Equally Weighted Portfolio (1/N)

The elegant power of naïve diversification

Overview

The Equally Weighted (EW) strategy assigns identical capital weights to every asset in the basket— a simple rule often written as $w_i = 1 / N$ for $i = 1,\dots,N$ assets. Despite its apparent naïveté, a long literature—from Sharpe (1964) to DeMiguel, Garlappi & Uppal (2009)—shows that EW performs surprisingly well out‑of‑sample because it sidesteps the estimation noise that plagues more sophisticated optimizers.

In our optimiser this method serves both as a robust baseline and a practical choice for users who favour transparency, ultra‑low turnover, and broad diversification without making any forecast about returns or covariances.

Intuitive Explanation

Think of splitting a pizza with friends. If everyone gets the same‑sized slice, no negotiation is needed and nobody feels short‑changed. Likewise, an equally weighted portfolio gives each asset an identical "slice" of capital, ensuring the portfolio's outcome is not dominated by any single name.

Every‑ingredient salad analogy: When you mix equal spoonfuls of many ingredients, the flavour of any one component is muted. Similarly, EW dilution keeps idiosyncratic shocks from any stock from overwhelming the total portfolio.

Detailed Mathematical Explanation

Given $N$ assets with expected return vector $\mu \in \mathbb{R}^N$ and covariance matrix $\Sigma \in \mathbb{R}^{N\times N}$ , Equally Weighted sets weight vector $w^{\text{EW}} = \tfrac{1}{N}\mathbf{1}$ , where $\mathbf{1}$ is a vector of ones.

Expected Portfolio Return

\mathbb{E}[R_p] = w^{\top}\mu = \frac{1}{N}\sum_{i=1}^{N} \mu_i

Portfolio Variance

\sigma_p^2 = w^{\top}\Sigma w = \frac{1}{N^2}\sum_{i=1}^{N}\sum_{j=1}^{N}\sigma_{ij}

If all pairwise correlations are zero and each asset shares the same variance $\sigma^2$ , the variance simplifies to $\sigma_p^2 = \sigma^2 / N$ . Thus risk falls at the familiar 1/√N rate—the core diversification benefit. In reality, correlations are positive so the decay is slower, but the intuition remains intact.

Implementation in Our Service

The backend class EquiWeightedOptimizer in srv.py creates the weight vector in one line:

w_i = \frac{1}{N}\;\;\forall\,i

Performance metrics (Sharpe, Sortino, CAPM beta, etc.) are then computed exactly the same way as other methods, letting you compare EW head‑to‑head with MVO, HRP, and more.

Worked Example

Suppose we invest in four stocks—A, B, C, D—each with different expected returns and volatilities. EW allocates 25 % to each. The portfolio's expected return is the simple average of individual returns, while variance is computed via the earlier formula. Even if stock D is twice as volatile as A, its impact is capped by the equal stake.

Advantages and Limitations

Advantages

Forecast-free robustness: No estimation of expected returns or covariances required, eliminating a major source of error in portfolio construction.
Low turnover: Weights only drift as prices move; periodic rebalancing keeps transaction costs minimal compared to optimization-based approaches.
Small-cap tilt: Relative to market-cap weighted portfolios, equally weighted naturally emphasizes smaller names—often harvesting size premia.
Benchmark baseline: Provides a clean yard-stick to test whether more complex strategies add value in out-of-sample performance.
Simplicity and transparency: Easy to explain and implement, with no "black box" elements that might raise concerns for stakeholders or clients.

Limitations

Risk blindness: Ignores that some assets are far more volatile than others, potentially including excessively risky assets with the same weight as stable ones.
Liquidity constraints: A 1/N schedule may overweight illiquid micro-caps in large portfolios, creating practical implementation challenges.
No covariance exploitation: Cannot achieve the lowest possible risk for a given return when reliable estimates exist, leaving diversification benefits on the table.
Concentration during bubbles: Without rebalancing, bubble assets can grow to dominate the portfolio as they inflate, leading to unintended concentration.
Sector imbalances: May lead to unintended sector or factor tilts depending on the initial universe of securities.

References

Sharpe, W. F. (1964). "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk." Journal of Finance, 19(3), 425–442.
DeMiguel, V., Garlappi, L., & Uppal, R. (2009). "Optimal Versus Naïve Diversification: How Inefficient Is the 1/N Portfolio Strategy?" Review of Financial Studies, 22(5), 1915–1953.
Benartzi, S. & Thaler, R. (2001). "Naïve Diversification Strategies in Defined Contribution Saving Plans." American Economic Review, 91(1), 79–98.