What are the 5th and 95th percentiles of a daily returns?

Economics by Geoffrey

All questions in this assignment should be answered using the Company 1 stock price data. Generate the daily returns from stock price data and answer the following questions.

 

Question 1: What are 1st, 2nd, 3rd quartiles and the IQR of daily returns?

 

 

Question 2: What are the 5th and 95th percentiles of a daily returns?

 

Question 3: What are Mean, Std. dev., Variance, Skewness, and Kurtosis of daily returns?

 

All three questions in this assignment should be answered using STATA simulation of random numbers.

 

Question 1: Suppose a stock market can go up with a probability 0.55 and can go down with a probability 0.45. Let U represents the number of days the stock market is up through a week (5 trading day). Tabulate the value of U

 

 

Question 2: What is the probability that a stock market rallies during all trading days during a week?

 

 

Question 3: What is the probability that a stock market declines during all trading days during a week?

 

All three questions in this assignment should be answered using STATA simulation of random numbers.

 

Question 1: I teach 80 students. The probability that a student will attend the class is p = 0.85. What is the probability that on a given date I have at least 60 students in class? (Please provide a STATA code, and STATA table, and justify your answer!)

 

 

Question 2: Online assignment consists of 10 questions. The probability that I answer all of them correctly is p = 0.30. What is the probability that it will take 3 attempts until I achieve a perfect score?

 

 

Question 3: I have office hours between 10:00 am to 12:00 none. On average, 4 students visit during office hrs. What is the probability that at least 5 students visit me during office hours between 10:00 am and 12:00 noon?

 

All three questions in this assignment should be answered using STATA simulation of random numbers. On each question, please provide a STATA code, and STATA table, and justify your answer!

 

 

Question 1 (Uniform Distribution): The amount of time, in minutes, I spend driving from home to work is uniformly distributed between 55 and 80 minutes, inclusive. What is the probability that it will take more than 60 minutes to drive from home to work?

 

 

Questions 2 and 3 (Exponential Distribution): I run a car repair shop. The amount of time it takes me to serve each customer has an exponential distribution with
the average service time of 45 minutes.

Question 2: What is the probability that I spend less than 10 minutes repairing a car?

 

Question 3: What is the probability that I spend more than 60 minutes repairing a car?

 

All three questions in this assignment should be answered using STATA simulation of random numbers.

 

Question: Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112.

 

Questions 1: What is the probability of an individual scoring above 500 on the GMAT? (Please provide a STATA code, and STATA table, and justify your answer!)

 

Questions 2: How high must an individual score on the GMAT in order to score in the top 5%? Bottom 5%?

 

Questions 3: What is the lower bound of 99% confidence interval of an individual score on the GMAT exam?

 

All three questions in this assignment should be answered using STATA simulation of random numbers.

 

There are 10 players who play a chess game against the Computer. Each player plays 6 times and the probability that he/she wins is 0.70. Let Xi , where i = 1,2,…,10, denotes the number of times player i wins. Let

 

 

 

denotes the average number of wins across players.

 

Question 1: What is the mean of ? (Please provide a STATA code, and STATA table, and justify your answer!)

 

 

Question 2: What is the standard deviation of ? (Please provide a STATA code, and STATA table, and justify your answer!)

 

Question 3: Draw two histograms of  (use 7 bins as there are 7 possible outcomes for ) and  (use 15 bins).

 

All questions in this assignment should be answered using the Company 1 stock price data.

 

Question 1: First generate the daily returns from stock price data and then construct the 75% confidence interval for the mean daily return.

 

 

 

Question 2: First generate the stock market decline indicator, “Ind”, taking the value of 1 if the daily return is negative and taking the value of 0 otherwise.  Then construct the 95% confidence interval for the proportion of days when the stock market declines.

 

To complete this assignment, please use the first ticker you are assigned with.

 

Question 1: Test at 99% confidence the null hypothesis that the mean daily return is 2%, H0: µ = 0.02, against the alternative that the mean daily return is not 2%, Ha: µ != 0.02 at 99% confidence. Please provide the STATA code, and STATA table, and explain your answer.

 

 

Question 2: Let p denotes the probability that the stock price declines on a given day. At 95% confidence, test the null hypothesis H0: p >= 60%, against the alternative Ha: p < 60%. Please provide the STATA code, and STATA table, and explain your answer.

 

Use 1st and 2nd tickers you are assigned.

 

Question 1: Test at 99% confidence the null hypothesis that the mean daily returns of Company 1 and Company 2 are the same. I.e.,

 

H0: µ1 = µ2  vs. Ha: µ1 != µ2

 

at 95% confidence level. Please provide the STATA code, and STATA table, and explain your answer.