Key takeaways
- Statman's 1987 paper set the classic threshold at 30 stocks for a borrowing investor and 40 for a lending one, purely on variance reduction.
- Just 1,092 US firms, 4.31% of the CRSP sample since 1926, account for all $34.82 trillion of net US stock market wealth creation.
- Bootstrapped 100-stock portfolios beat the cap-weighted market only 43.29% of the time over 90 years, with no variance advantage left to gain.
- Globally, 55.2% of US stocks and 57.4% of non-US stocks underperformed one-month Treasury bills in compound terms between 1990 and 2020.
- Goetzmann and Kumar found more than 25% of over 40,000 brokerage accounts held a single stock, and more than half held fewer than three.
Say two people each pick thirty stocks, carefully, out of the same market on the same morning. Neither has any special skill. Both just want a decent spread, and thirty is the number they've always heard. One of them happens to end up owning the company that becomes the decade's outlier. The other doesn't.
By the textbook test, you'd call both of them diversified. And by that test they are. Yet their outcomes won't look remotely alike, and the calculation behind the number can't see the difference — because it was never measuring that.
Here's where the textbook figure comes from. It's one calculation: how fast the standard deviation of a randomly chosen portfolio falls as you add names. Meir Statman's 1987 paper in the Journal of Financial and Quantitative Analysis put it at 30 stocks for a borrowing investor and 40 for a lending one. He was arguing upwards, against a then-common belief that about 10 was plenty.
Now a second number, from a different question. Across the CRSP database from 1926 to 2016, 1,092 companies accounted for all of the net wealth the US stock market created. That's 4.31% of the 25,332 firms in the sample. The other 96% collectively matched one-month Treasury bills and no more.
The first number tells you how much your portfolio wobbles. The second tells you whether you owned the companies that made the money. So which of those were you trying to solve when you counted your holdings?
Where the 20-to-30 answer to how many stocks is diversified came from
Statman's method was variance reduction. Take a randomly selected portfolio, add stocks one at a time, and watch the standard deviation fall towards the market's. The drop is steep early and flattens fast. Past some point the extra risk reduction isn't worth the cost of another holding. That point is where the classic answer sits.
Statman himself moved it later. In a 2004 Financial Analysts Journal paper he wrote that the optimal level of diversification under mean-variance rules exceeded 300 stocks, while the average investor held three or four. He called the gap a puzzle and answered it with behavioural portfolio theory: people build portfolios in layers, with a protective base and a lottery-ticket top. If your own holdings look like that, you're the average investor he was describing.
So the variance answer was never fixed. It moves with the correlation structure of the market. Campbell, Lettau, Malkiel and Xu documented that in 2001, showing that firm-level volatility rose relative to market volatility between 1962 and 1997. The number of stocks you'd need for a given risk level rose with it.
Their 2022 follow-up gets quoted far less. Idiosyncratic volatility spiked around 1999 and 2000, then declined. The share of firm-level variance in equal-weighted data fell from roughly 95% at the end of the original sample to around 80% in recent data. The authors say plainly that they never expected the upward trend to continue. They also wrote the update partly to answer two replication studies, by Chiah, Gharghori and Zhong and by Leippold and Svaton, whose samples stop in 2017 and 2016 respectively.
The honest summary is awkward. The variance-based answer sits somewhere between 20 and 300, it depends on the decade, and its own authors have revised it. All of which is before you ask whether variance is the thing you wanted measured.
What the skewness evidence measures instead
Hendrik Bessembinder's 2018 paper asked a blunter question. Take every common stock in CRSP since 1926, hold it from first appearance to delisting, and compare the result with rolling one-month Treasury bills over the matched window. Only 42.6% of stocks beat the bills. The single most frequent lifetime outcome, with returns rounded to the nearest 5%, is a loss of 100%.
Individual stocks also don't last long. The median time a stock spent in the CRSP database across those 90 years was seven and a half years. Just 36 stocks were present for the full period.
Put those two facts side by side and you get the shape of the problem. Pick a name at random and the likeliest lifetime outcome is a total loss, over a holding period that's finished inside a decade. That's the draw you're making each time you add one.
The wealth-creation side is more lopsided still. Net wealth creation across the sample came to $34.82 trillion. The top 90 firms, 0.36% of the total, produced half of it. The top 295 produced three quarters. Exxon Mobil alone accounted for 2.88%, and the top five firms for 10.07%.
