EQUITY MARKETS Leveraged ETFs Where is the Missing Performance? JULY 26, 2012 Richard Co Executive Director Equity Products 312-930-3227 Richard.co@cmegroup.com John W. Labuszewski Managing Director Research & Product Development 312-466-7469 jlab@cmegroup.com
We examine the underperformance typically associated with leveraged Exchange Traded Funds (ETFs) relative to the returns associated with the underlying index. We trace this phenomenon to rebalancing issues and suggest that stock index futures likewise offer leverage absent rebalancing issues or the attendant gamma losses. Leveraged Exchange Traded Funds (ETFs) were originally introduced in 2006 and have attracted much attention in recent years. The reasons are readily apparent. Leveraged ETFs provide investors a facile means by which to gain exposure to the portfolio underlying the ETF on a leveraged basis. 1 But the major criticism often leveled at leveraged ETFs is that they exhibit a tendency to underperform their respective indexes, after adjusting for leverage. This phenomenon may become acute during periods of high market volatility. This study traces this underperformance to the fact that leveraged ETFs must be rebalanced frequently in order to maintain the advertised leverage ratio. We suggest that stock index futures offer the benefits of leverage absent the need to rebalance or the so-called gamma losses often associated with leveraged ETFs. Daily Rebalancing A fund manager may realize a daily return equal to 100% of the returns associated with the Standard & Poor s (S&P 500) index by purchasing a portfolio that replicates the composition of the index utilizing 100% of assets under management (AUM). 2 Fund managers may replicate Index returns by holding stocks, stock index futures, equity swaps or some combination of these replicating assets. 1 Inverse ETFs provide an equally facile way for investors to short the market, as part of a hedging or speculative strategy. Inverse ETFs may be available on an unleveraged or on a leveraged basis. 2 While we reference the S&P 500 as the subject of our discussion, the same rationale would be applicable to any other index or portfolio inclusive of stocks, fixed income securities, commodities or other assets. Once established, no further adjustment of the portfolio s composition of replicating assets is necessitated unless the underlying index should be altered; or, fund investors should add or withdraw monies. Likewise, a fund manager may realize a daily return equal to 200% that of the index (or 2x exposure) by deploying leverage to accumulate twice as many stocks or other index replicating assets in the portfolio. But unless the Index value remains unchanged at the conclusion of any particular period, the portfolio will not reflect 200% of the Index holdings. Thus, unlike an unleveraged portfolio, the leveraged portfolio requires constant adjustment. This implies that managers of leveraged ETFs are faced with the necessity to rebalance on a periodic basis. If the Index advances over the course of a day, the portfolio will become under-leveraged. This is due to the fact that any increase in asset value accrues to the portfolio equity owners while the dollar value of debt undertaken to lever up the portfolio remains unchanged. This would necessitate the purchase of additional equities replicating the composition of the index, and taking on additional debt in the process, in order to maintain the 200% or 2x exposure. If the Index declines over the course of the day, the portfolio will become over-leveraged per the opposite dynamic. This would necessitate the liquidation of equities within the portfolio in order to maintain the 200% or 2x exposure. Market Advances Market Declines Buy replicating assets to maintain leverage ratio Liquidate replicating assets to maintain leverage ratio Leveraged ETFs normally aim to achieve the advertised leverage ratio on a daily basis. Thus, fund managers may rebalance the portfolio daily. But in so doing, the fund manager will encounter the risk associated with whipsaw markets. E.g., assume that the market is range-bound. The market advances and our portfolio manager buys additional replicating assets to reestablish the 2x leverage ratio. The subsequent day, the market 1 Stock Market Landscape July 26, 2012 CME GROUP
