The Dynamics of Leveraged and Inver
Exchange-Traded Funds
Minder Cheng and Ananth Madhavan
Barclays Global Investors
May9,2009
Abstract
Leveraged and inver Exchange-Traded Funds(ETFs)have attracted significant asts
lately.Unlike traditional ETFs,the funds have“leverage”explicitly embedded as part
of their product design.While the funds are primarily ud by short-term traders,they
are gaining popularity with individual investors placing leveraged bets or hedging their
portfolios.The structure of the funds,however,creates both intended and unintended
characteristics that are not en in traditional ETFs.This note provides a unified
framework to better understand the underlying dynamics of leveraged and inver ETFs,
their impact on market volatility and liquidity,unusual features of their product design,
and questions of investor suitability.We show that the daily re-leveraging of the funds
can exacerbate volatility towards the clo.We also show that the gross return of a
leveraged or inver ETF has an embedded path-dependent option that under certain
conditions can lead to value destruction for a buy-and-hold investor.The unsuitability
of the products for longer-term investors is reinforced by the drag on returns from
high transaction costs and tax inefficiency.†
1Introduction
Leveraged and inver Exchange-Traded Funds(ETFs)provide leveraged long or short exposure to t
he daily return of various indexes,ctors,and ast class.The funds have“leverage”explicitly embedded as part of their product design.The category has exploded since thefirst products were introduced in2006,especially in volatile ctors such as Financials,Real Estate,and Energy.As of end-January2009,there are now over106 leveraged and inver ETFs in the US alone with Asts Under Management(AUM)of about$22billion.1
†The views expresd here are tho of the authors alone and not necessarily tho of Barclays Global Investors,its officers or directors.This note is intended to stimulate further rearch and is not a recom-mendation of any particular curities or investment strategy.We thank Mark Coppejans,Matt Goff,Allan Lane,Hayne Leland,J.Parsons,Heather Pelant,Ira Shapiro,Mike Sobel,Richard Tsai and an anonymous referee for their helpful comments.
c 2009,Barclays Global Investors.All rights rerved.
1Thisfigure does not include leveraged mutual funds that have the same characteristics as leveraged ETFs except for the fact that they are not traded intradaily.
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The space now compris leveraged,inver,and leveraged inver ETFs offering2×or 3×long exposure or short exposure of−1×,−2×,or−3×the underlying index returns.The most recent products authorized by the US Securities and Exchange Commission(SEC)offer the highest leverage factors.However,the bulk of AUM remains in2×leveraged products. Coverage has also expanded beyond equities and includes commodities,fixed income and foreign exchange.There is strong growth in this space outside the US as well.In addition, option contracts on leveraged ETFs have also gained in popularity.Leveraged and inver mutual funds analogous to ETFs have also grown in popularity.Other than the fact that they offer investors liquidity at only one point in the day,the structure of the products is identical to leveraged and inver ETFs and hence our analysis is fully applicable to the funds too.
橙匕首Several factors explain the attraction of leveraged and inver ETFs.First,the funds offer short-term traders and hedge funds a structured product to express their directional views regarding a wide variety of equity indexes and ctors.Second,as investors can obtain levered exposure within the product,they need not rely on increasingly scarce outside capital or the u of derivatives,swaps,options,futures,or trading on margin.Third, individual investors–attracted by convenience and limited liability nature of the products –increasingly u them to place longer-term leveraged bets or to hedge their portfolios.
The structure of the funds,however,creates both intended and unintended character-istics.Indeed,despite their popularity,many of the features of the funds are not fully understood,even among professional ast managers and traders.This paper provides a unified framework to better understand some key aspects of the leveraged and inver ETFs,including their underlying dynamics,unusual features of their product design,their impact onfinancial market microstructure,and questions of investor suitability.
