Equally Weighted Portfolio (1/N)

The simplest portfolio construction rule: allocate equal capital to every asset in the universe. Despite its simplicity, this naive diversification strategy is a surprisingly strong benchmark.

Overview

The equally weighted (or 1/N) portfolio assigns the same weight to each of the assets in the investment universe. It requires no estimation of expected returns, variances, or correlations, making it completely free of estimation error. This property makes it a powerful benchmark: DeMiguel, Garlappi, and Uppal (2009) showed that none of the 14 optimized portfolio strategies they tested consistently outperformed the 1/N rule out of sample, due to the estimation error inherent in optimization-based approaches.

The strategy is also the simplest implementation of the "naive diversification" heuristic documented in behavioral finance. Benartzi and Thaler (2001) showed that retirement plan participants frequently spread their contributions evenly across the available options regardless of the options' characteristics.

Mathematical Formulation

Portfolio Weights

For a universe of assets, each asset receives an equal weight:

Portfolio Expected Return

The expected return of the equally weighted portfolio is the simple average of all individual asset expected returns:

where is the expected return of asset .

Portfolio Variance

The portfolio variance is:

This can be decomposed into variance and covariance components:

Which simplifies to the well-known expression using the average variance and average covariance :

As , the portfolio variance converges to the average covariance . This is the well-known result that diversification can eliminate idiosyncratic risk but not systematic (market) risk.

Simplified Case: Uncorrelated Assets

When all assets are uncorrelated and have equal variance , the portfolio variance reduces to:

This shows the diversification effect: doubling the number of uncorrelated assets reduces portfolio volatility by a factor of .

Advantages

Zero estimation error: No parameters need to be estimated, completely avoiding the estimation risk that plagues optimization-based methods.
Simplicity: Trivial to implement and explain to stakeholders.
Strong out-of-sample performance: Empirically competitive with or superior to many sophisticated optimization strategies on a risk-adjusted basis.
Low turnover: Only rebalancing to equal weights is needed, resulting in relatively low transaction costs.
Maximum diversification in weight space: The entropy of the weight vector is maximized, ensuring no single asset dominates.

Limitations

Ignores all information: Does not use any information about expected returns, risk, or correlations, even when reliable estimates are available.
Universe dependent: Performance depends entirely on the choice of asset universe. Adding a redundant or poor-quality asset mechanically reduces portfolio quality.
Unequal risk contributions: Despite equal capital allocation, risk contributions are highly unequal when assets have different volatilities.
No risk control: Portfolio risk is entirely determined by the characteristics of the asset universe, with no mechanism to target a specific risk level.

References

DeMiguel, V., Garlappi, L., & Uppal, R. (2009). "Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?" The Review of Financial Studies, 22(5), 1915-1953.
Benartzi, S. & Thaler, R.H. (2001). "Naive Diversification Strategies in Defined Contribution Saving Plans." American Economic Review, 91(1), 79-98.
Windcliff, H. & Boyle, P.P. (2004). "The 1/N Pension Investment Puzzle." North American Actuarial Journal, 8(3), 32-45.