Double and Triple Leveraged ETFs Revisited: The Real Decay

After reading a lot of blog posts, tweets on twitter, Facebook comments, and emails, I decided it was time to figure out the real decay behind the leveraged ETF's, both long and short. As I wrote about this in one of my previous blog posts, I wanted to revisit this issue of the double and triple leveraged ETF's, and why investor's should stay away from them, and to clear up some confusion. With the popularity of ETF's came these funds which use 200% and 300% leverage. Yes in any steady trend they can grow like weeds, but in a correction they will give back much of their gains. This is simple, and basic math.

First of all, these are extremely risky, and investor's shouldn't hold on to any leveraged ETF(s) for the "long run", they are almost sure to lose money. These instruments are ideal for traders not investors!

Second of all let's identify what a leveraged ETF does. A double leveraged ETF uses 200% (triple uses 300%) leverage to capture a specific basket, sector, or index move. Let's take the very popular SDS which is a 2X inverse tracking the S&P 500, for every 1% move up in the S&P 500 index SDS will move down by 2%, and for every 1% move down in the index SDS will move up by 2%. Similarly is the SSO which is the 2X tracking the S&P 500, for every 1% move up in the S&P 500 index SSO will move up by 2%, and for every 1% move down in the index SSO will move down by 2%.

If you're the person who says: It's a great way to hedge my portfolio, so what's the problem with them? Then clear all your other thoughts and read this post carefully- it may save you some money.

It's basic math that so many people overlook! Let's use the benchmark S&P 500 index for an example. Let's say we start off on the S&P 500 at 1000 and a double and triple leveraged ETF both at $100 per. If the benchmark index moves down 10% in 1 week to 900, and assuming both ETF's track perfectly it would put the double leveraged ETF at $80 per share, and the triple leveraged ETF at $70 per share. Here is where some investor's don't use those basic math skills they learned so many years ago, and assume that when the S&P gets back to 1000, the leveraged ETF will trade at the identical value as before, when the S&P was at 1000... THIS IS FALSE!

Basic math tells us this is not possible. In order for the benchmark to get back to 1000 it will need to go up by 11.11% which will correlate to a 22.22% and 33.33% move in the double and triple ETF's respectively. As we can see in order to get the double leveraged ETF back to 100 from 80, the benchmark will need to increase by 12.5% correlating to a 25% increase in the double ETF. The triple leveraged ETF will need an even greater move to get back to 100. In order for the triple ETF to get back to 100 from 70, the benchmark will need to increase by 14.283% correlating to a 42.85% increase in the triple ETF.

To show how this works I have created an Excel spreadsheet. I have downloaded historical data on the S&P 500 Index for exactly one year, back to the closing index value on July 11,2008. Assuming these leveraged ETF's track perfectly with the change in the index (which is incorrect but they do track very closely), the spreadsheet shows the changes for 4 different leveraged ETF's. The ETF's tracked are: Double Leveraged Long index, Triple Leveraged Long index, Double Leveraged Short index, and Triple Leveraged Short index. I also started each ETF at 100 on July 11, 2008 (this is not where they started, but will not make a difference in the % change). These ETF's don't assume any capital gains distributions, splits etc...

Click here to download the Spreadsheet (Excel 2007 and Firefox recommended)

As you can see, for the past year the index is down 29.07%, the double short ETF up 6.8%, however the triple leveraged Short ETF is also down 20.11%. Many would have assumed the double and triple leveraged short ETF's would be up 58.14% and 87.21 respectively over this period. This is certainly not the case. These ETFs seem to decay over time, again this is proven with basic math! I will show you some scenarios in the following three tables.

Scenario #1: The table below shows an index moving up by 1% on the first day, and down by 0.990099% on the following day. The same two day occurrence is repeated over 20 trading days (market moves exactly sideways over 20 trading periods).

	Index	2X Long	2X Short	3X Long	3X Short
Start price	1000	100	100	100	100
% Change
1	1010	102.00	98.00	103.00	97.00
-0.99009901	1000	99.98	99.94	99.94	99.88
1	1010	101.98	97.94	102.94	96.88
-0.99009901	1000	99.96	99.88	99.88	99.76
1	1010	101.96	97.88	102.88	96.77
-0.99009901	1000	99.94	99.82	99.82	99.64
1	1010	101.94	97.83	102.82	96.65
-0.99009901	1000	99.92	99.76	99.76	99.53
1	1010	101.92	97.77	102.76	96.54
-0.99009901	1000	99.90	99.70	99.70	99.41
1	1010	101.90	97.71	102.69	96.43
-0.99009901	1000	99.88	99.64	99.64	99.29
1	1010	101.88	97.65	102.63	96.31
-0.99009901	1000	99.86	99.58	99.58	99.17
1	1010	101.86	97.59	102.57	96.20
-0.99009901	1000	99.84	99.53	99.53	99.05
1	1010	101.84	97.54	102.51	96.08
-0.99009901	1000	99.82	99.47	99.47	98.94
1	1010	101.82	97.48	102.45	95.97
-0.99009901	1000	99.80	99.41	99.41	98.82

As you'll notice the index is back to even and all 4 of the leveraged ETF's are below their initial starting values, in just 2o trading days.

