Frequently Asked Questions: 1QBit

Who is 1QBit?

1QBit is a software company focused on solving intractable industry problems with the most advanced quantum and classical hardware available. 1QBit is backed by major corporations including Accenture, Allianz, CME Group, Fujitsu, Royal Bank of Scotland and the Siam Commercial Bank. Its hardware partners include D-Wave, Fujitsu, IBM, Microsoft, Rigetti and others. 1QBit’s publicly-announced client list includes DowDuPont, Biogen and NatWest.

1QBit’s 60+ researchers and developers hold over 100 university degrees in a wide variety of specialized areas including medicine and biology, machine learning, computational physics, chemistry, mathematics, computer science, business and engineering. 1QBit develops algorithms in a variety of fields and applies the synergies that occur when concepts and techniques cross from one field to another. This includes the analysis of market sentiment based on volume, price and open interest data available from sources like CME DataMine.

What is the Market Sentiment Meter (MSM)?

The Market Sentiment Meter is organized around the concept that typical bell-shaped risk-return probability distributions seriously underestimate tail risk and that just augmenting the tails of the distribution is not necessarily sufficient.

As an illustration, take event risk where traders might imagine two dissimilar outcomes. For example, since 2016, we have seen event risk associated with elections – UK Brexit Referendum of June 2016, U.S. Presidential election of November 2016, French and UK elections in 2017, Brazilian elections of October 2018, U.S. Congressional elections of November 2018, etc., where there were two possible scenarios. Before the event, the market typically prices the probability-weighted outcome, or the middle ground. After the event, when the outcome becomes known, the market immediately moves away from the middle ground to the “winning” scenario – a price break. For example, with Brexit, the leave vote generated a sharp downward move in the British pound (versus USD), while a Remain vote would have presumably generated a sharp almost instantaneous rally in the pound – either way, the pound was no longer going to trade in the middle.

To handle risk-return probability distributions that may not have bell-shaped curves and may be highly asymmetric, the MSM method uses a mixture distribution process, and gathers a variety of information from futures and options prices, volumes and intra-day activity to create a proxy for the actual unobservable distribution. While implied volatility from options prices is one of the metrics used in the MSM process, it is not the sole primary driver of the process and it is not allowed to bias the results toward bell-shaped solutions.

The MSM risk-return probability distribution has the four characteristic shapes shown below.

Balanced risk is the most common state and shows a bell-shaped risk-return probability distribution.

Complacent is when the risk-return probability distribution is tall and narrow. Market participants have relatively few worries.

Anxious is when the distribution broadens and may even move off-center. Market participants see worries everywhere.

Bi-Polar or Event Risk occurs when market participants are weighing the probabilities of two starkly different outcomes and the distribution has two modes. Bi-polar states are rare and typically short-lived, yet extremely important to recognize.

How is the MSM Calculated?

The MSM risk-return probability distribution is calculated using a proprietary process based on multiple metrics from the price, volume and intra-day activity of futures and options markets. Read our research paper on “Reimagining Probability Risk Distributions,” for an intuitive explanation of our process.

What does the MSM look like on a real product?

The time series below shows the states of the Market Sentiment Meter overlaid on the settlement price for the nearby futures contract (the front month) in Henry Hub Natural Gas physically delivered futures (NG).

Casual observation may suggest that bi-polar (event risk) periods are sometimes followed by important price moves. As a cautionary note, the concept of event risk is only that after an event, one of the two possible outcomes has clearly occurred, and that all of the market participants are now acting on this common knowledge. That said, the anticipated choice might have been between up or down, moving or staying still, high or low volatility, etc.

Are there risks in using the MSM to measure risk?

Prices, volumes and intra-day activity in futures and options markets are taken to represent the risks perceived by market participants and based on their observed actions. We do not claim any predictive value as we are only attempting to describe an unobservable risk-return distribution to inform discussions and analysis of marketplace risks.

What type of data does 1QBit provide?

