Investors often seek tools that can amplify their gains, hoping to turn a modest market rise into a significant profit. One such tool is the leveraged exchange-traded fund, a financial product designed to deliver a multiple of the daily return of an underlying asset, such as a stock index or a single company. If the market goes up by one percent, a fund with twice the leverage aims to go up by two percent. However, these funds operate on a strict daily reset: every night, the fund manager adjusts the portfolio to ensure the leverage ratio returns to its target for the next day. This mechanism creates a complex reality for anyone holding the fund for more than a single day. While the math works perfectly for a single day, the path the market takes over weeks or years matters immensely. A market that swings wildly up and down, even if it ends where it started, will erode the value of a leveraged fund due to the mathematics of compounding. This phenomenon, often called volatility drag, has long been known to reduce returns, but it tells only half the story of how these funds actually perform over time.

Two researchers at Harvard Business School, Chris Murray and Marco Sammon, have taken a fresh look at how we should measure the success of these products. They argue that the standard ways investors and analysts currently evaluate leveraged funds are deeply flawed and often lead to the wrong conclusions. In their analysis, they demonstrate that the most common metric used to judge performance—the arithmetic average return—can make a losing investment look like a winner. They show that this method can suggest that a fund is growing when it is actually shrinking, and it can even imply that using infinite leverage is the best strategy, a recommendation that would inevitably lead to total financial ruin. Instead, the researchers propose that the only true measure of success is how much an investor's actual money grows over time. They advocate for using a different mathematical approach, based on how wealth compounds, which accurately reflects the reality of holding these funds for the long term.

The core of the problem lies in how we calculate averages. Imagine a scenario where an asset starts at a price of one hundred dollars. In the first period, it rises by one percent to one hundred and one dollars. In the second period, it falls by just enough to return to exactly one hundred dollars. The asset has made zero percent progress overall. Now, consider a fund with twice the leverage. In the first period, it rises by two percent to one hundred and two dollars. In the second period, it must fall by a slightly larger percentage to return to the starting point, but because it is leveraged, the math works against it. The fund ends up with slightly less than one hundred dollars. The asset is unchanged, but the leveraged investor has lost money. Despite this loss, if you calculate the average of the daily returns for the leveraged fund, you get a positive number. If you then pretend the fund earned that positive average every single day, you would calculate a final value that is higher than the starting point. This creates a false picture where the math says the investor gained wealth, while the bank account shows a loss. This discrepancy is not a minor error; it is a fundamental flaw in using simple averages to predict long-term growth.

The researchers found that this misleading nature of averages is not just a theoretical curiosity but a practical danger. They examined how these funds behave over long periods, such as twenty years, using computer simulations based on historical market data. In one simulation involving a highly volatile stock, they looked at a hypothetical investment of ten thousand dollars in a fund with three times the leverage. The standard calculation, which relies on the average daily return, suggested that the investment would grow to an astronomical sum, far exceeding the total wealth of the entire planet. However, this result was driven by a tiny fraction of possible outcomes where the stock price skyrocketed in an almost impossible way. In reality, for the vast majority of paths the market could take, the investment would be wiped out, leaving the investor with almost nothing. The standard metric was being pulled up by these extreme, economically impossible scenarios, hiding the fact that the typical investor would lose everything. This suggests that relying on expected terminal wealth, a common measure in finance, gives a dangerously optimistic view of what an investor can expect to keep.

Another critical finding is that the frequency at which we measure returns changes the answer, even when the actual market path remains the same. If an analyst calculates the expected performance of a fund by looking at daily data, they might get one number. If they look at the same data but group it into weekly or monthly blocks, they might get a completely different number, sometimes even ranking the funds in the opposite order. This happens because the way returns are grouped changes how the math of compounding interacts with the market's ups and downs. The researchers argue that a good measure of performance should not change just because we decided to look at the data differently. They propose that using log returns, a method that focuses on the rate of growth rather than the simple average, solves this problem. This approach ensures that the ranking of funds depends on the actual wealth produced, not on how the data was sliced. It also correctly accounts for the fact that volatility hurts growth, preventing the dangerous conclusion that more leverage is always better.

The paper also highlights how real-world costs and the timing of investor money flow into and out of these funds can drastically alter the outcome. A fund might show a positive return over a year, but if most investors put their money in after the big gains had already happened, the average investor might still lose money. The researchers used data from leveraged funds tracking Korean stocks to show this clearly. They found that while the funds themselves had positive returns, the actual dollars gained or lost by the investors were negative because of when they entered and exited the market. This distinction is vital because it separates the performance of the product from the experience of the person buying it. Furthermore, they discussed the risks of funds that reset their leverage more frequently, such as hourly. While this might seem like a way to reduce the drag of daily swings, it introduces new risks related to trading costs and the ability of the fund to execute its trades without moving the market price against itself.

Perhaps the most striking example of the power of these funds comes from the performance of a single company, NVIDIA. In 2024, the stock of this company rose by 171 percent. A fund with twice the leverage returned 382 percent, which is more than double the stock's gain. This seems to defy the usual warnings about volatility drag. The researchers explain this by identifying a hidden force they call the convexity bonus. When an asset makes a very large move in one direction, the mathematics of the leveraged fund creates a bonus that adds to the return. This bonus can be so large that it overcomes the drag caused by volatility. In the case of NVIDIA, the bonus was so significant that the leveraged fund outperformed the simple multiple of the stock's return, even after accounting for fees and costs. This shows that while volatility usually hurts leveraged funds, a massive, sustained move in one direction can make them incredibly profitable, a nuance that simple averages often miss.

The researchers also point out the dangers of funds that can be closed out during the day. In one instance involving a company called Lucid, rumors caused the stock to drop more than 50 percent during the day. Although the stock recovered and closed down by a much smaller amount, the leveraged fund holding it was terminated by its trading partners before the recovery could happen. The fund was left with a negative value, and shareholders lost everything, even though the stock itself survived the day. This event underscores that the daily closing price is not always the whole story; the path the price takes during the day can trigger mechanisms that destroy the fund's value before the market has a chance to correct itself.

Ultimately, the work by Murray and Sammon serves as a guide for how to think clearly about these complex financial products. They argue that investors should stop looking at the average daily returns or the expected wealth across all possible futures, as these measures often tell a story that does not match reality. Instead, they should focus on how their actual capital compounds over time. By using the right mathematical tools, investors can see that volatility is a penalty that reduces growth, that infinite leverage is a path to ruin, and that the timing of their own money matters just as much as the market's performance. The goal is not to find a magic formula that guarantees wealth, but to understand the true mechanics of how these funds work, so that investors can make decisions based on what actually happens to their money, rather than on what a simplified average suggests might happen.