Regulators Finally Urge Caution on Leveraged Funds

Headline: FINRA Urges Caution on Leveraged Funds

Subhead: The Perils of Holding for More Than a Day

So FINRA has finally decided to warn brokers to warn their customers about leveraged ETFs. I covered this subject a long time ago. Back then, I noted that the math will never add up. It can’t. For these funds to work as people expect them beyond a day, the leverage would have to be some multiple of the logarithm of the price change, not a multiple of the percent price change. It’s a subtle difference, but over a period of more than a day, it makes a gigantic impact.

And that’s the key: “more than a day”. When I’ve written about these trading vehicles before, I’ve gotten comments like, “the users of these products should know that they don’t work as expected when the time frame is more than a day.” The thing is, as the Wall Street Journal noted, the purveyors of these leveraged funds claim that ”such funds are suitable for investors to use for longer than a day to pursue a variety of strategies to limit risk or pursue returns.” That’s confirmed when you look at the prospectus (pdf file) of these products (page 10) where you’ll see a “simulation” performance chart showing how the leveraged fund would have performed in an up market that lasted a year, and a down market that also lasted a year. In those simulations, the funds performed almost exactly 2-to-1 over the year. A reasonable person looking at that graph and those numbers would logically conclude that, even though the objective states that the correlation is limited to just one day, the information on page 10 of the prospectus implies that the 2-to-1 tracking lasts well beyond just a single day.

One other important point about this: ProShares tries to explain away the problem of tracking error as being caused by volatility’s impact on compounding. While that is true to a certain extent, this explanation reminds me of a magic act where the magician tries to get you to look away from where the real action is taking place. What I mean by that is, if the fund’s objective was different, there wouldn’t be this “volatility” problem. That is, volatility isn’t the problem. Instead, the flaw is the fund’s objective.

Remember, I said that for these funds to work as expected beyond a day, the objective would need to be based on the logarithm of the price change, not the percent. Here’s an extreme example (not so extreme if you were trading financials in late-2008): On Day 1, you have an index at 100. On Day 2, it drops -20% to 80. On Day 3, it rises 25%, back to 100.

Now let’s look at an ETF that moves double those percent changes. On Day 1, the ETF is at 100. On Day 2, it drops -40% (-20% x 2) to 60. On Day 3, it rises 50% (25% x 2) to 90. The daily tracking worked precisely as advertised with no volatility errors or any other problem. But the ETF is down -10%. In this instance, the fund achieved its objective perfectly, yet it still lost a lot of money.

The reason it still lost money is because it takes a 66-2/3% gain to overcome a 40% loss. That 50% gain is simply insufficient. That’s the problem!!!

Now I’m not going to get into the math of the logarithmic solution, at least not in this post. Let me just say this: as long as the objective of these funds is based on multiples of percentages, then they will always have tracking problems lasting more than a day.

UPDATE: You asked for it. Printout of Excel showing the math (pdf file).

Comments

[AndrewBaker:]

This is one very good example of why people should have learnt their math at school: calculators can give you an answer when you plug in the data, but you've really got to know the math if you want to play with these things.

Having said that, I entered a long position on FAZ last week, intending to hold for a while, and I intend to keep holding it a while longer. This is because I believe that the financials are way overpriced, and that the ramping that has been done over the past two months cannot go on that much longer.

Markets can be unreasonable for longer than I can be solvent though, so let's see if I get shaken out before I reap my profits.

Jun 24 11:52 AM