Contents
Under mean-variance portfolio theory, the optimal level of diversification today exceeds 300 stocks. The average investor holds three or four. That distance is one of the best documented anomalies in finance, and its cost has been measured: households with below-median financial literacy who rely on their own judgement lose an expected 50 basis points a year on average. But there is an uncomfortable result worth knowing before closing the case: in one sample of brokerage accounts, households with concentrated portfolios outperformed diversified ones. This article goes through what has been measured.
Summary: the seven findings that matter
Each row names the study and the year. It is worth separating the average cost from the tail cost: almost all the damage sits with a few.
| Finding | Result | Study and year |
|---|---|---|
| Optimal level against actual level | More than 300 stocks against 3 or 4 | Statman, Financial Analysts Journal (2004) |
| Extent of under-diversification | The vast majority of the accounts analysed | Goetzmann and Kumar, Review of Finance (2008) |
| Who diversifies least | Young, active, low income and non-professional | Goetzmann and Kumar (2008) |
| Expected loss of the worst-placed group | 50 basis points a year on average | Von Gaudecker, Journal of Finance (2015) |
| Where that loss concentrates | In the upper tail of the loss distribution | Von Gaudecker (2015) |
| The result that complicates the diagnosis | The concentrated outperformed the diversified | Ivkovich et al., J. Financial Quant. Analysis (2008) |
| What non-diversifiers are after | Positive skewness: the chance of a big win | Mitton and Vorkink, Rev. Financial Studies (2007) |
What you will find here
• The exact distance between the optimal and the actual, and why an index fund closes it.
- Who holds the least diversified portfolios, from data on tens of thousands of accounts.
• How much it costs in returns, and why the average hides what matters.
• The study in which concentrating the portfolio paid off.
• The explanation that turns the mistake into a deliberate choice.
Three hundred stocks against three
Meir Statman framed the problem in Financial Analysts Journal with the precision of someone who does the arithmetic. The current optimal level of diversification, measured by the rules of mean-variance portfolio theory, exceeds 300 stocks, while the average investor holds only three or four.
And he adds the calculation that makes the comparison even less favourable: he estimated the benefit of increasing diversification to the 3,444 stocks of a total market index fund with an annual cost of 0.20 %, and concluded that the total market fund offers a better way to diversify than a portfolio of 300 stocks or fewer.
The author also lists what aggravates the problem beyond the number of holdings: large positions in own-company stock inside employee plans, portfolio concentration in particular styles, and geographical bias.
Why he views it as a puzzle instead of a mistake
Statman’s contribution is not pointing out the distance but explaining it without resorting to incompetence. In behavioural portfolio theory, investors build their portfolios as layered pyramids: the lower layers are designed for downside protection and the upper ones for upside potential. Risk aversion gives way to risk seeking in the top layer, as the desire to avoid poverty gives way to the desire for riches.
And the key: what motivates that behaviour is investors’ aspirations, not their attitudes towards risk. Some fill the top layer with the few stocks of an undiversified portfolio; others with lottery tickets.
| Study | What it analysed | What it found | What it does not support |
|---|---|---|---|
| Statman (2004) | Optimal against observed level of diversification | More than 300 optimal stocks against 3 or 4 actual | It is a theoretical calculation plus a behavioural frame |
| Goetzmann and Kumar (2008) | More than 40,000 brokerage accounts, 1991-1996 | Widespread under-diversification and a clear profile | One discount broker in a bull period |
| Von Gaudecker (2015) | Households by financial literacy and advice | 50 basis points of expected loss in one group | Household survey data from one country |
| Ivkovich et al. (2008) | Households with concentrated against diversified accounts | The concentrated outperformed | Does not imply concentrating is a good idea in general |
| Mitton and Vorkink (2007) | 60,000 accounts and the preference for skewness | The inefficiency is explained by seeking skewness | Explains the choice; does not say it is right |
Who diversifies least
William Goetzmann and Alok Kumar examined in Review of Finance the portfolios of more than 40,000 equity investment accounts at a large discount brokerage over six years, from 1991 to 1996.
