Technical Analysis on Volatility (My Conceptual Framework)

This post is a continuation of research from my initial blog post "Introducing my Technical Analysis Framework For Options Trading".  My belief and thesis is that technical analysis can and should be applied to analyzing volatility, which could perhaps even help to predict future price behavior.


Technical Analysis on Volatility (My Conceptual Framework)

Does technical analysis work?  Take any of the countless number of technical indicators and confirm their effectiveness by simulating the trading rules over sufficient period of time and one would come to a disappointing conclusion.  Justifiably so, most people would say technical analysis does not work.

I believe the reason why technical analysis, in general, has not been so effective is because technical analysis has focused on analyzing Price and/or Volume over Time.  Yet, these arise from the outcomes of the continuous interaction and intersection of buyers and sellers in a market.  By definition, the moment price occurs, it is already in the past.  In other words, technical analysis and indicators on a chart show us what has happened, not what will or is likely to happen.  In hindsight, it is always easy to know the outcomes of a decision and go back and choose what would have been the “right” decision.

Perhaps, it is time to reapply technical analysis to what it is really good for.  Technical analysis, indicators and charts are really good tools for perception.  Markets, price, volume, time, trend, etc. are all metaphysical objects.  Ask the question, “What is a trend?” and you would get countless answers, which is the same as no one answer.  This is akin to asking the question “What is love?”.  In addressing the process of perception, I came up with my own philosophical concept to more objectively perceive any object, physical or metaphysical.[1]

The key to greater understanding and awareness is to perceive anything in multiple or higher dimensions.  Once again, technical analysis is a great tool for perception.  If we apply this tool to volatility (a different, perhaps higher dimension of price) I believe we can get a much better understanding of price and utilize this understanding for profit.

Profitability of buying or selling a stock is a function of volatility.  With zero volatility, zero profits.  Furthermore, when perceiving price through volatility, one does not have to try to predict the direction of price, but rather if there would be sufficient price movement in order to realize a profit.  In fact, in options/volatility trading, one could also potentially profit from little or no volatility.

I tested these conceptual assumptions with a volatility trading strategy on the SPDR S&P500 (SPY) ETF.  I utilized two volatility indicators and applied technical analysis tools on them for timing of when to buy an options straddle and when to sell an options iron butterfly with outside strikes 5% away from at-the-money strike.  Additional details include using nearest month options with expiration at least greater than 10-trading days away.  Commissions cost of 0.75 per contract and slippage of 0.05 for the entry & exit trades were included.  The contract size was set at 10 straddles and 10 iron butterflies.  Also, no delta hedging was involved.  Finally, the simulation was conducted from beginning of 2012 until August 2013 expiration, the first entry trade posted on 2/14/2012.  The simulation was conducted with thinkBack, a backtesting tool on the thinkorswim platform using end of day marks on options prices.

Strategy	Profits (Gross/Net) STDEV of Daily Net Profits Change Potential % Return
Buying next month straddle on expiration day (cyan)	$10,470 / $8,130 $642 (1) 56.9%
Selling next month iron butterfly w/outer strikes 5% away on expiration day (yellow)	-$18,055 / -$20,935  $463 (2) -100%
Selling iron butterfly w/outer strikes 5% away using volatility timing (red)	$5,790 / $2,910 $164 (3) 57.0%
Buying straddle, Selling iron butterfly using volatility timing (blue)	$9,420 / $4795 $510 (4) 57.1%

(1)   minimum account size required in hindsight would have been $14,285 to cover for $7,285 maximum loss and $7,000 to initiate a position.

(2)   Surprisingly over the time period, selling an iron butterfly at the start of each expiration month would have led to consistent losses.

(3)   A minimum of $5,100 would have been required in hindsight.

(4)   A minimum of $8,400 would have been required in hindsight.

The chart and the table shows simulated results and are for research and education purposes only.  More research would be required on longer time periods, out of sample data, and many more underlying instruments and options on those instruments in order to test the efficacy of technical analysis on volatility.  Yet, the strategy to buy and sell options based on volatility indicators seems to show promise.