Specifically,leveraged ETFs must re-balance their exposures on a daily basis to produce the promid leveraged returns.What may em counterintuitive is that irrespective of whether the ETFs are leveraged,inver or leveraged inver,their re-balancing activity is always in the same direction as the underlying index’s daily performance.The hedging flows from equivalent long and short leveraged ETFs thus do not“offt”each other.The magnitude of the potential impact is proportional to the amount of asts gathered by the ETFs,the leveraged multiple promid,and the underlying index’s daily returns. The impact is particularly significant for inver ETFs.For example,a double-inver ETF promising−2×the index return requires a hedge equal to6×the day’s change in the fund’s Net Ast Value(NAV),whereas a double-leveraged ETF requires only2×the day’s change. This daily re-leveraging has profound microstructure effects,exacerbating the volatility of the underlying index and the curities comprising the index.
While a leveraged or inver ETF replicates a multiple of the underlying index’s return on a daily basis,the gross return of the funds over afinite time period can be shown to have an embedded path-dependent option on the underlying index.We show that leveraged and inver ETFs are not suitable for buy-and-hold investors becau under certain circum-stances the long-run returns can be significantly below that of the appropriately levered underlying index.This is particularly true for volatile indexes and for inver ETFs.The unsuitability of the products for longer-term investors is reinforced by tax inefficiency and the cumulative drag on returns from transaction costs related to daily re-balancing activity.
The paper proceeds as follows:Section2shows how leveraged and inver ETF returns
are related to tho of the underlying index and provides an overview of the mechanics of the implied hedging demands resulting from the daily re-leveraging of the products;Section 3explains the microstructure implications and resulting return drag from trading costs associated with hedging activity;Section4analyzes the longer-term return characteristics of the products and the value of the embedded option within;and Section5summarizes our results and discuss their implications for public policy.
2The Mechanics of Leveraged Returns
2.1Producing Leveraged Returns
As leveraged returns cannot be created out of thin air,leveraged and inver ETFs gen-erally rely on the usage of total return swaps to produce returns that are a multiple of the underlying index returns.Futures contracts can also be ud in addition to,or instead of,total return swaps.However,given their exchange-impod standardized specification (to facilitate exchange-bad trading and clearing),futures are not as customizable as total return swaps and are more limited in terms of index reprentation.In addition,basis risk is more significant with the futures than with total return swaps.2
Leveraged returns also can be produced by trading in physicals on margin.In other words,by borrowing the required capital in excess of its AUM,a leveraged ETF can invest in a properly levered position of the curities comprising the ETF’s index benchmark.A negative implication of such an implementation strategy is that thefinancing cost will create a drag on the fund’s performance with respect to its promid leveraged return.On the other hand,an inver or leveraged inver ETF can short the curities comprising the ETF’s index benchmark and accrue interest income.Interestingly,a new breed of leveraged and inver ETFs has recently emerged that are managed against customized index benchmarks. The benchmarks explicitly incorporate thefinanci
麦田里的守望者ng cost(for leveraged ETFs)or accrued interest(for inver and leveraged inver ETFs)in index construction.Conquently,financing cost and accrued interest will not appear as a deviation against the funds’index benchmark.3Throughout this paper,we will assume that leveraged and inver ETFs rely on total return swaps to produce the promid leveraged returns.4Ourfindings remain unchanged regardless of how leveraged returns are produced,whether by trading in physicals on margin,equity linked notes,futures or other derivatives besides total return swaps.
Unlike traditional ETFs,leveraged and inver ETFs can be viewed as pre-packaged margin products,albeit without any restrictions on margin eligibility.It is also worth noting that creations and redemptions for leveraged and inver ETFs are in cash,while for traditional ETFs this is typically an“in-kind”or basket transfer.
2Basis risk refers to the risk associated with imperfect hedging,possibly arising from the differences in price,or a mismatch in sale and expiration dates,between the ast to be hedged and the corresponding derivative.
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3See,for example,Dow Jones STOXX Index Guide(2009).This structure is more common in Europe.
