# Duration required for stock beta calculation

I am using stock beta as a parameter for calculating intrinsic value of a stock using DCF method. I know how to calculate beta of stock, but I want to know what should be length of historical data (how many days of historical data) for both stock and benchmark index for this purpose. Also is there any way I can find benchmark index for a given stock ? Should it be based on which sector this stock belongs to?

There's not one "beta" for a stock - it's always relative to some benchmark. Typically the "beta" that is published is relative to some very broad benchmark like the S&P 500, with the theory that it is "close enough" to the entire market to calculate an accurate beta. In other words, if every single stock in the US were used instead of the S&P 500, bet wouldn't change materially.

You can use a sector index as a benchmark if you want to compare a stock's risk to its sector, but published betas typically use a broader index if they don't specify the benchmark used.

Time frame is a better question, and typically beta should match your investment time frame - meaning if you are investing for 10 years, then use a 10-year beta.

I have always considered beta more of a directional measure that focusing on hyper-accuracy. Do I care if a stock has a beta of 2.3 versus 2.6? Not really - I just know that both are about twice as "risky" as the market overall.

• I am using beta as one of the parameter to estimate intrinsic value of a stock so what would be best time frame? Also if I calculate two beta (one broader index and one sector index) , take weighted or simple harmonic mean , would that give realistic estimate of beta? Mar 31, 2023 at 6:35

I want to know what should be length of historical data (how many days of historical data) for both stock and benchmark index for this purpose.

Years, not days. I'd use at least one or two years, if not more.

Also is there any way I can find benchmark index for a given stock ? Should it be based on which sector this stock belongs to?

The sector is a good starting point but a broader index like SPX or NDX can be used if the sector isn't statistically significant. Alternative benchmarks can be used where it makes sense, e.g. bond or commodity ETFs shouldn't be benchmarked to equity indices.