The volatility indicator used for long straddle entry is my Realized Volatility indicator.  Details of the Realized Volatility indicator is discussed in my post “FairVolatility (VIX) Model & Indicator, part I”.  The volatility indicator used for short iron butterfly entry is the Standard Deviation indicator in Metastock software.  Logically, when Realized Volatility is seen increasing, one would want to buy the straddle in order to take advantage of  potential increase in implied volatility and expected price movement.  On the sell side, one would want to sell an iron butterfly if the directional movement of the underlying is expected to slow down or be range bound.  No distinction was made in this simulation as to the relative levels of implied volatility vs. realized volatility but could be parameters for further research.

More specifically, the rules were:

1)      Buy straddle when the criteria for Realized Volatility moving up was triggered. Simultaneously exit any open short iron butterfly position.

2)      Sell iron butterfly when the criteria for standard deviation indicator moving down was triggered.  Simultaneously exit any open long straddle position.

3)      Exit any open short iron butterfly position if criteria for standard deviation indicator moving up was triggered.  (Usually, the two indicators moved in same direction with Realized Volatility leading standard deviation.  There were few instances where Realized Volatility remained in a down move but standard deviation started to move up.  This happened in prolonged up move in SPY prices.  In these instances, the short iron butterfly position was exited w/o corresponding long straddle trigger.)

The technical analysis indicators used for timing on these volatility indicators for long and short entry will not be mentioned here, because I am certain through continued research that more effective timing indicators can be found.

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[1] http://thirdeyeinsight.wordpress.com/2013/02/03/what-is-love-the-path-towards-enlightenment/

Fair Volatility (VIX) Estimate Model & Indicator, Part II 8-20-13

This is the second part of the contents of the FVE Model & Indicator.  Once again, the purpose of the two posts is to share ideas.  Your feedback would be highly appreciated.

“Fear” Factors:

The “fear” factor is the second part that goes into my Fair Volatility (VIX) Estimate Model.  VIX is a measure of the implied volatility levels of options on the S&P500 Index with 30-day constant maturity.  VIX reflects the supply and demand for those options.  If demand/supply gets stronger relative to the other, VIX rises/falls.  Therefore, in order to model the “fear” factor, I thought about the several factors that would increase or decrease the demand & supply of options.  The following table summarizes those factors.

Demand & Supply Factors / Expression	Explanation
Volatility Factor
Expected Future Volatility / Use Realized Volatility Measure	Volatility Arbitrage looks at opportunities to profit from differences between expected future volatility of the underlying relative to current implied volatility (IV) level of options.  Demand/Supply for options will increase/decrease if current IV levels are low/high relative to expected volatility.
Fear Factors
Falling Prices / Inverse Correlation	While options are great instruments for use in any type of trading strategy, demand for options is strongest as protection against falling portfolio value.  The shape of the normal IV curve or skew would show the usual relationship between underlying’s price and IV direction.  For the S&P500 Index, there is a strong inverse relationship between VIX & the S&P500 Index.
Speed/Acceleration of Price changes /Slope of Trend	Speed is related to but different than volatility.  A stock in a strong uptrend could have low to stable volatility, but the speed would be relatively high.  Demand for options is strong when the speed of decline is high.
Price Trend of the underlying instrument / Relative Strength of Prices	Demand for options increases when the S&P500 index is in a down trend while supply of options increases when S&P500 Index is in a steady uptrend.  This is similar to inverse correlation, but more specific to the price trend.
Leading Factor, Wave Factor / Stochastic RSI of Prices	Options prices reflect the expectation of future price behavior of the underlying instrument.  In other words, the changes to implied volatility levels is believed to be a leading indicator to changes to volatility of the underlying.  While historically this has not always been the case, we should accommodate this assumption in our model, which is built using the underlying prices.  In technical analysis, oscillating indicators such as Stochastic Oscillator has some properties of turning before the actual prices do.

Let us try to model all the factors and assumptions described in the table by combining several technical analysis indicators[1].

Fair Volatility (VIX) Estimate or FVE Model & Indicator is a function of:

1)      Realized Volatility

2)      Inverse Correlation

3)      Slope of Price Trend

4)      Relative Strength Index (RSI)

5)      Stochastic RSI

6)      Adjustment Weight of each Indicator

7)      Adjustment constant for best fit with VIX.

First & major factor is the volatility of the S&P500 Index itself.  I developed the “Realized Volatility” measure discussed in the “Volatility Factor” section to model volatility.

