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Certain ETFs double the daily rate of return of certain indices. Can you use such ETFs to beat the market (not on a risk-adjusted basis, just in terms of pure returns)?

I have read that

When based on high volatility indexes, 2x leveraged ETFs can also be expected to decay to zero

But I don't see why this can be true.

My rationale is the following: My assumption is that typically, markets have a positive return expectation (otherwise, prices should drop such that this is true). If, on a daily basis, the expected return is positive then it should be profitable to double that return. And if this is true for one day, then surely this should be true for longer periods of time.

If you can win by following such a strategy, then who loses?

Uwat
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  • I would say related, the other question (and answer) seems to focus more on risk. – Uwat Feb 14 '12 at 19:54
  • Perhaps, but my answer there offers a mathematical explanation as to why leverged ETFs fail long term. – JTP - Apologise to Monica Feb 15 '12 at 02:54
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    The SEC would like to chime in with a real-world example - http://www.sec.gov/investor/pubs/leveragedetfs-alert.htm - "Between December 1, 2008, and April 30, 2009, a particular index gained 2 percent. However, a leveraged ETF seeking to deliver twice that index's daily return fell by 6 percent—and an inverse ETF seeking to deliver twice the inverse of the index's daily return fell by 25 percent." –  Feb 17 '12 at 06:37
  • Can I ask what "beat the market" means? – gef05 Feb 18 '12 at 17:02
  • @gef05 - you can, and it would be a valid standalone question! But to "beat the market" means to earn a better return than "the market" at large - typically represented by the S&P500 index. An S&P500 index fund is a good "where to invest if you don't actually have any specific good ideas about where to invest" and is an important baseline: if you are doing something more risky than investing in the market (e.g. in individual stocks, or real estate), you should expect higher returns - or, why take those risks? It is notoriously difficult to consistently beat the market. –  Feb 22 '12 at 01:26

5 Answers5

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If the index goes up every single day during your investment, you would indeed be better off with 2x ETFs, assuming no tracking errors.

However, this is basically never the case. Indexes fluctuate up and down. And the problem is, with these sorts of ETFs, you double your win on the upside but your downside is more than double. If an index goes up 10% one day and down 10% the next, you lose 1% of the value of your investment (1.1 * 0.9). If you are using 2x ETFs, you lose 4% of the value of your investment (1.2 * 0.8), not 2%. If you are using 3x ETFs, you lose 9% of the value of your investment (1.3 * 0.7), not 3%.

So, if the index will continue to rise during your holding period, yes, you are better off with these 2x or 3x ETFs. If the index falls on some days, but rises most other days, the added downside is all but certain to make you lose money even though the stock trends upward. That's why these ETFs are designed for single-day bets. Over the long-term, the volatility of the stock market, combined with your exponentially increased downside, guarantees you will lose money.

ChrisInEdmonton
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  • I could also make the following, amazingly similar argument: What if there were 0.5X ETFs (perhaps there are, I don't know)?

    If the 1X ETF earns 10% one day, loses 10% the other day, you lose 1% of the value. But the 0.5X ETF does not lose 0.5% of the value, but rather 0.25% of the value.

    Why, then, would 1X be the "magical" number?

     – Uwat Feb 15 '12 at 18:04
  • If you say that 2X does not beat 1X, then surely 1X is expected to beat 2X. Intuitively, 0.5X should also beat 1X. By repeating this argument indefinitely, 0X should beat 1X, which is clearly impossible.

    In this comment "beat" means that the expected returns are higher (on average)

     – Uwat Feb 15 '12 at 18:14
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    I did not say that a 2X ETF fails to beat a 1X ETF. I explicitly state that if the index goes up every single say, you would indeed be better off with a 2X ETF. Similarly, if the index goes down every single day, you are better off with a 1X ETF. What is often counter-intuitive is that, if there's a lot of volatility in the index, a 2X ETF will almost always come out worse than a 1X ETF, for mathematical reasons. – ChrisInEdmonton Feb 15 '12 at 18:58
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    To take your example, a 0.5X ETF will do worse than a 1X ETF if the index goes up every single day, better if the index goes down every single day. A 0X ETF would do much worse than a 1X ETF on rises, much better on drops. But you'll probably never see an ETF offered below 1X; the offering company is taking too much risk for the volatility. An index that started at 100, went up 50% to 150, then down 33% to return to 100 would mean that a 0.5X ETF ended up paying out 4. – ChrisInEdmonton Feb 15 '12 at 19:05
  • "What is often counter-intuitive is that, if there's a lot of volatility in the index, a 2X ETF will almost always come out worse than a 1X ETF, for mathematical reasons."

    Even though this is true, this does not imply that the 2X ETF will return lower results on average. My question is: Will the 2X ETF return better results on average?

