Finding the drift from historical stock data

Question

I'm currently working on a project that involves modelling stocks as Geometric Brownian motion, so my program takes as arguments: The annualized drift, the annualized volatility, the number of days to simulate and the start price. I have my project working when I set the values of these. What I'd now like to do would be to use historical stock price data from Bloomberg and estimate the drift and volatility and then put it into my model.

Example:

Prices = [100.00, 100.50, 100.62, 99.64, 101.21, 102.29, 101.75]

Drift = ?

Could it possibly be something as simple as $$\frac{\dfrac{0.5}{100} + \dfrac{0.12}{100.50} - \dfrac{1.98}{100.62} +\dfrac{1.57}{99.64} + \dfrac{1.08}{101.21} - \dfrac{0.54}{102.29}}{6} $$ to find the daily drift, and then multiply by 250 to find the annualized?

I've looked online, and there is plenty of information about finding the volatility but not much about finding the drift?

Thanks

Answer 1

Your approach is correct. You just have to multiply by $252$ which is assumed the standard number of workdays in a year.

I would also consider getting a longer sample, so your estimate is actually statistically meaningful.

Another correction possibly needed with stocks is to adjust for dividends (when needed).