Wednesday, December 16, 2009

Historical Volatility Pointing to a Sub-20 VIX

Just as I get in an extended discussion of historical volatility (HV), I note that the combination of 10/20/30/50/100 day HV has plummeted to levels not seen since mid-October 2007, which happens to be one week after the all-time high in the S&P 500 index.

It is worth noting that back in mid-October 2007 when the similar HV numbers were posted, the VIX was hovering around the 18.00 level.

With the VIX Holiday Crush starting to kick in and the drama associated with today’s FOMC meeting now behind us, I now believe there is about a 50% chance that the VIX dips below 20 in the next two days, even with the E-mini S&P 500 futures (/ES) down 4.50 as I type this. The alternative, which has been the status quo as of late, is that the 20 area acts as support for the VIX and triggers resistance in stocks.

Now the VIX does not have to follow historical volatility religiously, but if HV continues to fall, the case for a 20+ VIX will deteriorate rapidly. Substantial divergences tend to have a relatively short life. With the current divergence now at six trading days, the VIX can only defy gravity for a short while longer…

For more on related subjects, readers are encouraged to check out:

Disclosure: none

Tuesday, December 15, 2009

Adapting Annualized Volatility to Other Time Frames

In Calculating Centered and Non-centered Historical Volatility I attempted to walk through the steps and calculations necessary for determining of historical volatility (HV) using an Excel spreadsheet.

The second to last step in the calculation (before translating the final number into a percentage) is to annualize the standard deviation by multiplying it by the square root of the number of days in a year. In the example I chose, I used 252 trading days, reasoning that there are 365 days per year, 104 weekend days and approximately 9 holidays. One could also argue that while the markets are not open on weekends and holidays, there is market-moving news that makes the jump from Friday to Monday generally more volatility than a typical overnight period. By that line of reasoning, it could be appropriate to use 365 calendar days in the calculation. I am not aware of any options traders that use the square root of 365 in their calculations instead of 252, but note that such an approach would yield a historical volatility number about 20.4% higher (e.g., 18.81 instead of the 15.63 I arrived at in the example in Calculating Centered and Non-centered Historical Volatility.)

Most floor traders simplified the volatility calculation process by assuming 256 trading days in a year. With the square root of 256 an even 16, this greatly simplified the calculations that were done in one’s head.

Not everyone is interested in annualized volatility data. Traders who have options expiring in a week are more interested in determining historical volatility in weekly terms. In order to calculate weekly volatility instead of annualized volatility, simply substitute the square root of 52.14 (the number of weeks in a year) for the square root of 252. The multiplier becomes to determine weekly volatility thus becomes 7.22. Using the example referenced above, the 15.63 per cent annualized volatility translates into 7.11 per cent weekly volatility. A similar approach could be used to calculate historical volatility over other periods, such as a month or perhaps even two years.

Sometimes called statistical volatility or realized volatility, the 15.63 historical volatility means that looking backward, approximately 68% of the time (one standard deviation), the underlying (S&P 500 index) moved 15.63% or less on an annualized basis. Similarly, given the same data set, approximately 68% of the time the underlying moved 7.11% or less on a weekly basis.

Before I wrap up the current discussion of historical volatility, I will use the next two or three posts to talk about how investors might want to use historical volatility data.

For more on historical volatility, readers are encouraged to check out:

Disclosure: none

Monday, December 14, 2009

The BRIC Bull

The last time I wrote about the relative performance of the BRIC countries was a little over eight months ago, in Russia Leading the BRIC Rally. At that time, the bounce off of the March lows was barely a month old and Russia (RSX) was leading the way, followed closely by India (EPI), with Brazil (EWZ) and China (FXI) not rallying quite as sharply.

Fast forward eight months and Russia is still out in front, but starting to look a little tired. For all the talk of a Chinese bubble, FXI, the most popular Chinese ETF, is a distant fourth and falling farther behind the other BRIC ETFs with each passing week. Since the end of October, the top performers have been India and Brazil. In fact the top India ETF (EPI) is now 21% higher than it was the day before the Lehman Brothers bankruptcy, while the Brazil ETF is 29% higher than its was trading just before the Lehman debacle.

