A Wall Street firm is planning its strategy for next week (Monday through Friday). In particular, they are interested in day trading a particular stock. The firm plans to observe the price of the stock at 15 minute intervals each day, starting at 9:30am and ending at 4:00pm. The fluctuations in price in each of these intervals is assumed to be a normally distributed variable with a mean of 0.01 and a standard deviation of 0.25. Suppose that we have $10,000 to use for trading. The opening price each day is equal to the closing price of the previous day, and the stock began the week with a price of $100. We are interested in two possible trading schemes:

(a) Suppose the stock’s price to begin the day is t. We buy the stock the first time that we observe a price less than or equal to 99.5% of the day’s beginning price. In other words, if p is the price at which we buy the stock, it must be that p ≤ 0.995t. We sell our entire position when either (i) the price of the stock increases by at least 1% from where we bought it, i.e., if the price is 1.01p or more or (ii) when we reach the end of the day, whichever comes first. We never will buy twice in the same day.

(b) The same as (a), except that we buy whenever p ≥ 1.005t instead of when p ≤ 0.995t. Simulate 10 weeks of trading under each scenario and report on the average weekly profits/losses. Note: Whenever we buy, we use all of our money. So, for example, if on a particular day we have $9000, and we buy when the stock reaches $90, we would buy $9000/$90 = 100 shares

Simulate 10 weeks of trading under each scenario and report on the average weekly profits/losses. Note: Whenever we buy, we use all of our money. So, for example, if on a particular day we have $9000, and we buy when the stock reaches $90, we would buy $9000/$90 = 100 shares.

(please include excel work done for simulation)