# Hard Wheat

##### The unit of prices below is **USd** (¢) per bushel.

## Data Sources

The estimations reported for every day correspond to the model estimations using information available up to each corresponding day

## Technical Information

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Overview of this tool

The tool is based on a statistical model that formally models the behavior (fluctuations) of commodity price returns (i.e. day-to-day percentage changes of commodity prices) using futures market prices closest to maturity. The **first graph** above identifies abnormalities or excessive price variability (i.e. price volatility that exceeds a pre-established threshold). The red vertical lines on the first graph indicate when there is excessive price variability. This first graph can be compared to the price trend of hard wheat futures, shown in the **second graph** above.

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What the tool identifies

**Periods of excessive price variability.**This occurs when we observe a large number of extreme positive returns. An extreme positive return is defined as a return that exceeds a certain pre-established threshold. This threshold is normally taken to be a high order (95 or 99%) conditional quantile, (i.e. a value of return that is exceeded with low probability: 5 or 1%). In this model we use the 95% and 97.5% quantiles.**Days that are within periods of (high, moderate or low) price variability.**This reflects the number of continuous days in the current level of variability. For example, 20 days of low variability means that since the last instance of moderate or high variability, there have been 20 days of low variability.

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How the model works

The probability that we will observe k days of extreme price returns (returns above the 95% quantile as explained in the definition of excessive price variability) in a period of D consecutive days is defined as:

We implement a one-sided test based on a normal approximation for the binomial distribution. Using a period of 60 consecutive days that precede any date (i.e. D=60), we test whether the probability value obtained from our stochastic model of returns is larger than the chosen 5% or 2.5% probability of observing extreme return.

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Thresholds used in the tool to determine excessive price variability

The tool currently uses the Conditional Value-at-Risk (CVaR) of returns as a threshold to identify periods of excessive price variability:

- Standard measure of the risk of loss for investments in financial economics.
- Uses extremely high estimated quantiles of return (95% and 97.5%) as thresholds for “Excessive Variability.”

An additional threshold is being added based on conditional expected shortfall (CES): the expected log return above the 95% quantile, which serves as a more rigorous threshold for alerting on excessive variability than the CVaR.

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The decision rule embedded in the color system

**RED or Excessive Volatility**: If the probability value is less than or equal to 2.5%, the null that violations (i.e. days of extreme price returns) are consistent with expected violations is highly questionable, meaning that we are in a period of an excessive number of days of extreme price returns relative to that expected by the model ; therefore we characterize that date as belonging to a period of excessive volatility.**ORANGE or Moderate volatility**: If the probability value is bigger than 2.5% or less than or equal to 5%, the null that violations are consistent with expectations is questionable at a low level, meaning that we are in a period of moderate number of days of extreme price returns relative to that expected; therefore we characterize that date as belonging to a period of moderate volatility.**GREEN or Low volatility**: If the probability value is bigger than 5%, we accept the null that violations are consistent with expectations, meaning that the number of extreme price returns is consistent to what is expected from the model; therefore we characterize that date as belonging to is a period of low volatility.