Looking ahead to 2010, I expect Russia will have considerable difficulty remaining the top performer. I would not be surprised to see Brazil eclipse the bunch, followed by India and a resurgent China. One thing is certain: if investors can predict the plight of the BRIC ETFs in 2010, quite a few of the other pieces of the investment puzzle will magically begin fall into place.

For more on related subjects, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Sunday, December 13, 2009

Chart of the Week: A Month of New Sector Leadership

During the course of the past month or two, stocks have drifted sideways, lacking buying conviction and strong leadership.

In this week’s chart of the week below, I have tracked the performance of the nine AMEX sector SPDRs over the course of the past month. Note that former leaders financials (XLF) and energy (XLE) are now lagging, while defensive sectors such as utilities (XLU) and health care (XLV) are leading the way. Now I have nothing against utilities and health care, but the next time these two sectors lead a significant bull rally will be the first time in my memory. One or more of technology (XLK), consumer discretionary (XLY), materials (XLB) or perhaps financials needs to take a leadership role to give the next bullish leg the type of strength that portfolio managers can believe in.

A good defense may win championship, but it will not light a fire under potential buyers.

For more on related subjects, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Thursday, December 10, 2009

Put to Call Ratio and the Probability of a Downturn

In the last day or two I have been fielded several questions about put to call ratios. It seems as if some investors are concerned that there is a stealth movement by sophisticated investors who are making substantial bets on a downward move with large purchases of puts. Invariably, these concerns have led to questions about what I see in the put to call ratios that will confirm or deny this.

To quickly recap, the CBOE publishes three put to call ratios. In my preferred charting site, StockCharts.com, these are known as:

  • $CPCE – the ticker for the equity put to call ratio
  • $CPCI – the ticker for the index put to call ticker
  • $CPC – the ticker for the total equity + index data

For reasons I have discussed in the past, I prefer the CPCE ratio and use this as a contrarian signal. The problem with the CPCI data is that institutional order flow for index options tends to come in large chunks that can create misleading short-term signals.

Recently, however, the CPCE, CPCI and CPC have all had very similar looking charts. I have reproduced the six month chart of CPCE below and it shows no unusual spikes in put activity relative to call activity. If anything, the 10 day EMA that I use to smooth the sometimes noisy CPCE data shows an almost eerie flat line for the past month or so, just as was the case when I last wrote about put to call ratios when in Equity Put to Call Ratio Not Pointing to a Correction when the Dubai debt crisis hit.

For more on related subjects, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Wednesday, December 9, 2009

When Did Volatility Bottom?

If an investor were to have a VIX-centric view of the universe, he or she might reasonably conclude that as far as 2009 is concerned, volatility bottomed just before Thanksgiving, when the VIX made its intraday low for the year (20.05 on 11/25) or on the previous day, when the VIX had its lowest close of the year at 20.47.

In fact, if one considers only historical volatility then the lows in historical volatility for the 10 day, 20 day and 30 day measures all fell in the second half of September. Further, an even more comprehensive volatility measure, average true range (ATR), also shows volatility bottoming in the second half of September. As the chart below shows, ATR has not come close to touching its September and October lows during the last month. On the other hand, the VIX is in a more definitive downtrend and continued to make new lows in November.

What does all this mean? In short, it means that even as volatility has flattened out, market expectations of future volatility have continued to decline. With the holiday effect expected to put a more pronounced damper on volatility starting next Monday, I would not be surprised if the VIX takes one last run at the sub-20 level before the end of the year. After the first of the year, however, I would expect historical volatility and implied volatility measure such as the VIX to start to track more closely. Whether this means historical volatility will rise to meet the VIX or the VIX will fall toward historical volatility levels remains to be seen.

For more on related subjects, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Tuesday, December 8, 2009

Calculating Centered and Non-centered Historical Volatility

Yesterday in What Is Historical Volatility? I attempted to provide a brief overview of historical volatility (HV) and put it in a broader volatility context.

Today I will endeavor to address the most frequent question I get about historical volatility: exactly how is it calculated?

