FAS Is Now XLF

For someone who gets a kick out of volatility, the arrival of triple ETFs has been a little bit like manna from heaven. Of course the launch of the Direxion triple ETFs back in early November just happened to coincide with the highest VIX readings in history. There is nothing like record volatility, except perhaps record volatility times three.

But a lot has changed since November. The VIX traded in the 80s the month it was launched; today it was as low as 25.02. At the moment the VIX is exactly 1/3 as high as it was when it peaked in November at 81.38. For those who have been selling options, the ride down the volatility slide has been an unusually profitable one. In fact, it is likely that some of the premiums harvested in the last nine months or so will turn out to be the most bloated we will see in our trading lifetimes.

My personal interest in the triple ETFs notwithstanding, these vehicles have received mixed reviews, largely because their suitability as buy and hold investments degrades rapidly after just one trading session – with the problems exacerbated by increases in volatility. On the flip side, the recent decrease in volatility has muted some of the tracking and compounding errors inherent in leveraged ETFs. In fact, in the current environment, the 3x and -3x ETFs are starting to look somewhat tame relative to their history. The two charts below show the (30 day) historical volatility (purple line) and implied volatility (gold line) of the most popular financial sector ETF, XLF, and the 3x financial sector ETF that has taken the trading world by storm, FAS. While there are a number of interesting conclusions to be drawn from these charts, the point I wish to make is that current historical and implied volatility for FAS (top chart) is hovering around the 100 mark, which is about where HV and IV were for XLF (bottom chart) in February, March and April. In other words, the 3x ETF FAS is no more volatile or has more uncertainty in its stock price now than XLF did during the period from October through April. Tracking error aside, FAS is now effectively the ghost of XLF.

[source: iVolatility]

Clean vs. Not-So-Clean Energy

While I have not mentioned it much on the blog, one of my favorite sectors to invest in is the energy sector. When it comes to energy ETFs, the 800 pound gorilla is XLE, the energy select sector SPDR that trades over 20 million shares on a typical day. XLE’s holdings are heavily tilted toward the major integrated oil companies, with Exxon Mobil (XOM) and Chevron (CVX) accounting for slightly more the 1/3 of the ETFs holdings, followed by ConocoPhillips (COP), Schlumberger (SLB), Occidental Petroleum (OXY), etc.

With cap and trade legislation passing the House over the weekend, investing in the energy space is getting even more interesting. XLE is up this morning, as are the popular oil services ETF, OIH (the top five holdings favor drillers and include RIG, SLB, DO, BHI and NE) and the exploration and production ETF, XOP (top five holdings are XEC, PXD, EAC, INT and HK.)

There are a variety of ETFs out there in the clean/green space. Perhaps the best known of these and certainly the most popular is PowerShares WilderHill Clean Energy (PBW), whose largest holdings include a healthy dose of solar companies (top five holdings are FSYS, VLNC, SOLR, ESLR, SOL.) Among the more interesting alternatives is a sibling ETF, PowerShares WilderHill Progressive Energy (PUW), which places more emphasis on energy efficiency and nuclear power and has a list of top holdings which includes MX.TO, ES, PX, USU and CCO.TO. For a solar-only ETF play, Claymore/MAC Global Solar Energy (TAN) is an excellent bet. Note that many of the holdings of TAN are not traded on U.S. exchanges. The current top five holdings are MBTN.SW, FSLR, S92.BE, CTN.DU and SWV.BE. Also in the top ten holdings are two Chinese solar companies whose ADRs are available in the U.S.: STP and TSL.

In the chart below, I have highlighted my favorite all-purpose clean energy ETF, PBW and have included a ratio of PBW to XLE in order to get a sense of the relative performance of clean energy with respect to the broad energy sector. While PBW has pulled back with the broader market during the past three weeks, it has continued to perform strongly against the broad energy sector ETF. As the ratio chart hints at, pairs trades involving clean energy ETFs such as PBW, PUW and TAN vs. XLE, XOP and OIH are one way to play the Washington energy legislation game going forward.

[source: StockCharts]

Disclosure: Long OIH, DO, INT and TSL at time of writing.

Chart of the Week: Might Recent Volume Bottom Doom Stocks?

This week’s chart of the week could easily chronicle the recent decline in volatility, but that’s a story many pundits have already flogged to within an inch of its life, so it’s time for something else. Like volume.