Their general result: the vast majority of investors in the sample are under-diversified. And the cross-sectional examination gives the profile: young and active investors, and those in low-income and non-professional categories, hold the least diversified portfolios.
In an analysis extended to more than 60,000 accounts, the same authors specify what else accompanies under-diversification: less sophisticated investors, those who follow price trends, those who prefer local or familiar stocks, and those who display overconfidence hold relatively less diversified portfolios. The under-diversified also show strong style and sector preferences, and prefer more volatile, positively skewed stocks.
And they rule out the handiest practical explanations: factors such as small portfolio size, transaction costs and search costs are not likely determinants of diversification decisions. They state the consequence without hedging: the unexpectedly high idiosyncratic risk of investors’ portfolios produces a welfare loss.
How much it costs, and to whom
Hans-Martin von Gaudecker published in Journal of Finance the estimate most useful for a practical conversation, because it crosses diversification with two variables an investor can change: financial literacy and advice.
His primary finding brings comfort to the majority: virtually every household that demonstrates strong financial literacy, or seeks guidance from professional experts or personal acquaintances, secures satisfactory investment returns.
And the cost for the remaining group: compared with those groups, households with below-median financial literacy who trust their own decision-making capabilities lose an expected 50 basis points on average.
| Household profile | Investment outcome | Implication |
|---|---|---|
| High financial literacy | Reasonable | Literacy works as protection |
| Relies on professional advice | Reasonable | Delegating also solves the problem |
| Relies on private contacts | Reasonable | Simply not deciding alone is enough |
| Low literacy and self-reliant | −50 basis points on average | This is the combination that costs money |
| Where the difference sits | In the upper tail of losses | A few households lose a lot, not everyone a little |
That last row changes the reading most. All differences between groups stem from the upper tail of the loss distribution. It is not that the poorly informed investor systematically loses half a point: it is that a minority loses a great deal and drags the group average down.
The study in which concentrating paid off
Zoran Ivkovich, Clemens Sialm and Scott Weisbenner asked a different question in Journal of Financial and Quantitative Analysis: whether information advantages help explain why some individual investors concentrate their portfolios in a few stocks.
Their findings run counter to a straightforward interpretation: equities purchased by retail investors whose brokerage assets are concentrated in a limited number of positions yield higher returns than those belonging to individuals holding more balanced portfolios, a trend particularly pronounced among high-net-worth accounts.
And the pattern of that advantage points to its cause: the excess return of concentrated over diversified portfolios is larger in stocks not in the S&P 500 index and in local stocks, which may reflect concentrated investors successfully exploiting information asymmetries. Moreover, controlling for each household’s average investment ability, their trades and holdings perform better when their portfolio includes fewer holdings.
It warrants careful reading: the research doesn’t claim that focusing represents a sound approach, but rather that individuals who focus occasionally seem to have justification for doing so. The exact same rationale surfaces in home bias: knowledgeable under-diversification exists alongside blind under-diversification, and overall statistics blend them both.
The explanation that turns it into a choice
Todd Mitton and Keith Vorkink developed in Review of Financial Studies a model in which investors have heterogeneous preferences for skewness, which allows some not to diversify in equilibrium. And they tested it against a dataset of 60,000 individual investor accounts.
They find support for three implications. First: the portfolio returns of under-diversified investors are substantially more positively skewed than those of diversified investors.
Second, and this is the decisive one: the apparent mean-variance inefficiency of under-diversified investors can largely be explained by the fact that they sacrifice mean-variance efficiency in exchange for greater exposure to skewness.
And third, which rules out coincidence: the stocks most frequently chosen by under-diversified investors have substantially higher average skewness — especially idiosyncratic skewness — than those chosen by diversified investors.
Put simply: someone holding three stocks is not necessarily ignoring diversification; frequently, they are intentionally chasing the potential of a massive payout, and footing the bill through efficiency. What the data fails to establish is whether this strategy actually pays off for them.
How to apply this practically
Ordered by the strength of the evidence behind each point:
- Employ a comprehensive index fund as the portfolio’s foundation. The benchmark computation determines that this offers superior diversification compared to a basket consisting of 300 assets or fewer.
