Risk and Execution · Lesson 1 of 41234
The question
My stock ended the year about flat. Why did the 2x fund on it lose so much?
The idea
- You met the daily reset in Leveraged and inverse ETFs and the path effect in Leveraged decay in numbers. Over a whole year, what drives the path effect? Here "path" means the set of daily moves the stock made, not the order they came in. The answer: the size of the daily swings, measured as volatility (how widely daily moves spread, stated at a yearly rate). A rough guide for a fund that resets each day:
- Drag ≈ (multiple² − multiple) ÷ 2 × volatility²
- It is a guide, not an exact rule: it is closest when the year's move is small. Two things follow:Drag grows with the square of the swings: double the volatility, about 4 times the drag.Inverse funds pay more. For +2x the factor is (4 − 2) ÷ 2 = 1. For −2x it is (4 + 2) ÷ 2 = 3, the same as a +3x fund.
Worked example
One year, Nov 10, 2025 to Nov 10, 2026.
Case 1: a flat year with big swings (NVDA).
| Return | |
|---|---|
| NVDA | −14.95% |
| 2 × the year | −29.90% |
| 2x each day, compounded | −37.68% |
| NVDL (2x NVDA fund) | −44.02% |
The rough guide: NVDA's volatility was 38.46% a year. 1. Square it: 0.3846 × 0.3846 = 0.148. 2. Multiply by the factor for 2x, which is 1: 0.148, about 15 points of drag. 3. The real path effect: −37.68 − (−29.90) = −7.78 points.
Close. The swings, not NVDA's move, drove the compounded loss. NVDL's further −6.3 points is the fund's gap (fees and the cost of the swaps that give its exposure).
Case 2: both sides lost (TSLA). TSLA fell 14.70% with volatility of 45.74%.
| 2x long (TSLL) | −2x short (TSLQ) | |
|---|---|---|
| 2 × the year | −29.40% | +29.40% |
| Daily multiple, compounded | −41.53% | −26.30% |
| Fund | −48.44% | −20.45% |
TSLA fell, and the short fund still lost: its factor of 3 turned a "should-be" +29% into −26.30% before costs.
The common mistake
"Path dependence means the order of the days matters." For a fund that resets each day, it doesn't. The year's result multiplies each day's (1 + multiple × move), and a product is the same in any order. What matters is how big the daily moves were. "Shuffle the days" shows it.
Check your understanding
Pick an answer to see why. Two of three right passes the lesson.
1. Two stocks each end a year flat. Stock A had volatility of 20%, stock B 40%. Before costs, how does B's 2x daily fund's drag compare with A's?Answer: C. About 4 times as large. drag grows with volatility squared: 0.4² = 0.16 against 0.2² = 0.04, 4 times. Not B: volatility doubled, but the drag follows its square.2. An index rose 10% over a choppy year. Which fund is most likely to have lost money before costs?Answer: A. A −2x daily fund. the −2x fund starts 20 points behind and pays a factor of 3 on the swings, against 1 for +2x. Not B: +2x starts about 20 points ahead and has the smaller factor.3. You replay a 2x fund's year with the days in a different order. What happens to its compounded result before costs?Answer: D. It stays the same. the result multiplies each day's (1 + 2 × move), and order doesn't change a product. Not A: order matters for stop orders and multi-day stretches, not for a daily-reset fund's year.
Takeaways
- Check the underlying's volatility before the multiple: drag grows with its square.
- Inverse funds carry more drag: −2x pays about 3 times what +2x pays on the same swings.
- A flat or falling year can cost both the long and the short fund.