Next, we can combine the inverse correlation and slope of a price trend factors by using the Linear Regression Slope (LRS) indicator.  The LRS indicator moves above zero if the price trend over a specific time period is calculated to be rising and below zero if the price trend is calculated to be falling.  For inverse correlation, I subtract values from the FVE model when the LRS is positive and add values if the LRS is negative.  More specifically, however, instead of looking at the speed of a price trend, I believe looking at the acceleration of the price trend would be more optimal.  This can be accomplished by comparing the distance between the LRS indicator and its moving average.  Algorithmically, this is expressed by the following formula:

Negative of (Linear Regression Slope 11 day – simple 11-day moving average of the LRS (11)) * Adjustment Weight

Furthermore, we want to look at the current price of the S&P500 Index in relation to its past prices given a time frame.  This insight came to me after conducting analysis on historical VIX values.  The following chart shows the median VIX values when the S&P500 Index is in an uptrend or downtrend relative to several of its moving averages

The way to interpret this chart is as follows.  The black & grey lines show the long-term median VIX values since 1994.  The black line represents the median value of all VIX values when the S&P500 Index was above its moving averages, from 5-days to 240 days.  The grey line represents the median value of all VIX values when the S&P500 Index was below its moving averages.  The red and orange lines look at median VIX values during specific times of high volatility, for example between 2008-2012. The blue and cyan lines look at median VIX values during specific times of low volatility, for example between 2003-2007.

The current market since 2012 is that of a low volatility environment.  Therefore, given the current environment, as the S&P500 Index fluctuates above (for example) its 20-day moving average, we can expect with 50/50 probability that VIX would be around 13 (blue line).  When the S&P500 Index moves below its 20-day moving average, we can expect with 50/50 probability that VIX would be around 17 (cyan line).

We can use moving averages to express whether VIX values are expected to be lower or higher, but the 22-day Relative Strength Index expresses this more efficiently and is easier to calculate.  Therefore, the following formula represents expected incremental changes to VIX dependent on the price trend of the S&P500 Index.

(100 – RSI(22))*0.01 * Adjustment Weight

The leading or wave factor tries to take into account the assumption that implied volatility level of options is a leading indicator to price volatility of the underlying instrument.  Even when the S&P500 Index is moving in a clear trend, intraday or daily prices moves up & down in wave form.  VIX is not only affected by price trends but also is affected by intraday & day to day price behavior.  The Stochastic Relative Strength Index indicator moves quickly up & down with high sensitivity based on the intraday and day to day price behavior of the S&P500 Index.

We should take caution that no price based technical indicator acts as a true leading indicator.  They are lagging indicators.  Using them would be like driving a car looking at the rear-view mirror.  However, the sensitivity of the Stochastic RSI indicator serves the purpose of anticipating possible changes to VIX quickly and in combination with other factors serves its purpose better.  The algorithm for this leading or wave factor is as follows.

((100 – Stochastic RSI)*.01)*Adjustment Weight

You probably have noticed the “Adjustment Weight” attached to the three factors described above.  Honestly, this Adjustment Weight is a blunt calculation to adjust the weighting of the various factors to the absolute value of volatility.  In other words, a 10% move in VIX when VIX is at 30 is twice the amount as when VIX is at 15.  Since the FVE model takes the base Volatility Factor and adds the various components of the Fear Factors, I needed to increase the value of those components as volatility rises.  The Adjustment Weight was calculated as follows:

1 + (75% of Realized Volatility / long-term average of VIX which is around 21.5)

The final component of the FVE model is the Adjustment Constant.  This Adjustment Constant was used as a value for best fit to the actual VIX values.  Yes, this is curve fitting, but if we take a look at the long-term, 6-month average of the difference between VIX and FVE model without this Adjustment Constant, we can see that the difference has been ranged from 2.0 – 7.0 most of the time.  I have used 3.2 since developing the FVE model since May 2010.  Furthermore, this Adjustment Constant is in of itself a good indicator to show structural changes to VIX.  For example, one of the reasons why the FVE model’s trading performance has been lackluster since October of 2012 could be that volatility has been aggressively sold since the ECB’s OTM policy announcement on September 6, 2012, when much of the fear of Euro’s collapse that was built into volatility markets quickly subsided.  With the Adjustment Constant untouched, FVE Model has perhaps been overvaluing VIX in recent months.  Nevertheless, this Adjustment Constant can be but should not be changed.

