Please complete the following set of exercises.
Say you are a stock investor. You are considering to invest in MICROSOFT CORP. To that end, you download the stocks’ historical price data given in “Computer Exercise 2.xlsx”. More precisely, you analyze the end-of-month stock price from January 2003 to December 2013. Please answer the following questions.
1. To start, you want to get an idea of the monthly return that you could have obtained by buying in one month an selling in the next (assuming that there are no dividends). Compute the monthly net return; i.e. the proportionate change in prices.
2. Now you want to know in how many of the total months in your sample you would have made a positive net return. What is the number of months in which your net return would have been positive?
3. You decided that you want to invest in MICROSOFT CORP. Say that the outcome of your “experiment” (i.e. your investment) that you are interested in is whether you will receive a positive net return in the first month or not. That is, you define a Bernoulli random variable, X, that can take on values 1 (positive net return next month), and 0 (zero or negative net return next month). Since you don’t know how to otherwise approach the question (you are a first-time investor), you decide that the likelihood of success in the past should be an indication of the future probability of success. Hence, what is the probability of success (i.e. positive net return) based on the 2003-2013 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. in the expected value in 4.) really is.
6. Is the distribution of X symmetric about its mean? Why or why not?
7. Now assume that your investment horizon is 12 months, where in each month you can either gain a positive net return (Xi=1) or a negative net return (Xi=0). Assume that the random variables Xi, i=1, 2,…,12, are independent. The probability of success is still the same as in 3., and it is the same for all i. What is the probability that you will make a positive net return in 7 (out of the in total 12) following months)?
8. Under the same assumptions as in 7., what is the probability that you will make a positive net return in more than 6 (out of the in total 12) following months?
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