The Market Sentiment Meter is available as a subscription, which may be ordered for any of the following products:

  • CME S&P 500 Index E-Mini futures (ES) and options
  • CBOT 10-Year Treasury Note futures (TYF) and options
  • CME Euro/USD FX futures (EC) and options
  • NYMEX WTI Crude Oil futures (CL) and options
  • NYMEX Henry Hub Natural Gas futures (NG) and options
  • COMEX Gold futures (GC) and options
  • CBOT Soybean futures (S) and options
  • CBOT Corn futures (C) and options

The subscription includes:

  • Daily updates
  • Full history from January 2012
  • Curated Data File Package (CSV)

The Curated Data Files contain a wide variety of metrics, including futures settlement prices, futures and options volumes, a representative proxy for implied volatility for options, and many other derived series, as well as our market state classifier, which may be:

  • Balanced
  • Complacent
  • Anxious
  • Bi-polar (event risk).

Application notes and research papers will be made available to assist the subscriber as they are prepared and published.

What is the file format of the 1QBit data?

Subscription files are provided as Comma Separated Values (CSV).

Application notes and R&D papers will be made available either as a downloadable PDF or through a web page, to be determined.

What is the average daily file size?

Curated Data File Package (CSV) per product ranges from 7 MB to 13 MB. This depends on the number of zeros in the file, which are represented by “0”, as opposed to the standard 9-digit precision.

How many files are available per day?

The Curated Data File for each product is updated after each trading day. There are currently eight products available.

What is the delivery frequency of the data?

The files are updated after the close of each business day, as soon as the preliminary end-of-day settlement files (P files) have been published by CME Group and made available to 1QBit.

Refer to the CME DataMine EOD FAQ for details.

What time is delivery time of the data each day?

You can always download the most recently updated files from CME DataMine. The updated files will normally be available within four hours of their publication by CME Group. Typically, the files will be available between 2 a.m. and 5 a.m. Central Time (CT). However, from time to time, delays may occur.

Are files compressed?

The CSV files are not compressed.

Are sample files available?

Sample files will be available with details available in the future.

How far back historically is data available?

Time series in the Curated Data File starts on January 3, 2012, the first futures and options trading day of 2012.

Where does the futures settlement price and volume data come from?

All price and volume data comes from the End-of-Day (EOD) settlement files published by CME Group and offered for purchase by CME DataMine.

What settlement price is used on days that a market is closed?

The settlement price will always be the price published by CME Group.

In order to keep the time series for all of the products in exact alignment, the following special cases were handled as follows:

Good Friday

In recent years, no CME Group markets have been opened on Good Friday. In 2010, 2012 and 2015 however, the Equities, Rates and FX products were allowed to open on Thursday evening with Friday’s trade date, and allowed to trade overnight until 8 a.m. on Friday, after which the markets were closed and the trades booked on the Friday. The volume in all cases was small in comparison to that of nearby days. The Curated Data Files do not include any Good Friday data.

National Day of Mourning for former U.S. President George H. W. Bush (December 5, 2018)

There was no trading at all for interest rate products on December 5. CME Group published end-of-day settlement prices for December 5 that were identical to the prices reported for December 4. In equities, the markets were closed from 8:30 a.m. CT onward on December 5, but were open overnight, which made it possible for a regular settlement price to be published. All other markets remained open for their usually scheduled hours. The Curated Data Files contain the following data for interest rate futures and options:

  • Settlement prices published by CME Group
  • Total volume published by CME Group, which consisted of PNT (privately negotiated trades) that were cleared through CME Clearing. These PNT trades did not show up in high and low prices.
  • High and low prices interpolated from the previous day, based on the percentage spread. Our method keeps the time series for all the MSM products based on exactly the same days. It also ensures that time-dependent calculations using raw data in the CSV file will match the same calculations done using the processed data in the CSV file.

How does the roll from an expiring month affect the definition of the nearby month and other calculations, such as day-to-day return?

In most futures products, volume and open interest is largest in the contract with the nearest expiry date. However, as the expiry date draws nearer, volume and open interest move to the next available expiry. This is referred to as the roll and can be spread over many days.

The Market Sentiment Meter defines a nearby futures contract and second futures contract. The nearby contract is usually exactly that, i.e. the futures contract with the closest expiry and the greatest volume. Each day, however, the MSM program compares the volume in the nearby contract with the volume in all subsequent expiries. When the volume in a later contract surpasses the volume in the nearby contract, the definition of the nearby futures contract is updated to be the new contract with the largest volume. The definition does not move back, even if the volume in the expiring contract temporarily exceeds the volume in the new nearby.

