# 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

• I suggest to keep it simple. List the monthly returns. Calculate the average of monthly returns. Calculate the standard deviation of monthly returns. Calculate the correlation of monthly returns. Finally calculate "correlation coefficient multiplied with annualized standard deviation of stock A divide annualized standard deviation of market" which is $\rho \frac{\sqrt{12}*\sigma_A}{\sqrt{12}*\sigma_M}$. Note that the sqrt(12) in numerator and denominator cancel out. Jun 6 '20 at 20:29
• thanks for your help! Jun 7 '20 at 7:35

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

1. Correlation coefficient
2. Standard deviation of the stock
3. 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.

• thanks :) so so much! Jun 7 '20 at 7:35