Asset correlation: the key to diversification

Owning 15 different stocks isn't always being diversified. If all 15 are banks from the same country, or US tech companies, they'll probably rise and fall almost at the same time. What really reduces risk isn't the number of assets, but how differently they move from each other. That's measured with correlation.

What correlation is

Correlation is a number between −1 and +1 that shows how much two assets move together:

• +1: they move exactly alike. When one goes up, so does the other, in the same proportion.
• 0: no relationship. Knowing what one did tells you nothing about the other.
• −1: they move exactly opposite. When one goes up, the other goes down.

In practice, the extremes are almost never seen. Some approximate typical values:

Asset pair	Typical correlation
Two S&P 500 ETFs	~1.0
Apple and Microsoft	0.6 to 0.7
US and European stocks	0.7 to 0.9
US and Latin American stocks	0.5 to 0.7
Stocks and US government bonds	−0.3 to 0.4 (varies over time)
Stocks and gold	0 to 0.2

Why correlation lowers risk

Picture two assets with the same volatility, 20% a year, and put half your money in each. The portfolio's volatility depends on their correlation:

Correlation	50/50 portfolio volatility
+1.0	20%
+0.5	~17%
0	~14%
−0.5	10%

Illustrative calculation. With a correlation of +1, combining does nothing: you have the same risk. As correlation drops, risk falls without giving up return, because one asset's falls are partly offset by the other. That's why diversification is called "the only free lunch" in finance.

This is the principle behind the efficient frontier: the optimizer looks for combinations of assets that offset each other.

How to read the correlation matrix

When you calculate a portfolio in the optimizer, the results include a Correlations section. It's a table where each cell shows the correlation between two of your assets, color-coded:

• Strong colors on one side: assets that move alike. Together, they add little diversification.
• Colors on the other side or neutral: assets that move differently. These are the ones that help lower risk the most.

The "Group by region" option sorts assets by region. Blocks usually appear: Latin American stocks highly correlated with each other, Asian stocks with each other, and bonds on their own.

An exercise:

1. Load the "Global tech" example and calculate.
2. Look at the matrix: many cells will show high correlations, even though the companies are from different countries.
3. Now load the "Global diversified" example, with stocks from several regions, bonds and gold.
4. Compare the two matrices and each portfolio's volatility.

Three correlation traps

1. It rises in crises

In moments of panic, many assets that normally move differently start falling together. In 2008 and in March 2020, almost every stock market in the world fell at the same time. Diversifying across stocks from different countries helps, but it protects less exactly when you need it most. That's why it's worth including assets of a different nature, like high-quality government bonds. We explain it in bonds in a portfolio.

2. It changes over time

The correlation between stocks and bonds was negative for much of the 2000s and 2010s, and turned positive in 2022, when inflation hit both. A correlation calculated with 3 years of data may not repeat over the next 3.

3. Market hours distort it

Tokyo closes before New York opens. If you compare daily returns, a drop in New York shows up in Tokyo the next day, and the daily correlation looks lower than it really is. That's why, in automatic mode, the optimizer uses weekly returns when you mix Asia with the Americas: with weekly data, that lag almost disappears.