This was posted at Rambus Forum by Big Kahuna,

It is the best explanation for these things that I have heard.

FWIW :
………………..

The reason why the leverage ETFs ‘decay’ is because they are design to track 3x the Daily percentage move in the underlying and that has the following effect.

Imagine an asset with a price of $100

Day 1 it goes up to $125

Day 2 it goes back to $100

If you were invested in the asset you would be square on the trade (putting aside brokerage etc)

In percentage terms we have

Day 1 +25% (25/100)

Day 2 -20% (25/125)

Now the looking at the 3x Leverage ETF that tracks the Daily percentage movement and applying 3x these % moves.

Assume it also has a starting price of $100 for ease of calculations. But any number works.

Day 1 +75% (3*25%) = $175

Day 2 -60% (3×20%) of the new asset price of $175 = $70 (ie 175 – .60*175 = 175 – 105 = 70)

If you were invested in the 3x leverage asset you are down $30. (-30%) Versus square on the non-leveraged trade

An asset that goes +10%, -7.7%, +10%, -7.7%, etc etc will be up 16% after 20 days but the 3* Leverage asset will be at 0% increase

Because of this an asset could be in a slow grind bull market but the 3x product in a bear market.

IMO unless you are going “all in” (100% of your capital) it never makes sense to trade these things. You are better off putting 3x the capital in to the non-leveraged asset. And thus avoiding the ‘decay’.
I hope this helps.