Leveraged ETFs are Complex?

It’s not exactly grabbing headlines, but our nation’s regulatory watchdogs are on the scent of yet another scourge from which investors need to be protected: leveraged ETFs. Apparently, these things are like snakes in the grass, just waiting to spring at poor innocents who wander by.

Several brokerages have taken steps to discourage their clients from buyingNYSE-Mod-Small leveraged ETFs and in some cases prohibit it altogether. The folks at Motley Fool have been waving people off them. The association of state securities regulators named leveraged ETFs as one of their Top 10 Investor Traps, along with Ponzi schemes and currency and gold bullion scams.

And just last week, FINRA, the financial industry’s self-regulation body, announced changes to the margin requirements for buying leveraged ETFs that go a long way towards destroying their usefulness. A FINRA spokesman called leveraged ETFs ”very complicated, with a high element of risk."


I guess it all depends on what you are used to. Leveraged ETFs are more volatile than their unleveraged counterparts, but that’s hardly a hidden gotcha. It’s kinda the whole point. Most are based on indexes that are less volatile than individual stocks. FINRA doesn’t seem to have a problem with individuals buying volatile biotech stocks and even stock options.

And leveraged ETFs are more complicated than unleveraged ETFs. But let’s get real folks, they are way less complicated than all sorts of things we think consumers can handle. Auto leases and cell phone contracts pop into my head as examples.

A leveraged ETF is designed to magnify the returns of an underlying instrument, usually an index. So, for example, the Rydex 2x S&P 500 (ticker RSU) is engineered to produce twice the S&P return on any given day. It does this by borrowing money, but the mechanics aren’t that vital. The important point is that it and it’s brethren do a pretty solid job of what they say they do, which is, I repeat for emphasis, deliver a stated multiple of an index return over a single day.

The problem is that, apparently, practically all individual investors, pundits, brokers, and regulators think that an ETF that matches twice the S&P each day ought to therefore match twice the index over longer periods too. But the math, and in this case I am referring to junior high school algebra, doesn’t work that way.

Let A and B be the returns for two consecutive days. Then the return for the two day period is:

r = ((1 + A)(1 + B)) –1 = A + B + AB

Got it? That wasn’t so hard. Now suppose we have a fund that gives us twice the return. What is its two day return?

r = ((1 + 2A)(1 + 2B)) – 1 = 2A + 2B + 4AB

That’s not twice what the unlevered version got you over two days. You will note that if A and B are relatively small, for example 1%, then the AB term is tiny and ignorable. If they are large, e.g. 10%, then AB starts to matter. Also note that if one of A or B is negative, then the AB term will be negative. This is why if you gain and then lose (or lose and then gain) 10% you wind up with 99% of what you started with.

All this is pretty obvious stuff to some of us. But I’ve searched the web and can’t find anywhere that explains what is nothing more than a common misunderstanding about math. A few places give a hypothetical example and others a real-life one, but nowhere is the general principle explained. And many of the media reports give no explanation at all, leaving the reader with the vague impression that something sinister is afoot with these evil sounding leveraged ETFs.

I’m not sure that the world needs leveraged ETFs, so I’m not particularly upset at the effort to run them out of town. But the core problem here is not that Wall Street is preying on naive investors, it’s that nobody seems willing or able to help those investors become less naive.

No Comments

  • By ryan, September 8, 2009 @ 1:13 pm

    What’s ironic is that I’m sure many of the advisers who would discourage an investor from using leveraged ETF’s would advise a different client to not pay off a home mortgage but rather invest the extra cash in the stock market.

    It’s still a leveraged investment, either way.

  • By Mike Piper, September 8, 2009 @ 1:24 pm

    This reminds me very much of a quote from a recent William Bernstein piece.

    “As Scott Burns explained to me years ago, fractions are a stretch for 90% of the population. The Discounted Dividend Model, or at least the Gordon Equation? Geometric versus arithmetic return? Standard deviation? Correlation, for God’s sake? Fuggedaboudit!”

    It’s much like people’s generally poor grasp of the whole “Roth vs. Traditional” question. There are some fundamental math skills that just aren’t there.

  • By JoeTaxpayer, September 8, 2009 @ 1:43 pm

    There’s a problem with leveraged ETFs, expecially the inverse flavor. I wrote about this in http://www.joetaxpayer.com/etfed/ and the follow on article http://www.joetaxpayer.com/an-etf-lawsuit/ in which I discuss a leveraged inverse ETF that returned barely 10% over a year when the underlying index was down 50%. Your math above acknowledges small tracking error, but not like this.
    I’ve not put as much time reviewing the positive trackers. I’m sure they are not quite as bad.

  • By Neil, September 8, 2009 @ 2:21 pm

    I have not done a lot of research on this, but I believe the problem with many leveraged ETFs is that they don’t do what they claim to over the long term. I’ve been told that short ETFs may have lost you money at this point even if you bought them when the market was much higher than its current levels.

  • By Eric, September 8, 2009 @ 4:11 pm


    It is entirely possible especially with the violent up and down movements over the last year. These ETFs are designed to track a single day’s movement. All it takes is one or two crazy swings and the tracking will be increased.

  • By TFB, September 8, 2009 @ 7:55 pm

    Algebra? Are you kidding? I’m waiting for the day the newspapers will include a fifth grade math formula in an article.

  • By Mark Wolfinger, September 8, 2009 @ 8:44 pm

    The average American investor is just too ignorant (or too lazy to make any effort to understand what he/she is buying).

    It may not be the government’s responsibility to protect the ignorant. But why allow them to buy into an investment that’s far worse than an available alternative.

    Unleveraged ETFs are available, and for a small additional commission, the investor can invest an equal amount of money, and buy an ETF that does not have a downwards bias in price.

    The managers of these leverages ETFs are INTENTIONALLY hurting their clients – even when the publish warnings. they are greedy and profiting by hurting the ignorant.

    These items should be banned. Period.

  • By JoeTaxpayer, September 8, 2009 @ 9:09 pm

    Eric – I appreciate that the math may work out that way. But that means that if I were clairvoyant and knew the market (a given index) would drop 50% 12 months hence, the leveraged inverse ETF is actually not the right product to use. I suppose it should only be used for very short term trading, if the divergence over time is that wide.

  • By Matt, September 9, 2009 @ 7:33 pm

    In fact, they do almost exactly what they claim.

    The vast majority, however, are based on the DAILY return – they state this quite clearly and obviously, and warn against holding beyond a DAY.

    For example: “Fund Summary: The investment seeks to replicate, net of expenses, 200% of the daily performance of the S&P 500 Index”

    If you’re holding the 2x DAILY etf for months or years, are you washing your floors with Windex? Or washing your hair with dishsoap?

  • By JoeTaxpayer, September 11, 2009 @ 12:07 am

    I wrote a spreadsheet to simulate the variation in a 1X vs 2X ETF. Using a RND function in excel, I looked at the difference over a 240 day period. I then looked at the ratio for each simulation, 2.00 would be ideal, but as you pointed out, not expected. I found over about 100 trials, a min of 1.3 max of 2.2 with the most common result between 1.65 and 1.75.
    This is a far cry from the .2 I cited in my example. I’d look forward to your comment, if it avoids references to cleaning products. I can follow math.

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