The first column contains dates, the second column is the S&P500 index, daily closing prices for individual securities are listed from the 3rd column. Column headers contain ticker codes (generally, codes ending with “.N” and “.OQ” denote securities liste
economics
Description
File SP500data.csv contains daily closing prices that I downloaded from Thomson Reuters
Datastream for the period from 02-Jan-2003 to 30-Dec-2011 for 501 stocks listed on NASDAQ and NYSE.1
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1.
Convert your closing prices to log returns.
Note that each column is a separate stock.
2.
Construct M = 1, 000 equally-weighted random portfolios of sizes from 2-stock to 200-stock portfolios. [You will end up constructing 199×1,000=199,000 portfolios in total].
3.
Construct a boxplot of average portfolio returns with 199 “boxes”, each box representing portfolio size (that is, x-axis
is your number of stocks in a portfolio from 2-stock to 200-stock), and the
data used to construct each “box”
are average returns
of 1,000 random
n-stock portfolios from Step 3.
4.
Calculate standard deviation
of returns for each of the portfolios in Step 3.
5.
Plot the average standard
deviation of your portfolios on a graph where y-axis is “StDev of a
Portfolio” and x-axis is
“Portfolio size”.
6.
How quickly you can achieve
adequate portfolio diversification? Portfolio is adequately diversified when
90% of idiosyncratic (or firm-specific risk) can be diversified away. You may
assume that the level of firm specific
risk is equal to:
(a)
average standard deviation of
single-stock portfolios (or, simply, average
standard deviation of individual stocks) MINUS
(b)
standard deviation of an
equally-weighted portfolio consisting of all 501 stocks (there is only one way to construct an equally weighted
portfolio of all stocks, and thus, this portfolio is unique).
7.
On the same graph from Step 6 above, plot 90% confidence interval around the mean.
For
best results, annualize (scale) your average portfolio returns and portfolio
standard deviations by 252 and √252
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respectively.
1I removed stale stocks, stocks that have
been delisted for the major part of that period, or stocks that
exhibited extremely large price swings.
