Harry Markowitz: why diversification is the only free lunch, and how many stocks you really hold
A 1952 paper turned 'do not put all your eggs in one basket' into mathematics. What Markowitz proved, what he left out, and how concentrated six famous portfolios really are.
Who he was
Harry Markowitz (1927–2023) published a paper called Portfolio Selection in 1952, when he was a young graduate student, and won the Nobel Prize in economics for it in 1990, together with William Sharpe and Merton Miller. The paper is about 15 pages long and is the starting point of what is called modern portfolio theory.
Before it, investors thought about shares one by one: is this one good? Markowitz changed the question to: what does this share do to the whole portfolio?
The core ideas
He proposed to describe every investment by two numbers, the expected return and the risk, measured as the variation of returns. The risk of a portfolio, he showed, is not the average of the risks of its parts. It depends on how the parts move together. Two risky assets that do not rise and fall at the same time give a portfolio that is less risky than either, without lowering the expected return. That is the sense in which diversification has been called the only free lunch in investing.
From this follows the efficient frontier: for each level of risk there is a mix of assets with the highest expected return, and a rational investor chooses a point on this line. Everything that is not on the frontier takes more risk for the same expected return, or gives less return for the same risk.
How it works in practice
Take two assets with the same risk. If they always move together, mixing them does nothing. If they move independently, a half-and-half mix has a much lower risk than either, about 30% lower in the case of fully independent assets. The more assets with low correlation you add, the smaller the share of risk that comes from any single one, but the gains shrink quickly: the biggest benefit comes from the first dozen or two, and adding the hundredth stock changes very little.
Markowitz is reported to have said that he did not use his own method for his own retirement savings and instead split the money half and half between stocks and bonds, to avoid regret. This is often told as a joke against the theory, but it also shows the point: the method needs inputs that nobody knows, and simple rules can be nearly as good.
What six current portfolios show
The best way to see diversification is the column 'effective positions'. It tells you how many equal positions would be as concentrated as the real portfolio. Bridgewater has 990 positions but behaves like 23.9, because the S&P 500 fund alone is 16.3%. Duquesne's 94 positions behave like 22.2. Klarman's 23 positions behave like 13.4, Buffett's 26 like 8.1, Ackman's 10 like 6.9 and Pabrai's 4 like 2.9.
In the language of Markowitz, the concentrated investors are making a bet that their selection skill is large enough to pay for the risk they do not diversify away. Bridgewater, with about 30% in index funds, behaves in the opposite way: the equity sleeve is built to be diversified. Remember that a 13F shows only US-listed stocks, so each of these investors may hold other assets that change the whole picture.
Six real portfolios side by side, from the latest filing of each investor (Form 13F, US-listed stocks only). Effective positions is the number of equal-sized positions that would be as concentrated as the real portfolio: one divided by the sum of the squared shares. Opened or closed is the average over the four quarters of half the combined share of positions that were opened or closed.
| Investor | Reported stocks | Positions | Effective positions | Largest position | Ten largest | Opened or closed per quarter |
|---|---|---|---|---|---|---|
| Warren Buffett | $299.3 billion | 26 | 8.1 | 22.0% | 91.0% | 1.0% |
| Ray Dalio | $24.4 billion | 990 | 23.9 | 16.3% | 42.1% | 5.8% |
| Bill Ackman | $13.7 billion | 10 | 6.9 | 17.6% | 100.0% | 7.0% |
| Stanley Druckenmiller | $5.2 billion | 94 | 22.2 | 16.6% | 46.3% | 23.8% |
| Seth Klarman | $5.4 billion | 23 | 13.4 | 16.5% | 74.9% | 9.5% |
| Mohnish Pabrai | $0.3 billion | 4 | 2.9 | 43.3% | 100.0% | 4.4% |
Where it is challenged
There are three well-known problems. The inputs, the expected returns and the correlations, have to be estimated, and small errors in them produce very different portfolios; an optimiser tends to put the most weight exactly where the estimate is most wrong. Correlations are not constant: in a crisis assets that were independent often fall together, so the protection is weakest when it is most needed, as in 2008, when many assets fell together, and in 2022, when stocks and bonds fell at the same time. And risk is defined as the variation of returns, which counts a surprise upward as risk, while most people fear only a loss.
A well-known study from 2009 compared fourteen optimised portfolios with the simple rule of putting the same amount in every asset and found that the simple rule was hard to beat out of sample.
What to take from it
Own assets that do not all fail for the same reason. Check how concentrated you really are, not how many tickers you have: a hundred stocks of one sector, or several funds that hold the same shares, are less diversified than they look. Do not trust a precise optimisation built on imprecise forecasts. And accept that diversification is a protection against surprise, not a way to make money in every year.
It also has a price: you will never own the single best asset, and the part of the portfolio that does best will always be diluted.
Where it meets our bots
Several of our bots are built on the logic of Markowitz. The equal-risk bot sizes each of five asset classes by how much it swings, the permanent portfolio splits money equally among stocks, long bonds, gold and cash, and the 60/40 bot is the classic two-asset case. The comparison with the S&P 500 bot, which holds a single basket of stocks, is a live test of what diversification across asset classes does, in good years and bad.
All accounts are virtual and every trade is public. The guides below explain each rule.
Related strategy guides
Risk parity: sizing positions by how much they swing
The permanent portfolio: stocks, bonds, gold and cash
The 60/40 portfolio: stocks and bonds
Models
Portfolios
Graham 50/50
Origin and history since 1926
Faber Ivy (static)
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Portfolio builder
Set the shares of stocks, bonds, gold or take famous models, mix them, and see how such a portfolio lived through every era of history.
Goal finder
Say what you need — for example, 6 % a year over 10 years with a drop no deeper than −25 % — and see which models and mixes met it, and in what share of historical periods.
Retirement: how much to withdraw
The 4 % rule tested on 60 portfolios: which share of the money you could take out every year, and when it failed.