Empirical Analysis in Finance / Econometrics

[Hint: In some exercises, you might need to use the NORM.DIST and/or NORM.INV functions in Excel. For example, let a random variable X follow a normal distribution with mean 10 and standard deviation 20. If you are asked to compute the probability that a data value drawn from that distribution is below 8, you enter NORM. DIST(8, 10,20,1) to obtain 46%. Or, if you want to find x such that 90% of the population have the data value below x, or Pr(X1.5); (c) Pr(Zs+1.21); (d) Pr(-1.96SY=0) if Y~N(u=0, 0=2) (e) Pr(0 U-0.5) if U follows a uniform distribution between 0 and 2 (that is, any number between 0 and 2 is equally likely to happen) 2. X follows a normal distribution with u=1.8 and o=0.75. Determine the value x such that the probability mass to the left of x is 5%. That is, find the x shown in the figure below: p.d.f. of N(1.8,0.75) Pr(XSx)=0.05 X 3. Wall Street analysts regularly issue stock recommendations. A buy recommendation by an analyst issued for stock S at day t means the analyst believes the stock S will perform well in the one-year period following t. A large sample study collected the one-year return following each recommendation. The study found that the average one-year return was 5.75%, with a standard deviation of 19.2%. Assume that one-year returns following recommendations can be approximated by a normal distribution. Let's see whether these analysts are doing a good job. Many of them do not specify exactly what "perform well" means, so let's assume that a good performance means beating the market. The average one-year return on the market is 6.5%. Compute the fraction of recommendations that thus performed well. (That is, compute the fraction of recommendations with one-year returns above 6.5%). 4. SAT scores across can be approximated by a normal distribution with mean 500 and standard deviation 100. a) If you pick one SAT exam at random, what is the probability that the score is: (i) Below 500; (ii) Below 300; (iii) Between 300 and 700? b) You intend to use the SAT to screen out applicants; you want to retain only applicants on the top 1% of the SAT distribution. What is the SAT threshold you should use? (Such that you accept an applicant only if her SAT score is above that threshold.)