Homework 4: An Insufficiently Random Walk
Down Wall Street
36-402, Advanced Data Analysis
Due at the start of class, 8 February 2011
In this assignment, you will use the same data set of values for the S& P 500
stock index that was used in the lecture notes for 1 February. You will need to
download SPhistory.short.csv from the class website.
Problems 2 and 3 are about estimating the first percentile of the return dis-
tribution, Q(0.01), under various assumptions. The returns will be larger than
this 99% of the time, so Q(0.01) gives an idea of how bad the bad performance
will be, which is useful for planning. Note that a calendar year contains about
250 trading days, and so should average two or three days when returns are
even worse than Q(0.01).
Include code for all problems as an appendix. Clearly indicate which block
of code is for which problem. Comment your code when at all possible.
1. (5 points) Load the data file, take the last column (containing the daily
closing price), and calculate the logarithmic returns. Note that the file
is in reverse chronological order (newest first). When you are done, if
everything worked right, running summary on the returns series should
give
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.094700 -0.006440 0.000467 -0.000064 0.006310 0.110000
Hint: Read the notes for 1 February.
2. In many applications in finance, it is common to model daily returns as
independent Gaussian variables.
(a) (5 points) Find the mean and standard deviation of the best-fitting
Gaussian, and the Q(0.01) it implies.
(b) (5 points) Write a function which simulates a data set of the same
size as the real data, using the independent Gaussian model you
fit in part 2, and returns a list, with components named mean and
sd, containing the parameter values estimated from the simulation
output.
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