Diversification: benefits and limitations

“Don’t put all your eggs in one basket” is probably the most repeated investment advice. It is right, but incomplete. Diversifying reduces one type of risk and leaves another untouched, and there are ways of “diversifying” that reduce almost nothing.

This article explains what diversification does, where the theory comes from, how to measure the effect with simple calculations and where the limits are. The numbers are hypothetical and serve to illustrate the reasoning. Nothing here recommends any asset, fund or portfolio. If the concepts of risk and return are not yet clear, start with How to interpret investment risk and return.

What diversifying means

The “Introduction to Investments” handbook from the CVM (Comissão de Valores Mobiliários, Brazil’s securities regulator) defines diversification as splitting money among different classes and types of investment to reduce risk. The SEC, on Investor.gov, describes two layers:

• across asset classes, such as stocks, bonds and cash. Conditions that hurt one class may favor another;
• within each class, with several issuers and sectors. If one company or sector does badly, other positions can make up for it.

Dividing wealth among classes is called asset allocation. It is a personal decision, which depends on each person’s time horizon and risk tolerance, according to the same Investor.gov.

Specific risk and systematic risk

The central distinction lies here. The CVM uses an example: if health inspectors discover that a food company is breaking hygiene rules, its shares tend to fall. Most other companies are not affected, and some competitors may even benefit.

This is specific risk, or diversifiable risk: an event that hits one company, one sector or one issuer. Someone holding only that stock feels the whole drop. Someone with a portfolio of many stocks feels a fraction.

Other events hit almost everything in the same direction. The CVM cites the expectation of a recession, which tends to push down the prices of practically all assets. This is systematic risk, or non-diversifiable risk. Adding more assets does not eliminate it.

Where the theory comes from

The idea of spreading risk is old. The person who turned it into theory was the American economist Harry Markowitz, in the article “Portfolio Selection”, published in the Journal of Finance in 1952. The work earned him the 1990 Nobel Prize in Economics, shared with Merton Miller and William Sharpe.

The Nobel press release sums up the contribution in three points:

• choosing a portfolio can be reduced to two dimensions: expected return and variance (a measure of fluctuation);
• a portfolio’s risk depends not only on the risk of each asset, but also on the covariances between them, that is, on how they move together;
• therefore, what matters in an asset is not its risk in isolation, but how much it contributes to the risk of the whole.

The same release records the limit: because asset returns are correlated in practice, risk “cannot be completely eliminated”, no matter how many securities the portfolio holds.

Correlation in practice

Correlation is a measure, from −1 to +1, of how two assets move together. Near +1, they rise and fall together. Near 0, they are unrelated. Near −1, one tends to rise when the other falls.

An example with two scenarios

Imagine two hypothetical assets and two equally likely scenarios for next year:

	Scenario 1	Scenario 2	Expected return
Asset X	+20%	−10%	5%
Asset Y	−10%	+20%	5%
Portfolio 50% X + 50% Y	+5%	+5%	5%

On its own, each asset may return +20% or −10%. Half in each returns +5% in any scenario: in scenario 1, 0.5 × 20% + 0.5 × (−10%) = 5%; in scenario 2, the calculation reverses and gives the same. The expected return did not change, and the fluctuation disappeared.

Now imagine Y behaves exactly like X (+20% in scenario 1 and −10% in scenario 2). The half-and-half portfolio returns exactly the same as each asset alone. Two assets, no diversification.

Both cases are extremes and hardly exist in real markets. They serve to show that the benefit comes from the difference in behavior, not from the number of names in the portfolio.

An example with volatility

Now with a more commonly used measure. Suppose two hypothetical assets, each with volatility (annual standard deviation of returns) of 20%, and a portfolio with half in each. By Markowitz’s formula for two assets, the portfolio’s volatility depends on the correlation:

Correlation between the two assets	Volatility of the 50/50 portfolio
+1	20.0%
+0.5	17.3%
0	14.1%
−1	0%

The calculation, for anyone who wants to check: with equal weights and the same volatility σ in both assets, the portfolio’s volatility is σ × √[(1 + ρ) ÷ 2], where ρ is the correlation. With σ = 20% and ρ = 0, it comes to 20% × √0.5 ≈ 14.1%.