None of this contradicts the variance work. It measures something the variance work never priced: the chance that your small portfolio simply misses the companies that mattered. That's a different failure mode from a bumpy ride, and it doesn't show up in a standard deviation. The distinction is close to the one between volatility as a statistic and the drawdowns investors actually feel, except here the mismeasured thing is upside rather than downside.
A five-stock example you can follow in your head
Heaton, Polson and Witte built the cleanest illustration in their 2017 paper "Why Indexing Works". Imagine an index of five securities. Four of them return 10% over the year and one returns 50%. The equally weighted index returns 18%.
Say you have £100 to put in, and no way of telling the five apart. Buy the whole index and you get the 18%, every time, guaranteed by the arithmetic. Buy one or two of the five instead — as a stock-picker would — and there are 15 possible portfolios you could end up holding. Ten of them contain only the 10% names. Five contain the winner.
The average across all 15 is 18%, identical to the index, exactly as the arithmetic requires. The median is 10%. So two thirds of the time your £100 does the 10%, and the index result you gave up was never a matter of skill.
Nothing in that example involves volatility, correlation or risk tolerance. It's pure distribution shape. The mean and the median of a skewed distribution sit in different places, and a small portfolio lands near the median.
Variance converges long before outcomes do, so the number of stocks in a portfolio answers only half of it
So how many names does it take to close that gap? Bessembinder separated the two effects with bootstrap simulations, drawing random value-weighted portfolios 20,000 times and linking monthly returns over one-year, decade and 90-year horizons.
Two things fall out, and they move at very different speeds. Skewness, the lopsidedness that variance work never priced, collapses almost at once. The share of portfolios that actually beat the market barely shifts.
| Holdings | Skewness of annual returns | Share beating the market |
|---|---|---|
| Single stock | 6.99 | not reported |
| Five stocks | 1.08 | 22.68% |
| 25 stocks | 0.10 | 36.81% |
| 50 stocks | -0.09 | 40.94% |
| 100 stocks | -0.21 | 43.29% |
By any variance-based test, a 50-stock portfolio is fully diversified. No fees or trading costs are deducted from any of the win rates in the last column.
Read that last column again, slowly. Going from 25 holdings to 100 buys you about six and a half percentage points, and still leaves you likelier to lose to the index than to beat it. The variance gap had closed by 50 names. The outcome gap was still open at 100.
Against Treasury bills the picture is friendlier, which matters if your benchmark is cash rather than an index. At the decade horizon, the share of bootstrapped portfolios beating bills rose from 47.77% for a single stock to 72.29% at five, 86.86% at 25 and 93.08% at 100. Diversification does reliable work against cash. It does much slower work against the market.
The same pattern outside the US
Bessembinder, Chen, Choi and Wei extended the study to more than 64,000 global stocks over 1990 to 2020. In compound terms, 55.2% of US stocks and 57.4% of non-US stocks underperformed one-month US Treasury bills. The top-performing 2.4% of firms accounted for all $75.7 trillion of net global wealth creation. Outside the US, 1.41% of firms accounted for $30.7 trillion.
The UK figure is worth pulling out if that's where your picks live. Of the 4,192 UK stocks in that sample, 26.2% beat the value-weighted market over their lifetimes. Germany came in at 25.5%, Hong Kong at 21.1% and Japan at 17.7%. In 41 of the 43 markets studied, fewer than half of listed stocks beat their own market index.
The portfolio-size result repeats abroad as well. Among non-US stocks over the full 31 years, the share of bootstrapped portfolios beating US Treasury bills ran 26.8% at one stock, 53.3% at five, 75.9% at 25, 83.2% at 50 and 89.0% at 100. Against the value-weighted market, 100-stock portfolios won 39.6% of the time in US stocks and 45.4% in non-US stocks. Since a UK or European sleeve is often where a portfolio's concentration quietly hides, this bears on how much of an equity allocation ends up outside the home market.
Three caveats belong next to those numbers. The aggregate isn't a universal law: in twelve of the markets more than half of individual stocks did beat US Treasury bills, and more than 60% did in Saudi Arabia, Israel, Switzerland and Finland. Where accurate delisting returns were unavailable for non-US firms, the authors imputed a return of -30%, which is an assumption rather than a measurement. And Bessembinder discloses financial support from Baillie Gifford, a manager whose investment case rests on concentrated exposure to extreme winners.
