# Historical beta: Beta estimation for which time horizon?

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?

• 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. – noob2 Oct 27 '16 at 13:34
• 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? – Plazi Oct 27 '16 at 13:53
• 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. – noob2 Oct 27 '16 at 14:47
• 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. – noob2 Oct 27 '16 at 14:53
• 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? – Plazi Oct 27 '16 at 16:51