     – Uwat Feb 15 '12 at 19:21
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    No, a 2X ETF will return worse results on average, given AVERAGE index volatility. Given a monotonically increasing index, a 2X ETF will return better results. You will most certainly be able to find periods of time WITH VOLATILITY where a 2X ETF will win out, though perhaps not by as much as you think, but over the long haul, it does not. Try plugging in numbers in your spreadsheet. You CAN make money. You CAN make more money. Even with volatility. But over the long-run, it is statistically improbable, given average volatility. – ChrisInEdmonton Feb 15 '12 at 19:33
  • And again, it's going to depend on your time span, and the volatility. A day? A week? A month? A year? Ten years? I'd be absolutely stunned if you could find an index where a 2X (daily) ETFs would have had a positive return over 10 years, though I'm sure you could find an example over a month. To avoid using this as a chat forum, I'm going to refrain from commenting further. – ChrisInEdmonton Feb 15 '12 at 19:35
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    Uwat - sorry, it's intuitive for me. I know that (x+y)(x-y)=x^2-y^2 so the idea that a number of 2X gains and losses just become larger losses stands to reason. – JTP - Apologise to Monica Feb 16 '12 at 05:52
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You miss the step where the return being doubled is daily.

Consider you invested $100 today, went up 10%, and tomorrow you went down 10%. Third day market went up 1.01% and without leverage - got even.

Here's the calculation for you:

day - start - end

1 $100 $120 - +10% doubled

2 $120 $96 - -10% doubled

3 $96 $97.94 - +1.01% doubled

So in fact you're in $2.06 loss, while without leveraging you would break even. That means that if the trend is generally positive, but volatile - you'll end up barely breaking even while the non-leveraged investment would make profits. That's what the quote means.

edit to summarize the long and fruitless discussion in the comments:

The reason that the leveraged ETF's are very good for day-trading is exactly the same reason why they are bad for continuous investment. You should buy them when there's a reasonable expectation for the market to immediately go in the direction you expect. If for whatever reason you believe the markets will plunge, or soar, tomorrow - you should buy a leveraged ETF, ride the plunge, and sell it in the end of the day. But you asked the question about volatile markets, not markets going in one direction. There - you lose.

littleadv
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  • Thanks for your answer. I understand that rates are doubled on a daily basis. However, consider the following:
    1. If you were to invest for only one day, would you think it would be profitable to invest in a leveraged ETF (assuming its expectation is positive)?
    2. If you answered yes to (1), then after selling the stock at day n, why not buy it again at day n+1?
    3. If you should buy it at day n+1 as in (2), you might as well keep the stock forever.

    Also, your answer presents only an hypothetical situation -- it does not in any way prove that returns would be lower or negative.

     – Uwat Feb 14 '12 at 19:51
  • littleadv is correct. Take a look at the charts of any leveraged ETF. You'll find that over the long term, they all decay. If the market has an extended swing in one direction, then you can realize significant profits. However, high return always comes with high risk. Even according to the companies that sell them, these products are meant for sophisticated (day-)traders only. – Jason R Feb 14 '12 at 19:54
  • @Uwat if I were able to definitely predict index behaviors, I wouldn't be telling it to you, rest assured:-) Going up one day, and down the same percentage the next day is pretty frequent from my observations, and that is why leveraged ETF's are dangerous. – littleadv Feb 14 '12 at 19:56
  • @Uwat: I would also beware applying principles of statistics such as expectations too freely; while your assertion may be correct over a very large ensemble of daily returns for a given index, there is a very practical saying: "the market can stay irrational longer than I can stay solvent." Your statistical analysis wouldn't help you if you invested in a double-long fund in early September 2008 (although there were much fewer back then). True, there is potential for high reward, but also very high risk with such an approach. – Jason R Feb 14 '12 at 19:56
  • I understand that such a strategy is excessively risky. And even if it were true that say, the probability of a leveraged ETF going down over a year was 75%, this would not necessarily indicate that the expectation would be lower than the non leveraged ETF (which could be assumed to go down over a year 50% of the time) since those low returns might be compensated by very high returns the other 25% times. – Uwat Feb 14 '12 at 20:05
  • What part(s) of my comment(s) makes you say this: "I'm not sure you understand how percentage calculations works.... "? – Uwat Feb 14 '12 at 20:24
  • I believe you are the one misunderstanding the situation. Can you reply with yes or no to part 1 of my comment #1? – Uwat Feb 14 '12 at 20:34
  • @littleadv So you would reply with "yes" to part 1 of my comment #1, correct? If so, then why does (2) and (3) not follow? If not, then why not? – Uwat Feb 14 '12 at 20:43
  • @Uwat - I explained to you why not. Unless you know with a very high level of certainty that the market is going in one direction, you're likely to lose money. I also calculated an example to show you how exactly it happens. The fact that you can't grasp the example is exactly why I think you misunderstand how the percentage calculations work. – littleadv Feb 14 '12 at 20:45
  • I understand perfectly well your example. Also the fact that "you're likely to lose money" is in no way a proof that the net expectation is lower. I will come back with a simulation that will demonstrate this fact. I think you might misunderstand the word expectation. There are several investments that I would gladly make even if I expected to lose money 95% of the time. – Uwat Feb 14 '12 at 20:55
  • @Uwat - I'm not sure you understand. You asked about a specific quote, and you couldn't understand why it would be true. I showed you how it can be true. Showing me that in other cases your assumption that you win works is meaningless, because you're wrong in the assumption that you always win, not that you may win. The point of this ETF's is that by using them right (day trading at the right time) you can win a lot. But the risk is very high when misusing them (i.e.: not day-trading but holding for prolonged periods, as one example), and that what the quote, and my answer, are about. – littleadv Feb 14 '12 at 20:58
  • @littleadv I have never ever assumed that the double long ETF will always return higher returns. I'm just saying that although perhaps the probability of losing over a long period might be significantly higher with a leveraged ETF, I believe that THE EXPECTATION SHOULD BE HIGHER. And absolutely nothing about your answer/comments have proved this to be wrong. Perhaps you should read about this – Uwat Feb 14 '12 at 21:06
  • @Uwat "I believe that THE EXPECTATION SHOULD BE HIGHER." - based on what? Again, as long as the market is going in one direction - that may be true. Once the market becomes volatile, regardless of the trend - the more leveraged the ETF is - the more you're going to lose. How? See the example in my answer. – littleadv Feb 14 '12 at 21:09
  • Well, this is fantastic. I didn't know that proof by example was a valid way to prove things. So apparently whenever you multiply a number by 3 you obtain 90. Proof: 30*3 = 90