The volume story rarely gets the air (electron?) time it deserves, so I have plucked out a chart in hopes of being provocative.

In the StockCharts lexicon, $NYTV is one of several measures of NYSE volume. Specifically, it is the daily NYSE volume figure reported by the Wall Street Journal and the one I have chosen to standardize on for my own charts. The chart below uses the NYTV numbers to plot NYSE total volume (dotted black line) against the backdrop of a solid gray area chart for the SPX, with data going back to May 2008. To smooth out some of the fluctuations and holiday-induced dips in volume, I have added a 9-day exponential moving average (EMA) as a solid blue line. I have also included a 10-day rate of change (ROC) study below the main chart.

While readers will undoubtedly draw their own conclusions from the chart, I have chosen to highlight three bottoms in the 9-day volume EMA. The first one occurs in late August 2008, just before the Lehman-induced September swoon. The second bottom is from late December, just before the January top. With Friday’s late volume surge triggered by the Russell index reconstitution, the spike in volume is almost certain to confirm that the mid-June volume drought will now become another bottom. The dip in volume coincided with the most recent top in the SPX and it is possible that for the third time in 1 ½ years, the volume bottom could signal a multi-month drop in the SPX.

[source: StockCharts]

VIX Convergence Zone in Mid-20s

Since Fridays are days in which recent VIX lows are often tested, I thought this might be a good time to step back from the typical VIX daily chart and look at a weekly chart. In the chart below, I have elected to go back to the beginning of 2006 to capture the details of what was arguably the lowest volatility year on record so it could be compared with the most volatile year we have witnessed, 2008.

While volatility first began to spike in February 2007, it was not until July 2007 that investors began to come to terms with the potential magnitude of the damage should the subprime mortgage crisis morph into a global financial contagion. From July 2007 to September 2008, volatility was elevated, but seemingly contained in the 16-35 range represented by the blue box in the chart. It just so happens that the midpoint of that range roughly coincides with the 2006 VIX high of 23.81 that is represented by the horizontal green line.

To complete the picture, I have added a dotted green trend line that connects the December 2006 low to the May 2008 low. Like the 2006 high and the median for the blue box, it projects to about the 24-25 range.

This is not to say that the VIX cannot go below 24-25, but given the 3.06% drop in the SPX on Monday and the 2.14% gain yesterday, the current 26.65 level in the VIX does seem inconsistent with recent single day volatility.

[source: StockCharts]

Disclosure: Long VIX at time of writing.

VIX:VXV Ratio Sell/Short Signal

The VIX closed at 26.36 today, down 15.4% from Monday’s close of 31.17 to the lowest closing level since the 25.66 close on September 12, 2008 – the last trading day before the Lehman Brothers bankruptcy was announced.

According to the classic 10 day simple moving average measure, which has the VIX currently sitting 11.7% below that level, the VIX is now in an ‘oversold’ position according to the TradingMarkets 5% Rule as well as a more stringent 10% threshold used by other traders.

From a volatility term structure perspective, the VIX is also oversold. Notably, the VIX:VXV ratio, which compares 30-day volatility of SPX options to 93-day volatility (using the VXV index), closed today at 0.896 today. In the chart below, you can see that when this ratio closes at 0.92 or below, the bears tend to have an upper hand for at least several weeks. When the ratio drops below 0.90, as was the case today, the odds shift even more favorably in the direction of the bears.

In brief, the low current levels in the VIX:VXV ratio suggest that options traders are too bullish and complacent in their 30 day outlook (event volatility) relative to their 93 day outlook (structural volatility.) While these two volatility measures can be brought back into line by lowering estimates of long-term structural volatility, the path of least resistance is for short-term event volatility to rise. This means the odds favor that the VIX will move in the direction of the VXV, which closed at 29.41 today. Of course rising volatility tends to favor the bears at the expense of the bulls. Even with today’s exceptionally strong close, longs should consider taking profits and/or initiating short positions.

[source: StockCharts]

Disclosure: Long VIX at time of writing.

The Next Big Thing?

This morning ProShares launched two new triple ETFs. Now before you exclaim, “Enough already!” consider that the new ETFs are designed to track the daily moves of the S&P 500 index. As such, these are the first 3x and -3x ETFs that track the SPX directly. For this reason alone, the two new ETFs are can’t miss products. While these triple ETFs will have some interesting hedging applications, the fact that they have a target tracking period of one trading day, like the Direxion Daily ETFs, means they will probably become very hot in the day trading space. Don’t be surprised to see 100 million shares traded in both of these within a few months.

