Leveraged ETFs (2x, 3x) - House always wins

As I mentioned in my previous post I am attaching my analysis of the 2x leveraged ETFs. I took the real-time data of the Dow Jones and analyzed the performance of the 2x long (Ticker: DDM) and 2x short (Ticker: DXD) ETFs. I chose a period in which the Dow starts with particular level, drops down and few days later ends up slightly lower than the starting level.

In this period the Dow index is down ~15%. You would see the DDM (2x long) is down ~32% (As you would expect). BUT look at the DXD (2x short) is only up ~15%!!! You would think you would be up ~32%

No matter what the management get its fees. The house always wins!

All that glitters is not gold - Understanding Leveraged ETFs

Leveraged ETF are ETF funds that amplify (by a factor of the levered ratio) the daily returns of a specific index. For example: (Ticker SSO) is 2x levered ETF that tracks S&P500. If S&P500 index moves +1% in a day, SSO will return +2% and likewise a -1% move in S&P500 will be -2% in SSO's value.

At first glance, leveraged ETFs looks good:
What is not obvious is the fact that leveraged ETFs are not 2x the annual return of the index. To be clear, suppose

Assume:

no management fees for the following example

Today: S&P500 is 1000 and the SSO is $50

1 year from now: S&P500 is 1100 (10% up from today). You cannot expect SSO to be $60 (2 x 10% = 20% growth)

The reason is the markets must have moved up and down before gradually growing to 1100 points from 1000. Each day the daily return or the move in the index in % is amplified by 2. This will affect the total return you would expect in leveraged ETF.

I will try to post a real analysis of leveraged ETF and it correlation to the markets