Diversification: The Magic of Correlation
The more assets you hold that don't move in perfect sync, the less your portfolio swings. But correlation sets the limit on how far diversification can go.
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Text version · Quant Basics, lesson 3: “Diversification: The Magic of Correlation”
The more assets you hold that don't move in perfect sync, the less your portfolio swings. But correlation sets the limit on how far diversification can go.
Out of sync, so they offset each other
The lower the correlation between assets, the more likely one holds up when another falls, and the lower the portfolio's volatility. That's diversification.
Diversification has limits
The more you hold, the more thoroughly each stock's idiosyncratic risk is diluted, but the systematic risk they all share can't be diversified away. In a crisis, correlations tend to rise, which raises this floor.
More holdings ≠ more diversification
Six bank stocks all rise and fall together on the same interest-rate news, so they don't diversify much. One stock, one bond and one gold holding is fewer assets, yet diversifies better.
Key takeaways
- The lower the correlation between assets, the more portfolio volatility falls.
- Adding more assets removes stock-specific risk but not the market risk they all share: the floor = single-asset volatility × √correlation.
- The first 10–20 assets give the most diversification benefit; after that each extra one adds less and less.
- Correlations often rise together in a crisis, so diversification that works in normal times can fail just when you need it most.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Correlation 0.3: going from 1 asset to 10, what does portfolio volatility drop from and to? And from 10 to 100?
- Set the correlation to 0: what's the volatility of a 100-asset portfolio?
- Set the correlation to 1: does adding more assets lower volatility at all?
- Simulate a crisis: with 100 assets, the correlation rises from 0.3 to 0.8. What does portfolio volatility go from and to?
Quiz and explanations
- 1. An equal-weighted portfolio of 10 stocks that are all perfectly correlated with each other (correlation 1) will have volatility that…
- Answer: Matches a single stock.Putting assets that move in perfect sync together gives no diversification at all.
- 2. Which risk can diversification NOT remove?
- Answer: The whole market falling.Systematic risk is shared by every stock.
- 3. Assets each have 20% volatility and a pairwise correlation of 0.25. Holding a very large number of them, roughly what's the portfolio volatility?
- Answer: 10%.Floor = 20% × √0.25 = 10%.
Terms in this lesson
- correlation (Correlation): How much two prices move together, from −1 to 1; the closer to 1, the more in sync.
- diversification (Diversification): Holding several assets that don't move in perfect sync to lower the portfolio's overall swings.
- idiosyncratic risk (Idiosyncratic Risk): Risk specific to one company (earnings, accidents and so on) that market instruments can't hedge; only diversification helps.
- systematic risk (Systematic Risk): Risk the whole market shares and diversification can't remove, such as recessions or interest rate changes.