4In addition to swaps,leveraged funds’asts typically include a pool of futures contracts to manage l
iquidity demands and reduce transaction costs.Some long leveraged funds listed in the US are guided by a no-action letter from the SEC that stipulates a ,80%or more)of asts should be in the underlying.However,this does not apply to the inver funds.关于拜年的作文
2.2Conceptual Framework
We turn now to the development of a unified conceptual framework to analyze inver and leveraged ETFs.We will utilize a continuous time framework.All extant leveraged and inver ETFs promi to deliver a multiple of its underlying benchmark’s daily returns,so we will focus on the dynamics of the index and of the corresponding leveraged and inver ETFs over a discrete number of trading days indexed by n where n=0,1,2,...,N.Let t n reprent the calendar time of day n,measured as a real number(in years)from day0. We assume t0=0initially,a convenient normalization.Note the frequency of n does not have to be daily.If there are leveraged or inver ETFs designed to produce a multiple of the underlying benchmark’s return over a different ,hourly,weekly,monthly, quarterly,etc.),we can redefine n accordingly without any loss of generality.
Let S t reprent the index level which a leveraged or inver ETF references as its underlying benc
hmark at calendar time t.Later,in ction4we will explicitly describe the continuous time process underlying the evolution of the index level,but for now let r t
n−1,t n reprent the return of the underlying index from t n−1to t n,where
兼职创业项目r t
n−1,t n =
S t
n
S t
n−1
−1(1)
We will assume there are no dividends throughout to focus on the price and return dynamics without any loss of generality.Let x reprent the leveraged multiple of a leveraged or inver ETF.Therefore
x=−2,-1,2and3correspond to double-inver,inver,double-leveraged and triple-leveraged ETFs.
2.3Return Divergence and Path Dependency
It will become clear later that the exposures of total return swaps underpinning leveraged and inver ETFs need to be re-balanced or re-t daily in order to produce the promid leveraged returns.In effect,the funds are designed to replicate a multiple of the underlying index’s return on a daily basis.The compounding of the daily leveraged moves can result in longer-term returns,as expresd by:
ΠN n=1(1+x r t
n−1,t n
)(2) that have a very different relationship to the longer-term returns of the underlying index leveraged statically,as given by:
(1+x r t
一本正经造句0,t N
)(3) We can u a double-leveraged ETF(x=2)with an initial NAV of$100as an example.It tracks an index that starts at100,falls10%one day and then goes up10%the subquent day.Over the two-day period,the index declines by-1%(down to90,and then climbing to99).While an investor might expect the leveraged fund to decline by twice as much, or-2%,over the two-day period,it actually declines further,by-4%.Why?Doubling the index’s10%fall on thefirst day pushes the fund’s NAV to$80.The next day,the fund’s NAV climbs to$96upon doubling the index’s10%gain.This example illustrates the path dependency of leveraged ETF returns,a topic we return to more formally when we model the continuous time evolution of ast prices in ction4.
Figure1:DUG versus DIG(March2-6,2009)
Figure2:DUG versus DIG(September2008-March2009)
2.3.1Example:DUG and DIG
完怎么写Real world examples of the effects noted above–and the confusion they cau among retail investors–are not difficult tofind.The relation between short-and long-run performance of leveraged ETFs is well illustrated in the ca of the−2×ProShares UltraShort Oil& Gas(DUG)and its2×long ProShares counterpart(DIG)that track the daily performance of the Dow Jones US Oil&Gas index.As shown in Figure1,the funds are mirror images of each other over short periods of time,in this ca a few trading days in March.Over longer periods,however,the performance is materially different as s
hown in the six month period in Figure2.Indeed between September of2008and February of2009,both ETFs were down substantially.The examples illustrate the path-dependency highlighted in the analysis.
2.4Re-balancing and Hedging Demands
The re-balancing of inver and leveraged funds implies certain hedging demands.Since extant funds promi a multiple of the day’s return,it makes n to focus on end-of-day hedging demands.One benefit of modeling returns in continuous time,however,is that our analysis generalizes to any arbitrary re-balancing interval.Indeed,there has been recent discussion of new leveraged funds that track an index on a monthly versus daily basis.