When the nearby futures contract is advanced to a later expiry, the second futures contract also advances.

For contracts such as Corn, which trades in March, May, July, September and December, the next expiry may be more than a month away. There are also contracts, such as Gold, that trade the nearest calendar months in addition to the standard months. The roll logic is driven by volume and does not attempt to select the expiry that “ought” to be next.

In order to keep day-to-day ratio data consistently defined across a roll, the Curated Data File reports the previous nearby reference price. This is the settlement price on the previous day for the contract being reported as the nearby contract.

For example, in CME Euro/USD FX futures (EC), the 2016 the Market Sentiment Meter’s nearby roll, from the December 2016 ECZ16 contract to the March 2017 ECH17 contract, took place on December 16. The second futures contract advanced from March to June on the same day.

  • On December 15, the nearby contract was ECZ16, and the previous nearby reference price was $1.05605, the settlement price for ECZ16 on December 14
  • On December 16, the nearby contract was ECH17, and the previous nearby reference price was $1.04715, the settlement price for ECZ17 on December 16

The return in the nearby contract is always computed from the previous nearby reference price.

Why is there sometimes no high or low price data in the second futures contract columns?

Blank price data can be present for several reasons.

For example, if there was no volume traded in the second futures contract, there will be no high or low price to report. Bids and asks that do not trade are not used in the MSM calculations.

In some cases, there may be volume traded in a way that does not establish a high or low price, for example:

  • Volume from trade-at-settlement orders
  • Privately negotiated trades that are cleared by CME Group without price reporting

This situation occurs most frequently in 10 Year Treasury Note futures, which trade for March, June, September and December. When open interest is rolling from (say) March to June, there is typically not much activity in the September contract.

CME Group calculates a settlement price for all listed contracts, even if there is no trading on any given day. It is not uncommon for contracts with distant expiry dates to slowly accumulate open interest over many low-volume (and no-volume) days.

What is a smoothed time series? How does long-term differ from short-term?

The Curated Data File contains a variety of smoothed time series. Our research has indicated that comparing short-term smoothed metrics to long-term smoothed metrics can lead to very useful insights into how market risk perceptions are evolving.

Smoothing is exponential. For example:

(today’s smoothed IVOL) = k * (today's IVOL) + ( k-1 ) * (yesterday's smoothed IVOL),

where k = 1/(number of smoothing days).

For short-term smoothed series, the number of smoothing days has been arbitrarily set at 30 and for long-term smoothing is set at 200 days. The number of days is configurable by product and we are continuing to conduct research related to the most appropriate smoothing processes.

We prefer an exponential smoothing process to a moving average window process. Exponential smoothing values recent data more highly than older data. In a moving average window, the data points within the time window are all considered equal, and we strongly believe that market participants do not process information in this manner. With a moving average window method, if a large movement occurs and then is reversed, the large temporary movement would retain the same impact even as it fades into history. With exponential smoothing, the large temporary movement loses influence every day.

What does the volume data include?

Volume data reported in the Curated Data Files is the total daily volume reported by CME Group. This includes:

  • CME Globex volume,
  • Floor volume (where it exists)
  • Exchange for Related Position (EFRP) volume
  • Privately Negotiated Trades (PNT) cleared through CME Clearing
  • Other volume subcategories designated by CME Group (these are typically quite small)

An EFRP can be an exchange for physical (EFP), e.g. from financially-settled futures to physical futures such as CL, NG, etc., an exchange of futures for risk (EFR), or an exchange of options for options (EOO). For additional detail on EFRP transactions in a specific product, consult the relevant sections of the Exchange Rule Book.

How is historical volatility calculated?

Historical volatility within the Market Sentiment Meter uses exponential smoothing as described above. For volatility, a weighted historical standard deviation is calculated from a Daily Variance Proxy, defined as the square of the percent change in price. The daily variance proxy is weighted exponentially, so that more recent price movements contribute more to this historically weighted standard deviation. This method mimics the traditional definition of volatility as the standard deviation of the distribution of percent price movements (as it is in the Black-Scholes model).

The Market Sentiment Meter is influenced by differences between the forward-looking volatility estimates seen in options prices, and the backward-looking volatility estimates made from the settlement prices in the underlying futures contracts.

The historical standard deviation is annualized so that it can be compared to other volatilities, most notably the implied volatilities published by CME Group.