 Compiling all the factors together, the FVE indicator is built as follows:

1)      11-day exponential moving average of 75% of Realized Volatility Calculation Value[2] +

2)      Negative of (Linear Regression Slope 11 day – simple 11-day moving average of the LRS (11)) * Adjustment Weight +

3)      (100 – RSI(22))*0.01 * Adjustment Weight +

4)      ((100 – Stochastic RSI)*.01)*Adjustment Weight +

5)      Adjustment Constant of 3.2

The following chart shows graphically each component of the FVE indicator.

In summary, the Fair Volatility (VIX) Estimate Model and Indicator is just that--an attempt to model VIX.  FVE indicator is a graphical representation of all the assumptions used to construct the model in its attempt to show how VIX would move in real-time based on prices of SPY.  Because of the numerous variables and the crudeness of the math, the danger that FVE model over fits past data is ever present.  However, I have analyzed FVE model on VIX for over three years now since its creation.  The efficacy of the FVE model (I believe) lends support to the assumptions that I have built into the model.

Of course, because FVE model is represented as an indicator, trading strategies can be devised rather easily using the FVE indicator.  For example, let us assume the following simple strategy.

Buy front month VIX futures if FVE > FVE 11 days ago AND
VIX futures price < FVE,

Sell front month VIX futures if FVE < FVE 11 days ago AND
VIX futures price > FVE.

Or

Buy VXX if FVE > FVE 11 days ago AND VIX futures price < FVE,

Sell VXX if FVE < FVE 11 days ago AND VIX futures price > FVE.

The simulated results would be as follows on VIX front month futures since 1/30/2008

includes 0.075 points slippage & $2.50 per contract commission costs

The simulated results would be as follows on VXX since 1/30/2009

includes 0.05 cents slippage & $25 commissions cost

However, the potential for FVE model utilized in a trading system is much greater.  Recently, I have simulated a trading system with an additional factor included in the FVE model for the purposes of using it as a trading model.  Once again, however, I am reluctant to disclose the adjustment to the FVE model and trading rules because I am highly aware that the adjustments could just be curve fitting or over optimization to past data.  This adjustment and new rules would need to stand the test of time.

I am, however, very interested to find out if my insights to making the adjustment to the FVE model would prove to be sound.  Once again, please take the simulated results with heavy skepticism.  This next graph only shows the maximum potential, not the likelihood of performance.

includes 0.075 points slippage & $2.50 per contract commission costs

Thank you for reading these latest two posts on FVE model & indicator and my blog.  I hope you found it educational.  I have built the FVE indicator in Metastock and had them built for eSignal platforms.  I will try to share these in the not too distant future (although I may have to charge a small fee for processing...sorry).  Finally, I am sharing my research and ideas freely.  However, if you utilize them, please at least acknowledge my research and efforts.  Better yet, share these posts.  As you can see, I am not trying to profit from them.  Thanks.

Steven Lee

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[1] There are many resources to describe the formulas and assumptions behind most widely used and known technical analysis indicators.  Just search for them on the web.

[2] I actually use a filtered version of Realized Volatility Measure that takes out the outlier effects, for example flash crash of 2010

Fair Volatility (VIX) Estimate Model & Indicator Part I, 8-19-13

Here is a section of content that I have written and have yet to write much more.  I do not know what the final structure of the amalgamation of my research over the years would be, whether that would take shape in an ebook, an educational manual, or just many more posts in my blog.  This blog has served as a personal journal of my interests in the financial markets and in volatility.  Perhaps it is time I start to engage more with those that visit this site.  I would highly appreciate any feedback you could provide.  Thank you.

Fair Volatility (VIX) Estimate Model & Indicator 8-19-13

After the financial crisis of 2008, I believed the market structure had changed significantly and new models—or at least the discarding of previous rules--were needed to generate a trading “edge”.  So, I designed Fair Volatility (VIX) Estimate Model & FVE Indicator in May 2010.  Trading VIX Derivatives and VIX Exchange Traded Products seemed like the ideal assets class to utilize my trading experiences from both the directional and volatility trading worlds.

