# Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?

@article{DeMiguel2009OptimalVN, title={Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?}, author={Victor DeMiguel and Lorenzo Garlappi and Raman Uppal}, journal={Review of Financial Studies}, year={2009}, volume={22}, pages={1915-1953} }

We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1-N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated…

## 2,701 Citations

### An Updated Review of (Sub-)Optimal Diversification Models

- Economics
- 2018

In the past decade many researchers have proposed new optimal portfolio selection strategies to show that sophisticated diversification can outperform the na\"ive 1/N strategy in out-of-sample…

### How good is the out-of-sample performance of optimized portfolios : an empirical comparison of optimal versus naive diversification

- Economics
- 2014

Preceding research is inconclusive on the empirical performance of optimized portfolios. In this thesis I evaluate the out-of-sample performance of a minimum-variance portfolio, a meanvariance…

### Approximating the numéraire portfolio by naive diversification

- Economics
- 2010

Estimation theory has shown, owing to the limited estimation window available for real asset data, that the sample-based Markowitz mean-variance approach produces unreliable weights that fluctuate…

### Optimal Granularity for Portfolio Choice

- EconomicsJournal of Empirical Finance
- 2019

Many optimization-based portfolio rules fail to beat the simple 1/N rule out-of-sample because of parameter uncertainty. In this paper we suggest a grouping strategy in which we first form groups of…

### Optimizing the Performance of Sample Mean-Variance Efficient Portfolios

- Economics
- 2012

We propose a comprehensive empirical strategy for optimizing the out-of-sample performance of sample mean-variance efficient portfolios. After constructing a sample objective function that accounts…

### Does Greater Diversification Really Improve Performance in Portfolio Selection?

- Economics
- 2014

One of the fundamental principles in portfolio selection models is minimization of risk through diversification of the investment. This seems to require that in a given working universe, or market,…

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

- Computer ScienceSSRN Electronic Journal
- 2020

It is demonstrated that risk-based diversification - which rely solely on the variance-covariance matrix - strongly outperform the 1/N naive rule in terms of Sharpe ratio, certainty equivalent returns and turnover and that machine learning and clustering techniques can be used to enhance the benefits from diversification when using risk- based allocation rules.

### Being Naive about Naive Diversification: Can Investment Theory be Consistently Useful

- Economics
- 2008

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and taught in MBA texts. DeMiguel, Garlappi and Uppal (2007), however, show that, due to estimation errors,…

### An optimal combination of risk-return and naive hedging

- Economics
- 2015

Taking an approach contrary to the mean-variance portfolio, recent studies have appealed to an older wisdom, ”the naive rule provides the best solution,” to improve out-of-sample performance in…

### Shortfall minimization and the Naive (1/N) portfolio: an out-of-sample comparison

- Economics
- 2016

ABSTRACT Naive portfolio selection, wherein an investor allocates an equal portion of their wealth to the field of candidate assets, is a simple ad-hoc way to create a portfolio. Naive portfolio…

## References

SHOWING 1-10 OF 69 REFERENCES

### Parametric Portfolio Policies: Exploiting Characteristics in the Cross Section of Equity Returns

- Economics
- 2004

This work proposes a novel approach to optimizing portfolios with large numbers of assets by model directly the portfolio weight in each asset as a function of the assetâ€™s characteristics, and presents an empirical implementation for the universe of all stocks in the CRSP-Compustat dataset.

### Optimal Portfolio Choice with Parameter Uncertainty

- EconomicsJournal of Financial and Quantitative Analysis
- 2007

Abstract In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical…

### International Portfolio Diversification with Estimation Risk

- Economics
- 1985

International portfolio diversification has long been advocated as a way of enhancing average returns while reducing portfolio risk for the investor who considers diversifying into foreign…

### On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results

- Economics
- 1991

This paper investigates the sensitivity of mean-variance(MV)-efficient portfolios to changes in the means of individual assets. When only a budget constraint is imposed on the investment problem, the…

### When Will Mean-Variance Efficient Portfolios Be Well Diversified?

- Economics
- 1992

The authors characterize the conditions under which efficient portfolios put small weights on individual assets. These conditions bound mean returns with measures of average absolute covariability…

### An Empirical Bayes Approach to Efficient Portfolio Selection

- Economics, Computer ScienceJournal of Financial and Quantitative Analysis
- 1986

This empirical Bayes method is shown to select portfolios whose performance is superior to that achieved, given the assumption of a noninformative prior or by using classical sample estimates.

### Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps

- Economics
- 2002

Mean-variance efficient portfolios constructed using sample moments often involve taking extreme long and short positions. Hence practitioners often impose portfolio weight constraints when…

### Portfolio Resampling: Review and Critique

- Economics
- 2002

A well-understood fact of asset allocation is that the traditional portfolio optimization algorithm is too powerful for the quality of the inputs. Recently, a new concept called “resampled…

### Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach

- Economics
- 2004

In this paper, we show how an investor can incorporate uncertainty about expected returns when choosing a mean-variance optimal portfolio. In contrast to the Bayesian approach to estimation error,…