How Diversified Is My Portfolio? A Correlation Guide

Why twenty stocks can still be one bet

Adding a stock lowers the portfolio’s risk only to the extent that the new stock does something the others do not. If every holding reacts to the same news — the same interest-rate move, the same consumer slowdown, the same enthusiasm for one theme — the portfolio behaves like one large position, however many tickers it lists.

The arithmetic makes the point clearly. Take stocks that each swing about 30% a year (their volatility), held in equal amounts. How far diversification can bring that down depends almost entirely on the average correlation between them:

Illustrative: portfolio volatility for equal-weight holdings of 30% volatility each, from the standard formula 30% × √(1/n + (1 − 1/n) × correlation).

Two things stand out. Past a couple of dozen holdings, adding more barely moves the number. And the floor is set by correlation, not by count: at 0.7, an unlimited number of stocks still leaves you with most of a single stock’s volatility, while five stocks at 0.3 already do better than twenty at 0.7.

What correlation tells you, and what it does not

Correlation is a number from −1 to +1 that describes how consistently two return series move in the same direction. The glossary entry covers the definition; for a diversification check, four practical points matter more:

• It is about direction, not size. Two stocks can be correlated at 0.9 while one moves twice as far as the other. Correlation tells you they move together; volatility and beta tell you by how much.
• It depends on the window. Measured over a few weeks it is mostly noise. A year of daily returns is a sensible minimum, and comparing a one-year reading with a longer one shows whether a relationship is stable.
• It is not a probability. A correlation of 0.5 does not mean two stocks move together half the time. It means their returns share a moderate linear relationship.
• It is weakest when you need it most. In broad sell-offs correlations between stocks tend to rise, so a portfolio that looks diversified in a calm year can fall more uniformly in a bad one. Treat a low correlation as helpful, not as a guarantee.

How to read a correlation matrix, holding by holding

A correlation matrix puts every pair of holdings in one grid. Here is an invented five-stock portfolio, with each holding’s weight in brackets:

Read it in this order:

1. Skip the diagonal and half the grid. Every stock correlates 1 with itself, and the grid is a mirror: A–B and B–A are the same number.
2. Find each holding’s strongest tie. A’s is 0.85 (with B), C’s is 0.80 (with A), E’s is only 0.20 (with D). A holding whose strongest tie is low is the one doing the diversifying.
3. Look for blocks. A, B and C correlate between 0.75 and 0.85 with each other. They are three names for one exposure.
4. Add up the weights of each block. A, B and C together are 30% + 25% + 20% = 75% of the portfolio. Five holdings, but three-quarters of the money rides on one driver.
5. Then ask what links the block. The matrix shows that holdings move together, not why. The answer is usually a shared sector, a shared customer base or a shared sensitivity to rates — and knowing which tells you what would hurt all of them at once.

Negative numbers are rare between ordinary stocks. When one appears, check the window before relying on it; a short history can produce a negative reading that does not last.

Sector concentration

Sector weights are the quickest check and need no statistics: add up what you hold in each sector as a share of the portfolio. Companies in one industry share demand, costs and regulation, so they tend to correlate more with each other than with companies elsewhere, and a heavy sector weight usually shows up as a block in the matrix too.

Two cautions keep the check honest:

• Different sectors can share a driver. A homebuilder, a bank and a furniture retailer sit in three sectors and can all depend on the housing market. The sector table will look spread out; the correlation matrix will not.
• Funds overlap with what you hold directly. A broad index fund already owns the largest companies in the market. Holding the fund and several of its biggest constituents separately concentrates you in those names more than either line suggests on its own.

There is no universal right weight per sector. What matters is that the weight you hold is one you chose, so write down a ceiling and check against it.

Factor exposure: the tilt behind the names

Factors are characteristics shared by many stocks across sectors — company size, valuation, profitability, growth, sensitivity to the market — that help explain why groups of stocks move together. A portfolio spread over eight sectors can still be all small companies, all on high multiples of earnings, or all high-beta, and then it will behave as one bet whenever that characteristic falls out of favour.

Factor exposure answers “which way does the portfolio lean as a whole?” You read it as a tilt against the market rather than as a pass or fail: leaning towards smaller companies or cheaper P/E ratios is a legitimate choice, as long as you know you have made it. The useful question is whether the tilts are the ones you intended, and whether they all point the same way.

A practical diversification check

Run through these in order; each takes minutes once the data is in front of you.

1. Top-heavy? Add up the weights of your five largest positions. If one position alone is a large share of the portfolio, no correlation reading will offset it.
2. Sector weights. Compare each sector’s share with the ceiling you set yourself.
3. Correlation blocks. Over at least a year, find the clusters of high correlation and add up their weight, as in the example above.
4. Factor tilts. Check whether size, valuation and market sensitivity all lean the same way.
5. The bad months. Look at your worst months and your maximum drawdown: did most holdings fall together? That is the correlation that mattered, measured in the conditions you care about.
6. One question to finish. Name the single event that would hurt most of the portfolio at once. If you can name it quickly, that is your real concentration.

None of this says a concentrated portfolio is wrong. It says you should know where the concentration is, and size it on purpose.

Running the check in Lemma Analysis

Sector weights come with portfolio tracking. The dashboard’s Sector mix card shows the portfolio’s weight by sector, heaviest first; on the portfolio screen, Allocation drift lets you set a target per sector with Edit targets and shows target against actual.

The rest is on the portfolio analytics board:

• Correlation matrix — who really moves together is built from your holdings’ price returns over the window selected on the board, never shorter than a year; under a shorter chart window the card says 1Y window. Hover a cell for the pair in plain words, from “move almost as one” to “barely related”. When there are more companies than fit the card, it shows the most connected ones — ranked by each company’s strongest tie with any other holding, whatever its sign — says so (showing the 16 most connected of 34 companies), and Show all → opens the full grid.
• Factor exposures — in plain English draws six bars: Quality, Momentum, Growth, Size, Value and Volatility. Each places your portfolio’s weighted average for one characteristic on a 0 to 1 scale against the companies we track. The definitions are ours, so read the caption under each bar for what it is built from rather than assuming the textbook version. When we have no data for the holdings behind a factor the bar shows a dash and says so, never a made-up middle value; when the data covers too little of the portfolio to be trusted, the bar says how much of it the figure covers.
• Select Combined portfolio in the header and both cards cover every holding across your portfolios. Two portfolios that each look diversified can turn out to be the same bet twice, and only the combined view shows it.

The analytics board is part of Ultimate; tracking a portfolio, including the sector mix and allocation drift, is free. Every new account gets Ultimate for seven days once the email address is confirmed.

Educational only. Not investment advice.