Naive diversification

Naive diversification is a portfolio construction strategy that consists of investing in a large number of instruments or assets without considering their risk or return characteristics. Naive diversification is based on the notion that by investing in a large number of assets, we can potentially reduce the risk of the portfolio and achieve more stable returns over time.

An alternative approach would be to use a statistical approach such as Modern Portfolio Theory of Markowitz, which allows investors to construct portfolios with better return-risk profiles by combining a large number of securities. While this approach will generally lead to a efficient portfolios, the approach is quite sensitive to the inputs and can lead to corner solutions.

In addition, statistical approacher are complicated, sensitive to small changes in the parameters, and often infeasible in practice. A naive diversification approach on the other hand, is very simple and easy to implement. At the same time, it still honors the key message of Modern Portfolio Theory (MPT) that is investment diversification.

Approaches to naive diversification

There are several ways in in which we can apply naive diversificaton:

  1. Equal weighting: allocate equal amounts of capital to each instrument in the portfolio. This is known as equal weighting, and it involves dividing the capital equally among the assets without considering their characteristics.
  2. Market capitalization weighting: allocate capital to the assets based on their market capitalization. This approach is known as market cap weighting, and it involves allocating more capital to the larger companies and less capital to the smaller companies.
  3. Random weighting: allocate capital to the assets randomly. This is known as random weighting since we assign random weights to the assets and do not consider their risk or return characteristics.

The most popular approach to naive diversification is the so-called 1/n approach. We discuss this approach in more detail below. The approach can easily be implemented using an Excel spreadsheet and does not require specialised software.

Naive diversification – the theory

The following equation shows a ‘1-factor market model’ that describes the excess return of a security as a function of its ‘abnormal’ return, α, its systematic risk β towards the market, and its idiosyncratic risk ε

r_i - r_f = \alpha_i + \beta_i \cdot (r_m - r_f) + \epsilon_i

When we construct a portfolio from multiple assets, our portfolio return can be described as

r_p - r_f = \alpha_p + \beta_p \cdot (r_m - r_f) + \epsilon_p

Suppose we increase the number of securities a lot. In that case the above equation reduces to:

r_p = r_f + \beta_p \cdot (r_m - r_f)

This is because both the ‘abnormal’ return α and firm-specific risk ε disappear.At the same time, systematic risk component (β) converges to 1 (i.e. equals market risk).

\alpha_p = \lim_{i \to \infty}\dfrac{1}{N}\sum_{i=1}^{N}\alpha_i = 0

\beta_p = \lim_{i \to \infty}\dfrac{1}{N}\sum_{i=1}^{N}\beta_i = \beta_m = 1

\epsilon_p = \lim_{i \to \infty}\dfrac{1}{N}\sum_{i=1}^{N}\epsilon_i = 0

In other words, investors that wish to construct a proper portfolio don’t need to involve themselves with a complicated approach such as MPT. Instead, they are able to form an ‘optimal’ by just investing (equally) in a large number amount of assets. The portfolio is called a 1/n portfolio. Such a portfolio will, theoretically, have an exposure to market risk that is equal to 1. Investors who are risk-averse and that are content with lower levels of expected return, can decide to invest only part of their portfolio in the 1/n portfolio, and keep the rest in cash.

As long as the amount of securities is large enough and investment in any single security is not overstated, investors can obtain, through naive diversification, the market return.  Although an equal-weighted portfolio is the most common way to apply naive diversification, the theory actually is independent of the amount invested in any single security. At least, as long as the number of securities is large enough. In practical terms, this underlying idea initially contributed to the emergence of ETFs in the 90s.

Advantages of naive diversification

Naive diversification has several advantages:

  • First, unlike a lot of other approaches available to investors, constructing a naive portfolio is not computationally intensive. There are no parameters that have to be estimated
  • Second, the approach is not sensitive to estimation error. As such, a naive portfolio is a more robust approach to investing
  • Finally, research suggests that a naive portfolio in practice does almost as well as more sophisticated approaches

Summary

Investing in a large number of securities allows investors to reduce overall portfolio risk. As long as the number of investments is sufficiently high, the return on any single security will not affect the risk-return profile of the entire portfolio.

Naive diversification, by investing using arbitrarily chosen weights, (e.g. equally-weighted, value-weighted,…), will thus perform sufficiently well if enough assets are included in the portfolio.  This portfolio construction can easily be done using an Excel spreadsheet.