Question: (10 points) The following examines the probability of stock market returns. Use STATA

to answer this question. The relevant data can be found in the file "SP500Prices.csv"

1. (1 point) Use the price series to generate returns according to the following specification: Returns = ln(Pricet/Pricet-1). Hint: you may use the STATA syntax "variable[_n]" to call the nth observation of a variable, and "variable[_ n-1]" to call the nth - 1 observation.
2. (1 point) Generate a dummy variable for positive returns. Specifically, the variable "positive" must equal 1 for any day returns are positive and must equal 0 for any day returns are negative. Hint: you can use the "replace" command.
3. (1 point) Do you believe the daily returns series can be described by a Bernoulli trial?
   Why or why not?
4. (1 point) Assume the daily return is well described by a Bernoulli trial. Compute the probability of success, where success is defined as a positive return. Hint: use the "sum" command.
5. (1 point) Assume the distribution of returns will remain unchanged over the next week.
   Use the cdf of the Binomial distribution to determine the probability that at least 3 of the next five days will have a positive return.
6. (1 point) Assume the distribution of returns will remain unchanged over the next week.
   Use the pdf of the Binomial distribution to determine the probability that at least 3 of the next five days will have a positive return.
7. (1 point) Define a stock market crash as a daily return less than or equal to -0.09.
   Find the number of crashes in the sample. List the dates of these crashes.
8. (1 point) Determine the number of "trading years" in the sample as follows: floor (#Observations / 250), where 250 is the approximate number of trading days per year.
9. (1 point) Find the average number of crashes per year.
10. (1 point) Assume the distribution of stock market crashes is well described by a Poisson distribution. Find the probability that there will be 2 crashes in any given year.

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