The official names of the new ETFs are the Ultra ProShares (UPRO) and Short ProShares (SPXU). For more information on these ETFs, check out their prospectus.

On Twitter

Sooner or later, I feel I needed to share my thoughts about Twitter; since I have added some 1,000 or so followers in the past few days, this seems like a good time as any to speak up.

I have probably been using Twitter on and off for close to two years. From the start, I have had a love-hate relationship with the platform, for a variety of reasons. Initially it was largely a case of poor stability and reliability, then as Twitter made it into the mainstream, it seemed as if it was one too many communications channels – both inbound and outbound. As a result, I have a history of using Twitter in periodic bursts of activity, becoming disillusioned, swearing it off for awhile, then eventually poking my head back in to see if I should give it another test drive. If it sounds like a crazy process, I tried the same approach with classical music for several years and one day suddenly discovered I was in love. (Fortunately, I never took this approach to dating…)

In the last two months I have finally made my peace with Twitter. There is no longer any love or hate, but I think I have finally come to terms with how I would like to use this communications channel. The easy part is outbound communications, where I have decided to differentiate my Twitter posts from the blog by focusing on three areas, in descending order of importance (at least as I see it):

1. ‘Retweeting’ commentary and analysis (largely but not entirely investment-related) that I believe deserves a wider audience
2. Notifying readers of a new post up on VIX and More
3. Offering impromptu comments about intraday market activity

For those who are interested in following me on Twitter, you can find me at Twitter.com/VIXandMore

From my perspective, the more difficult side of Twitter has always been inbound communications, where I prefer not to drink for the proverbial fire hose in real time. I have found that I can keep up with only 2-3 dozen of my favorite Twitter sources – and only for those who tweet no more than a few times per day. So while I get only a small slice of the Twitter community, I get quality input in real time. For the other 300 or so of my regular sources of information, I can always grab their RSS feeds via Google Reader or Bloglines and read the material at my leisure.

I have tried a variety of applications which I thought might significantly improve my Twitter experience, including TweetDeck and others, but none of these has revolutionized my Twitter experience. For my purposes, the best Twitter application I have used so far is Twitterfall, which I first heard about in Traders Atwitter Over New Apps from Theresa Carey’s excellent Investor Brain blog. Part of the reason I have become a Twitterfall fan is that I can use it to set up filters for keywords such as VIX and VXX – so I can scan the entire Twitterverse in real time to see what is being said about these subjects.

Going forward, I hope to continue to use Twitter as an extension of the blog, to highlight some interesting links as I happen upon them and to offer some intraday market commentary that is probably more appropriate for a microblogging platform than for posting in this space.

The 1000th Post

If Blogger’s math is to be believed, this is my millennial post. I had originally intended to roll this post out with limited fanfare, but a strange confluence of events has caused me to reconsider. First, over the weekend, the blog received substantial accolades from Barron’s options columnist Steven Sears in For the Markets, How Tweet It Is. Today, the Wall Street Journal’s MarketBeat columnist Matt Phillips referred to the “VIX-obsessed blog VIX and More” in his Ugly Start of Week for Stocks as Oil Drops, VIX Jumps.

So today I have decided to (briefly) discuss a little bit of the origins and evolution of the blog and to help point the many new readers to some of the highlights from the first 1000 posts.

A Non-Volatile Birth

The story begins in December 2006, with the VIX hovering around 10.00. At the time, I was looking for an online location to serve as a searchable repository for some of my research on the VIX. After sampling some online message boards and determining these were too unwieldy, I decided to try blogging. In the first week of January, I determined Blogger was the easiest way to take the plunge. The VIX handle had already been claimed by another blogger and I figured I didn’t want to box myself into such a narrow subject area anyway, so I settled on the “and More” escape hatch and plunged in with VIX and More: An Introduction. With the VIX barely out of single digits and left for dead by most, I did not expect to see much in the way of traffic, but after a couple of weeks, a few hearty souls started dropping in. To highlight the absurdity of devoting a blog entirely to the VIX, I added the tagline, “Your one-stop VIX-centric view of the universe…” and hoped that the ellipses would be a signal to readers that everything was tongue in cheek.