VIX is calculated from a weighted average of implied volatilities from options prices of multiple strikes on the S&P500 Index with a constant maturity of 30 days to expiration.  For example, a VIX number of 15 technically reflects the option market participants’ expectation that the S&P 500 Index would move within a ~4.33% range up or down (with confidence of one standard deviation or 68%), within a one-month time frame.  Because VIX represents an annualized volatility number, we need to divide 15 by the square root of 12 (months in a year) in order to come up with a one-month equivalent number.

In reality, however, VIX reflects the market’s expectation of price volatility, fluctuation AND behavior of the S&P500 Index looking 30-days into the future.

S&P500 Index options are bought as insurance to protect against potential decline in the value of equity portfolios.  Obviously, the higher the demand, higher the value of protection and thus higher VIX levels.  This is why VIX is commonly referred to as the “Fear Index”.  It is well known that VIX usually moves in opposite direction as the S&P500 Index.  This inverse correlation is seen 70 – 80% of the time.  Therefore, in building a VIX model, we should look at more than just volatility.

VIX is a function of Volatility Factor & “Fear” Factor.

Before I delve in to these factors, I want to explain that any model with multiple variables that look highly promising in simulation and research could flop when applied to markets real-time.  Most often, this is due to either poor design and/or "curve fitting", which is selecting specific parameters that would have delivered strong performance given very specific conditions as experienced in the past, but utterly flop in current and future market environments because markets are never the same.  That being said, I have simulated the Fair Volatility Estimate indicator using simple trading rules on VIX futures and VXX for over three years now.  I wanted to share my designs, even if they are crude, for educational purposes.  The attractiveness and utility in trading volatility as an asset class is too good not to learn more about it.

 Chart of FVE & VIX 8-19-13

FVE Trading Simulation on Front Month VIX Futures 8-16-13

Volatility Factor:

Based in options theory, it is my understanding that the core component of any volatility model is a way to efficiently calculate realized volatility, otherwise known as historical volatility or statistical volatility.  I prefer the term “realized volatility” because there is a strategy in options volatility trading known as gamma scalping, which is a form of volatility arbitrage

In gamma scalping, one would buy for example the options straddle of an underlying stock or index and then at certain price or time intervals hedge the delta exposure of the options straddle by buying or selling the underlying instrument.  Let me explain this process in greater detail.

For example, let us say you bought 100 September straddles (long Sep 37 call, long Sep 37 put, each 100 contracts) for the combined price of 2.25 and implied volatility of 24% on XXX stock.  This straddle purchase would cost you $22,500.  Now let us also imagine an extreme case that XXX stock price for the next one-month period remains unchanged on a day-to-day closing price of 37.  In this case, at expiration, you would lose the entire $22,500 by holding the straddle as it expires completely worthless

However, let us also assume in this extreme example that intraday, XXX stock price fluctuates up or down by $1 and back to the closing price of 37.  Let us also assume that you hedge your delta exposure of the straddle by buying and selling XXX stock as the price fluctuates intraday.  If the gamma on the 37 strike options is 0.14, then with XXX stock $1 lower to 36 intraday, the delta of the calls would change from +0.50 to +0.36, and the delta of the puts would change from –0.50 to –0.64.  The new net delta of the straddle with stock price at $36 would have changed to -0.28 from zero.  On an options position of 100 straddles, this would mean buying 2800 shares (-0.28 * 100 straddles * 100 unit shares/per option) of XXX stock at the price of 36 to bring the net delta exposure to zero.  Finally, as the price of XXX stock moves back to 37 by market close, you would sell the 2800 shares that were bought at XXX stock price of 36 in order to bring the net delta exposure back to zero.  On the flip side, if the stock moves up from 37 to 38 intraday, then you would short sell 2800 shares of XXX stock at 38 to hedge the new delta exposure of the straddle of +0.28.  Once again, as the stock price closes at 37, you would buy back the 2800 shares stock sold short at 38. 

This is a simplistic and unrealistic example which does not account for the change in gamma over time as well as execution costs.  However, if you were to repeat this process each and every day for 21 trading days or one month time frame, you would have lost the entire $22,500 you paid for the options straddle but profited $58,800 from the delta hedging process of buying and selling stock for a net profit of $36,300!

This is where the term “realized volatility” comes from.  A $1 price fluctuation intraday of a $37 stock is equivalent to a 42.9% volatility (1/37 * square root of 252-- # of trading days per year).  Remember that the September 37 straddle was bought at 24% implied volatility.  The rule in any profitable trading is to buy/sell lower/higher and sell/buy higher/lower.  In gamma scalping, one is buying/selling implied volatility of options and selling/buying by capturing or “realizing” stock volatility.

