Among the quotes attributed to Mark Twain is this one: “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

This highlights one of the challenges of personal finance: that the data and the conclusions we rely on for decision-making can never be accepted with absolute certainty. That’s for a few reasons. First, because the world changes and markets change, our approach must change as well. And second, academic research is necessarily imperfect. Because personal finance includes an element of human behavior, it can never be studied with scientific precision. Below are four areas where our understanding has evolved over time—and may yet evolve further.

Market drivers. In the 1950s, a PhD student named Harry Markowitz developed a mathematical approach to building portfolios that’s now known as Modern Portfolio Theory. With detailed formulas, Markowitz showed investors how to build “efficient” portfolios—those which optimized the tradeoff between risk and return. For years, this approach was seen as the gold standard, and others built on it.

William Sharpe, a professor at Stanford University, developed a tool—now known as the Sharpe Ratio—to help investors compare the performance of different assets on a risk-adjusted basis. And Eugene Fama, a professor at the University of Chicago, proposed the idea that markets are “efficient,” meaning that stock prices adjust almost immediately to new information, thus making it virtually impossible to beat the market.

For their work, all three won Nobel Prizes in economics. More recently, however, a new school of thought has arisen. Behavioral finance, pioneered by Daniel Kahneman and Amos Tversky, challenged the old, strictly numerical approach. They were the first to argue that human emotion also plays a part in financial decisions. Most notable among their contributions was prospect theory. Kahneman and Tversky found that when people experience a loss, it feels about twice as bad as an equivalent gain. This idea—that people are averse to losses—now seems intuitive, but it wasn’t previously understood. In the old world of Modern Portfolio Theory, investors were instead seen as being emotionless.

Since Kahneman and Tversky’s work, researchers have uncovered dozens more biases that affect financial decision-making. Because of that, the pendulum has swung in most investors’ understanding of what really drives markets. The implication for individual investors: Many people now view behavioral factors as being at least as important in explaining market movements as traditional quantitative factors.

In making financial decisions, then, we should acknowledge that the market is only sometimes rational. That’s why it’s so important to develop an investment strategy that’s durable enough to carry you through those periods when irrationality takes over.

Diversification. In 1970, Lawrence Fisher and James Lorie published a paper titled “Some Studies of Variability of Returns on Investments in Common Stocks.” They wanted to better understand the dynamics of portfolio diversification. Their conclusion: “95% of the benefit of diversification is captured with a 30 stock portfolio.” As a result, for decades, a portfolio composed of 30 stocks was viewed as a magic formula. To be on the safe side, many investment firms included 40 or 50, but anything in that neighborhood was viewed as sufficient to diversify away the risk posed by any one stock.

That thinking has changed. In 2017, Hendrik Bessembinder, a professor at Arizona State University, published a paper titled “Do Stocks Outperform Treasury Bills?” His surprising conclusion: Between 1926 and 2016, just 4% of stocks accounted for all of the net gains in the U.S. market above the return of Treasury bills. In other words, the other 96% of stocks, as a group, did no better than Treasurys, which delivered about 2% per year. Bessembinder has since found that the same conclusion holds outside the U.S.

This completely upended investors’ thinking about diversification. Where earlier research focused on the downside risk posed by the underperformance, or even failure, of an individual stock, Bessembinder focused on an entirely different risk: the upside risk when a portfolio fails to hold one of the market’s star performers.

This is yet another reason why, in my view, index funds make so much sense. S&P 500 and total-stock-market funds hold the handful of stocks in the 4% that’ve led the market over the past decade. Just as importantly, they probably hold the 4% that will lead the market over the next decade.

Risk. When Markowitz developed the concept of an efficient portfolio, he chose portfolio volatility as his preferred measure of risk. Volatility is a statistic that measures the degree to which an investment’s price bounces around over time. Markowitz deemed portfolios with more variable prices as being more risky.

Using this yardstick, Markowitz then argued that there’s an ironclad relationship between risk and return. If an investor wants higher returns, he or she needs to accept more risk. Or if an investor wants less risk, that can only be achieved by settling for lower returns. This fundamental tradeoff was an accepted truth for many years. But today, many see it differently, including hedge fund manager Seth Klarman. He’s argued that the use of volatility to measure risk is “preposterous” and that investors don’t need to take on more risk to earn greater returns.

Klarman’s firm, Baupost Group, specializes in securities that are distressed and selling at steep discounts. In interviews, he’s argued that this approach actually reduces risk while increasing potential returns:

“You’re buying things that are cheaper, which means that you have less downside, and more upside…If [a stock trading at $6] suddenly falls to $3, does that make it more risky because it’s more volatile, or does that make it a ludicrously good bargain because it’s now trading for half the price, and you could only lose half as much and you could make way proportionally more if things work out?”

What does this mean for individual investors? The stocks that Klarman is referring to are called value stocks. And though they have underperformed in recent years, they’ve outperformed over longer periods. Klarman’s argument, in my view, provides a logical explanation for that outperformance. For that reason, a value-oriented fund may deserve a place in your portfolio, especially today, when the broader market is heavily tilted toward growth stocks.

Beating the market. For years, textbook finance aligned with Fama’s assertion that it was impossible to beat the market. Because prices adjusted so quickly to new information, there was no way to buy or sell quickly enough to get in front of those price movements. But in recent years, evidence has mounted on the other side of this argument.

Though it’s exceedingly difficult, a number of investors have proven it is possible to beat the market, because prices don’t adjust as quickly as Fama argued. Numerous funds have demonstrated this: For years, Renaissance Technologies beat the market with computer-driven trading. Gotham Capital delivered outsized returns with old-fashioned, value-driven stock-picking. The Magellan Fund under Peter Lynch did it by identifying growth stocks. And most recently, Pershing Square Capital Management did it through shrewd market timing when COVID knocked down markets in 2020. To be sure, it’s not easy to beat the market, but these funds do nonetheless disprove the theory of market efficiency.

Especially since these market-beating funds aren’t broadly available to the public, what’s the lesson here for individual investors? In my view, there’s a broader point: Because they disprove established research, they’re a reminder that we should be wary of any conclusion that seems too declarative. To be sure, academic research is useful as a guide. But it should never be seen as carved in stone.