For some additional context and to underscore the absurdity of the venture, at the time I was trading almost 100% stocks – very few options – and did not include the VIX in my stable of indicators. I did, however, have a strong belief that most of what we learn comes from getting out of our comfort zones, so I embraced this electronic journey as a potential learning opportunity.

Toward the end of February, when some asked what I wanted for my birthday, I joked, “A 20% spike in the VIX, of course.” Well I got a record 64% spike for my birthday and quite a few curious souls who showed up wondering what it all meant. The joke, it turns out, was on me.

By the time Bear Stearns collapsed and the sub-prime meltdown had transformed into a full-blown financial crisis, I discovered that I was probably the only person who had been thinking about and writing about the VIX and volatility almost every day for two years. What started out as a lark has become a serious venture, quoted in such publications as the Wall Street Journal, Financial Times, Barron’s, Globe and Mail, etc.

Blog Highlights to Date…

My hope has always been that this blog can be both serious and fun. It seems like only yesterday that a reader asked for wine pairings with my VIX Weekly Sentiment Indicator and I was glad to oblige. Recently, I decided to tag a select group of posts with the “lighter side” label to demonstrate that the fear indicator can indeed coexist with an occasional attempt at humor.

For some of the most widely read posts, readers can check out the most read posts of 2007 as well as their 2008 counterparts. I will also have the first installment of the top posts of 2009 ready after the first half of the year and I have begun to flag a handful of posts for which I have received the most positive feedback with a hall of fame label.

Finally, those who are relatively new to the VIX and volatility are encouraged to check out posts I have tagged with the educational label or skip directly to the one post everyone should read, Ten Things Everyone Should Know About the VIX.

Innovations

I am particularly pleased by a number of ideas that were born on this blog. These include the VIX:VXV ratio, VIX macro cycles, the Global Volatility Index, fearograms, an options opportunity matrix, “event volatility” vs. “structural volatility”, a conceptual framework for volatility events, the ratio of the VIX to the yield on 3-month T-bills, and even some semi-serious ideas, such as the LEHVIX and the OHFdex (Overripe High Fliers Index).

More Education Than Market Calls

The intent of this blog has always been to stimulate new ideas and make better fishermen out of all of us, as I strongly believe that ultimately we are all self-coached. Occasionally, however, I have not been able to resist making some market calls – and I have had the good fortune to nail several of them. When I make calls, I usually do so to be provocative and because my thinking is clearly contrarian. When to Short China? is one of my most popular posts of all-time, as is Prediction: Direxion Triple ETFs Will Revolutionize Day Trading. In retrospect, these look like no brainers, but at the time, they cut sharply against the grain.

More often than not, I call things early, but close enough. A recent example was calling a bottom on March 5^th – one day early and 21 points too high.

Moving Forward

I am not sure what the future will bring in this space. Some 2 ½ years after diving in I now believe that my analysis of volatility and market sentiment provide me with the bulk of my edge and I find that most of my trades involve options on ETFs, yet I still intend to keep my trading and the blog largely separate. I have a passion for education, market sentiment and options and I think there is a lot of work to be done in terms of elevating the discussion in these areas.

I have also enjoyed seeing the chart of the week become a regular feature and clearly take pleasure in putting together some strange and unusual charts. I expect there will be more wacky charts in the future as well as more synthesis of charts, market sentiment and fundamentals.

The blog has already spawned a subscriber newsletter and a nearly complete manuscript for a book (Trading with the VIX, to be published by Wiley & Sons). I certainly would not have predicted either of these developments and I am keeping an open mind about the future.

Thanks to all who have helped to make this blog possible and have shared their ideas along the way. In the end, it is my firm belief that investing does not have to be a zero-sum game, particularly if the scorecard acknowledges some non-financial benefits.

Chart of the Week: Lack of Volume and Breadth Threatens Bull Move

In the last few weeks, stocks have struggled to add to recent gains, suffering even more from a lack of buying interest than from selling pressure.

The chart of the week below is an attempt to use two basic indicators to capture the lack of volume and market breadth that has undermined the March to mid-June rally. As a measure of market volume, I have chosen to highlight on balance volume (OBV), which is a running total of the volume on up days minus the volume on down days. This indicator is excellent at highlighting trends which are at risk due to declining volume, which is exactly what the warning suggested when there was a peak in OBV during the first two weeks of May.