    You applied the same logic and provided nothing else of any value.

     – Uwat Feb 14 '12 at 21:39
  • @Uwat - I didn't try to prove anything. You asked how that quote could be true - I showed you. – littleadv Feb 14 '12 at 21:43
  • Wrong. You proved that "When based on high volatility indexes, 2x leveraged ETFs can also decay to zero" Instead of the actual quote. Besides, the quote wasn't the full content of my question. – Uwat Feb 14 '12 at 21:59
  • You know what, forget it. – littleadv Feb 14 '12 at 22:04
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Here is a simple example of how daily leverage fails, when applied over periods longer than a day. It is specifically adjusted to be more extreme than the actual market so you can see the effects more readily.

You buy a daily leveraged fund and the index is at 1000. Suddenly the market goes crazy, and goes up to 2000 - a 100% gain! Because you have a 2x ETF, you will find your return to be somewhere near 200% (if the ETF did its job). Then tomorrow it goes back to normal and falls back down to 1000. This is a fall of 50%. If your ETF did its job, you should find your loss is somewhere near twice that: 100%. You have wiped out all your money. Forever. You lose. :)

The stock market does not, in practice, make jumps that huge in a single day. But it does go up and down, not just up, and if you're doing a daily leveraged ETF, your money will be gradually eroded. It doesn't matter whether it's 2x leveraged or 8x leveraged or inverse (-1x) or anything else. Do the math, get some historical data, run some simulations.

You're right that it is possible to beat the market using a 2x ETF, in the short run. But the longer you hold the stock, the more ups and downs you experience along the way, and the more opportunity your money has to decay.

If you really want to double your exposure to the market over the intermediate term, borrow the money yourself. This is why they invented the margin account: Your broker will essentially give you a loan using your existing portfolio as collateral. You can then invest the borrowed money, increasing your exposure even more. Alternatively, if you have existing assets like, say, a house, you can take out a mortgage on it and invest the proceeds. (This isn't necessarily a good idea, but it's not really worse than a margin account; investing with borrowed money is investing with borrowed money, and you might get a better interest rate. Actually, a lot of rich people who could pay off their mortgages don't, and invest the money instead, and keep the tax deduction for mortgage interest. But I digress.) Remember that assets shrink; liabilities (loans) never shrink.

If you really want to double your return over the long term, invest twice as much money.

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NO.

All the leveraged ETFs are designed to multiply the performance of the underlying asset FOR THAT DAY, read the prospectus. Their price is adjusted at the end of the day to reflect what is called a NAV unit. Basically, they know that their price is subject to fluctuations due to supply and demand throughout the day - simply because they trade in a quote driven system. But the price is automatically corrected at the end of the day regardless.

In practice though, all sorts of crazy things happen with leveraged ETFs that will simply make them more and more unfavorable to hold long term, the longer you look at it.

CQM
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See http://blogs.reuters.com/felix-salmon/2011/04/30/why-the-sec-should-look-at-levered-etfs/?dlvrit=60132, http://symmetricinfo.org/2011/04/are-investors-in-levered-short-treasury-etfs-a-disaster-waiting-to-happen-pt1/, and the articles linked from it:

The issue with holding a levered ETF past 1 day is that investors expose themselves to path dependency in the underlying....

The reason for the difference in payouts comes from the fact that the manager of the levered ETF promises you a multiple of the daily returns of the underlying. To be able to promise you these daily returns, the ETF manager has to buy/sell some of the underlying every day to position himself to have a constant leverage ratio the next day. The short video below explains this process in detail for a 2x long ETF, but the same result holds for a 2x short ETF: the manager has to buy more of the underlying on a day when the underlying increases in value and sell more of the underlying when the underlying goes down in value .

poolie
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