I'm reflecting on whether historically estimated $\beta$ is a "good" estimator of future $\beta$.

Consider the problem as follows:

  • Let $r_1$, $r_2$, ...., $r_{36}$ be the last 36 months of returns for a security
  • let $m_1$, $m_2$, ...., $m_{36}$ be the market returns.

You can use this data to calculate a line of best fit: $r =\alpha+ \beta m + \epsilon$

However, I'm seeing that the resulting $\beta$ is not particularly stable over time, which somewhat brings into question the entire purpose of its existence.

Is there any reason to believe that $\beta$ is stable over time? beyond just using overlapping datasets to estimate it.


1 Answer 1


No, betas are not stable over time. That's not even true for portfolios (for individual stocks it's even worse). One of the seminal references is: Lewllen and Nagel (2006). Take a look at figure 2 from their paper, where they report the conditional betas of value, size and momentum anomalies:

enter image description here

This is also one of the reasons why Bloomberg reports adjusted beta for individual securities:

$$\beta^{adjusted} = (1/3) + (2/3) \times \beta$$

The intuition being that securities with high beta (above 1) should see a decline in beta towards one over time and the opposite for securities with low beta.

  • 3
    $\begingroup$ The technique used by Bloomberg to improve stability is widely used and is generally called Shrinkage. You can find papers discussing various beta shrinkage methods. $\endgroup$
    – nbbo2
    Commented Feb 6, 2023 at 17:12
  • $\begingroup$ @MYK There are better ways to phrase that comment or maybe pose it as a new question. $\endgroup$
    – Bob Jansen
    Commented Feb 7, 2023 at 7:34
  • $\begingroup$ Yeah, fair enough, I was a bit annoyed last night. $\endgroup$
    – MYK
    Commented Feb 7, 2023 at 12:19
  • $\begingroup$ I suppose the underlying question was about the utility of beta for forward looking applications - if any. $\endgroup$
    – MYK
    Commented Feb 7, 2023 at 12:19
  • $\begingroup$ I think that is a good question, but that's better discussed in a new question or it has been asked already. $\endgroup$
    – Bob Jansen
    Commented Feb 7, 2023 at 15:17

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