How are moving averages calculated?

While our MSM metrics process uses exponentially smoothed time series data, for ease of user comparisons and for use in momentum trading models, we also provide some pre-calculated moving averages. Each moving price average is the uniform windowed average of today’s settlement price and the settlement prices from prior days.

For example, the 20-day moving average is computed from today’s settlement price and the settlement prices from 19 prior days. The average is given to nine decimal places, regardless of the price ticking.

The Curated Data Files begin on January 3, 2012. The moving price averages, peak prices and other time-dependent data have been initialized with values based on settlement files prior to that date.

The moving price averages are calculated for the nearby futures contract settlement price. The 200-day moving price average will therefore contain one or more contract rolls. Even the 20-day moving average will contain a roll day in some contracts. Although there may be a small jump in the price when moving from expiry to the next, it is assumed that the averaging will give greater emphasis to the much larger number of non-roll days. That said, the interpretation of a 60-day moving price average in Crude Oil futures (which roll monthly) will have to be different from the interpretation of a 60-day moving price average in 10-Year Treasury Note futures, which roll quarterly.

What are the descriptive parameters of the risk-return probability distribution?

The risk-return probability distribution is a proprietary process using a mixture distribution method. See our related research papers for more in-depth explanations.

How are the probabilities of reaching price targets calculated?

The probabilities are calculated using today's risk-return probability distribution.

For example, to calculate the probability of reaching 20% above today’s 60-day average in the coming year: The price value for 20% above the 60-day moving average is expressed as a return relative to the today's settlement price and the distribution used to calculate the probability of this return being exceeded.

The target return is used as the left-hand side of a semi-infinite interval, and the probability calculated as the area under the tail of the distribution.

Data Structure

CsvHeaderName

Description

Typical Value

BizDate

Business date for the settlement price and other data reported on this row. In general, this will be the last trading date. Expressed as a string.

2018-Oct-23

Y

YEAR of the business date, as an integer

2018

M

MONTH of the business date, as an integer

10

D

DAY of the business date, as an integer

23

Futures Product Code

Product code used by CME DataMine for the futures contract, in upper case

TYF

Options Product Code

Product code used by CME DataMine for the options contract being used in the model on this day. In most cases, the options code does not change through time; however, there is an exception for the option used for the Euro FX (USD per EUR). The original option code was ZC from 2012 to 2017, but EUU afterwards, after a shift in the product option type. This field always shows the option that was in use on the corresponding business date.

TC

Nearby Futures Settlement Price

The nearby future is the futures contract with the largest daily volume. When trading “rolls” from one expiry to the next, the nearby future moves as soon as the next expiry has a larger volume and does not move back.

118.265625

Nearby Futures High Price

CME Globex High price as published by CME Group in the EOD settlement P File. For the nearby futures contract.

118.65625

Nearby Futures Low Price

CME Globex Low price as published by CME Group in the EOD settlement P File. For the nearby futures contract.

117.96875

Nearby Futures Contract Year

The year of the delivery month that defines the nearby futures contract. Given as an integer. For example, the SH19 (March 2019) Soybean future has a contract year of 2019.

2018

Nearby Futures Contract Month

The delivery month that defines the nearby futures contract. Given as an integer. For example, the SH19 (March 2019) Soybean future has a contract month of 3.

12

Nearby Futures Contract Volume

Total volume traded and settled on the business day in the nearby future. Includes CME Globex volume, floor volume (where it exists), EFRP (exchange for a related position). Total volume also includes PNT (privately negotiated trades) that are cleared through CME Clearing.

2923885

Second Futures Settlement Price

The second future is the most actively traded futures contract with a date after the nearby future

118

Second Futures High Price

Same definition as for the corresponding nearby futures contract, but for the second future

118.375

Second Futures Low Price

Same definition as for the corresponding nearby futures contract, but for the second future

117.78125

Second Futures Contract Year

Same definition as for the corresponding nearby futures contract, but for the second future

2019

Second Futures Contract Month

Same definition as for the corresponding nearby futures contract, but for the second future

3

Second Futures Contract Volume

Same definition as for the corresponding nearby futures contract, but for the second future

13050

Total Futures Volume

Total futures volume as reported by CME Group

2936935

Representative Implied Volatility

Representative IVOL is chosen from the values published by CME Group using the following criteria: furthest expiry with a daily volume greater than 10 lots and a reported delta between 0.45 and 0.55. Of these, the contract with the largest traded volume is chosen, which may be a put or a call.