More assets, up to a point

The same reasoning applies to many assets. Suppose an equally weighted portfolio of N hypothetical assets, all with 20% volatility and a correlation of 0.3 between each pair:

Number of assets	Portfolio volatility
1	20.0%
4	13.8%
25	11.5%
100	11.1%
Infinite	11.0%

The drop is steep with the first assets and almost stops after that. The floor, of about 11%, is the part that comes from the correlation between assets: the systematic risk in the example. (Calculation: volatility = 20% × √[1/N + (1 − 1/N) × 0.3]; as N grows, it tends to 20% × √0.3 ≈ 11.0%.) If the assets were completely independent (zero correlation), volatility would fall to 20% ÷ √N and approach zero. This is what the Nobel release points to when it says the “law of large numbers” does not fully apply to portfolios.

The benefits

• Less dependence on a single event. An issuer’s default or a sector crisis hits only the part of the portfolio exposed to it.
• Less fluctuation for the same expected return. As in the two-scenario example, combining assets that do not move together can reduce variation without reducing expected return. Less fluctuation also reduces the negative effect of volatility on the compounded result, explained in the article on risk and return.
• Better odds of sticking to the plan. A portfolio that fluctuates less tends to be easier to endure in bad times, which reduces the risk of selling at the worst moment. This is the newsroom’s assessment, not a guaranteed result.

Investor.gov sums up the effect with caution: diversification does not guarantee that your investments will not suffer if the market drops, but it can improve the chances that you will not lose money, or that you will lose less than you would without diversifying (Diversify Your Investments).

The limitations

It does not eliminate systematic risk. A recession, a sharp rise in interest rates or a crisis of confidence can bring almost everything down at the same time. How interest rates affect several assets at once is covered in Global interest rates and their effects on assets.

Correlations change. The correlation used in the calculations is estimated from past data. Nothing guarantees that two assets that moved independently will keep doing so, and the protection may be smaller than history suggests precisely when it is most needed.

Quantity is not diversity. Ten assets from the same sector or ten funds buying the same things concentrate the same risk. Investor.gov warns that a fund concentrated in one sector does not diversify and recommends checking each fund’s largest holdings to see whether they are really different.

It limits the gain. The CVM points out the other side: if a positive event affects only one company, someone who held only that stock gains more than someone with a diversified portfolio. Diversifying means giving up the best case to protect yourself from the worst.

It does not improve a bad asset. Combining several high-risk assets, or unregistered products, does not make them safe. Diversifying among fraudulent offerings is still losing money.

It has costs and requires monitoring. More positions can mean more fees, more work to understand each one and more difficulty keeping track. In the newsroom’s assessment, a portfolio you do not understand does not become safer just because it has many items.

It does not replace guarantees or an emergency fund. Spreading bank investments across institutions may be relevant because of the per-institution limit of the FGC (Brazil’s deposit guarantee fund), explained in Fixed income and equities. But that is protection against credit risk, not against market fluctuation. And the emergency fund, according to the CVM on its Investor Portal, should prioritize low risk and high liquidity.

Rebalancing: diversification unravels on its own

Over time, the assets that rise most come to weigh more. Investor.gov gives an example: a portfolio that started with 60% in stocks may reach 80% after a period of gains. As a result, the portfolio’s risk changed without you deciding anything.

Rebalancing means returning to the original proportions, selling part of what rose or investing more in what lagged. According to Investor.gov, some experts suggest doing this at fixed intervals, such as every 6 or 12 months, and others when a class drifts more than a set percentage. In either case, the agency notes that the practice tends to work best when not done too often. Selling may generate taxes and costs, which also factor into the decision.

Tokenization and crypto do not change the logic

Digital assets are not exempt from this math. Diversifying across several tokens that depend on the same market, the same infrastructure or the same issuer may mean little real diversification. And tokenizing an asset does not change the risk of the underlying asset, as shown in Why tokenizing an asset does not eliminate risk.

Key takeaways

• Diversifying reduces specific risk (of a company, sector or issuer), but not systematic risk, which hits the market as a whole.
• The effect depends on how assets behave together. Many similar assets are equivalent to a few; a few truly different assets can significantly reduce fluctuation.
• Diversification does not guarantee profit or prevent losses, limits the maximum gain, has costs and requires rebalancing. The right mix depends on your time horizon, goal and profile.