declines to the original level and our portfolio manager liquidates replicating assets to reestablish the 2x leverage ratio. In the process, our portfolio manager is whipsawed by buying high and selling low. The cumulative effect of whipsaw markets may detract from the value of the portfolio, resulting in returns that fall short of the target that the portfolio manager intends to achieve. The same dynamic may be at work for short or inverse ETFs as well. If the index declines, portfolio equity increases disproportionately, necessitating more shorting. These positions would be bought back if the market should subsequently advance. Thus, the daily rebalancing act compels fund manager constantly to chase their positions and possibly become subject to the risk of whipsaw markets. Note the prospectuses of leveraged ETFs typically purport to track daily returns and not necessarily compounded returns over extended periods. Simple Mathematical Argument A little rudimentary arithmetic offers some insight and perspective. Assume that we are holding the leveraged ETF for days. Further, we use to denote the desired leverage. Thus, an exposure of 200% may be represented as a beta of 2 or 2. We denote the underlying daily index performance as for the i th day. The value of the portfolio after N days may be expressed as follows. 1 This is derived by nothing more than compounding the daily returns of the index on N consecutive days. This equation may be recast in logarithmic terms as follows. exp ln 1 If we apply a 2 nd order Taylor series expansion and approximate the right-hand side of the equation, the value is approximated by the following formula. 3 1 exp 1 2 1 Where This expression is less daunting than it appears. represents the average daily return for the index during the period. The first half of the expression is no more than the compounded returns based on the average daily performance over the period. This compounded daily return is scaled by the second term that has a magnitude smaller than 1. This is where the under-performance may be observed. Note that is the sample variance of the daily return. The correction is a function of market volatility during the holding period. From this approximation, we easily may verify that during the course of a range-bound or sideways but nonetheless volatile holding period, i.e., 0, the value of the portfolio would be less than the initial value ( exp ) and would actually decline significantly. The severity of this decline is dependent upon the magnitude of realized variance of the underlying index and leverage deployed. Tracking Error The phenomenon described above is reminiscent of the balancing act that option traders face every day. Option traders who seek to carry a delta-neutral position by balancing options with offsetting positions in the underlying market are faced with the necessity of adjusting the offsetting position as the delta associated with their options fluctuates in response to market movements. In particular, a short delta-neutral option position is associated with negative gamma. This implies that losses may be proportional to the square of changes 3 This approximation is rather crude by design and there are several ways in which to improve upon the exactitude of the expression. But to the extent that we have already accomplished what we set out to demonstrate, we forego the additional steps required to tidy up any loose ends. 2 Stock Market Landscape July 26, 2012 CME GROUP
in the underlying price, offsetting the time decay of the option premium. Thus, we refer to this variance-related loss as the gamma loss. To verify the occurrence of such gamma losses, we endeavored to measure the degree to which the monthly total return (inclusive of price fluctuations plus dividends) of popular S&P 500 based ETFs deviate from the return that they are purported to track. We may refer to these comparisons as tracking error. Tracking errors may stem from multiple sources including gamma losses as well as other factors as follows. Market Price vs. NAV The market price of an ETF, which is fundamentally a function of the buy and sell order flow, may exhibit a disconnect from the Net Asset Value (NAV) or the value of replicating assets held in the trust. Creation Unit Imprecision The replicating assets held as creation units may not precisely reflect the composition and value of the underlying index. Distribution Patterns ETFs typically make distributions on a quarterly basis in March, June, September and December. This lumpy payment pattern may represent another source of tracking error between an ETF and the underlying index. Fees ETFs extract fees or expenses which are not reflected in the value of the underlying index. E.g., the SPDR S&P 500 ETF Trust charges 0.09% while the ProShares UltraShort ETF charges 0.89%. Thus, we compare the monthly return of the SPDR S&P 500 ETF Trust ( SPY ), a +1x to the monthly return of the S&P 500. Likewise we compare the monthly return of the ProShares Short S&P 500 ( SH ) ETF, a -1x product to the inverse of the S&P 500 s monthly return. Similarly, we compare the monthly return of the ProShares Ultra ( SSO ) ETF, a +2x product, to twice that of the S&P 500. Finally, we compare the monthly return of the ProShares UltraShort ETFs ( SDS ) ETF, a -2x product, to the inverse of twice the S&P 500 return. The tracking errors associated with the long and short non-leveraged ETFs averaged close to zero although there were some notable deviations. But the tracking errors associated with the long and short leveraged ETFs averaged almost a full half percentage point below the targeted index returns. We might generally attribute