funds will have median returns less than a - 2.0x. Thus, only
with a correct market call over short time periods or during
low-volatility conditions will a 4.0x fund likely outperform its
lower leverage fund competitors.
In addition, this study demonstrates an alternative long-term
strategy for LETFs within a portfolio context. The benefit
of leverage is that a 3.0x LETF, for example, can attain
100-percent exposure to the market with only one-third of
an investor’s portfolio. The remainder can be invested in a
relatively safe bond portfolio counteracting declines in the
market. In effect, the LETF can act as a pseudo option or
futures position without the need for special accounts, concerns about expiring contracts, or the extreme risk associated
with an open futures position.
Within this framework, this study shows an actively traded
2.0x, 3.0x, or 4.0x can be used in combination with T-bills
to outperform the S&P 500 Index while reducing risk over
extended periods of time. The 3.0x LETF/T-bill combination
using 33 percent in the 3.0x LETF and 67 percent in T-bills
was the best performer for time horizons out to at least five
years. Thus, contrary to the consensus that these instruments
are for short-term trading only, LETFs can be used for
extended periods and even reduce risk.
For the 4.0x funds, returns from an individual or portfolio setting do not look as attractive for any extended holding period
in a normal market relative to LETFs with less leverage.
However, with enough trend and in low-volatility environments, a 4.0x will perform well. Except for the clairvoyant,
investors should direct this latest incarnation of LETFs toward
short-term trading strategies.
DATA AND METHODOLOGY
Daily return data from January 1926 to December 2016 were
retrieved from The Center for Research in Security Prices value-weighted index of the S&P 500 universe. To estimate the gamut
of possible LETF returns, daily data was resampled 10,000 times
to simulate possible future return sequences. Theoretical returns
for - 4.0x to 4.0x leverage ratios were derived assuming an
annual 1.0-percent expense ratio because LETFs have much
higher expense ratios than typical ETFs. 3 Because the new 4.0x
funds are based on the S&P 500 futures and not on the index
itself, there are a few differences between the proposed 4.0x
LETFs and others on the index. The main difference is most
LETFs magnify the total return on the underlying index including dividends. An investor in futures does not receive dividends.
Thus, the proposed 4.0x ForceShares and ProShares products
are not exactly equivalent to magnifying the underlying index.
The adjustment is detailed below.
The S&P 500 futures generally will be higher than the S&P
Index (contango) if interest rates exceed the dividend yield
where LRT is the return to the leveraged fund, XRT is the under-
lying index return, β is the daily leverage ratio, T is time in
days, µr is the mean daily return, and σr2 is the standard daily
population variance. 2 Equation ( 1) shows the realized leverage
is positively related to trend and negatively related to the vari-
= β +
LRT T (T– ;) – [ ; σ ] (β 2 – β) 2r 2r 2
= β +
LRT T (T– ;) – [ ; σ ] (β 2 – β) 2r 2r 2
* is negative, which is usually the
case, the realized leverage over time will be less than the daily
leverage. It should also be pointed out that the leverage over
time even for a - 1.0x inverse fund is subject to decay because
(β2 - β)/2 is 1.0 and not zero.
Equation ( 1) also shows why the introduction of 4.0x funds
will result in greater leverage decay by a magnitude. Any
decay realized by a 4.0x is substantially increased even relative
to a 3.0x because the 3.0x fund’s (β2 - β)/2 term is only 3 and
a 4.0x fund’s (β2 - β)/2 multiple is 6. For an inverse fund, the
- 4.0x fund has a multiple of 10, explaining why inverse funds
suffer from decay to a much greater extent than their bullish
counterparts. It also explains why so many inverse funds lost
money during the financial crisis despite the declining market.
This led to a variety of complaints at the time (Justice 2009;
Maxey 2009; Zwieg 2009). In addition, a decay multiple of 10 is
unlikely to perform well in even moderate volatility conditions.
With the introduction of 4.0x and - 4.0x funds, it is not clear
how quickly the leverage decay will counter the higher leverage
ratio even if the index increases or decreases as the investor
predicts. Although there can be a case for holding leverage
funds for extended periods of time (Trainor 2011b; Loehr and
Lamb 2013; DiLellio et al. 2014), is this still the case for a 4.0x?
At what point is leverage too high?
Leveraged funds are marketed as short-term trading vehicles,
but Guedj et al. (2010) suggest that up to 25 percent of investors hold these funds for more than a month and up to
8 percent hold them for more than a quarter. In addition, the
number of investment advisors using these funds in portfolio
construction is increasing, and it is likely the LETFs in these
accounts are being held for significant periods of time (Lau
2014). One only needs to read investment bulletin boards
to learn about individual investors holding these funds for
extended periods of time. Thus, realistic expectations of
long-term return dynamics are essential, especially because
expectations might have become exceedingly unrealistic based
on the ongoing low-volatility bull market.
This study shows how new 4.0x and - 4.0x funds are likely to
perform both individually and within a portfolio setting if and
when they are formally introduced in the market. Under
average volatility conditions, results show the higher decay
associated with a 4.0x leverage ratio results in median returns
basically equal to a 3.0x LETF within one month and returns
less than a 2.0x LETF in one year. For the inverse funds, even
when the market decreases over the year, both - 3.0x and - 4.0x