The re-indexing problem of leveraged ETFs stems from the arithmetic effect of volatility of the underlying index. Take, for example, an index that begins at 100 and a 2X fund based on that index that also starts at 100. In a first trading period (for example, a day), the index rises 10% to 110. The 2X fund will then rise 20% to 120. The index then drops back to 100 (a drop of 9.09%), so that it is now even. The drop in the 2X fund will be 18.18% (2*9.09). But 18.18% of 120 is 21.82. This puts the value of the 2X fund at 98.18. Even though the index is unchanged after two trading periods, an investor in the 2X fund would have lost 1.82%. This decline in value can be even greater for inverse funds (leveraged funds with negative multipliers such as -1, -2, or -3). It always occurs when the change in value of the underlying index changes direction. And the decay in value increases with volatility of the underlying index.