In a similar vein, the McClellan Summation Index (aka the NYSE Summation Index or NYSI) shows market breadth as derived from the net daily advancing stocks minus declining stocks. The McClellan Summation Index did turn up at the end of February, just before the March bottom and is generally an excellent tool for gauging trends in market breadth.

In addition to the May highs, note that both OBV and the McClellan Summation Index have recently made lower highs as well. While OBV shows some indications of steadying at current levels, the larger concern is the decline in market breadth issues highlighted by the McClellan Summation Index.

Like all indicators, these two are far from perfect, but they often provide important information about the decline in strength and potential for reversal in major trends.

For additional information on the subjects above try:

• The McClellan Summation Index (4/3/07)
• Two Thoughts on the McClellan Summation Index (10/25/07)
• McClellan Summation Index Turns Positive (2/29/09)
• Whither COF? (5/27/08)

[graphic: StockCharts]

VIX at Seasonal Cycle Low

With the VIX now getting comfortable in the 20s, there has been a fair amount of discussion about just how low we can expect the VIX to go in the next few months.

Back in April, in The New VIX Macro Cycle Picture, I predicted that the VIX will likely not drop below the 25-27 area in the current bull market. That prediction has held up so far, but will almost certainly be tested during the summer months.

Most investors tend to think of the summer season as something of a horse latitudes of sorts for trading, with volume tailing off, portfolio managers on vacation and stocks sometimes set to cruise control. As a result, most people equate summer with lower volatility.

While the VIX does tend to follow a distinct seasonal cycle, the truth of the matter is that we are now at the seasonal cycle low, with volatility historically increasing dramatically from June through October. In fact, over the course of the past two decades the increase in volatility has been highest from June to July, increasing by over 10% (1.82 points.) The pattern is quite distinct in the chart below, which shows composite monthly volatility from January 1990 through last month, using 100 as the series mean.

So…while volatility may indeed trend lower as some of the concerns about the global recession are put to rest in the next few months, lower volatility will have to counter the established seasonal cycle.

For some previous posts on the same subject, try:

• The VIX Annual Cycle (12/24/08)
  
  
• A Month By Month Look at the VIX (1/31/07)

[graphic: VIXandMore]

Disclosure: Neutral position in VIX via options at time of writing

Who Trades the VIX and VXX?

Several times in the past, I have had some fun the Trading Patterns feature at optionsXpress, including a February 2008 post, optionsXpress Trading Patterns and the VIX, which examined the securities that optionsXpress customers who traded the VIX were also trading.

Given all that has happened in the past 16 months, I thought it might be interesting to see what the current crop of VIX traders are trading – and also to contrast this with traders of VXX, the VIX ETN.

First, the VIX trader snapshot from February 28, 2008 shows leveraged short positions in real estate, technology and oil.

I have expanded today’s snapshot of the VIX trader to include a larger list of securities. Clearly, some themes remain, such as the bias for leveraged short positions in real estate and finance, as well as interest in some of the most volatile momentum stock plays.

Finally, looking at the VXX trader, both ETFs in general and the leveraged ETF plays in particular are even more important parts of the trading approach.

In terms of conclusions, I am cognizant that the optionsXpress customer base is a retail-oriented subset of the broader trading crowd and not necessarily representative of the bulk of the volume of VIX and VXX trades. From the graphics above, however, it is difficult to make the case that traders are using the VIX and VXX for hedging. Based on available data, traders who trade the VIX and VXX are typically trading the most volatile leveraged securities available. At the very least, the connection between the VIX and leveraged ETFs appears to be very strong among those traders who prefer to focus on the most volatile nuclear-tipped trading vehicles.

[source: optionsXpress]

Disclosure: Long VXX and neutral position in VIX via options at time of writing

VXX:VXZ Ratio

Since its launch on January 30^th, the iPath S&P 500 VIX Short-Term Futures ETN (VXX) has generated an enthusiastic following, with an average volume of 400,000 shares traded each day. The same claim cannot be made of VXX’s more problematic sibling, the iPath S&P 500 VIX Mid-Term Futures ETN (VXZ), where 100,000 share days are more the exception than the rule.

In spite of the lack of popularity, VXZ, which attempts to replicate the changes in VIX futures approximately five months out, should not be overlooked. In fact, comparisons between the movements of VXZ and VXX provide some interesting insights into the ebb and flow of volatility expectations.

