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

• Published date: 01 November 2014
• Date: 01 November 2014
• DOI: http://doi.org/10.1111/fire.12055

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

Abstract

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.

C2014 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