Tristan Yates and Lye Kok (IndexRoll) submit: The Constant Leverage Trap is a well-known problem in financial modeling. Attempting to maintain a constant leverage ratio in a portfolio over a long period of time will eventually lead to the portfolio selling off almost all of its assets in the worst of market conditions. This problem was largely academic until recently, when two companies, ProShares and Rydex launched a set of leveraged ETFs that seek to track double the return of the S&P 500 Index.
The leveraged ETFs are: ProShares Ultra QQQ ETF (NYSEARCA:QLD), ProShares Ultra S&P500 ETF (NYSEARCA:SSO), ProShares Ultra MidCap400 ETF (NYSEARCA:MVV), ProShares Ultra Dow30 ETF (NYSEARCA:DDM), ProShares Ultra Russell2000 ETF (NYSEARCA:UWM), ProShares Ultra SmallCap600 ETF (NYSEARCA:SAA), ProShares Ultra Russell1000 Value ETF (NYSEARCA:UVG), ProShares Ultra Russell1000 Growth ETF (NYSEARCA:UKF), ProShares Ultra Russell MidCap Value ETF (NYSEARCA:UVU), ProShares Ultra Russell MidCap Growth ETF (NYSEARCA:UKW), ProShares Ultra Russell2000 Value ETF (NYSEARCA:UVT), ProShares Ultra Russell2000 Growth ETF (NYSEARCA:UKK), ProShares Ultra Basic Materials ETF (NYSEARCA:UYM), ProShares Ultra Consumer Goods ETF (NYSEARCA:UGE), ProShares Ultra Consumer Services ETF (NYSEARCA:UCC), ProShares Ultra Financials ETF (NYSEARCA:UYG), ProShares Ultra Health Care ETF (NYSEARCA:RXL), ProShares Ultra Industrials ETF (NYSEARCA:UXI), ProShares Ultra Oil & Gas ETF (NYSEARCA:DIG), ProShares Ultra Real Estate ETF (NYSEARCA:URE), ProShares Ultra Semiconductors ETF (NYSEARCA:USD), ProShares Ultra Technology ETF (NYSEARCA:ROM), and the ProShares Ultra Utilities ETF (NYSEARCA:UPW).
The mechanics of maintaining constant is trivial. At the beginning of the market day, hold a portfolio of equal proportions equity and debt. At the end of the day, if the market has gone up, the fund will have more equity than debt, so it buys additional shares. If instead, the market went down, the fund sells shares. This is called daily rebalancing.
Intuition says that this is likely a bad investing strategy. Buying every time the market climbs and selling when it falls sounds like buying high and selling low. And backtesting using historical data confirms these suspicions.
Finding The Trap
A model was created to find the Constant Leverage Trap. Using historical pricing data from January 1993 to March 2007, a fund simulated buying and selling shares at the end of each day in order to maintain constant leverage. No interest is calculated at first – the object is simply to see the results of daily rebalancing.
In the simulation, the fund started with 10,000 shares of SPY in Jan 1993 and bought additional shares during the bull market of the 1990s, finally arriving at over 32,000 shares in Jan 2000. Then, during the downturn the fund has to start selling shares to maintain a constant leverage ratio, liquidating almost 16,000 shares during the bear market of the next three years. 2,400 shares were sold just in the market week after 9/11/2001.
An interesting finding is that while the Constant Leverage Trap did force the fund to sell huge amounts of shares during a downturn, it also prevents the fund from going down to zero. The fund will always have some shares left, even if it’s just a small fraction of the original total.
The most important question for a long-term investor is whether the constant leverage fund significantly beats the index. The answer is yes, to some extent, if you pick the right starting year. If you pick the wrong year, you have serious problems.
When interest payments were added to the model using a cost of debt of 5%, the fund still had to buy heavily during the run-up and then sell during the bear market, but also continually liquidate shares to pay interest. During a fourteen year period the fund beat the S&P 500 by 34%.
But this outperformance is largely a function of the starting year. A fund investor that bought at the beginning of 1993, 1994, 1995, or 2003 would have beat the index by about 30 points over the period. Unfortunately an investor that bought in 1998, 1999, 2000, or 2001 would have underperformed by 30%. And anyone that invested in the other years would have matched the index, give or take about ten percent.
And the volatility was very high. In the best year, the constant leverage fund gained 81% and in the worst year it lost 43%.
Purchase and Walk Away
Now this could be seen as a repudiation of leveraged investing – but that would be drawing the wrong conclusions.
If the fund simply never bought or sold any additional shares after the original 1993 investment, the investor would have 6% more money, and a lot less short-term gains, transactions, and a lot loss volatility. It’s clear that a reinvestment strategy based on maintaining constant leverage doesn’t add significant value – if anything it reduces it.
Of course, if a fund doesn’t buy any additional shares, the leverage will reduce over time. In the model the fund’s leverage fell from 2x to 1.2x over a fourteen-year period as the underlying assets appreciated. Still, this may be exactly what an investor wants as they get closer to retirement.
In order to show that it is possible to construct a simple reinvestment model that adds value, we then built a model in which a fund very slowly and steadily increases the number of index shares by about 3% a year, using simple dollar cost averaging to buy more shares when prices fall and fewer shares when prices rise.
This model allowed the fund to avoid accumulating as many shares during the upturn, and then to accelerate its purchases during the bear market. The leverage ratio, initially 2x, falls to 1.3x at the height of the bull market, and then rises to 1.8 at the end of the bear market. We take on more leverage as the market gets cheaper, which boosts our future returns.
Over a ten-year period, 1997 to 2006, $1 invested in the dollar cost averaging [DCA] leverage fund would be worth $2.47, as compared to $2.19 for the index fund, and $2.04 for the Constant Leverage Fund. Investments made in individual years perform well also, beating the index in ten of the fourteen years, but the advantages become more apparent over longer holding periods.
Avoiding Hari Kari
The most important benefit of a DCA Leverage fund is that it saves investors from financial suicide if they happen to invest in Jan 2000 at the top of the market. In the downturn, the Constant Leverage fund takes the worst possible action – it sells most of its shares at a loss. That means that it has a much smaller share base in the next upturn and can’t recover.
During the three bear years examined, 2000 to 2002, the index loses 33%, a DCA leverage fund loses 50%, and a Constant Leverage fund loses 68%. The index then recovers its losses over three years, a DCA leverage fund recovers over four years, and a Constant Leverage fund never recovers at all.
Note that I am not advocating this specific dollar cost averaging investing model for investors, but simply showing that it is possible to use leverage and simple regular reinvestment strategies to create value rather than destroy it like the Constant Leverage Trap does.
I understand why companies like ProShares and Ryder are maintaining constant leverage – because they want to market their portfolio in a specific way, and create a tool that investors can use for capturing daily appreciation. The risks of holding a constant leverage fund for longer periods are disclosed in the prospectuses, but I don’t believe that they have been adequately discussed by the management companies or by the financial media in general.
As of now, even though models clearly show that there are benefits to using leverage in index-based portfolios held for long periods of time, there is still no practical solution for investors. Currently, their only choices are to use margin, rolled Index Options, or rolled Index ETF LEAP call options. However, using margin creates margin call risk of course, and option mechanics are not generally well understood, making mistakes easy.
Perhaps a company will offer a leveraged fund or ETF at some point that does not use constant leverage, but instead uses a better re-investment solution such as dollar-cost averaging. If the fund also had the ability to borrow cheaply and could manage the leverage ratio well, it would provide considerable value to long-term investors.
[Note: The entire model with all of the prices, calculations, and findings used in this article can be downloaded.]