# Alpay Kaya, CFA

La vérité existe. On n'invente que le mensonge. —Braque (Truth exists. One only invents falsehood.)

# Leveraged ETF Mythology (Circa 2013)

Just as markets are positioned at the crossroads of mathematics and human behavior, they serve as a showcase of the interplay between objectivity and subjectivity. One popular way people display their flippant attitude towards objectivity is by proclaiming causal relationships without any accompanying verification (or any attempt at such). I am referring to a Wall Street Journal MarketWatch commentary (Thomas Kee; The Trading Deck, 29 November 2012) in which Leveraged ETF (LETF) decay is incorrectly attributed to 2 sources: ‘liquidity risk’ and ‘rollover risk’.

The author offers a few examples over a 2-year timeframe. As he did not specify dates or number of trading days (and his numbers seem to coincide with non-adjusted prices) the numbers shown below are my own calculations. As for the definition of the ideal LETF referenced in the tables, it assumes zero financing costs, zero management fee, zero transaction costs, and perfect tracking.

False Claim #1: Liquidity Risk   LETFs with a specific focus (e.g., single commodity, equity sector) suffer from manipulated prices due to the small market of assets with which to back the fund. The idea is that market makers manipulate prices, having predicted when & how portfolio managers will rebalance a fund’s assets. Since market makers are not running charities, the explanation is not outright nonsensical. Of course, that is a far cry from verification.

The author cited two financial ETFs, the +1x XLF and +2x UYG, as examples. Using adjusted prices, these funds’ growth factors over the 2 years (500 trading days) leading up to the article’s date (12/3/10 to 11/29/12) are shown below.

$\begin{array}{lc} \mbox{} & \mathtt{Price\ Ratios} \\[0.5ex] \mathtt{+1x\ XLF} & 1.073 \\ \mathtt{+2x\ UYG} & 1.055 \\ \mathtt{+2x\ LETF\ (Ideal)} & 0.998\end{array}$

The author claimed XLF was up 9%, but UYG was up only 11% (not the expected 18%). From the ideal LETF’s ratio, it is clear his expectation is incorrect. The case ‘liquidity risk’ has not been made, and the example does not explain decay.

As an example of a leveraged ETF with general focus (i.e., lacking liquidity risk) the +2x S&P 500 LETF SSO was given because its percent change over the same period was twice that of the S&P 500. This is a coincidence. Its use is an example of data mining with a sprinkling of confirmation bias.

False Claim #2: Rollover Risk   LETFs with higher gearing (e.g., 3x) decay due to excessive transaction costs because they are rebalanced “much more often” than a 2x ETF. This claim actually does border on being outright nonsensical as ETF sponsors claim a daily return objective regardless of leverage.

The author offers the +3x S&P 500 LETF UPRO as an example. The price ratios are calculated using adjusted prices over the same 500 trading days as above.

$\begin{array}{lc} \mbox{} & \mathtt{Price\ Ratios} \\[0.5ex] \mathtt{S\& P\ 500} & 1.156 \\ \mathtt{+3x\ UPRO} & 1.374 \\ \mathtt{+3x\ LETF\ (Ideal)} & 1.251\end{array}$

Is the ideal LETF subject to ‘rollover risk’. . . in the absence of transaction costs? Other than for a single day, no one should expect the percent change of a leveraged ETF’s price to be that of the index times leverage.

ASIDE  The price ratios in the tables bring up another question… how could a leveraged ETF outperform an ideal version? They do not exactly satisfy the stated daily return objective every day. Over the period in question, UPRO’s average daily leverage was slightly greater on days the S&P 500 was up than on days it was down (3.36 vs. 3.12). The same is true if the leverage average is weighted by the percent change in the index’s price (2.99 on up days vs. 2.95 on down days).

Claims should be substantiated in an objective manner when possible and qualified as subjective when objective analysis is not possible. It goes without saying that the litmus test, “does that sound like it could make sense,” does not serve to satisfy the former.