0.0377374

Year of Implied Volatility Contract

Year of the delivery month date for the selected options contract. The delivery month for an options contract is typically the same as the delivery month for its underlying futures contract.

2019

Month of Implied Volatility Contract

Delivery month for the selected options contract

3

Put Option Volume

Total put options volume as reported by CME Group

435889

Call Option Volume

Total call options volume as reported by CME Group

964321

Total Option Volume

Total options volume as reported by CME Group. This is the sum of the total put and total call volumes.

1400210

Put Option Open Interest

Total put options open interest as reported by CME Group

2158047

Call Option Open Interest

Total call options open interest as reported by CME Group

2145525

Total Option Open Interest

Total options open interest as reported by CME Group. This is the sum of the total put and total call options open interest.

4303572

Nearby Futures Previous Day Reference Price

Settlement price for today's nearby futures contract on the previous trading day.

118

Daily Percent Change in Price

Ratio calculated as the difference of natural logs

0.002248529

Excess Return Index

The simple return index (i.e. without subtracting an estimated risk-free return). The index is set to 1.0 on the Curated Data Start Date of January 3, 2012. For later days, it is calculated from the daily returns, so that it always applies to the nearby futures contract (which changes across the rolls).

1.4733518461

Short-Term Smoothed Implied Volatility

Smoothing is exponential, i.e. (today’s smoothed IVOL) = k * (today's IVOL) + ( k-1 ) * (yesterday's SMOOTHED IVOL), where k = 1/(short term days).

 

The number of days for short-term smoothing is 30.

0.036760346

Long-Term Smoothed Implied Volatility

Same as short term smoothing, except with a scale factor of 200 days.

0.040106398

Daily Variance Proxy

The daily variance proxy is the square of the daily percent change in price.

5.05588E-06

Short-Term Smoothed Historical Standard Deviation

The short-term smoothed historical standard deviation is computed by smoothing the daily variance proxy with a time constant of 30 days, and then taking the square root. The value in the file is annualized.

0.032103478

Long-Term Smoothed Historical Standard Deviation

The long-term smoothed historical standard deviation is computed by exponentially smoothing the daily variance proxy with a time constant of 200 days, and then taking the square root. The value in the file is annualized.

0.066664962

Ratio of Short-Term to Long-Term Smoothed Standard Deviation

The ratio of the short-term smoothed historical standard deviation to the long-term smoothed historical standard deviation, as defined above.

0.48156449

Ratio of Short-Term HISTORICAL STD DEV to Current Implied Volatility

The ratio of the short-term smoothed historical standard deviation the implied volatility of the underlying futures product, computed from the most distant but still actively traded options.

0.850707209

High Price to Low Price Ratio as Percent Spread

High price minus the low price, divided by the low price. For the nearby futures contract. Computed as a difference of logs.

0.005810899

Short-Term Smoothed High-Low Percentage Spread

Same as other short term smoothed data. Exponentially smoothed with a time constant of 30 days.

0.003180144

Long-Term Smoothed High-Low Percentage Spread

Same as other long term smoothed data. Exponentially smoothed with a time constant of 200 days.

0.00355142

Ratio of Short-Term Smoothed to Long-Term Smoothed High-Low Percentage Spread

The ratio of the short-term smoothed high-low percentage spread to the long-term high-low percentage spread. Indicates when a change in the high-low percentage spread has been sustained for some time.

0.895457119

Short-Term Smoothed Put Option Volume

Same as other short term smoothed data. Exponentially smoothed Put Option Volume with a time constant of 30 days.

270539.8194

Long-Term Smoothed Put Option Volume

Same as other long term smoothed data. Exponentially smoothed Put Option Volume with a time constant of 200 days.

233339.6376

Ratio of Short-Term Smoothed to Long-Term Smoothed Put Option Volume

The ratio of Short-Term Smoothed Put Option Volume to the Long-Term Smoothed Put Option Volume. Indicates when a change in the put option volume has been sustained for some time.

