DJIA Daily Return Distribution, 1928-2009

The financial market meltdown has caused many to re-evaluate their models for expected market returns.

In reality, though, the recent market swings are not out of the ordinary in terms of what has been observed in the past. They are still within the fringes of the ‘long tail’ of the distribution of daily market returns.

If there is an unpredictable and high impact event, waiting to spring on the market and challenge the perception of normal or ‘expected’, the “dot-com” bust, 9/11 and financial market meltdowns have not revealed any. None have been a ‘Black Swan’, to use Nassim Nicholas Taleb‘s term.

DJIA Daily Return Difference Distribution, 1928-2009

When it comes to the financial markets, if there is a large-impact event which requires counter-factual reasoning to model or comprehend, it has not yet occurred.

Daily leveraged funds have been the topic of numerous articles recently which have questioned whether they should be held for periods longer than a single trading session, and in turn, whether they are suitable for individual investors.

YTD Russell 2000 Index vs. Daily Leveraged Funds

Take, for example, the Russell 2000 Index (^RUT), the iShares Russell 2000 ETF (IWM), which tracks the index, and the various daily leveraged funds which attempt to track the index to the tune of -3x (TZA, Direxion Daily Small Cap Bear 3X Shares), -2x (TWM, UltraShort Russell2000 ProShares), -1x (RWM, Short Russell2000 ProShares), 2x (UWM, Ultra Russell2000 ProShares) and 3x (TNA, Direxion Daily Small Cap Bull 3X Shares).

Over the YTD period through 6/19/09, all daily leveraged equivalents of the fund, both the bullish and bearish versions, have underperformed the index.

Indeed, the market’s extraordinary recent volatility highlights the perils of daily leveraged funds. Daily rebalancing over periods of price fluctuation, without successive days of monotonic price decrease or increase, have a significant negative impact on the value of leveraged funds.

Performance and Holding Period

Does that mean that leveraged ETF’s are always inappropriate for investment over periods longer than a trading session?

Leveraged funds are a relatively new invention in the ETF world, and most don’t have sufficient history to compare longer-term performance vs benchmarks.

Russell 2000 vs. Daily Leverage - Actual & Calculated

Performance – Real vs. ‘Ideal’

Leveraged ETF’s do, though, track relatively closely the benchmarks they follow, with daily performance magnified by the intended degree of leverage. Take, for example, the +2x and +3x daily leveraged equivalents of the Russell 2000 index, over the first two months of Q2.

‘Ideal’ leverage can be calculated by applying a factor of ‘x’ to the daily returns of the Russell 2000 benchmark and comparing the result to the returns of the corresponding daily leveraged ETF. In reality, the daily leveraged ETF’s underperform slightly the synthesized ‘ideal’ returns. The difference represents tracking error and fund expenses, including management fees and the fund’s internal costs of borrowing to maintain leverage.

In this example, at the end of the period, the value of $1000 invested, and held, would be:

• +3x: $2117 – ideal (synthesized)
• +3x: $2080 – TNA (Direxion Daily Small Cap Bull 3X Shares)
• +2x: $1750 – ideal (synthesized)
• +2x: $1746 – UWM (Ultra Russell2000 ProShares)
• +1x: $1364 – ideal (Russell 2000 Benchmark)
• +1x: $1363 – IWM (iShares Russell 2000 Index)

Tracking Error and Expenses

The +3x leveraged fund (TNA) underperformed the ideal by $37 or 1.7%. The 2x leveraged fund (UWM) underperformed the ideal by $4 or 0.2%. And, the 1x leveraged fund (IWM) underperformed the Russell 2000 benchmark by just $1.

So, the leveraged funds do a pretty good job of tracking ideal leverage, even over periods far longer than a single trading session.

Long-Term Performance

How about performance; can daily leveraged funds produce performance proportional to the daily leverage rate, over longer periods? In this example, during which market gains were mostly monotonic, they do. The benchmark was up 36.3%, the 2x fund up 74.6% (2.05x the benchmark), and the 3x fund up 108% (2.97x the benchmark).

This example period, though, was chosen with the benefit of hindsight, just as the selection of other, more volatile periods, can be chosen to highlight the risks.

Synthesized Long-Term Performance

Nasdaq vs. Calculated 2x and 3x Daily Leverage

How, then, do leveraged ETF’s perform over much longer holding periods? The data does not exist, because leveraged funds don’t have sufficient history, but using methods similar to those used to calculate the ‘ideal’ data points highlighted in the charts above, data can be synthesized by applying daily leverage to historical market data.

How would the $1000 invested in the NASDAQ composite perform versus $1000 invested in 2x and 3x leveraged versions of the index, over a very long period, such as since the index’s inception?

Certainly, not very well, since leveraged ETF’s aren’t appropriate for long holding periods, and since NASDAQ has been wracked by the “dot-com bust” and the recent world financial crisis and “meltdown”? Right?

Wrong. To the contrary, even if the recent recovery is excluded, daily leveraged investments perform handsomely, outperforming the index by factors which far exceed the daily leverage target:

$1000 invested in NASDAQ since inception (2/5/71) to 3/20/09…

• unleveraged: $14,572
• leveraged 2x: $46,236
• leveraged 3x: $31,026

Sure, leverage is not without its risk. And, the risk is significant.

For example, a $1000 investment in leveraged versions of the index, at the height of the “dot-com boom”, through 3/20/09, is nearly wiped out…

• unleveraged: $289
• leveraged 2x: $35
• leveraged 3x: $2

But, when timing is more fortunate, leveraged versions of the index can far exceed their advertised daily performance targets, even over long periods. $1000 invested in NASDAQ from 7/6/95 to end of .com boom (3/10/2000)…

• unleveraged: $5,360
• leveraged 2x: $22,456
• leveraged 3x: $73,262

Conclusion

Leveraged ETF’s are good at what they advertise, magnifying daily performance by their leverage ratio.

The performance of leveraged funds are influenced both by daily results and by the compounding leveraged effects of those results, which are affected more heavily than unleveraged funds, by the volatility of the target investment.

The real risk inherent in daily leveraged ETF’s isn’t really their performance or behavior when held long term; it is the fact that such funds are more volatile than the unleveraged versions by factors which exceed the advertised leverage ratio. Over longer periods, this translates into disproportionate risk which isn’t necessarily compensated by the leverage ratio.