Diversification — How Many Stocks Are Enough?

What is Diversification?

Diversification is a strategy of spreading investments across various assets to reduce the impact of a single stock's loss on the overall portfolio. The key is not simply increasing the number of stocks, but combining assets that move differently to offset risk. If you hold 20 stocks from the same industry, even with many holdings, the diversification effect will not be significant.

Risk is divided into two types: unsystematic risk (also known as specific risk), which is unique to a particular stock, such as a company's poor earnings performance, and systematic risk (also known as market risk), which affects the entire market, such as interest rates, economic conditions, or exchange rates. Diversification can only reduce unsystematic risk; systematic risk remains no matter how many stocks you add. This article is an educational explanation of the principles and does not recommend buying specific stocks.

How Does Risk Decrease as the Number of Stocks Increases?

Assuming stocks move completely independently (correlation coefficient of 0) and each stock has the same volatility, the volatility of a portfolio composed of N stocks converges to the individual volatility divided by √N. For example, if individual volatility is 30% annually, it drops to 30÷√4 = 15% with 4 stocks, and 30÷√16 = 7.5% with 16 stocks.

However, actual stocks belong to the same market and tend to move together to some extent, so their correlation coefficient is not 0. If the average correlation coefficient between stocks is ρ, even if you increase the number of stocks indefinitely, portfolio volatility does not reach 0 but stops at a level equal to individual volatility multiplied by √ρ. If the correlation coefficient is 0.3 and individual volatility is 30%, the lower limit of diversification is 30×√0.3 ≈ 16.4%. This limit is the systematic risk that cannot be eliminated.

Therefore, there is a clear diminishing return to increasing the number of stocks. While risk decreases rapidly when adding the first few stocks, beyond a certain number, the risk reduction from adding one more stock is minimal.

What is the Optimal Number of Stocks?

Classic studies suggest that most unsystematic risk is eliminated when holding approximately 20-30 randomly selected stocks. Referring to the √N example above, volatility decreases from 30% with 1 stock to about 9.5% with 10 stocks, and about 6.7% with 20 stocks. After 20 stocks, the additional reduction is only in decimal points.

However, these numbers apply when correlations are low. Stocks in overlapping industries or concentrated in a single theme have high correlation coefficients, meaning that even with 30 holdings, you might only achieve diversification similar to holding 5-6 stocks. Conversely, mixing asset classes with low correlation, such as stocks, bonds, and international assets, can achieve greater diversification with fewer holdings.

In conclusion, the optimal number of stocks is not a fixed answer but a function of how differently the held stocks move. Instead of only accumulating large-cap export-oriented stocks, mixing stocks with different characteristics—such as domestic-focused, export-oriented, financial, and dividend stocks—will create a more stable portfolio with the same number of holdings.

How to Apply This in Practice?

It is difficult for individual investors to calculate correlation coefficients for each stock. A practical alternative is to avoid overlap by diversifying across broad categories like industries, regions, and asset classes. For example, if you already hold one semiconductor stock, instead of adding another, fill the next slot with a stock from a different sector.

Instead of aggressively increasing the number of individual stocks, another approach is to achieve diversification across hundreds of stocks with a single ETF. A single index ETF inherently provides diversification across the entire market. Therefore, a core-satellite strategy—using ETFs for broad exposure and adding a few individual stocks as satellites—can effectively manage both administrative burden and diversification.

Weight management is also part of diversification. Even with 10 stocks, if 60% of your portfolio is concentrated in one stock, the actual diversification is closer to holding just that one stock. Allocating weights close to equal and regularly rebalancing to restore target allocations when they drift over time is a mechanism to maintain intended diversification.

Pitfalls and Limitations of Diversification

First, there's 'over-diversification,' where investors feel secure simply by looking at the number of stocks. If you hold more than 50 stocks, the additional diversification effect is minimal, while it becomes difficult to track and manage each stock, and returns get diluted by average-performing stocks, ultimately resembling an index. In such cases, an index ETF is superior in terms of cost and management.

Second, there's the phenomenon where correlations tend to spike to 1 during crises. Assets that normally move independently tend to fall together during sharp market downturns, weakening diversification precisely when it's most needed. This is another way of saying that diversification only reduces unsystematic risk and does not eliminate systematic risk.

Third, diversification is a mechanism to mitigate losses, not an insurance policy to eliminate them. A diversified portfolio will still decline if the entire market falls, so it works best when used in conjunction with other risk management strategies like stop-loss orders and position sizing.

Summary and Checkpoints

The answer to the optimal number of stocks is not 'how many,' but 'how differently they move.' Mixing stocks with low correlation is sufficient with fewer holdings, while accumulating only similar stocks will not provide diversification even with many holdings. Generally, for a well-diversified individual stock portfolio, risk reduction tends to flatten out in the 20-30 stock range.

There are three checkpoints: (1) Are your holdings concentrated in the same industry or theme? (2) Is any single stock's weight excessively large? (3) Is the number of stocks growing beyond a manageable level? This article is an educational resource explaining principles, and actual investment decisions and responsibilities lie with the investor.