You can choose to invest your money in one particular stock or put it in a savings account. Your initial capital is 1000 dollars. The initial stock price is 100 dollars. The interest rate r is 0.5% per month and does not change. Your stochastic model for the stock price is as follows:

next month the price is the same as this month with probability 1/2,

with probability 1/4 it is 5% lower,

and with probability 1/4 it is 5% higher.

The principle applies for every new month. There are no transaction costs when you buy or sell stock.

Your investment strategy for the next 5 years is:

convert all your money to stock when the price drops below 95 dollars,

and sell all stock and put the money in the bank when the stock price exceeds 110 dollars.

Describe how to simulate the results of this strategy for the model given.

Determine number of simulation so the Monte Carlo study would attain the margin of error ±0.01 with probability 0.99.

How does this strategy compared to gains from the savings account for the same period of time? Determine success rate the above strategy related to gains from the savings account.

Calculate 95% confidence interval for estimated strategy success rate.

Assume another investment strategy when you put money in stock when price drops below 100 dollars and sell these stocks when price is above 115 dollars.

Is there a significant difference between two strategies?

Is it true that the difference between strategies is less then 50 dollars?

Formulate and test the hypotheses at a level α=0.05.