Those who live very long lives sometimes face an unfair irony: The accomplishments of even towering figures can lose their luster over time—not because they’re proven wrong but because the ideas they developed become so widely accepted that we forget they were once new. The investment world lost one such towering figure last week: the economist Harry Markowitz, who was 95.

Markowitz first came to prominence in the early 1950s, when his PhD thesis, titled “Portfolio Selection,” offered an entirely new approach to investing. Prior to Markowitz, what constituted investment theory would have fit on an index card. For years, in fact, the only framework available to investors was the “prudent man” rule, which had its roots in an 1830 court ruling. At issue in that case was the management of a trust which had been established for the benefit of Harvard College and Massachusetts General Hospital. Over time, the two institutions became unhappy with the trust’s performance and sued the trustee, arguing that he had been negligent.

The trustee prevailed, however. “All that can be required of a trustee,” the court wrote, “is to observe how men of prudence, discretion and intelligence manage their own affairs…” In other words, investment markets inherently carry risk. All an investor can do, therefore, is to exercise judgment in choosing investments.

This became known as the prudent man rule. And despite being highly subjective, it was the lens through which investments were evaluated for more than 100 years, until the economist John Burr Williams suggested a better way. In his 1937 book, The Theory of Investment Value, Williams developed the concept now known as intrinsic value. Williams introduced the idea with this poem:

A cow for her milk,
A hen for her eggs,
And a stock, by heck,
For her dividends

An orchard for fruit
Bees for their honey,
And stocks, besides,
For their dividends.

In other words, “a stock is worth only what you can get out of it.” And for that reason, stock prices should reflect the profits of their underlying companies. While this might seem like an obvious concept today, Williams was the first to see it. This new quantitative approach to choosing investments offered a big step forward from the prudent man rule, which wasn’t quantitative at all.

Williams’s work in the 1930s led directly to Markowitz’s in the 1950s. As Markowitz described it, when he later received the Nobel Prize in economics, “The basic concepts of portfolio theory came to me one afternoon in the library while reading John Burr Williams’s Theory of Investment Value.”

Markowitz agreed with Williams’s approach to valuing individual investments. It was far better than the old prudent man approach. But Markowitz still saw it as incomplete. The shortcoming: While it’s important to evaluate individual investments, it’s equally important—if not more so—to consider how a collection of investments will work together in a portfolio. Markowitz was the first, in other words, to show investors how to effectively diversify a portfolio.

In his 1959 book, Portfolio Selection, adapted from his thesis, Markowitz provided this example: “A portfolio with sixty different railway securities, for example, would not be as well diversified as the same size portfolio with some railroad, some public utility, mining, various sort of manufacturing, etc. The reason is that it is generally more likely for firms within the same industry to do poorly at the same time than for firms in dissimilar industries.”

As noted above, today this might seem obvious, but before Markowitz, it had never occurred to anyone. And it wasn’t just a casual observation. Portfolio Selection runs more than 300 pages, dense with formulas. In it, Markowitz provided a framework for building optimal portfolios—those that offered either the maximum possible return for a given level of risk, or the least possible risk for a given level of return. Markowitz called these portfolios “efficient,” and presented them visually in a diagram he called the efficient frontier.

In the decades since Markowitz developed the efficient frontier, no one has challenged his math, the concept still stands, and it’s a mainstay of Finance 101 courses everywhere. His theories have received some criticism, though: In particular, many argue that the statistic Markowitz chose to measure risk—the standard deviation of an investment—isn’t valid.

Standard deviation, also known as volatility, is the degree to which a stock’s price tends to move in a relatively straight line or to bounce around. Consider, for example, the stock of a company like Procter & Gamble. P&G’s business is relatively stable, and thus its stock price is quite steady compared to the overall market. Now let’s compare that to Amazon’s stock. Reflecting the business it’s in, and its growth rate, Amazon’s stock price acts more like a roller coaster. From a mathematical perspective, Amazon’s stock has been far more volatile. But which would you have wanted to own?

Over the past 10 years, P&G’s stock has gained 154%—not bad. But Amazon’s shares have gained nearly 830%, reflecting its enormous profit growth. Through the lens of modern portfolio theory, however, we would deem Amazon’s stock very risky simply because it’s moved so much. Many see this conclusion as nonsensical. While Amazon may be an extreme example, it illustrates why volatility is a controversial idea.

While I agree that it’s difficult to distill risk down to a single number, this criticism is also a little unfair. That’s because, in his 1959 book, Markowitz explained why he chose volatility as a risk yardstick: “…for conservative investors, a loss of 2L dollars is more than twice as bad as a loss of L dollars…” Investors, in other words, are human. We really dislike losses. The uncertainty of a volatile stock can be upsetting, and the reality is that stocks like Amazon don’t only go up.

We saw this just last year. In 2022, when the S&P 500 dropped 19%, Amazon shares lost more than 50%. Meanwhile, P&G shares dropped less than 5%. It’s not hard to see, then, why Markowitz saw volatility as being a reasonable proxy for risk. He was acknowledging that investors have emotions. In his book about risk, Against the Gods, Peter Bernstein notes that more volatile stocks have been more prone to permanent loss, so there is both an emotional and a quantitative justification for that metric.

Over the years, others have tried to develop alternative risk measures, but as I discussed earlier this year, there is no single perfect measure. Each provides a different perspective. From the investor’s point of view, I find it helpful to consider different risk measures as a mosaic, helping to form a more complete picture. It’s to Markowitz’s credit that he was the first to use any quantitative measure at all in attempting to assess risk. While volatility isn’t perfect, it’s certainly more rigorous than the old prudent man standard.

Putting aside this question, Markowitz’s lasting contribution is that he taught investors how to think about diversification, and few people debate that.