Use Consistent Observation Periods When Calculating Beta

Summary

The document clarifies how to choose a time scale when estimating a stock’s beta from correlation and standard deviations. Its central rule is to calculate the correlation, the stock’s standard deviation, and the market’s standard deviation from returns measured over matching observation periods. The components might use monthly or annual data, or a shorter interval such as intraday observations, as long as the period is consistent across all three.

The response illustrates that the choice of interval can reflect the volatility horizon being studied, mentioning long-term windows as well as an intraday window. It does not prescribe one universally correct period, provide a worked beta estimate, or discuss annualizing returns and volatility in detail. Estimates may differ with the sampling frequency and length of the data window, so the chosen horizon should fit the analysis and be applied consistently.

Key ideas

• Calculate correlation and both standard deviations using returns sampled over the same observation period.
• The period may be monthly, yearly, or intraday, depending on the horizon being studied.
• The document gives no universal preferred frequency or worked beta estimate.
• Changing the sampling period can change the volatility horizon represented by the estimate.

Tags

# Beta and standard deviation


# Beta and standard deviation












IS beta of a stock formula equals to correlation coefficient multiply with annualized standard deviation of stock A divide annualized standard deviation of market . i am not sure whether to use average monthly return or annualized return. please help me

## Answer by AllBlooming (score 2)

https://quant.stackexchange.com/a/54705

As long as you use the same observation period (month, year, or whatever you choose) for all components in the formula, you're good. So the three parts of it

- Correlation coefficient

- Standard deviation of the stock

- Standard deviation of the market

all need to be calculated over the same period, e.g. a month or a year.

So you could look at long term volatility by using a year (or 5 years, or 10 years) as the underlying time period.

You could also look at intraday volatility, and use e.g. two hours.

The important thing is to use the same time period for all three components of the formula.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.