A New Method to Measure the Performance of Leveraged Exchange‐Traded Funds

Published date01 November 2014
Date01 November 2014
The Financial Review 49 (2014) 735–763
A New Method to Measure the Performance
of Leveraged Exchange-Traded Funds
Narat Charupat
McMaster University
Peter Miu
McMaster University
We examine the effects of daily return compounding, financing costs, and management
factors on the performance of leveraged exchange-traded funds (LETFs) over variousholding
periods. We propose a new method to measure LETFs’ tracking errors that allows us to
disentangle these effects. Our results show that the compounding effect generally has more
influence on tracking errors than other factors, especially for long holding periods and in a
“sideways” market. The explicitcosts (i.e., the expense ratios) and other factors (e.g., financing
costs) can materially affect the performance of LETFs, especially for those with high leverage
ratios and bear funds.
Keywords: exchange-traded funds, leverage, tracking errors, regression analysis, bull funds,
bear funds
JEL Classifications: G10, G12, G23
Corresponding author: DeGroote School of Business, McMaster University, 1280 Main Street West,
Hamilton, Ontario L8S 4M4, Canada; Phone: (905) 525-9140, ext. 23987; Fax: (905) 521-8995;
E-mail: charupat@mcmaster.ca.
The authors thank the anonymous referee and the editor for their helpful suggestions. The authors also
thank Donghui Chen and YueZhang for research assistance. The financial support from the Social Science
and Humanities Research Council is gratefully acknowledged.
C2014 The Eastern Finance Association 735
736 N. Charupat and P.Miu/ The FinancialReview 49 (2014) 735–763
1. Introduction
A leveragedexchange-traded fund (LETF) is a publicly traded fund that promises
to provide daily returns that are in a multiple (positive or negative) of the returns on
an index. To meet that promise, the fund uses leverage, which is typically obtained
through derivatives such as futures contracts, forward contracts, and total-return
swaps. The amount of leverage is adjusted daily so that the proportional leverage
(and thus the multiple) remains constant from day to day.
In the U.S. market, the first LETF was introduced in 2006. By the end of 2012,
there were over 200 LETFs with total assets of approximately $30 billion. Their
underlying indices include stock indices, bonds, currencies, commodities, and real
estate. The available multiples are double leverage(+2x and 2x) and triple leverage
(+3x and 3x). There are also inverse ETFs, which provide daily returns equal to
the negative of the underlying index returns (i.e., multiple =−1).
LETFs are not for long-term, buy-and-hold investors,because the constant main-
taining of leverage ratios will cause LETFs’ long-term compounded return to deviate
from the multiple of the underlying index return over the same period. The magnitude
and the direction of the deviation depend on the length of the holding period and the
path that the underlying benchmark takes during that period. For a given holding
period, the higher the multiple (in absolute terms) or the more volatile the underlying
index returns, or both, the greater the chance that an LETF’s realized return will differ
from its stated multiple.
The performance of ETFs is measured by tracking error, commonly defined
as the deviation of the returns on net asset values (NAVs) from the returns on the
underlying indices. Conventionally,a fund’s tracking errors may be estimated by: (1)
calculating the standard deviation of the difference between the fund’s NAV returns
and the returns on its underlying index; and (2) regressing the fund’s NAV returns on
the underlying index’s returns. These approaches are commonly used in studies on
traditional (i.e., +1x) ETFs and index mutual funds (e.g., Frino and Gallagher, 2001;
Elton, Gruber, Comer and Li, 2002; Gastineau, 2004). However, these conventional
approaches can lead to ambiguous results when used with LETFs and inverse ETFs
(hereafter, collectively referred to as LETFs). This is because the tracking errors of
these funds are dictated not only by factors that are under the control of the fund
issuers (e.g., fees, expenses, replication techniques, transaction costs, and the accrual
of cash), but also by factors that are outside of their control (e.g., compounding effect
and financing costs).
It is important to understand how compounding effect, financing costs, and
management factors influence LETFs’ tracking errors. In this study, we analyze
these effects and propose a new method to measure tracking errors that explicitly
controls for the compounding effect. We then apply this method to a sample of
inverse, double- and triple-leveraged funds. We show that, depending on the return
paths of the underlying indices, the effect of compounding can constitute a very large
portion of the total tracking errors. By screening out the compounding effect, our

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