Say you are a stock investor. You are considering to invest in AMAZON. To that end, you download the stocks historical price data given in Computer Exercise 2.xlsx. More precisely, you analyze the daily market-closing stock prices from January 3, 2007 to December 31, 2018. Please answer the following questions.

1. To start, you want to get an idea of the daily return that you could have obtained by buying on one trading day and selling on the next (assuming that there are no dividends). Compute the daily net return; i.e. the proportionate change in prices.

2. Now you want to know on how many of the total trading days in your sample you would have made a net return greater than 0.005. What is the number of days on which your net return would have been above 0.005?

3. You decided that you want to invest in AMAZON. Say that the outcome of your experiment (i.e. your investment) that you are interested in is whether you will win a net return larger than 0.005 on the first day or not. That is, you define a Bernoulli random variable, X, that can take on values 1 (net return > 0.005 on first day), and 0 (net return <=0.005 on first day).

   Since you dont know how to otherwise approach the question (you are a first-time investor), you decide that the likelihood of successes in the past should be an indication of the future probability of success. Hence, what is the probability of success (i.e. net return > 0.005) based on the 2007-2018 sample?

4. What is the expected value/population mean of your Bernoulli variable X?

5. What are the (population) variance and standard deviation of X? Having computed the latter,

   comment on how good your guess for X (i.e. the expected value in 4.) really is.

6. Is the distribution of X symmetric about its mean? Why or why not?

7. Instead, now assume that your investment horizon is 14 trading days, where on each day you

   either can gain a net return larger than 0.005 (Xi=1) or a net return <= 0.005 (Xi=0). Assume that the random variables Xi, i=1, 2,...,14, are independent. The probability of success is still the same as in question 3. above, and it is the same for all i.

   What is the probability that you will make a net return > 0.005 on 9 (out of the in total 14)

   following trading days?

8. Under the same assumptions as in question 7. above, what is the probability that you will make

   a net return above 0.005 on more than 11 (out of the in total 14) following trading days?