that recent extensions of mean-variance optimization due to Kirby and Ostdiek (2012) are successful in curbing estimation risk and turnover. Despite these facts, my results indicate that no strategy consistently outperforms naive diversification in terms of mean excess return, Sharpe ratio, and turnover. I introduce a statistic, the time series average of the cross-sectional mean absolute deviation of risk and return, to explain why I observe these results. Data limitations and dataset characteristics contribute the most to the performance of a candidate strategy. I also propose several extensions to active timing strategies and include new characteristics in a parametric portfolio choice framework. Naive diversification continues to prevail, suggesting practical optimization techniques are inferior to naive diversification when forming portfolios of individual stocks.

### Naive Diversification Isn’t So Naive After All – Introduction

Modern Portfolio Theory of course began with the seminal work of Markowitz (1952) who developed the workhorse theory of mean-variance efficiency. The two central conditions of Markowitz’s fundamental model are that: (1) investors must desire to act according to the mean-variance efficient outcome and (2) investors must be able to arrive at a reasonable estimate for the mean return and covariance structure of asset choices. Estimation risk is a common term which emphasizes he failure of Markowitz’s second condition. Estimation risk is the foundation of my work and the related literature. Samuelson (1967) notably added to Markowitz’s work by proving that a 1=N (naive), equally weighted portfolio was the optimal strategy when return distributions are independently and identically distributed (IID). An implication of naive investing is an assumption that ll moments of returns are equal; specifically the mean and variance for mean-variance investors . These assumptions, while likely not realistic, give rise to some appealing features regarding naive diversification. As discussed by Demiguel, Garlappi, and Uppal (2009) and Kirby and Ostdiek (2012), some of these features include: no estimation error, no optimization, no matrix inversion, no shorts, extremely low turnover, and easy application to a large number of assets.

This paper directly compliments the work of Demiguel et al. (2009) and Kirby and Ostdiek (2012). These authors both present compelling arguments but offer very different conclusions. This study presents a middle ground between these authors’ positions and provides evidence consistent with both. I find simply that naive diversification is hard to beat and perhaps naive investing isn’t so naive after all. I conduct a horse-race of the most recent innovations in portfolio optimization techniques using actual stock data, most similar to the study presented by Demiguel et al. (2009). To create my empirical datasets I use the sequential cross-sectional regression methodology described in Dickson (2015) to predict top performing stocks. Following from comments by both Demiguel et al. (2009) and Kirby and Ostdiek (2012), I introduce a statistic to measure the cross-sectional dispersion of the conditional means and volatilities of my data. Consistent with Kirby and Ostdiek (2012), I conclude that the cross-sectional dispersion of the Sharpe ratios in my top performing stock portfolios are simply too small for mean-variance extensions to outperform naive diversification. These results add to the mounting evidence of the poor performance of portfolio optimization techniques. Using robust simulations, I do confirm that the extensions proposed by Kirby and Ostdiek (2012) are successful at improving the performance of mean-variance optimization. However, due to the very issues that these authors discuss, these techniques are incapable of outperforming naive diversification using actual stock data.

Demiguel et al. (2009) compared the out-of-sample performance of 14 competing portfolio strategies and ultimately determined that estimation risk eroded nearly all the gains from sophisticated optimization techniques. Simply put, no strategy consistently outperformed naive diversification. Kirby and Ostdiek (2012) presented evidence to refute this claim and argued that the research design of Demiguel et al. (2009) placed mean-variance optimization at a severe disadvantage in terms of estimation risk and turnover. They developed simple extensions of mean-variance optimization designed to reduce estimation risk and portfolio turnover, and showed that their extensions outperform naive diversification even in the presence of high trading costs. Furthermore, they present evidence that the performance of their extensions is driven by characteristics of the datasets tested. Specifically, datasets that do not have large cross-sectional dispersions in means and variances will likely not perform well using strategies designed to exploit this dispersion, i.e. mean-variance strategies.

I contribute to this line of work in several key ways. First I conduct a comprehensive portfolio analysis using individual stock data and not portfolios of stocks. While some authors such as Green and Hollifield (1992), Jagannathan and Ma (2003), and Brandt, Santa-Clara, and Valkanov (2009) used individual stock data in a portfolio analysis, my study is the first to present a horse-race of the most recent innovations in portfolio optimization using individual stocks. Both Demiguel et al. (2009) and Kirby and Ostdiek (2012), as well as many other authors such as Kan and Guofu (2007), Garlappi, Uppal, and Wang (2007), Kirby and Ostdiek (2015), and DeMiguel, Martin-Utrera, and Nogales (2013) et al., only consider portfolios of stocks when testing competing models. Demiguel et al. (2009) comment that this gives naive diversification an advantage because diversified portfolios have lower idiosyncratic volatility than stocks, so the loss from using naive diversification as opposed to optimal strategies is smaller (p.1920). Their comment hints at what is claimed by Kirby and Ostdiek (2012), i.e. that the cross-sectional dispersions in means and variances of the datasets drives performance. In addition to attenuating the apparent advantage towards naive diversification, using individual stock data has another practical benefit; that is, it more accurately replicates a fund manager’s portfolio construction dilemma. Common datasets used in the aforementioned studies include the readily available characteristic based portfolios from Ken French’s data library, industry portfolios, or country indices. Fund managers are generally more interested in investing in a particular group of stocks or sectors that are more likely to outperform as provided by their team of analysts. They are likely less interested in investing in portfolios of stocks that are not traded, like the data found in Ken French’s data library, or simply all sectors and countries taken as a whole. The procedure described by Dickson (2015) aggregates forecasting signals from multiple sources known at time t, and predicts stock returns. These portfolios then serve as an excellent proxy for a group of actual stocks that are likely to outperform. The added advantage of an analysis with these data is that these results are tradeable and complete with aggressive adjustments for portfolio turnover.

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