Compounding effect

More than two years ago I noticed something that didn't seem right, that the 2x and the 3x ETFs did not offer 2x or 3x gains or losses compared to the ETF they were following. I was especially puzzled by FAS-FAZ that were both going down instead one going up and the other going down as expected. They were going in different directions in one single day but over a longer period (two year in this case) they were both losing value. I asked people around but nobody could give me a reasonable answer. Then I tried on paper, I simulated 1x, 2x and 3x transactions and I found part of the answer, namely why a 3x ETF does not give one a 3x loss or gain over a period of time. The reason is the so called "compounding effect".

For example, let's say an ETF is valued $100 , we have the following situations:

1) the ETF is going 10% up two days in a row, the first day it will be valued $110 but the second day is not going to be valued $120, since the second day it will be 10% out of 110 not the initial 100. After two days the gain will be 21%. So we are going into "weird" kind of mathematics:

+10%+10%= +21%

2) 10% down in the first day, 10% down the second day. That will be $90 first day and $81 second day.

-10%-10%=-19%

3) 10% up the first day, 10% down the second day. That will be $110 in the first day and $99 second day.
+10%-10%=-1%

Now let's skip the 2x ETFs and go directly to 3x ETFs. Assume that the 3x ETF is following the 1x ETF. So instead of having 10% up or down we are going to have 30%

a) 30% up+30% up. That will be $130 first day and %169 second day.

30%+30%=+69%

Notice that 69% is higher that 3x21%, the three times 1x ETF gain.

b) 30% down first day, 30% down second day. That will be $70 first day and $49 second day.

-30%-30%=-51%

This time 51% is lower than 3x(-19%)

c) 30% up first day, 30% down second day. That will be $130 first day and $91 second day.

+30%-30%=-9%

Pay attention to c) and also compare it with 3). This is 9 times the loss suffered by the underlying 1x ETF !!! 

This is very important result and the reason of writing this article. So, in other words, if market is volatile, if the 1x ETF doesn't have a clear direction, either up or down the 3x ETF is losing it's value at a very high pace. So I said "what if I am going to short both FAS and FAZ or ERY and ERX. What is going to happen in a one year time frame?" I was expecting the following results: if market was going to be volatile, I was going to gain, if it was going to go mostly up or mostly down I was going to lose. 

 I placed these ETFs in a fake account (on "Wall Street Survivor") in November 2010. Here are the results, after one year, in November 2011.

This was absolutely amazing, every single ETF was going down and since I shorted them, they were all in green. The wining pair was FAS-FAZ. I gained 49.85% by shorting FAS and 12.22% by shorting FAZ for a median profit of 31%. Second best pair was ERY-ERX with 20% gain and the worst was QLD-QID, as expected since this pair is 2x. SQQQ-TQQQ pair (that are 3x QQQ) were also pretty good with a 20% average gain.

A few day ago, after two years,  I looked again at my fake account and here are the results:

FAS-FAZ pair was once again the winner, this time with a 38.5% average gain. It didn't get too much since last year but is still good. Overall the account went up 10% in the last year. Notice that only QLD and TQQQ are in red.

Timing the entry is pretty important, is good to enter after a decent leg up or leg down since market sometimes goes sideways for a while. I also noticed that is good to enter at a level that is going to be visited again. The longer it takes the market to come back to the entry level the higher the gain. For example I entered in the middle of a rally and I started with a loss for a few months. Not a big loss but a loss nevertheless. 

The beauty of this system is that you don't care if the market goes up or down you are winning anyway if the market is volatile. And guess what, market is always volatile over long periods of time!

I don't know if you can make actually money with this system, for example my broker doesn't let me short FAS or FAZ or any other 2x or 3x ETF. If you know a broker that let you short these ETFs please let me know. Even if you are allowed to short them you may start with a loss and you may get a margin call and forced to cover.

Even though you cannot make money with this system keep in mind that your 2x and especially 3x ETFs are losing value all the time. Keep in mind that the compounding effect is not the only one responsible for 3x ETFs decreasing value but I think is the most important. The financials were indeed the most volatile and no wonder that the FAS-FAZ pair was the winning one. What is hard to "digest" is the incredible loss both ETFs have suffered since inception.

I can easily make 30% profit per year but I need to work hard, I need to be very objective and why not, I need a little bit of luck. But getting 30% profit for sure no matter if market is going up or down, this I can take any day. 

Please let me know your opinion. You can send me an e-mail at babaro13@yahoo.com if you prefer.

babaro