You would think the calculation would be a straightforward affair, but this is not necessarily the case. As best I can in plain English (and since I have not mastered Word’s equation editor), the steps for calculating historical volatility are as follows:

  1. Select a desired lookback period in trading days (lookback period)
  2. Gather closing prices for the full lookback period, plus one additional day (lookback +1)
  3. Calculate the daily close-to-close price changes in a security for each day in the lookback period (daily change)
  4. Determine the natural log of each daily percentage change (log of daily changes)
  5. Calculate the mean of all the natural logs of the closing prices for the lookback period (log lookback mean)
  6. For each day, subtract the lookback mean from the log of daily changes (daily difference)
  7. Square all the differences between the mean and the daily change (daily variance)
  8. Sum all the squares of the differences (sum of variances)
  9. Divide the sum of the squares of the variances by the lookback period (lookback variance)
  10. Take the square root of the lookback variance (historical volatility, expressed as a standard deviation)

Finally, to convert the standard deviation into an annual volatility percentage take the HV expressed as a standard deviation and multiply it by the square root of the number of trading days in a year (approximately 252) and then by 100 (historical volatility).

An Excel example will help to illustrate the steps and calculations. The table below uses closing data for the SPX for the last eleven trading sessions. The second row has a date of 11/24/09 in column A, a close of 1105.65 in column B and the natural log of the close for 11/24 divided by 11/23 in the column C [=LN (b3:b2)]. Column D is an average of the natural logs in column C [=average (c3:c12)], while column E simply subtracts column D from column C [=c3-d3]. Finally, Column F squares the results of column E [=e3^2] and cell F13 sums all the squares [=sum(f3:f12)].

The calculations below the main table start by repeating the value of F13 in A16 [=f13] and stating the number of lookback periods in A17. In A19, A16 is divided by A17 [=a16/a17]. A21 then takes the square root of the result from A19 [=a19^1/2]. A23 takes the result from A21 and multiplies it by the square root of 252 [=a21*sqrt(252)]. Last but not least, A25 converts to result from A23 to a percentage [=a23*100], yielding a 10-day historical volatility of 15.63.

To replicate the entire table, the formulas from row 3 can just be copied down to the bottom of the table, with one exception. That exception is column D, where the mean value – not the formula – is repeated throughout the table.

If this seems like a lot of calculations to arrive at historical volatility value, there is a much shorter and slightly different way – and one that I believe generates a better number for traders.

The above calculations reflect a centered approach in which daily price changes are characterized relative to a mean value for the entire period. Another way to look at the same problem is to assume that in the long run, the mean change in price approaches zero and is not meaningful. As a corollary, if the mean is not meaningful, there is no reason to subtract it from the daily changes, so all the calculations involving the mean can be dropped. This is the non-centered approach to calculating historical volatility and is sometimes known as “ditching the mean”.

The resulting table below is much more manageable and easier to follow. The first three columns (date, close and natural log of the daily price change) are identical to those above. The fourth column simply takes the standard deviation of the natural log of the daily price changes, multiplies it by the square root of the number of trading days in a year (252) and coverts it to an annualized volatility percentage by multiplying by 100. As a consequence, the formula in cell d12 below is simply =stdev(c3:c12)*sqrt(252)*100. This formula can now be copied to the rows below to calculate subsequent historical volatility values. Note that unlike the centered approach, there are no additional calculations required beyond those in the main table.

Here the non-centered approach also yields a 10-day historical volatility of 15.63.

For the next part in this series, I will expand upon what some of the formulas mean, how they can be modified, and why traders might prefer the non-centered historical volatility data to the centered historical volatility data.

For more on historical volatility, readers are encouraged to check out:

Disclosure: none

Monday, December 7, 2009

What Is Historical Volatility?

The volatility universe splits fairly neatly into two halves: historical volatility (HV) and implied volatility (IV). I tend to place slightly more emphasis on implied volatility because implied volatility looks to the future, is derived from options prices, and can provide some clues about the current sentiment of options investors. Of course, the CBOE Volatility Index, commonly known as the VIX, is an index that measures implied volatility in S&P 500 index options, so that may persuade me to favor IV over HV a little as well.

