Finance · Leverage & investor psychology
How a 2× fund loses 1.82% while the index breaks even
By Prof. Alessandro Buffoli, PhD
Two trading days are enough to show why “daily” deserves as much attention as “2×”.
An index rises from 100 to 110, then falls back to 100. A fund delivering exactly twice each daily return would finish at 98.18. It could meet its target on both days and still lose money over the period.
This is the calculation I want on a leveraged fund’s product page. It exposes a misunderstanding that a large “2×” and a small “daily” can leave intact.
Here is the arithmetic. The first day’s index gain is 10%, so the hypothetical fund gains 20%. Returning from 110 to 100 then requires a fall of about 9.09%. Double that daily loss and apply it to the fund’s new balance of 120. The result is 98.18. Assume exact daily tracking, with no fees or other costs.
| Point in time | Index | 2× daily fund |
|---|---|---|
| Start | 100.00 | 100.00 |
| After the rise | 110.00 | 120.00 |
| After the reversal | 100.00 | 98.18 |
The SEC’s explanation of leveraged ETFs makes the distinction clear: the target typically applies to each day. A longer holding period can produce a very different multiple.
Compounding can also help. With two consecutive 10% index gains, the index reaches 121 and our hypothetical fund reaches 144. That is a 44% gain against 21%. The path matters; the final index level alone cannot tell you what the fund should have returned.
Put the reversal beside the buy button
My concern is how easily a buyer could carry the multiplier into the wrong calculation: “I expect the index to gain 10% this month, so I expect about 20%.” Reading the word “daily” does not tell us whether the buyer has understood its effect.
A product page could show both of the paths above, then ask the reader to predict the fund’s ending value in a third example. Someone who expects the fund to break even whenever the index does has shown exactly what needs explaining. That is a more useful comprehension check than asking whether they have read the disclosure.
Costs and tracking differences still need explaining. But first, I want the buyer to understand how the product works even when it does exactly what it promises. Start with the two days. Let them calculate the loss.
Hypothetical calculations assume exact daily tracking and exclude costs. They illustrate product mechanics, not expected investment returns.
Prof. Alessandro Buffoli, PhD
Assistant Professor of Marketing at The Hang Seng University of Hong Kong.