Thursday, July 28, 2011

How Leveraged ETFs Lose Money

Leveraged ETFs are designed to return double or triple the return of an index each day, but they come with disclaimers warning that they won’t double or triple returns over longer periods of time due to a mysterious compounding effect. I’ve come up with a more concrete explanation that is hopefully more understandable.

An example of a leveraged ETF is the Horizons BetaPro S&P/TSX 60 Bull ETF (ticker: HXU). If the TSX 60 goes up 1% on a given day, HXU goes up 2%. The confusing part is that if the TSX 60 goes up 10% in a year, HXU doesn’t go up 20% that year.

A partial reason is the management fees charged to run HXD, but this doesn’t fully explain the seemingly missing returns. To understand what is going on, imagine a volatile 2 days where the TSX 60 goes up 10% then goes down 10%. Let’s track a $100 investment in the TSX 60 for the 2 days:

TSX 60: Start: $100, after up day: $110, after down day: $99

So, by the magic of compounding we lost a dollar. Here is the unsatisfying explanation of why things are worse than expected for our $100 investment in HXU:

HXU: Start: $100, after up day: $120, after down day: $96

For some reason we’ve lost $4. But it seems like we should only have lost $2 because HXU is designed to double the TSX 60 return. Just imagine what it would be like for a 10x leveraged ETF: our money doubles the first day and then we lose it all the second day!

To understand why the HXU losses are larger than we expected, let’s look in more detail at the holdings of HXU. To double the return of the TSX 60 with a $100 investment, HXU would have to borrow $100 so that it can hold $200 worth of TSX 60.

After the up day, HXU would hold $220 worth of TSX 60 and after accounting for the borrowed $100, we have $120 net. However, we’re supposed to be leveraged 2:1. HXU has to borrow another $20 to buy more TSX 60 so that it holds $240 worth of TSX 60 and owes $120.

After the down day, the TSX 60 investment drops by $24 to $216. HXU owes $120 leaving a new net value of $96. To get back to 2:1 leverage, HXU must sell $24 worth of TSX 60 and repay part of the loan leaving it with $192 of TSX 60 and a loan of $96.

After each up day, HXU must buy stock and after each down day it must sell stock. If this sounds like a buy high and sell low strategy, you’re right. The actual mechanism leveraged ETFs use to get exposure to an index may be more complex and make use of derivatives, but this doesn’t change the fundamental problem of buying high and selling low. Note that this explanation didn’t involve MERs, trading costs, or borrowing costs. These things only add to the drag on returns.

Of course, the TSX 60 doesn’t usually swing up and down by 10% each day. So the losses due to volatility are smaller than this example each day, but they add up over the course of a year. Over a long period of time, the HXU return will be significantly less than double the TSX 60 return.


  1. Thank you.

    The warnings are everywhere, but are totally ignored.

    I'm hoping your careful explanation gets through to the masses who own these vehicles.

  2. @Mark: I'll be happy if this explanation helps just one person (other than me).

  3. Nice clear explanation. I recently corresponded with an investor who believed that a 2x leveraged ETF would be a great buy-and-hold investment for a young person, because it would provide double the return of the market. Even after I explained the concept you outline here, he still thought it was the same as simply borrowing to invest. The daily reset is what people trip over.

  4. "HXU: Start: $100, after up day: $120, after down day: $96"

    I don't understand why you say we are missing $4 here. Can't this just be explained by "the magic of compounding" again? i.e.

    HXU up 20%: $100 x 1.20 = $120
    HXU down 20%: $120 x 0.80 = $96

  5. @Anonymous: The mysterious part is, why do we get 4x the losses if we're only 2x leveraged?

  6. @Anonymous and @Patrick: It's a matter of taste whether the compounding explanation is ssatisfying. It works for me with my math background because I know that compounding losses should grow as the square of the leverage, but I've found this explanation doesn't resonate with most people. I'm hoping the "buy high, sell low" explanation drives the point home better for most readers. Patrick captured the nature of people's expectations nicely.

  7. Excellent post. You clarified some long-standing curiosities I've had about these types of investment vehicles.

    My overall investment strategy (and personal investment policy) forces me to stay clear for the most part with these types of ETFs.

    With that being said however, I do have a 'discetionary' portion that I allocate to more exotic plays.

    I recently purchased a small position in Horizons Beta Pro Gold Bear (HGD).

    I find your findings to be interesting as it relates to high and low % increases in the markets and how they don't apply proportionately to the ETF's direction in unit price.

  8. @Wealthy Canadian: Thanks for the kind words. I get ideas about the direction of investments like gold as well, but I no longer act on them. Good luck.

  9. Michael, thank you for the explanation.
    I had an argument with a friend who read your post and from "Over a long period of time, the HXU return will be significantly less than double the TSX 60 return" derived that you expect HXU to outperform TSX though not by 2x. That's not what I concluded from your explanations.
    Please set the record straight.

    1. Hi AnatoliN,

      I definitely didn't intend to imply that HXU would beat the TSX 60. It might do so, but I was just addressing the misconception that it should double the TSX 60.

      Let me venture into mathland for a moment. If we assume the TSX 60 will have 7% compound average returns with 20% standard deviation, then the arithmetic average return is about 9% (the gap is roughly half the square of the standard deviation or about (1/2)(20%)^2 = 2%). For the 2X version, the arithmetic average return is 18%, and the standard deviation is 40%. The compound average return works out to 10%. Then we have to subtract HXU costs. Based on these assumptions, HXU might perform better than the TSX 60. However, we know that stock market returns are wilder than the lognormal distribution the above reasoning is based on. So, we can't be sure of how HXU will perform.

    2. Hello Michael, I've been discussing this with AN above as I made a fairly simple excel model that instead of doing the math you describe just picks two random dates for when you enter and exit the market and calculates performance of a index ETF vs HXU (and HQU) based on daily paid MER & daily value recalculation (to account for the daily re-balance).
      I then run the model a few thousand times (keeping the dates random) and look at results. On average I get a higher annual return with HXU than with the unleveraged ETF based on historical TSX data.
      I understand you reasoning about it not being as good as double the index, but it seems to be outperforming the index on average and in the majority of the thousands of simulations I run. It's more volatile, but long term performance seems better. Where is my mistake? (Is there one?)

    3. Unknown,

      I don't think you've necessarily made a mistake. The 2X ETF could easily outperform the TSX 60 over a given period of time. It might even outperform over most periods of time. It will tend to lose during periods of high volatility.

    4. Sorry, I thought my last comment didn't post. Thus a repeat of some information in the new comment.
      Reading your posts it seems like you advise against leveraged stocks like HXU. If you concur that it's possible for it to outperform index funds over most periods of time, why advise against it?

      P.S. I really appreciate your insight and spending time giving advice to random people on the internet.

    5. Unknown,

      I'm glad you appreciate my insights, but please understand that I don't give advice on my blog; I provide information for others so they can think for themselves.

      I wouldn't own leveraged ETFs myself. Let's imagine a wild scenario where stocks drop 40% one day and return to their previous level the next day (a 67% increase). An index owner can sleep through this without losing anything. The 2X leveraged investor would lose 53% of his investment (down 80%, and then up 133%). I use this extreme example to illustrate how a period of unusually high volatility can punish 2X ETFs. Less extreme cases wouldn't be as bad, but they could still be bad.