1.159425043

Short-Term Smoothed Call Option Volume

Same as other short term smoothed data. Exponentially smoothed Call Option Volume with a time constant of 30 days.

254917.8039

Long-Term Smoothed Call Option Volume

Same as other long term smoothed data. Exponentially smoothed Call Option Volume with a time constant of 200 days.

223050.7492

Ratio of Short-Term to Long-Term Smoothed Call Option Volume

The ratio of Short-Term Smoothed Call Option Volume to the Long-Term Smoothed Call Option Volume. Indicates when a change in the Call Option Volume has been sustained for some time.

1.142869077

Ratio of Short-Term Smoothed Put Option Volume to Short Term Smoothed Call Option Volume

Put-to-call ratio using short-term exponentially smoothed volumes. The ratio of the of Short-Term Smoothed Put Option Volume to the Short-Term Smoothed Call Option Volume.

1.06128256

Ratio of Long-Term Smoothed Put Option Volume to Long-Term Smoothed Call Option Volume

Put-to-call ratio using long-term exponentially smoothed volumes. The ratio of the of Long-Term Smoothed Put Option Volume to the Long-Term Smoothed Call Option Volume.

1.046128015

Percentage Difference Short-Term to Long-Term Ratio of Put to Call Volume

Difference in percentage points between the short-term smoothed put-to-call ratio and the long-term put-to-call ratio.

0.015154544

Short-Term Smoothed Return Momentum

The single-day return momentum is defined as the percent change in price, computed as a difference of natural logs. The short-term smoothed return momentum is the exponentially-smoothed average of these percent changes, with a time constant of 30 days.

-0.000180041

Long-Term Smoothed Return Momentum

The long-term smoothed return momentum is the exponentially-smoothed average single-day return momentum with a time constant of 200 days.

-0.000121053

Ratio of Short-Term to Long-Term Smoothed Return Momentum

The ratio of the short term (30d) smoothed return momentum to the long-term (200d) smoothed return momentum.

1.487289033

Ratio of Short-Term Return Momentum to Short-Term Standard Deviation

Ratio of the short term smoothed return momentum to the short term smoothed standard deviation. Provides a measure of how much the price of the nearby future has changed as opposed to simply moving around over the most recent 30-day period (the time constant for short-term smoothing)

-0.005608151

Ratio of Long-Term Return Momentum to Long-Term Standard Deviation

Ratio of the long term smoothed return momentum to the long term smoothed standard deviation. Provides a measure of how much the price of the nearby future has changed, as opposed to simply moving around over the 200-day period associated with long term smoothing

-0.001815845

20-Day Price Moving Average

Average settlement price for the nearby future over a 20-day window, i.e. today's business date and the previous 19 business dates.

118.209375

60-Day Price Moving Average

Average settlement price for the nearby future over a 60-day window.

119.2205729

200-Day Price Moving Average

Average settlement price for the nearby future over a 200-day window.

120.0017969

Percentage Difference Current Price to 200-Day Moving Average

Ratio of today’s nearby futures contract settlement price to the 200-day moving average.

0.985532118

Percentage Difference 20-Day Price Moving Average to 200-Day Price Moving Average

Ratio of the 20-day moving average to the 200 day moving average.

0.985063375

Peak price over total period

Highest nearby futures contract settlement since January 3, 2012.

135.265625

Peak Price of Nearby Futures in Last 200 Days

Highest nearby futures contract settlement price in the last 200 days, including today.

123.125

20 pct below peak price in last 200-business days

A reference price level calculated from the peak price in the last 200 days.

98.5

20 pct above 60-business day moving average

A reference price level calculated from the 60-day moving average, for upward movements.

143.0646875

Target 1 Nearest round number around 20 pct above 60-business day moving average

A reference price level for upward movement, calculated from the 60-day average, but rounded heuristically to a number that is easy to grasp, and expected to remain constant over a period of time, as might be used in media commentary.

145.0

Target 2 Nearest round number around 20 pct below 60-business day moving average

A reference price level for downward movement, calculated from the 60-day average, but rounded heuristically to a number that is easy to grasp, and expected to remain constant over a period of time, as might be used in media commentary.

95.0

20 pct Below 60-day moving average of price level

A reference price level calculated from the 60-day moving average, for downward movements.