Let us take a look at an example of selling implied volatility or selling 100 straddles using the same scenario as above, except that instead of $1, XXX stock is assumed to fluctuate just $0.30 intraday.  To hedge the delta exposure with stock price at 36.70 and 37.30, you would buy and sell 840 shares of XXX stock.  The net result would be $22,500 profit from options less $5,292 from delta hedging process for a net profit of $17,208.  A $0.30 price fluctuation on a 37 stock price is equivalent to a 12.9% realized volatility.  In this reverse example, one would have sold 24% implied volatility and bought at a 12.9% realized volatility.

Volatility arbitrage is the main reason why implied volatility and realized volatility move hand in hand.  If they did not, then there would be tremendous opportunities to buy or sell implied volatility against stock volatility.  The most important and critical challenge, however, in deciding whether to buy or sell volatility is to determine future volatility of the underlying instrument.  Ah, of course!  The future is unknown and uncertain.

However, volatility I believe is actually more predictable than the price direction of a stock.  Think of volatility as a volt meter.  We know from physical reality, that energy moves back and forth from high intensity to low intensity, unlike stock prices which could continue to move up or down.

There are several ways to measure a stock’s price volatility.  Historical volatility of closing prices is the simplest & most widely known.  The following lists other more efficient ways.

1)      Historical volatility: close to close

2)      Exponentially Weighted

3)      Parkinson: High to Low

4)      Garman-Klass: Open/High/Low/Close

5)      Rogers-Satchell: Open/High/Low/Close

6)      Yang-Zhang: Open/High/Low/Close

7)      GARCH & EGARCH models[1]

8)      Average True Range[2]

9)      My “Realized Volatility” calculation

The following report provides an excellent summary of the various ways to measuring historical volatility from 1 – 6 in the above list--(http://www.todaysgroep.nl/media/236846/measuring_historic_volatility.pdf.

GARCH models are also widely looked at as a way to predict future volatility.  The Average True Range indicator is widely used in technical analysis, but seldom mentioned in volatility modeling circles.

When designing my “Realized Volatility” measure, I wanted something that was both simple and usable.  I analyzed my own delta hedging actions while I was an options market maker and came up with the following formula.

Realized Volatility = 11 trading day exponential moving average of [If (Absolute Value(Log(High/Prior Close))>Absolute Value(Log(Low/Prior Close)), then Absolute Value(Log(High/Prior Close))*square root(252), else Absolute Value(Log(Low/Prior Close))*square root(252))*Adjustment Factor].

Basically, I look at how much the market pushes the price up or down from the prior closing price and translate this into an annualized volatility measure.  Then I take the 11-day exponential moving average of those values to come up with my Realized Volatility calculation.  The adjustment factor can be 0.80 – 1.00, depending on the longer-term implied volatility levels of the underlying instrument.  This Realized Volatility measure does not take into account the general rise in implied volatility levels prior to earnings announcements or other events, therefore, should not be applied to stocks, except for periods prior to one month before and 2 weeks after such events.  It is appropriate for indices, commodities and sector ETFs.  The adjustment factor also serves as a tool to use if I want to have a bias of being short or long options, in general, but this adjustment factor makes this measure a tool and not necessarily a theoretical model.

Here is what the Realized Volatility indicator looks (blue), compared to VIX (black) and the traditional historical volatility measure 11-days (green), & the FVE indicator (red).

Fear Factors:

Part II is continued in the August 20, 2013 post.

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[1] http://vlab.stern.nyu.edu/doc/1?topic=apps

[2] http://en.wikipedia.org/wiki/Average_true_range

Easy Volatility Investing by Tony Cooper

This is the link for an abstract.  The research is very similar to what I have been conducting with my Fair Volatility Estimate model in that VIX Exchange Trade Products trading has shown tremendous profit potential.  His research is conducted in a much more organized manner than mine.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2255327


Upon closer reading, some strategies presented in the paper would not make viable "trading systems". One of the strategies has not shown a trade since late 2011. Such few trades does not a trading system make... Good read, though...

(this post was adjusted on August 22nd to correct for some errors)