Correlation
Correlation measures how much two investments move in step. It decides whether diversification works, and unfortunately it doesn't always stay the same.
Learning objective: After this lesson you can explain why correlation is decisive for diversification and why it can change.
A correlation of plus one means two investments always move the same way. Minus one means always exactly the opposite. Zero means there's no connection.
Values for Diversification
For diversification you want values well below one. Two European stock funds often have more than 0.9 with each other, that's hardly any diversification. Stocks and safe government bonds were usually much lower in the past, often around zero.
Correlations Change
The unpleasant side: correlations change. In calm times investments often move differently. In a panic a lot falls together, because everyone wants to sell at once. And in 2022 even stocks and bonds fell together, because interest rates rose fast.
Planning With a Cushion
That's why diversification often helps least exactly when you need it most. If you know that, you plan differently: with a real cushion of safe investments rather than the hope that everything will balance out.
The usual Pearson correlation only measures straight line relationships. It doesn't capture dependencies that aren't straight line, for example with options or in very extreme moves. Two investments can have a correlation close to zero on normal days and still crash together on the worst days.
Correlation in Crises
That correlations rise in crises is well documented. There are three reasons. Many people need money at the same time and sell whatever they can. Those who invested with leverage are forced to sell. And a shared risk factor that's masked by the quirks of individual investments in calm times suddenly decides everything. Correlations estimated from normal times therefore overestimate how much diversification helps when it counts.
Two Calculations
It makes sense, then, to do two calculations: once the correlation over the whole period and once only over phases when the market fell sharply. The second number shows whether an investment really protects you when it matters. If an investment only balances things out in the first calculation, it's no good as a hedge.
Summary
- Correlation only measures straight line relationships.
- In crises correlations rise and diversification works worse.
- Also check correlations for crisis periods alone, not just on average.
Did you get it?
What does the usual correlation not capture?
Relationships that aren't straight line, especially in extreme moves.
Why do correlations rise in crises?
Because many people need money at once, leveraged positions are force sold and a shared risk factor dominates everything.
How do you realistically check whether diversification protects you?
By also calculating correlation only for phases of sharp declines.
Check your understanding
Your task
Write down two holdings from your portfolio or planned portfolio and estimate whether their correlation is close to one, close to zero, or below. Give your reason in one sentence. Then enter your positions in the portfolio x-ray and check whether your portfolio is heavily concentrated in one asset class.
Sources and further reading
- The study by Longin and Solnik (2001) in the Journal of Finance uses extreme value theory to show that the correlation of international stock markets rises sharply in falling markets but barely in rising ones. View source ↗
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- DiversificationStage 3
- VolatilityStage 5
- Gold and precious metalsStage 1
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