The case against: doesn't an index fund settle how many stocks is diversified?
That's the strongest objection, and it lands. A cap-weighted total-market fund owns the 4% by construction, so the skewness evidence is an argument for indexing rather than a live puzzle about how many names you hold. Heaton, Polson and Witte put it in their title. Bessembinder's own abstract argues that his results help explain why poorly diversified active strategies most often underperform market averages. On the mechanism, the critics are right.
The objection is weaker on what it implies about the number. If the answer is to own the index, then the answer to "how many stocks?" isn't 30. It's roughly all of them, weighted the way the market weights them. Indexing doesn't dissolve the question. It answers it with a figure two orders of magnitude larger than the textbook one, while the textbook number keeps circulating as guidance for people who pick stocks.
And people do pick stocks. Goetzmann and Kumar examined more than 40,000 accounts at a large US discount brokerage over 1991 to 1996. More than 25% held a single stock. More than half held fewer than three. Statman's 2004 figure of three or four names for the average investor points the same way. That brokerage sample is old and self-selected, and the authors acknowledge they have probably picked up speculators, but no plausible correction turns three stocks into thirty.
There's also a middle case the objection skips past, and it's probably where you are. Plenty of portfolios sit between one stock and the whole market: a concentrated active fund, a thematic tracker, or several broad funds that quietly hold the same giants. Our look at five popular funds sharing 39% of assets across ten companies is one version of that problem, and two decades of SPIVA data on active fund underperformance is the aggregate scoreboard the skewness argument predicts.
What would change the conclusion
Several things, and the first is already published.
Oh and Wachter's 2018 NBER working paper is the sharpest response to Bessembinder. They argue that the headline result, most stocks losing to Treasury bills, is exactly what a standard lognormal return model predicts, and so poses no challenge to that model. They find 48% of monthly stock returns exceed the bill return in the data, and 48% in their simulated economy too. Their criticism runs the other way: the lognormal model fails on the magnitude of monthly cross-sectional skewness, which far exceeds what the model implies, and it overstates skewness in long-run returns. This is a working paper rather than a peer-reviewed article, and it doesn't dispute the arithmetic. It disputes how surprising the arithmetic ought to be.
That distinction is worth sitting with. If the skew is mostly mechanical, what happens to your small portfolio is unchanged, because it still lands near the median. But the finding becomes evidence about compounding rather than evidence about markets.
Sample composition is the second lever. Bessembinder is explicit that the failure to beat Treasury bills is concentrated in stocks below median market capitalisation and in stocks that entered the database after the mid-1960s. If your universe is large, established companies, you're facing a milder version of this distribution.
Third is the counting method. Every firm counts once, whether it was a micro-cap that survived four years or a mega-cap that ran for nine decades. "Most stocks" and "most of the money" use different denominators, and a capitalisation-weighted count would flatter the result.
Fourth is the holding period. These are lifetime buy-and-hold returns to delisting, on a median life of seven and a half years. Real portfolios rebalance, sell and replace, and this evidence doesn't settle whether that helps or hurts. It also says nothing about the exits open to someone already holding a concentrated stock position, which is a separate question with its own arithmetic.
Fifth is the trend itself. If firm-level volatility keeps falling relative to market volatility, as the 2022 Campbell, Lettau, Malkiel and Xu update indicates it has since 2000, then the variance answer and the skewness answer both shrink together.
What the two answers to how many stocks is diversified actually say
Variance-based diversification is close to finished somewhere between 25 and 50 stocks. That part of the textbook survives. What it never covered is the chance of missing the winners, and that stays material at 100 holdings: 43.29% of 100-stock portfolios beat the cap-weighted market over 90 years, and 39.6% did over the 31-year global sample.
So the two figures answer different questions, and the older one got treated as though it answered both. Go back to the two people who each picked thirty names. If what they wanted was a smoother ride, thirty does most of the work for both of them. If what they wanted was to reliably own a distribution in which about 4% of companies produced all the gains, no realistic number of hand-picked holdings gets either of them there. Which of the two did you think you were buying?