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I was wondering how one should choose parameters such as "frequency" of returns (daily, monthly etc.), "time frame" (1 or 3 or 5 years of historical data etc), benchmark (same of the portfolio or the specific one of the market of each asset etc. - i.e. AAPL.US and ^GSPC.US, LUX.MI and FTSEMIB.MI) in computing beta coefficient of a given asset against a given benchmark (i.e. AAPL.US and ^GSPC.US) with simple linear regression model.

Different data providers show different beta coefficient of a same asset so is there a best practice maybe related to the personal "investment horizon"?

Please bare in mind this from the view point of estimating returns via CAPM for a better mean-variance portfolio optimization.

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  • $\begingroup$ it seems like you answered your own question...different providers calc different beta for the same asset. if there was a 'right' way, they'd likely all use it. $\endgroup$
    – Chris
    May 22, 2019 at 22:00
  • $\begingroup$ FWIW I like AQR's method of calculating beta. They use it for their own Betting Against Beta portfolios and I assume they settled on this method after carefully studying different approaches. IIRC it is described in the paper by Frazzini et al. $\endgroup$
    – nbbo2
    May 22, 2019 at 22:54
  • $\begingroup$ @Chris among all the provided betas one should choose which use according to some kind of criteria.. I'm quite novice in this field so I was wondering which are the guidelines. I perfectly understand there is no single best formula which is suitable for all assets or investments tecniques. $\endgroup$
    – Nipper
    May 23, 2019 at 11:00
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    $\begingroup$ The best approach is a dynamic linear model solved via the Kalman filter - use the whole sample at the highest frequency available. $\endgroup$
    – Lisa Ann
    May 23, 2019 at 16:11
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    $\begingroup$ Since my previous comment I have read an article by Novy-Marx in which he criticizes Frazzini's AQR BAB method for computing Beta as non-standard and biased by changes in market volatility. Therefore I no longer recommend this method. $\endgroup$
    – nbbo2
    Jun 22, 2019 at 0:09

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A widely accepted method to estimate Beta is the Vasicek (1973) method, which computes a preliminary estimate of Beta by linear regression and then "shrinks it" (adjusts it) towards 1 to compensate for the fact that the OLS Betas tend to be too extreme (too far from 1) in the cross section. I consider it the standard.

Recently Ivo Welch has published a new method which is relatively simple and he claims is superior to a variety of other methods, including the Vasicek method. It has the potential to become a new standard. His paper is Simpler Better Market Betas (SSRN link) and includes an exhaustive (somewhat exhausting) discussion of previously known methods to calculate Beta.

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There is no single answer here as beta is just a statistics. Do not let the qualitative-finance world tell you what beta is (or isn't). Beta, in corporate finance, can be stated somewhat differently - so know your audience.

Beta over 3-months will change more quickly, and a 5-year beta will change more slowly. You need to think about the question you are trying to answer, and decide from there what is correct for your problem.

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  • $\begingroup$ Thanks for the reply. I.e. regarding the time frame, from the empirical point of view a shorter time frame is usually suited to compute beta for short time investment and and vice versa? $\endgroup$
    – Nipper
    May 23, 2019 at 11:12
  • $\begingroup$ @Nipper Not necessarily. Let's say you assumed stock A was undervalued, and you wanted to buy stock A, but eliminate any systematic risk to the market. How much of the stock market do you short relative to your long? This becomes a judgement call but will be heavily influenced by the beta you choose. There is no single answer. $\endgroup$
    – jason m
    May 23, 2019 at 13:32

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