How Many Stocks to Diversify? Test of 1,023 Portfolios

Volatility is the typical size of a portfolio's daily swings, scaled to a year (annualised). Across the ten single stocks in our price data, portfolios of one stock had a mean (average) volatility of 44.3% a year. The portfolio of all ten had 30.6%. Five stocks reached 32.5%, which is 86% of the way from the first figure to the second.

This guide tests every possible equal-weight portfolio of one to ten of those stocks, 1,023 in all, from 30 September 2020 to 26 October 2026. It shows how fast the swings shrink as stocks are added. It also shows how little the later stocks add.

Volatility measures how much a result swings. We calculate it as the standard deviation of daily returns, multiplied by the square root of 252, the number of trading days in a year. A return is the percentage change in price over one day, with dividends counted. Our guides to volatility and standard deviation cover the measure.

The ten stocks are Advanced Micro Devices (AMD), Amazon, Alphabet, Intel, Meta Platforms, Microsoft, Netflix, Nvidia, Palantir and Taiwan Semiconductor Manufacturing (TSMC). They are the only single stocks in our price files. All ten are large technology-related companies. All were still trading on 26 October 2026.

A different set of stocks would give different numbers.

The window starts on 30 September 2020, the first price in Palantir's file. It ends on 26 October 2026. It holds 1,525 daily prices and 1,524 daily returns, over 6.1 years.

We built every possible equal-weight portfolio of one to ten stocks. Equal-weight means each stock gets the same share, reset to equal every day. Our guide to equal weight against market-cap weight covers the idea.

There are 10 portfolios of one stock, 45 of two, 120 of three and 252 of five, with the other sizes in the table. That makes 1,023 in all. We drew none at random, because we counted them all.

For each portfolio we measured volatility and the worst fall. The worst fall is the largest drop from a closing high to a later closing low, which we searched over every close in the window. Our guide to the drawdown defines it. We took the mean across all portfolios of that size for every result.

Chart 1 plots the mean volatility for each portfolio size. The band shows the lowest and highest portfolio of that size.

A single stock had volatility from 27.2% (Microsoft) to 69.7% (Palantir), with a mean of 44.3%. Two stocks cut the mean to 37.6%. Five stocks gave 32.5%, while ten gave 30.6%.

We measured each size as a share of the whole fall, from 44.3% with one stock to 30.6% with ten. Two stocks achieved 49% of it, three achieved 68%, five achieved 86% and six achieved 90%. The table gives every size.

Annualised volatility of equal-weight portfolios of the ten stocks, from 1,524 daily returns, 1 October 2020 to 26 October 2026, with dividends counted. We reset equal weights every day. Share of the fall: the fall in mean volatility from one stock to this size, as a share of the fall from one stock to ten. Source: YX Insights price data

Chart 2 shows how much each extra stock cut mean volatility. The second stock cut the mean by 6.7 points. The third cut it by 2.7 points, the fifth by 0.9 points and the tenth by 0.2 points.

Which stocks the portfolio held also mattered. The 252 five-stock portfolios ranged from 25.8% to 39.3%. Of those, 62 had lower volatility than the ten-stock portfolio's 30.6%. Microsoft alone, at 27.2%, also had less.

Part of each stock's movement belongs to that company. Part is shared with the other nine. Holding more stocks averages away the first part, but the shared part stays.

Correlation shows how large the shared part is. It is a number from -1 to +1 that shows how closely two returns move together. The mean correlation across the 45 pairs of the ten stocks was 0.43.

For these ten, the shared part alone implies a floor of 28.3% a year, the level mean volatility approaches as more stocks of the same kind are added. We calculated it from the average of the 45 pair covariances, scaled to a year. The ten-stock portfolio's 30.6% sits 2.2 points above it.

An S&P 500 exchange-traded fund (ETF) had 16.6% over the same days. An ETF is a fund that trades like a share. This one holds the 500 companies in the S&P 500. The ten-stock portfolio had 1.8 times that volatility.

Chart 3 shows the mean worst fall for each portfolio size, with the S&P 500 fund beside it.

The mean worst fall was 63.4% for one stock, 54.6% for five and 53.0% for ten. Going from one stock to ten removed 10.4 points. The S&P 500 fund's worst fall was 24.5%.

The ten-stock portfolio's worst fall ran from 19 November 2021 to 3 November 2022. The S&P 500 fund's ran from 3 January 2022 to 12 October 2022. Palantir's was the deepest of the ten stocks, at 84.6% from 27 January 2021 to 27 December 2022. Microsoft's was the shallowest, at 37.1%.

We reran the test 14 ways. Four reruns changed the data. One used weekly returns, Friday close to Friday close, giving 316 weekly returns.

One dropped Palantir, which left nine stocks and a window from 21 May 2012, with 3,629 daily returns. Two split the main window into halves of 762 daily returns each.

The other ten reruns left out each stock in turn, giving ten sets of nine stocks over the main window. Each rerun measures the share against its own one-stock and full-set volatility.

The number of stocks needed to reach 50% of the fall in mean volatility was three in 13 reruns and two in one. For 75% it was four in all 14. For 90% it was six in 13 reruns and seven in one. Five stocks achieved between 85% and 88% of the fall in mean volatility in every rerun.

The test measures swings and falls, not returns. It covers ten stocks over 6.1 years, so it says nothing about portfolios of 20 or 30 stocks. Our files hold only ten single stocks.

The ten are large, technology-related and still trading, which is a narrow sample that excludes stocks that stopped trading. We reset equal weights every day. The figures ignore costs and tax. The test makes no forecast.

In this test, five of the ten stocks achieved 86% of the fall in mean volatility. Six achieved 90%. The ten still moved together enough to leave volatility at 30.6%, against 16.6% for an S&P 500 fund.

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No single number applies, because it depends on how closely the stocks move together. In our test of ten large technology-related stocks, five stocks achieved 86% of the fall in mean volatility that ten achieved. The test covers one set of ten stocks over 6.1 years and makes no forecast.

Our test cannot say, because our files hold only ten single stocks, so it stops at ten. In those ten, the ninth stock cut mean volatility by 0.3 points and the tenth by 0.2 points. We did not test portfolios beyond ten stocks.

No. On average, each extra stock lowered mean volatility in our test, but Microsoft alone (27.2%) had less volatility than all ten (30.6%). The tenth stock cut the mean by 0.2 points. The ten-stock portfolio had 1.8 times the volatility of an S&P 500 fund.

Yes. In our test, the ten-stock equal-weight portfolio fell 53.0% from 19 November 2021 to 3 November 2022. The S&P 500 fund fell 24.5% from 3 January 2022 to 12 October 2022. A worst fall is the largest drop from a closing high to a later closing low.

DISCLAIMER: This article is intended for educational purposes only. Any information or analysis in this note does not constitute an offer to sell or a solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice, nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.