In practice historical beta is the most used approach for calculating beta.

Some one can use i.e. the last 6 month daily returns of stock i and market m to calculcate this.

Nevertheless I am wondering which horizon this estimate wants to forecast?

Following the example above: The next 6 month?

So is it always: Used time horizon length = Forecasted time horizon?

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    $\begingroup$ time horizon length = forecasted time horizon is a reasonable criterion, I am not aware that it has been proven "correct" however. Some people try to estimate a model of changing Betas (for ex an AR(1) model) and do forecasting accordingly. $\endgroup$ – noob2 Oct 27 '16 at 13:34
  • $\begingroup$ I dont exactly understand why it is reasonable? Is there any intuitive explanation? why not using half year history as a forecast for a year since? Does a beta of 2 calculated based on historical one year data means that we are expecting the a beta of 2 if we perform the same analysis in exactly one year? $\endgroup$ – Plazi Oct 27 '16 at 13:53
  • $\begingroup$ For volatility (not beta) I know it has empirically tested and found true that "time horizon length = forecasted time horizon is a reasonable criterion", for beta it is plausible to me, I don't remember whether I looked at the data for beta or not. $\endgroup$ – noob2 Oct 27 '16 at 14:47
  • $\begingroup$ Another technique you can do is to have say 3 measures of beta: for last M, N and Q months and find out by linear regression how to linearly combine them into a forecast for the next X months that you are interested. I have seen this done. $\endgroup$ – noob2 Oct 27 '16 at 14:53
  • $\begingroup$ thanks. I actually need to combine different "models" for estimating beta and test if a combined approach can forecast beta better than every single model alone. I though I could use "three different models" just by varying the horizon but I doubt its so easy. Do you think with linear regression I could do? For example the regression model is better predicting M, N, or Q beta than the single models? $\endgroup$ – Plazi Oct 27 '16 at 16:51

Estimation horizon does not depend on forecast horizon but rather on market regime relevance. Using long historical time periods (i.e. 5yrs vs. 1yr) improves estimation confidence but decreases usefulness since the market environment today may be different from the environment 5yrs ago (interest rate level, regulation, different company - M&A etc.). In case you want to estimate historical beta (v.s. Fundamental - see Barra) you can either use Kalman Filters, or estimate beta using various look-back periods and test robustness. Regarding return frequency (daily vs. weekly vs. monthly), this depends on your trading/hedging horizon.


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