Leveraged ETFs: A Value Destruction Trap?

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 (QLD), ProShares Ultra S&P500 ETF (SSO), ProShares Ultra MidCap400 ETF (MVV), ProShares Ultra Dow30 ETF (DDM), ProShares Ultra Russell2000 ETF (UWM), ProShares Ultra SmallCap600 ETF (SAA), ProShares Ultra Russell1000 Value ETF (UVG), ProShares Ultra Russell1000 Growth ETF (UKF), ProShares Ultra Russell MidCap Value ETF (UVU), ProShares Ultra Russell MidCap Growth ETF (UKW), ProShares Ultra Russell2000 Value ETF (UVT), ProShares Ultra Russell2000 Growth ETF (UKK), ProShares Ultra Basic Materials ETF (UYM), ProShares Ultra Consumer Goods ETF (UGE), ProShares Ultra Consumer Services ETF (UCC), ProShares Ultra Financials ETF (UYG), ProShares Ultra Health Care ETF (RXL), ProShares Ultra Industrials ETF (UXI), ProShares Ultra Oil & Gas ETF (DIG), ProShares Ultra Real Estate ETF (URE), ProShares Ultra Semiconductors ETF (USD), ProShares Ultra Technology ETF (ROM), and the ProShares Ultra Utilities ETF (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.

Performance

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.

Intelligent Re-investing

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.

Commentary

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.]

Comments

[David Jackson]

Fascinating. Question for you, Tristan: If an investor is looking for a bearish strategy, expecting an impending downturn in the market, which is better: shorting a leveraged Rydex ETF, buying a Rydex leveraged short ETF ("UltraShort"... or shorting a simple ETF?

[Tristan Yates]

A reader just let me know about an older ProShares mutual fund that tracked the NASDAQ with constant leverage.
The ticker is UOPIX, and the long-term chart is pretty scary and illustrates the constant leverage trap very well. And if you're thinking of profiting from the constant value trap by shorting the leveraged long, the chart shows that it would likely be successful eventually, but it that it could be a very wild ride.

As for David's brain teaser - is it better to be long the leveraged short or short the leveraged long? Well, you could go quadruple short if you buy the leveraged short on 50% margin. How does that sound?

[David Jackson]

Surely if you buy the leveraged short ETF then you'll get caught in the constant leverage trap that you describe. So it's better to short the leveraged long ETF, no? That way the constant leverage trap works in your favor.

[gparkanyi]

Hi Tristan,

Thanks for commenting on my blog at stockadventures.wordpr.../ .

I will have to double-check how these ETFs are actually invested, but my suspicion is that they rely heavily on index futures. If this is the case, then most of the assets are ostensibly invested in T-Bills - used as margin for the futures, with enough index futures purchased to mimic the 2X movement of the index. A 2:1 leverage can be maintained with relatively minor adjustments to the weighting of the index futures being used (the maximum leverage of these contracts can go to 50:1 or more - depending on the prevailing futures exchange margin requirements - so 2:1 is very conservative for index futures.)

The T-bills will generate income, so I doubt there is a net interest "cost-of-money&qu... Where it gets interesting is what happens when the index drops by 50%? The 2:1 leverage will in theory cause the capital to wiped out.

Either way, you can monitor the net asset value of these ETFs on a daily basis. If the market value begins to adversely diverge from the net asset value, then that would be your warning flag to get out. The net asset value should track %-wise the daily movement of the underlying index (2X if it is leveraged).

This may not apply to leveraged ETFs that could not take advantage of index futures. The dynamic then would be closer to what you have described, if the buying and selling of shares is required.

Cheers,
Allocator

[Tristan Yates]

Thanks for your comment. When you review the prospectus of one of these funds it mentions that a +10% daily rise in the fund followed by a -10% drop will result in a -4% total drop rather than -1% if you owned the index. That validates the share buying/selling computations that we used in the model.

I agree with you that they most likely do use a combination of index futures and T-bills, but when the futures go up, your leverage ratio will go down and when the futures go down, your leverage ratio will go back up, and you're still stuck rebalancing - either buying more futures or selling more futures. The effect is the same.

However, you're correct that we don't know the exact cost of debt. We just used the broker rate of options, which is about 5% right now, and yes, having money in T-bills could make that cheaper. But there is also high expense ratio too that we didn't model.

Anyway, check out the UOPIX chart also and see what you think.

[beidlerp]

I find this article very interesting. It sounds to me as if one would NOT want to use leveraged ETFs in a long-term buy-and-hold portfolio because of the significant down-side risk. Rather, these ETFs would be used for short-term plays. You'd want to wait for, say, a February 28th, buy in, and look for a good time to get out. Am I wrong?

Question: Let's say you feel good about the market on February 28th--you know it's coming back You buy 100 QLD or something, and lets say the index is back up to record levels 2 months later. Index up 10%, QLD up (say) 18%. You expect either a sloppy market or another correction. Do you sell and go into an index, or do you buy the double short nasdaq fund?

[rkaydanian]

Tristan, I like to thank you for the article, you explained the problem that we will face with these ETF's clearly and you offered what could be a solution by DCA 3% annually and I know 3% that you mentioned is not a magic number. Since these funds buy more shares as the underlying index trades higher and sell shares as it drops what do you think of using Bollinger bands and rebalance your position as it hits the upper and lower bands. Technically this will force you to sell when the price trades higher rapidly when it hits the upper band and buy more shares when prices decline rapidly when it hits the lower band.
Thanks in advance for your thoughts. Rob

[mg]

great article - however the historical results don't seem to bear this out. I checked closing prices daily of SSO since incepton vs. the SPX and calculated the % gains/loses from varying start and end dates corresponding to highs - to -lows, lows - to highs, and many random dates to others. WHat I found is that the SSO ETF does match the SPX indes with a return of approximately 2:1 . ( the worst variance on the low side was 1.79 / 1 and the biggest variance on the high side was 2.3/1) . SO my question is this - where is the value destruction ? From the historical prices these funds seem to provide roughly 2/1 leverage at all times. can you provide a specific ETF that demonstrates this trap?

[pdsro]

Tristan, im very thankful about your article. But im wondering how the leverage etf work by using this derivatives. Excatly how they can double the index using a future contract or a swap agreement?

[James Tobin Student]

The leveraged DCA approach exposes the investor to portfolio ruin much more significantly than the constant leverage approach. suppose the markets drop 10% per day for 7 days (unlikely, but it makes the point). The DCA approach results in total portfolio loss, whereas the constant leverage approach results in a damaged, but in tact, portfolio. the investor must determine if the increased risk of portfolio ruin is worth the tradeoff in returns. proshares and rydex probably know that anything but a daily mirroring of the index would be unviable because of the risk of portfolio ruin. The "daily" aspect of the 2x etfs may, in fact, be the very feature that makes them viable investment choices. Less efficient than 50% margin, but total avoidance of a margin call and very little change, comparatively, of receiving a margin call.

[TomO]

Tristan ----
I did the same thing "mg" did (9/28/07 questoin) and my results are identical. Ditto for UYG, the 2x financial sector ETF. So for the long-term investor, where's the down-side. What are we missing? A reply would be appreciated. Thanks.