• If you decide alone and your literacy is limited, get a second opinion. Turning to a professional or to contacts is enough for the outcome to become reasonable.
- Watch the tail, not the average. The differences between groups stem from the upper part of the loss distribution.
• Keep the bet out of the portfolio. If what you want is the chance of a big win, cap it and do not confuse it with your investment plan.
• Do not confuse informed concentration with blind concentration. The favourable result was measured in large portfolios and in local or off-index stocks.
Frequently asked questions
How many stocks do you need to be diversified?
More than almost anyone holds. According to the calculation published in Financial Analysts Journal, the optimal level of diversification measured by the rules of mean-variance theory today exceeds 300 stocks, while the average investor holds only three or four, and a total market index fund with 3,444 holdings and an annual cost of 0.20 % diversifies better than a portfolio of 300 stocks or fewer.
Who holds the worst diversified portfolios?
Across the two extensive datasets available, a consistent demographic pattern emerges. Looking at upwards of 40,000 discount brokerage portfolios managed between 1991 and 1996, minimal portfolio diversification was notably exhibited by young, highly active traders, alongside individuals belonging to non-professional and lower-income brackets, while expanding the scope to 60,000 accounts further incorporates trend-followers, proponents of domestic equities, and those exhibiting strong overconfidence.
How much does not diversifying cost?
It depends heavily on the profile, and the average is misleading. Almost all households with high financial literacy or who rely on professional advice or private contacts achieve reasonable outcomes; households with below-median literacy who trust their own capabilities lose an expected 50 basis points on average, and all differences between groups stem from the upper tail of the loss distribution.
Is it always a mistake to concentrate the portfolio?
Absent from every dataset. As reported by a study featured in the Journal of Financial and Quantitative Analysis, household investments that concentrate accounts within a handful of holdings surpass the performance of more diversified portfolios—particularly among larger portfolios—while yielding even greater excess returns on equities beyond the S&P 500 alongside local shares, signaling the strategic exploitation of information asymmetries.
Why do people not diversify if it is good for them?
Because many are acquiring an alternative. The framework evaluated across 60,000 accounts reveals that the portfolios belonging to the insufficiently diversified exhibit significantly more positive skewness, that their apparent mean-variance inefficiency is largely accounted for by trading off that efficiency in pursuit of skewness exposure, and that the equities they predominantly select possess much greater idiosyncratic skewness.
What we do not know
• What share of concentration is informed. There is evidence of an information advantage and of a welfare loss at once, with no quantified split.
- How much it costs in terms of risk taken. Loss figures are presented as expected returns, which fail to capture adequately the heightened likelihood of severe negative events.
• Whether financial literacy solves the aggregate. The analysis of a whole country suggests that raising it among the majority holding few stocks would cut the total loss only modestly.
- How it has changed with cheap index funds. Most account measurements predate the spread of low-cost indexing.
References
1. Statman, M. The Diversification Puzzle. Financial Analysts Journal, 2004. DOI: 10.2469/faj.v60.n4.2636
2. Goetzmann, W. N. and Kumar, A. Equity Portfolio Diversification. Review of Finance, 2008. DOI: 10.1093/rof/rfn005
3. Von Gaudecker, H.-M. How Does Household Portfolio Diversification Vary with Financial Literacy and Financial Advice?Journal of Finance, 2015. DOI: 10.1111/jofi.12231
4. Ivkovich, Z., Sialm, C. and Weisbenner, S. Portfolio Concentration and the Performance of Individual Investors. Journal of Financial and Quantitative Analysis, 2008. DOI: 10.1017/s0022109000004233
5. Mitton, T. and Vorkink, K. Equilibrium Underdiversification and the Preference for Skewness. Review of Financial Studies, 2007. DOI: 10.2139/ssrn.630821
This material serves purely informational purposes and should not be construed as financial advice or an investment recommendation. The referenced research evaluates distinct samples and timeframes that lack comparability, and none of these analyses makes it possible to determine the proper asset allocation for any specific portfolio.
