Adjusted β – It’s important to understand that statistical analysis provides an approximate rather than a “true” beta. Different commercial sources (as shown in the table) provide different data because they rely on different assumptions.
The differences in assumptions pertain to the time frame over which beta is calculated (e.g., month) and the total period considered (e.g., 5 years).
For example, #Yahoo Finance publishes a beta for the past 5 years calculated monthly, while #Bloomberg provides a beta for the last two years, calculated weekly. What’s happening here?
Firstly, we need to understand that beta is a measure of systemic risk and is theoretically consistent across any time frame – daily, weekly, or monthly beta should be the same.
However, the shorter the period over which beta is calculated, the higher the statistical problem of autocorrelation, meaning the trend increases the likelihood of correlation with the previous period, resulting in a higher level of “statistical noise.”
Finally, the longer the total period considered (2 years, 5 years), the greater the likelihood of significant changes in operational and financial risks during that period, potentially distorting historical measures from reflecting the true expectations. Reducing the total period also means fewer time segments, potentially affecting the minimum necessary data points for statistical analysis.
A very important finding by Marshal Blume is that beta for the next period is correlated with the beta from the previous period through this formula:
β[i1] = 0.371 + 0.635 β[i2]
Finding these figures required complex statistical analysis*, but the key takeaway is that historically calculated beta does not match reality (or future beta).
Specifically – if beta is greater than 1, the statistical figure is higher than the actual, and conversely, when it is less than 1, the statistical beta is lower than the actual. In other words, the actual beta regresses towards one.
For this reason, Bloomberg also publishes Adjusted Beta = 0.33 + 0.67 β.
*Corporate Valuation Theory, Evidence and Practice
Mark E. Zmijewski; Robert W. Holthausen
Second Edition