Similarly this can be said if we reverse the order of the % changes, as in the first day the index goes down 1% and the follow day the index returns to the start by moving up by 1.0101%. The changes are insignificant over a 20 days period, but as you can see if the first day results in a loss versus a gain, the value of the ETF at the end of the 20 day period is a bit lower.

	Index	2X Long	2X Short	3X Long	3X Short
Start price	1000	100	100	100	100
% Change
-1	990	98.00	102.00	97.00	103.00
1.01010101	1000	99.98	99.94	99.94	99.88
-1	990	97.98	101.94	96.94	102.88
1.01010101	1000	99.96	99.88	99.88	99.76
-1	990	97.96	101.88	96.88	102.75
1.01010101	1000	99.94	99.82	99.82	99.64
-1	990	97.94	101.81	96.82	102.63
1.01010101	1000	99.92	99.76	99.76	99.52
-1	990	97.92	101.75	96.77	102.50
1.01010101	1000	99.90	99.70	99.70	99.40
-1	990	97.90	101.69	96.71	102.38
1.01010101	1000	99.88	99.64	99.64	99.27
-1	990	97.88	101.63	96.65	102.25
1.01010101	1000	99.86	99.58	99.58	99.15
-1	990	97.86	101.57	96.59	102.13
1.01010101	1000	99.84	99.52	99.52	99.03
-1	990	97.84	101.51	96.53	102.01
1.01010101	1000	99.82	99.46	99.46	98.91
-1	990	97.82	101.44	96.47	101.88
1.01010101	1000	99.80	99.40	99.40	98.79

Scenario #2: Let's say the market rallies 25.02% (1.5% a day for 15 days in a row), and then corrects 15.32% (from high) in the following 11 trading days (down 1.5% a day for 11 days). In the table below I will plot exactly this example, once again using basic math.

	Index	2X Long	2X Short	3X Long	3X Short
Start price	1000	100	100	100	100
% Change
1.5	1015	103.00	97.00	104.50	95.50
1.5	1030.23	106.09	94.09	109.20	91.20
1.5	1045.68	109.27	91.27	114.12	87.10
1.5	1061.36	112.55	88.53	119.25	83.18
1.5	1077.28	115.93	85.87	124.62	79.44
1.5	1093.44	119.41	83.30	130.23	75.86
1.5	1109.84	122.99	80.80	136.09	72.45
1.5	1126.49	126.68	78.37	142.21	69.19
1.5	1143.39	130.48	76.02	148.61	66.07
1.5	1160.54	134.39	73.74	155.30	63.10
1.5	1177.95	138.42	71.53	162.29	60.26
1.5	1195.62	142.58	69.38	169.59	57.55
1.5	1213.55	146.85	67.30	177.22	54.96
1.5	1231.76	151.26	65.28	185.19	52.49
1.5	1250.23	155.80	63.33	193.53	50.12
-1.5	1231.48	151.12	65.22	184.82	52.38
-1.5	1213.01	146.59	67.18	176.50	54.74
-1.5	1194.81	142.19	69.20	168.56	57.20
-1.5	1176.89	137.93	71.27	160.97	59.77
-1.5	1159.24	133.79	73.41	153.73	62.46
-1.5	1141.85	129.77	75.61	146.81	65.28
-1.5	1124.72	125.88	77.88	140.21	68.21
-1.5	1107.85	122.10	80.22	133.90	71.28
-1.5	1091.23	118.44	82.62	127.87	74.49
-1.5	1074.86	114.89	85.10	122.12	77.84
-1.5	1058.74	111.44	87.66	116.62	81.34
% Change	5.87	11.44	-12.34	16.62	-18.66
Assumes%		11.75	-11.75	17.62	-17.62

As you can see the net gain for the index was 5.87%, however all 4 of the leveraged ETF's did not perform as they were suppose to. Note that this is only over 26 trading days about 10% of the trading year.

You will also notice at the bottom of the spreadsheet I created, a simulation to show how the index (over the next 250 days) could get back to even the level it was at on July 11, 2008, and the resulting % changes from $100 per share for each leveraged ETF. This proves how dangerous they are... They are all down even when the index is back to even!

The question you may be asking me is: You blog about these ETF's all the time, don't you use them? My answer is absolutely, I actually prefer these to any given stock. This is because I am a trader of these instruments (not to mention young with high risk tolerance), and I use them for short covered call/naked put option strategies. The reason behind this is simply because they have such large premiums on the options, they can be used many different ways to create additional income for my portfolio. I do not think any investor should be in these, but I know many are. This post only talks about what I call the less risky of the leveraged ETF's, this is because I talk about the leveraged ETFs that track the indexes. Some of the most popular leveraged ETF's are ones that track specific sectors, like the super volatile: FAS, FAZ, SKF, UYG, TNA, TZA, URE, SRS, and many more.

In conclusion, it certainly depends on the price these ETF's are purchased, but over the long run, based on simple mathematics, and the assumption that the market wont go in one direction forever, they are sure to deteriorate. This is why these are great instruments to trade, not invest.


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