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I am working on a Python library for financial calculations based on Time series data. One of the functions I'm implementing is beta. This will allow the user to pass two sets of time-series data, one for the market and one for the stock/asset and get the beta.

However, I am stuck at whether I should annualise the returns. I have tried reading about it and I see that different people use different return periods, some use 1-day returns while some use 1-month returns. However, I can't seem to find if they use absolute returns or annualised returns.

While this doesn't drastically alter the Beta, it is an important detail. I can leave it up to the user as well, but I want to have helpful defaults, so that users don't have to pass every parameter.

gouravkr
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    Keep it simple (and correct) by using the data that you have available. If you have daily data use daily returns (for both the stock, the market and the risk free rate), if you have monthly data use monthly returns, etc. Consistency is important (don't subtract a 1% annual risk free rate from a 1% daily stock return). Annualization (for example multpilying all daily rets by 260) is not necessary or useful (result of regression will be the same when all returns are multiplied by a constant). – nbbo2 May 31 '22 at 04:28
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    I agree with @nbbo2. What may be of interest is adjusted beta, as proposed by Blume (Betas and their regression tendencies, 1975) computed as ( 0.66666 * Raw BETA ) + ( 0.33333 * 1 ), which assumes that beta moves towards the market mean (1). Also, you need to think of what to do with missing data, especially when a data point is missing on one but not the other due to different exchange holidays. – AKdemy May 31 '22 at 19:36
  • annualization by multiplying does not change the beta estimates (changes the alpha though), but annualization by resampling does; unless there might be mismatch in the time at which the returns are snapped (New York time for American stocks, Tokyo time for Japanese...), i would use the highest frequency – Igor Pozdeev Jun 01 '22 at 06:08

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