Compared to implied volatility, historical volatility seems like a relatively simple concept. It looks backward at price action and measures the degree of change in the price of a security. Things get a little more complicated, however, when one asks two seemingly innocuous questions:

  1. How long of a period?

  2. What method of measurement is used?

The issue of a lookback period is really not much of a complication, but it does lead to a proliferation of historical volatility numbers. As historical volatility looks only at trading days, it is important to note that the historical volatility calendar differs from the implied volatility calendar. As a result, the standard implied volatility time horizon of 30 (calendar) days (such as is used by the VIX) translates to about 21 trading days, assuming the usual NYSE nine holidays per year. Even with the different calendars, the most frequently used historical volatility measurement is HV 30, which translates to about 43 calendar days.

The appropriate lookback period to use for historical volatility calculations is ultimately a matter of personal taste. As noted above, most providers of HV data tend to standardize on HV 30, but I generally prefer HV 20 or HV 21, as this is a better approximation of a trading month. One can use shorter time frames, but investors should be wary of the amount of noise in calculations that look back less than 20 days. Still, I like to look at HV 10 to get a sense of the most recent volatility trend. Looking farther out, HV 50 or HV 60 are popular ways to capture almost an entire earnings cycle, while HV 90, HV 100, HV 180 and HV 200 are all excellent ways to capture the long-term volatility trend. In order to incorporate a full year of historical volatility, HV 250 is recommended. Some options traders like to look at two full years of historical volatility data with the likes of HV 500, but I rarely find much value looking back a second year unless – as is the case right now – the most recent year is filled with quite a few statistical outliers.

Any good options broker will have one of more historical volatility calculations built in, but HV data is also available from various options service providers such as Livevol or iVolatility.

Note that standard historical volatility data are the result of a calculation involving close-to-close prices, specifically end of day prices. As such, historical volatility does not capture the magnitude of any intraday price movements, which are better served by calculations such as an average true range.

Finally, while there are many ways to calculate historical volatility, by convention historical volatility is calculated by taking the standard deviation of the difference between the natural log of the daily changes in the price of the underlying and the mean value during the lookback period. This sounds a lot uglier than it turns out to be in Excel. Since this is the holiday season, however, tomorrow I will provide a recipe for the traditional historical volatility calculation as well as a modification that I find simpler and more useful.

For more on historical volatility, readers are encouraged to check out:

Disclosure: LiveVol is an advertiser on VIX and More

Sunday, December 6, 2009

Chart of the Week: Dollar Rising?

Friday was a reminder that the dollar will not go down every single day in an orderly, straight line fashion. In fact, there will be days when the dollar reverses sharply and sends traders who are short the currency scrambling to cover their positions, as was the case with Friday’s 1.44% gain.

In this week’s chart of the week below, I track the fall of the dollar and simultaneous rise in the S&P 500 index that began during the first week in March. Since that time there has been only one day in which the dollar gained more than 1.44%. I have highlighted that day with blue arrows to underscore that while the prior large move in the dollar did precede a two week bounce in the currency and a four week selloff in stocks, it did not affect the underlying trend in either the dollar or stocks.

Of course it could be different this time around. For starters, the dollar closed above the 50 day moving average for the first time since mid-April. From a technical perspective, however, I would not tend to get excited about Friday’s rally until it leads to a higher high above 77 and a higher low above 75. For now at least, the current rally should be treated as just another opportunity for some new shorts to join the dollar carry trade party.

For more on the dollar, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Friday, December 4, 2009

New Dr. Brett Series on Lessons for Developing Traders

If there is one blog on the web where I never seem to find the appropriate amount of time required to digest all the nuggets of wisdom it contains, that site is undoubtedly Brett Steenbarger’s TraderFeed. Filled with insights that range from quantitative analysis and system development to what is arguably the best collection of content on the web in the realm of trader psychology, TraderFeed continues to be – at least in my opinion – the top all-purpose investment blog on the web.

For this reason, when Brett mentioned in Lessons for Developing Traders: What Moves Markets that he is “going to write about topics that no one told me about when I was learning the ropes,” I thought that instead of waiting until the series is finished to highlight it I would flag it now for anyone who is not already on the Steenbarger bandwagon.