Take the VXX:VXZ ratio, for instance. In some respects this indicator is similar to the VIX:VXV ratio I introduced back in 2007. There are some important differences between the two ratios, however, which are worth noting. First and foremost, you can trade both VXX and VXZ; neither VIX nor VXV can be traded directly. Second, and related, both VXX and VXZ are exchange-traded notes (ETNs), while VIX and VXV are indices. Finally, whereas VXX and VXZ look out one month and five months, the VIX and VXV indices look out one month and three months.

For those seeking to compare near-term volatility expectations with volatility expectations several months out, both the VIX:VXV ratio and the VXX:VXZ ratio are excellent tools. From a data perspective, the index ratio has 19 months of real-time historical data. Unfortunately, the VXX:VXZ ratio has only 4 ½ months of real-time (i.e., non-reconstructed) data to draw from. On the other hand, data for the VXV index is sometimes difficult to come by, while VXX and VXZ data are widely distributed.


The chart below shows the full history of the VXX:VXZ ratio, using a 4-day EMA (blue line) as a smoothing factor. While this indicator is still quite youthful, I find it encouraging that the recent bottom in the ratio coincided with a topping pattern in the SPX. Further, the double top in the ratio that completed on March 9^th also coincides with the bottom in the SPX.

Going forward, I will compare the VXX:VXZ ratio to the VIX:VXV ratio and subject both ratios to some additional scrutiny.

[source: StockCharts.com] 

Disclosure: Long VXX and neutral position in VIX via options at time of writing

Selling VIX Puts Pre-Expiration

Selling naked puts on the VIX just prior to expiration can be a surprisingly low risk volatility play.

Normally, selling naked puts is a dangerous strategy because of the risk that negative news can overwhelm the underlying, causing it to gap down and create a large loss. With the VIX, however, spikes are almost always upward, because while threats to equities are relatively easy to identify, it is much more difficult to discern when these threats are suddenly extinguished.

For this reason – and because the VIX has lately shown some reluctance to drop below the recent floor of 27 – selling a naked put on the VIX is a lot less risky than selling naked puts on other securities. Risk to the down side is definitely limited, yet the limitations are not perfectly mathematically quantifiable.

A sale of the June 30 put illustrates one potential naked put sale opportunity. The profit and loss chart below outlines what the trade looks like. With yesterday’s closing price of 30.81, the trade is profitable if the VIX rises, drifts sideways or loses up to 1.61 prior to tomorrow's special opening quotation. The gain is $80 per contract. The profit and loss chart shows that a loss of $170 per contract occurs at 27.50. Assuming 27.00 is a floor in the VIX, then the maximum loss is likely to be capped at $220. While a 12.3% drop in the VIX in one day cannot be ruled out, it is obviously not a very likely scenario.

Reminder: VIX options expire on Wednesdays. The June VIX options expire June 17^th this cycle. The last trading day for these options is today, Tuesday, June 16^rd. (See the 2009 options expiration calendar for more the full 2009 options expiration schedule.)

[source: optionsXpress]

Disclosure: Neutral position in VIX via options at time of writing.

Stock of the Week Winning Streak Ends at 13 Weeks

It was a fun ride while it lasted, but the Stock of the Week (SOTW) winning streak finally came to an end last week, after 13 consecutive weekly winning selections. In the end, it was a scant 0.14 weekly decline in LSB Industries (LXU) that brought an end to the ride, but even with that loss, the SOTW ‘Sequential Portfolio’ is still up 136.9% so far for 2009 and a gravity-defying 368.4% in the 14 ½ months since I introduced that feature as a part of my subscriber newsletter.

For anyone who is interested, I will update the performance of the SOTW in another two weeks and at the end of each quarter on the VIX and More Subscriber Blog.

For more information on the Stock of the Week, try VIX and More Stock of the Week Selection Up 343% in 14 Months.

Open Thread: Do Fibonacci Retracements Work?

Following my recent Dueling Fibonaccis for the SPX, a reader asked if I knew of any 'scientific' studies that attempted to evaluate the usefulness of Fibonacci retracement levels. The short answer is that I am unaware of any detailed studies, nor was I able to dig up anything meaningful with a search of SSRN.

So I turn this topic over to readers:

• Do Fibonacci numbers work as a trading tool?
  
  
• Are you aware of any published analysis which evealuates Fibonacci retracement levels?