Leveraged ETFs are known for their natural decay. On the long term, holding a position in an N-times leveraged ETF is generally worse than holding an N-times leveraged position in the underlying asset. But few people really understand the reason, which is called beta-slippage.

To understand what is beta-slippage, imagine a very volatile asset that goes up 25% one day and down 20% the day after. A perfect double leveraged ETF goes up 50% the first day and down 40% the second day. On the close of the second day, the underlying asset is back to its initial price:

(1 + 0.25) x (1 - 0.2) = 1

And the perfect leveraged ETF?

(1 + 0.5) x (1 - 0.4) = 0.9

Nothing has changed for the underlying asset, and 10% of your money has disappeared. Beta-slippage is not a scam. It is the normal mathematical behavior of a leveraged and rebalanced portfolio. In case you manage a leveraged portfolio and rebalance it on a regular basis, you create your own beta-slippage. The previous example is simple, but beta-slippage is not simple. It cannot be calculated from statistical parameters. It depends on a specific sequence of gains and losses.

At this point, I'm sure that some smart readers have seen an opportunity: if we lose money on the long side, we make a profit on the short side, right?

The reality is more complicated for various reasons.

First, these products may be very volatile.

Second, to sell them short, you need to borrow shares from your broker. The interest rate is variable and sometimes prohibitive.

Third, borrowed shares can be called back at any time for any reason by the broker.

Smart people had the idea to take market-neutral short positions in opposed leveraged ETFs. Unfortunately, such strategies may be very sensitive to starting dates (article here).

Are all leveraged ETFs losers on the long side and dangerous on the short side? Not for some of them. For example, leveraged S&P 500 ETFs have a lower beta-slippage than most leveraged ETFs, which makes SPXU-OLD and SDS good candidates for hedging a stock portfolio (article here).

In a trending market, beta-slippage can even become positive. Let's go back to the math: the simplest trending market is two consecutive days in the same direction. Imagine an asset going up 10% two days in a row.

On the second day, the asset has gone up 21%:

(1 + 0.1) * (1 + 0.1) = 1.21

The perfect 2x leveraged ETFs is up 44%, more than twice 21%:

(1 + 0.2) * (1 + 0.2) = 1.44

A leveraged ETF in a steady bullish trend may outperform its leveraging factor. But it depends on the sequence of losses and gains, and cannot be predicted or even calculated with a statistical model.

Here is an example with UPRO in the last twelve months:

12-month return 11/25/2012 to 11/25/2013 | |

S&P 500 | 27.5% |

UPRO | 114.4% |

The "intuitive" return of UPRO should be 27.5 x 3 = 82.5%.

Another past example using SLV (silver) and AGQ (silver 2x):

6-month return 11/1/2010 to 4/30/2011 | |

SLV | 81.1% |

AGQ | 195.3% |

During this rally, AGQ returned more than twice SLV's return.

Does it also work with leveraged inverse ETFs in bearish markets? The math works, not psychology. Fear generally makes bearish markets chaotic, not trending.

Beta-slippage is path-dependent. If the underlying gains 50% on day 1 and loses 33.33% on day 2, it is back to its initial value, exactly like in the first example. This time, the 2x ETF loses one third of its value, which is much worse than 10% in the first case:

(1 + 1) x (1 - 0.6667) = 0.6667

Without a demonstration, it shows that the higher the volatility, the higher the decay. Hence, its name: "beta" is a statistical measure of volatility. However, it is a bit misleading because the decay cannot be calculated from beta.

I publish a monthly dashboard with current decays of leveraged ETFs in stock indices, sectors, oil, gas, gold and silver. It is a must read for investors using leveraged ETFs for trading or hedging. To be notified, click "follow" at the top of this article.

**Disclosure:** I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Disclosure:** I am/we are long SDS.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **long SDS for hedging purposes