Econometrica Exam

Problem 1.

I choose Starbucks as a company I would like to analyze.

1. Here is a histogram of monthly excess log returns

[pic 1]

[pic 2]

As we can see from Chi-square statistics with p-value < 0.01, a null hypothesis of normal distribution is rejected at 1% significance level

Here is summary statistics for variable

Test for normality of ER:

 Doornik-Hansen test = 36.7722, with p-value 1.03521e-008

 Shapiro-Wilk W = 0.952764, with p-value 6.62222e-008

 Lilliefors test = 0.082186, with p-value ~= 0

 Jarque-Bera test = 121.283, with p-value 4.61093e-027

All three test rejected the null hypothesis of normal distribution of the variable at 1% significance level → variable doesn’t follow normal distribution

1. Adjusted close price of the stock

[pic 3]

We can sees that until 2007 the price had a steady growth, however from 2007 to 2009 it dropped dramatically and reached 2004 level due to the volatile markets. But after that plunge the price has been growing really fast increasing approximately 10 times from the 2004 level.

ER and excess return on the market portfolio:

[pic 4]

 Generally, ER have had a much higher volatility than market in general, especially in 1990-2003 years and 2008-2010 years.

1. Here is a data on one factor model:

Model 3: OLS, using observations 1992:07-2015:12 (T = 282)

Dependent variable: ER

HAC standard errors, bandwidth 4 (Bartlett kernel)

             coefficient   std. error   t-ratio    p-value

  ---------------------------------------------------------

  const      0.00925456    0.00490621    1.886    0.0603    *

  MktRF      1.13462       0.142757      7.948    4.68e-014 ***