There's volatility, and then there's path dependency.
A few weeks ago, Brendan Conway and Barron's published an excellent reminder about how different the returns of leveraged ETFs can be compared with a simple multiple of the underlying index.
Conway pointed out that Mariana Bush and Daniel Brown of Wells Fargo had warned that levered and inverse funds may surprise holders by returning less—or more—than the 2x or 3x (or even -1x) holding-period return if held for longer than the reset period.
Here's Bush and Brown's punch line: "Too many users incorrectly assume that accurately guessing the direction of a geared ETP's underlying index is sufficient. It is not! Correctly guessing low enough volatility is necessary as well."
Mariana and Dan are correct, but I worry that they packed too much into the word "volatility."
No argument from me: Low volatility does yield the best results for levered and inverse funds, but classic volatility, the variation of daily returns, is not the only driver of returns for these funds.
Levered and inverse funds are "path dependent," which means the return investors receive depends on the exact price history of the index tracked. For leveraged funds, up Monday and down Tuesday is different from down Monday and up Tuesday, even if they wind up unchanged overall.
Volatility, or its more commonly cited cousin, the standard deviation of daily returns, measures the average daily movement in a data series.
Investors in nonpath-dependent funds can—and probably should—ignore day-to-day volatility, because all that affects them is the price they paid to get in, and the price they receive when they sell.
But path-dependent funds bear the mark of every step along the way.
The two indexes shown below have identical volatilities, but very different paths. Even though they both start the week at 100, and end at 110, index A had one large move, and then held steady the rest of the week, while index B rode ups and downs.
Index A and B have the same volatility—see volatility's cousin, standard deviation—despite A's four flat days. That's because index A's 10 percent move on Monday weighs heavily on its average deviation. Because of the way we calculate volatility, it took index B five days of 4-plus percent swings to match that one 10 percent day. Outliers, like a 10 percent move, weighly heavily on our volatility calculations, because we calculate volatility by finding the difference of each day's return from the mean, and then squaring that difference. The squaring amplifies the effect of outliers.
Maybe this isn't the best way to express volatility, but it is still the industry standard. Some might argue that index B looks more volatile than A, and that investor experience in B is more stressful. Would they say that if index A had dropped 10 percent in a single day?
Index A has a different path than index B, and this takes its toll on B's returns.
Table 2 illustrates the different prices for 3x daily levered funds tracking index A versus index B.