Testing a Hypothesized Mean for Trading Stock Options


This is not a HW problem. For the purpose of trading stock options, I am trying to learn statistics on my own.

A stock is currently selling at $50 . The terms of a call option specify that the stock will raise to $70 in 18 weeks. That is, the stock is expected to increase about 2%/week.

(1) To assess the reasonableness of the 2%, I would perform a t test for testing a hypothesized mean. Am I right?

(2) If the t test shows that the average historical growth rate is 2.1%, I would be able to calculate the 95% probability that the average historical growth rate of 2.1% is equal to or higher than 2.1%. Or, equal to or higher than 2%. That is, 2.1% and 2.0% are the hypothesized means. Am I right?

(3) How far back should I go (# of historical observations)? Can the sample size be calculated by performing a “power test”? How do I do it?

(4) Is there a test better than the t test?

Thank you!

Doctor T
Hi Doctor T,

To use a T-test, you assume the data is collected from a normal distribution.
I think this is a flawed assumption for the stock market. Normal distribution is usually used for the natural and social sciences.

If the average height in grade 10 students was 170cm, it is reasonable to assume that it will be similar average in the next year grade 10.
In contrast, the fact that the average historical growth rate was 2.1% in the last 3 years doesn't promise you that the average will be similar in the following year. It may be -3% in the next year ...

Regards O