Understanding Upper Bound of Standardized Transaction Amount

When tracking data over time, like monthly temperatures or insider transactions, it's helpful to use statistical tools to make sense of the numbers. One such tool is UBSTA, which stands for Upper Band of Standardized Transaction Amount. In this post, we'll walk you through how UBSTA works, starting with a simple example and then applying it to insider transaction amounts.

A Simple Example: Average Monthly Temperatures in Oslo, Norway

Let's imagine we're tracking the average monthly temperatures in Oslo, Norway, over the past year. Here are the average temperatures in degrees Celsius:

To understand how UBSTA works, we first need to calculate a few key statistics:

• Mean (Average): Add up all the temperatures and divide by the number of months.
• Standard Deviation (STDEV): Measures the amount of variation or dispersion in the temperatures.

Calculating the Mean

Add up all the temperatures: -2 + (-1) + 2 + 6 + 12 + 16 + 18 + 17 + 13 + 8 + 3 + (-1) = 91

Divide by the number of months (12): 91 / 12 ≈ 7.58

So, the mean (average) temperature is about 7.58°C.

Calculating the Standard Deviation

To find the standard deviation, follow these steps:

• Subtract the mean from each temperature and square the result.
• Calculate the average of these squared differences.
• Take the square root of this average.

Here’s a simplified version of the calculations:

• Differences squared: (e.g., (-2 - 7.58)² = 91.35, ...)
• Sum of squared differences: (sum all squared differences)
• Average of squared differences: (sum of squared differences) / 12
• Standard Deviation: √(average of squared differences)

Let’s assume the standard deviation is about 7.2°C after calculations.

Calculating the Upper Band (UBSTA)

The Upper Band is typically calculated as: Upper Band = Mean + (𝑛 × Standard Deviation)

Using 1 standard deviation means there is a 68% chance, while using 2 standard deviations means there is a 95% chance. In SIT, we use 2 standard deviations for our calculations.

1 standard deviation:
UBSTA = 7.58 + (1 × 7.2) ≈ 14.78

2 standard deviations:
UBSTA = 7.58 + (2 × 7.2) ≈ 21.98

This means that there is a 68% probability (1 standard deviation) that the temperature is expected to stay below 14.78°C, and a 95% probability (2 standard deviations) that the temperature is expected to stay below 21.98°C.

Let's visualize the average temperature in Oslo along with the areas representing 1 standard deviation (1 STD) and 2 standard deviations (2 STD) on the following chart.

Now you can see how unusual a temperature above the green line (2 STD) would be.

Applying UBSTA to Insider Transactions. Why Use UBSTA?

Example: Insider Transaction Amounts

Let’s say we track the transaction amounts (in thousands of dollars) for a company ABC Inc. over a year:

Calculating the Mean and Standard Deviation

Mean: Add up all amounts and divide by 12. Mean = (50+60+55+70+80+90+85+95+100+110+105+120)/12=90

Standard Deviation:
Follow the same steps as before to find the variation in transaction amounts. Let’s assume it’s 20 after calculations.

Calculating the Upper Band (UBSTA)

Using 2 standard deviations: UBSTA=90+(2×20)=130

This means insider transaction amounts are expected to stay below 130 thousand dollars most of the time. If a transaction exceeds this value, it might be significant.

NB: This is UBSTA calculated for the past 12 months (periods). If next month insiders initiate significant buy/sell transactions, then UBSTA would change its value; it would be higher

Unlike measuring temperature, which is accessible for everyone, insider transactions are sometimes limited by the data available. We might only have access to data from the last few years or months.

Conclusion

Imagine if the temperature in Oslo suddenly reached +30°C. You can be certain that everyone would be talking about it online. Such an extreme temperature would fall outside the expected range, representing only a 5% statistical error. Similarly, when you see insider transactions that exceed the UBSTA, it's crucial to pay attention, as these transactions are statistically significant.

When applying the UBSTA principle to insider transactions, it's important to remember that UBSTA is a dynamic value that changes over time. While climate change occurs at a fast pace, it doesn't change as quickly as the UBSTA calculated for a specific company.

UBSTA helps identify significant transactions or patterns. In our examples, an insider transaction amount above the UBSTA might signal important trading activity (anomaly). After all, this is exactly the situation that people often refer to when they say 'someone knows something', highlighting the potential significance of transactions exceeding the UBSTA threshold.

Of course, UBSTA is not a magic key that unlocks all doors. It's important to analyze other attributes of insider activity, such as insider position, market conditions, and investment style. For example, some insiders employ speculative strategies.

We update the UBSTA value for each company whenever new insider transaction data comes in. You can access the UBSTA through our API or via a connector to the Google BigQuery dataset, both of which are available to our paid customers