Lesson 3 of 7
How diversification works
See what adding holdings removes from a portfolio's swings, and what correlation leaves behind.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
Who writes thisEditorial processLinkedIn (opens in a new tab)X (opens in a new tab)
In one minute
- Adding holdings that do not move in lockstep lowers a portfolio's swings, and the drop is steepest with the first few names.
- What is left over, however many holdings you add, is set by how much they move together: their correlation.
- Past a certain number of holdings, adding another does little for the swings and costs more to research and track.
Diversification works by cancelling out the risk specific to one company while leaving behind the risk every company in the mix shares. How much it removes, and how fast, depends on how correlated the holdings are with each other. What it removes is measured here as volatility, how widely a holding's yearly returns swing around their average.
What adding holdings does to a portfolio's swings
- 1 holding40.0%
- 2 holdings32.2%
- 5 holdings26.5%
- 10 holdings24.3%
- 20 holdings23.2%
- 50 holdings22.4%
Floor set by a 0.3 correlation: 21.9%
Two kinds of risk
Risk specific to one company
- A lost customer, a failed product, a change of management.
- Falls as you add holdings that do not share the same cause.
- Can, in principle, be spread away almost entirely.
Risk shared by the whole market
- A recession, a rate rise, a shift in how investors price risk in general.
- Touches every holding at once, in the same direction.
- No number of holdings removes it.
Diversification cancels the first kind. It cannot touch the second.
Why correlation sets the floor
The chart above never reaches zero because the holdings are not assumed to be independent: on average, each pair moves together with a correlation of 0.3. The more they share in common, the higher the floor. A set of holdings that moved completely independently of each other would keep falling towards zero instead. Markowitz set out this trade-off in his 1952 paper "Portfolio Selection": what a portfolio's risk depends on is not only how risky each holding is on its own, but how much they move together.
Diminishing returns
For 10 holdings: 40 x the square root of (0.3 + 0.07) is 40 x 0.608, or 24.3.
Most of the fall happens early. Going from 1 holding to 5 removes 13.5 points of volatility in this example. Going from 10 holdings to 50 removes only 1.9 points. Evans and Archer, measuring random portfolios in their 1968 study, found most of the fall came with the first handful of holdings, and questioned the economic case for adding many more.
Fewer swings is the side effect. The purpose is that no single permanent loss can reach much of the whole.
Check yourself
What does adding more holdings mainly reduce?
- The risk specific to each company
- The risk shared by the whole market
- All risk, without limit
Show the answer
Answer: A.
Diversification cancels the risk that is specific to one company. The risk every holding shares with the market as a whole stays no matter how many names you hold.In the illustrative example, with an average correlation of 0.3 between holdings, what is the lowest volatility a portfolio can reach, however many holdings it adds?
- 0 percent
- About 21.9 percent
- 40 percent
Show the answer
Answer: B.
The floor is 40 times the square root of the correlation itself, 0.3, which is about 21.9 percent. Correlation, not the number of holdings, sets this floor.Between 10 and 50 holdings in the example, how much further does volatility fall?
- 15.7 points
- 1.9 points
- 0 points
Show the answer
Answer: B.
Volatility moves from 24.3 percent to 22.4 percent, a fall of 1.9 points, for 40 additional holdings to research and track.Sources
- Markowitz, "Portfolio Selection", Journal of Finance, 1952, on how a portfolio's risk depends on the covariance between holdings, not only the risk of each one alone.
- Evans and Archer, "Diversification and the Reduction of Dispersion", Journal of Finance, 1968, on the diminishing benefit of adding holdings past a modest number.
What this leaves out
- The 40 percent volatility, the 0.3 correlation and every point on the line are illustrative, chosen to show the shape rather than to describe any real portfolio.
- The example assumes equal-sized, equally volatile holdings and one fixed correlation. Real holdings differ in size, in volatility, and their correlation with each other changes over time, often rising sharply in a downturn.
- Nothing here says how many holdings any reader should own. It is not advice about any security.