This new series also got me thinking to about the three things I wish I had been told (assuming I was smart enough to follow that advice) at the beginning of my trading career. The answers are personal ones, but I believe they capture insights that led to quantum advances in my trading:

  1. Standardize on one time horizon…and make it consistent with your trading approach and personality

  2. Make research and analysis of risk management at least as important as R&D on stocks, indicators and strategies

  3. Focus more time on developing expertise in managing (and exiting) existing positions than on discovering new high potential entries

For the record, a close fourth in this exercise was understanding the tenets of behavioral finance and the associated decision-making pitfalls that investors should learn to avoid. Those who wish to get a better sense of how I see the learning process for developing traders may wish to investigate my trader development stage model.

Readers, feel free to use the comments section to spell out the 3-4 things you wished someone had told you when you first started trading.

For more on these subjects, readers are encouraged to check out:

Disclosure: none

Thursday, December 3, 2009

VIX of 20 Spurring Market Correction?

As the chart below shows, the last two times the VIX has taken a run at 20 (late October and late November), stocks have responded by selling off and spiking volatility. It is possible that a VIX of 20 may still be something that investors are not yet ready to accept (availability bias), but with historical volatility hovering around 16 and the long-term trend in the VIX still moving downward, it is likely just a matter of time before we see a VIX in the 19s.

In addition to the absolute levels of the VIX, one must always watch relative VIX levels, which is where the moving average envelopes come in. Displayed as a blue zone in the middle of the trading range on the chart, the 10 day simple moving average envelopes make it easy to identify when the VIX is extended to the high side or the low side. While the 20 level has been well out of the moving average envelopes for the last two drops in the VIX, that is not likely to be the case going forward. This sets the possibility of a battle between the absolute VIX (support at 20) vs. the relative VIX (support at the bottom of the envelope) in the near future, with an increased likelihood that the 20 level does not hold the next time around.

Finally, it is that time of year where I feel compelled to remind everyone that seasonal factors also indicate that volatility should be moving lower. I have discussed the holiday effect several times in the past in this space and essentially the historical pattern calls for the VIX to hold relatively steady for the first two weeks of December, then drop sharply (probably about 1.5 points at current levels) as Christmas approaches.

For more on these subjects, readers are encouraged to check out:

[source: StockCharts]

Disclosure: none

Wednesday, December 2, 2009

Where Is VIX and More Headed?

I failed to mention it when it first came out a month ago, but anyone who missed The Periodic Table of Finance Bloggers by Joshua Brown at The Reformed Broker not only missed out on a great resource for identifying and classifying some of the top bloggers in the investment world, but also missed out on two elements that are often in short supply in the investment blogger space: subtlety and humor.

I got to thinking about the periodic table when I happened on Horizontal vs. Vertical Blogging from Michael Stokes at MarketSci.

When VIX and More started out, three years ago next month, financial blogging was still in its early stages and the options space in particular was wide open. In fact, Adam Warner at Daily Options Report pretty much had the entire options blogosphere to himself at the time. When I arrived on the scene, I envisioned taking ten minutes or so once a week to recap what had happened with the VIX and volatility during the week so I would be able to have some sort of archival historical overlay of my (almost) real-time thoughts on volatility. At least that was the idea…

Within a couple of days, the idea of a weekly post morphed into a daily post and not wanting to beat the VIX drum day after day, I started branching out into some tangential subject areas. I took up put to call ratios in short order, then expanded into the broader subject of market sentiment, decided to dive into the options space, adopted ETFs and particularly leveraged ETFs, and recently have ventured into behavioral finance, drafted a trader development stage model and have set out on a number of more distant tangents.

Part of the reason for the increase in breadth is to keep the content fresh and to be able to draw connections that are farther afield (e.g., VIX Data to Support Availability Bias and Disaster Imprinting Hypothesis.) Another reason is that I like the variety and never wish to be a slave to routine. Frankly, a third reason for my increasingly horizontal approach is that another wave of options bloggers has taken up the cause in the last year or so. As a result, I no longer feel that if I fail to comment on a particular zig or zag in the VIX or on another subject in my wheelhouse, that it won’t get said.

