# solution

Assignment

The Assignment B for this Workshop is to perform an analysis which computes the theoretical allocation, the actual allocation, and compares the two. You will be working with daily return data for the Market Index, consisting of 30 stocks. The work involved is the following:

1. Load the necessary data. The required data files are all listed in the Syllabus table under â€œWorkshopâ€ at the bottom the AMS 511 course page.

1. 1.1. Import[]thedailyreturnvectorforthereturnsoftheMarketIndexwhichwillrepresentthemarket. This is a vector of length 1471 with each element representing a different date.

2. 1.2. Import[]thedailyreturnsmatrixforthethirtymembersoftheMarketIndex.Thisisamatrixof dimension 1471Ã—30 with each row representing a different date and each column a different stock.

3. 1.3. Bothoftheabovearealignedproperly.

1. Perform a CAPM linear regression to estimate the betas and error variances of each member of the Market Index. For simplicity assume an annual risk free rate of 1.6%. Approximate the daily rate as (1 + 0.016)^(1/250) – 1.

2. Use these estimates of the betas and error variances to compute the proportional allocations of each stock as predicted by the CAPM and normalize them so they sum to one..

3. Import[ ] the actual market capitalization of each of the 30 stocks. Use these data to produce the proportional market allocations.

4. Plot histograms of the empirical PDFs of the betas and error variances. For each case, use the code

Histogram[data, Automatic, “PDF”]

5. UseListPlot[]toplottheCAPMallocationsestimatedin(3.)vstheobservedbasedon capitalization in (4.).

6. Perform whatever additional comparisons you feel would be useful to characterize what you found.

7. What discrepancies do you note? How might you explain them?

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