the discrepancies in tracking errors associated with the leveraged vs. non-leveraged ETFs to gamma losses. S&P 500 ETF Monthly Tracking Errors (August 2006-June 2012) SPDR SH SSO SDS Average -0.01% -0.05% -0.47% -0.49% Standard Deviation 0.18% 0.78% 0.82% 2.34% Maximum 0.66% 1.37% 1.20% 1.59% Minimum -0.50% -3.38% -3.13% -13.83% NOTES Total monthly returns calculated as function of price fluctuation plus receipt of dividends. Note that we observed some rather wide shortfalls from the anticipated returns were observed. The most dramatic of these shortfalls tended to occur during volatile market episodes such as those experienced at the height of the subprime mortgage crisis in 2008; and, in late 2011 in response to a flare-up in the ongoing European sovereign debt. Monthly Total Return 4% 2% 0% -2% -4% -6% -8% -10% -12% -14% Tracking Error of S&P 500 ETFs Aug-06 Feb-07 Aug-07 Feb-08 Aug-08 Feb-09 Aug-09 Feb-10 Aug-10 Feb-11 Aug-11 Feb-12 65% 55% 45% 35% 25% 15% 5% SSO SDS SPY SH VIX Gamma losses associated with the leveraged ETFs correlate closely with volatility in the S&P 500 as measured by the S&P 500 Volatility Index or VIX. S&P 500 Volatility Index 3 Stock Market Landscape July 26, 2012 CME GROUP
To verify that gamma loss is proportional to the square of beta in the leveraged portfolio, we might compare tracking errors in leveraged vs. unleveraged ETFs during periods of peak volatility. Such a comparison suggests that tracking errors associated with leveraged ETFs spotted roughly 4x as much as those associated with unleveraged ETFs. Thus, gamma losses generally scale as suggested by our derivation. Investment Implications These gamma losses are attributed to the fact that daily rebalancing is necessary to maintain the advertised risk exposure associated with leveraged ETFs, whether long or short (inverse) in nature. Gamma losses may be obscured in the short-term by directionally driven profits and losses and go unnoticed. But they can accumulate over time to become quite significant. Thus, as the holding period for one s leveraged investment grows longer, the choice of trading instrument becomes increasingly significant. The use of stock index futures as an alternative to leveraged ETFs represents a simple way of avoiding gamma losses. Note further that CME Group now offers futures based upon S&P Select Sector Indexes. Many of these indexes are supported by leveraged ETFs as well. These sector futures represent an effective way of replicating index performance on a leveraged basis either long or short with reduced tracking error relative to these leveraged ETFs. Copyright 2012 CME Group All Rights Reserved. Futures trading is not suitable for all investors, and involves the risk of loss. Futures are a leveraged investment, and because only a percentage of a contract s value is required to trade, it is possible to lose more than the amount of money deposited for a futures position. Therefore, traders should only use funds that they can afford to lose without affecting their lifestyles. And only a portion of those funds should be devoted to any one trade because they cannot expect to profit on every trade. All examples in this brochure are hypothetical situations, used for explanation purposes only, and should not be considered investment advice or the results of actual market experience. Swaps trading is not suitable for all investors, involves the risk of loss and should only be undertaken by investors who are ECPs within the meaning of section 1(a)12 of the Commodity Exchange Act. Swaps are a leveraged investment, and because only a percentage of a contract s value is required to trade, it is possible to lose more than the amount of money deposited for a swaps position. Therefore, traders should only use funds that they can afford to lose without affecting their lifestyles. And only a portion of those funds should be devoted to any one trade because they cannot expect to profit on every trade. CME Group is a trademark of CME Group Inc. The Globe logo, E-mini, Globex, CME and Chicago Mercantile Exchange are trademarks of Chicago Mercantile Exchange Inc. Chicago Board of Trade is a trademark of the Board of Trade of the City of Chicago, Inc. NYMEX is a trademark of the New York Mercantile Exchange, Inc. The information within this document has been compiled by CME Group for general purposes only and has not taken into account the specific situations of any recipients of the information. CME Group assumes no responsibility for any errors or omissions. Additionally, all examples contained herein are hypothetical situations, used for explanation purposes only, and should not be considered investment advice or the results of actual market experience. All matters pertaining to rules and specifications herein are made subject to and are superseded by official CME, NYMEX and CBOT rules. Current CME/CBOT/NYMEX rules should be consulted in all cases before taking any action. 4 Stock Market Landscape July 26, 2012 CME GROUP