Before the month is over, I will be delighted to welcome my 1,000,000th unique visitor. So while the content on this blog has unfolded in a somewhat haphazard fashion, I am glad to see that it is resonating with a broad audience.

Going forward, I envision a broader net than might have been implied by the original tongue-in-cheek tagline: “Your One Stop VIX-Centric View of the Universe…” It’s still (mostly) the same universe, but I think it’s time to explore more of the “and More” portion of this blog. Maybe it's time to visit the lighter side more often too...

For related posts, readers are encouraged to check out:

Disclosure: none

Tuesday, December 1, 2009

Equity Put to Call Ratio Not Pointing to Correction

The recent Dubai debt crisis has spurred some investors to take some profits, protect their portfolios and contemplate both the acknowledged and hidden threats to the global economy. From Wednesday’s close to Friday’s intraday low, the S&P 500 index (SPX) only fell 17 points or 2.4%, hardly the type of selloff that typically strikes fear into the hearts of bulls. Fearing that further declines may be in the cards, however, investors snapped up puts aggressively, particularly on Monday, when the put buying pushed the CBOE equity put to call ratio (CPCE) to elevated levels.

In the chart below, I have reproduced the CPCE along with a 10 day exponential moving average (dotted blue line) to smooth the data over a two week period. The chart shows that since the July leg of the current bull market, significant pullbacks in the SPX (solid black line) have been preceded by drops in the 10-day EMA of the CPCE below the 0.58 level. In fact, for the last 5 ½ weeks, the 10-day EMA has never threatened the 0.58 area and at the current 0.625, the CPCE shows no signs of an impending correction.

For related posts on the CPCE, readers are encouraged to check out:

Disclosure: none

Monday, November 30, 2009

Frontier ETFs

In yesterday’s chart of the week, I looked at three ETFs with exposure to the Middle East:

  • Market Vectors Gulf States ETF (MES)
  • Wisdom Tree Middle East Dividend ETF (GULF)
  • SPDR S&P Emerging Middle East and Africa ETF (GAF)

It is a little known fact that Middle Eastern ETFs are actually subset of a relatively new class of ETFs called frontier ETFs. Many of these frontier ETFs are single country ETFs, but two in particular stand out as diversified frontier plays:

  • PowerShares MENA Frontier Countries Portfolio ETF (PMNA)
  • Claymore/BNY Mellon Frontier Markets ETF (FRN)

I list PMNA (holdings) first because it is not a global, but a regional ETF, based on the NASDAQ OMX Middle East North Africa Index. At present the fund has a strong emphasis on the Persian Gulf and should be considered as a slightly more liquid (but still relatively illiquid) alternative to MES and GAF, trading approximately 10,000 shares per day. As of last week, the top country allocations were in the United Arab Emirates (22.6%), Egypt (20.2%) and Kuwait (16.9%).

In contrast to PMNA, FRN (holdings) has taken a much broader and more geographically diversified global approach, without a particular regional emphasis. Specifically, the ETF is designed to track the Bank of New York Mellon New Frontier DR Index. As of September 30, the top country allocations were Chile (28.6%), Poland (15.9%) and Egypt (15.4%).

The chart below shows that the while PMNA and FRN were very similar in terms of performance for the first five months of 2009, the more diversified FRN had been a much stronger performer during the latter half of the year. Not surprisingly, given PMNA's exposure to the Persian Gulf, the gap has widened significantly during the last few days.

In addition to these multi-country frontier ETFs and regional frontier ETFs such as Market Vectors Africa (AFK), it is important to keep in mind that there are many single country ETFs available, with an increasing amount of geographical diversity. Just last week, the first Poland ETF (PLND) was launched. For investors who are interested in single country Middle Eastern ETFs, Van Eck is planning to launch new ETFs for Egypt and Kuwait.

Finally, consider that frontier ETFs are likely to appeal only to investors who can tolerate high levels of risk. The multi-country and single country variants suffer from low liquidity and high volatility, making it unwise to build up large positions until trading volumes increase dramatically from current levels.

[source: StockCharts.com]

Disclosure: none