95.37645833

One 504-Day Standard Deviation Above the Mean

The "mean" here is the mean of the 504 most recent values for the Mean of the Mixture Probability Distribution (2 year’s worth). The current model fixes the mean at 0.0, which effectively fixes its standard deviation at zero.

0.0

One 504-Day Standard Deviation Below the Mean

The current model fixes this field to zero.

0.0

Kurtosis 504-Day Moving Average

The kurtosis (fourth moment) of the Mixture Probability Distribution is taken at the 504 most recent business dates (including today) and averaged.

3.198579951

Kurtosis 504-Day Standard Deviation

The kurtosis (fourth moment) of the Mixture Probability Distribution is taken at the 504 most recent business dates (including today). The standard deviation is then calculated for these 504 samples.

0.325183199

Skewness 504-Day Moving Average

The skewness (third moment) of the Mixture Probability Distribution is taken at the 504 most recent business dates (including today) and averaged.

0.005028247

Skewness 504-Day Standard Deviation

The skewness (third moment) of the Mixture Probability Distribution is taken at the 504 most recent business dates (including today). The standard deviation is then calculated for these 504 samples.

0.120287122

Probability of Rising Above 20 pct above 60-business day moving average

Calculated using today's Mixture Probability Distribution. The price value for 20 % above the 60- day moving average is expressed as a return relative to the today's settlement price, and the distribution used to calculate the probability of this return being exceeded.

 

1.30943E-08

Probability of Rising Above Target 1 (up)

Calculated using today's Mixture Probability Distribution, but with the rounded price target instead of the pure +20%. The rounding is typically away from the current price, so the probability will be smaller. The price value target is expressed as a return relative to the today's settlement price, and the distribution used to calculate the probability of this return being exceeded.

1.3E-08

Probability of Falling Below Target 2 (down)

Calculated using today's Mixture Probability Distribution, but with the rounded downward price movement target instead of the pure minus 20%. The rounding is typically away from the current price, so the probability will be smaller. The price value target is expressed as a return relative to the today's settlement price, and the distribution used to calculate the probability of this return being exceeded.

2.0E-07

Probability of Falling Below 20 pct below 60-business day moving average

Calculated using today's Mixture Probability Distribution. The price value for 20 % above the 60- day moving average is expressed as a return relative to the today's settlement price, and the distribution used to calculate the probability of this return being exceeded.

2.09266E-07

Mean of Mixture Probability Distribution

Computed according to the model. At present, this value is fixed to zero in the calculations.

0.0

Median of Mixture Probability Distribution

The median of a distribution is the point on the horizontal axis where the area to the left is the same as the area to the right. This is computed from the vector representation of the distribution by integrating numerically until the accumulated sum is 0.5.

-0.01

Primary Mode of Mixture Probability Distribution

A mode of a distribution is a point on the horizontal where the distribution has a local maximum. The risk-return probability distribution may have one or two modes. The primary mode is the first mode encountered in iterating along the vector representation of the distribution.

0.0

Secondary Mode of Mixture Probability Distribution

If the distribution is bimodal, this will be the location of the second peak.

0.0

Skew of Mixture Probability Distribution

The third moment of risk-return probability distribution.

0.022213535

Kurtosis of Mixture Probability Distribution

The fourth moment of risk-return probability distribution.

3.37197243

State of Mixture Probability Distribution

The state is determined by comparing the standard deviation of today’s Mixture Probability Distribution with thresholds computed from a rolling 252-day window of standard deviations. The upper threshold is for wide, and the lower threshold is for narrow.

 

Current state definitions include Complacent, Balanced, Anxious and Event Risk, a.k.a. Bi-Modal or Bi-Polar.

Balanced

Risk Index

To be defined.

0.0

Origin for Distribution

-1.00

-1

Stepsize for Distribution

0.01

0.01

Number of elements in the distribution vector

Currently 256

256

-0.01

Column headers run from -0.01 to +1.55. The data for any one business day represents the Mixture Probability.

0

-0.99

Computed values that differ from zero by small amounts, currently 0.000000001 (the 9th decimal place), are forced to zero.

0

-0.98

Data is scaled so that the vector will integrate numerically to unity. If the distribution is very wide and the tails are chopped off, then the data points in the interval are puffed up slightly to compensate.

0

 . . .

 

varies

1.53

 

0

1.54

 

0

1.55

 

0