## 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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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 listed on NYSE and NASDAQ, respectively.

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 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.