Reference no: EM133072573

Instructions for project 1 Data Preparation.

1. 1. Download the datasets for the 5-industry returns and the risk-free rate. This dataset contains the time series of 5 industry returns from 1926/07 to 2021/07.
   2. All the analysis should be conducted on Excess Returns. Excess return of an asset equals the return to that asset minus the risk-free rate. The data for the risk-free rate is available in the Rf file.

1. Estimations using the total sample (in-sample tests).
   1. table of summary statistics that reports mean and SD of excess industry returns and the covariance matrix.
   2. Estimate optimal weights using the matrix approach and report this result.
   3. Estimate optimal weights and their associated t-values using the regression approach and report the results.
   4. Compute the time series of returns to the optimal portfolio (the portfolio that uses optimal weights from part b or part c for investment) and report its mean, SD, and Sharpe ratio. This is the maximum in-sample Sharpe ratio in this data.

1. Out-of-sample tests.
   1. Divide the sample into two subsamples: first half and second half. Each subsample covers about 570 months of returns.
   2. Use the data for the first half to compute the optimal weights.[1]
   3. Use the optimal weights of the first half to form a portfolio for the second half. Compute this portfolio's mean, SD, and Sharpe ratio. Since this portfolio uses data from the first half for trading, its return, SD, and Share ratio are out-of-sample.
   4. DeMiguel et al (2009) argues that the 1/N approach dominates the MVE approach out of the sample. Compute the returns to the portfolio that trades the 1/N strategy in the second half and compute its mean, SD, and Sharpe ratio. Compare the Sharpe ratio of this portfolio to that of the MVE approach from part 3.c.

1. Evaluate the impact of N on results.
   1. Download the 10-industry dataset and compute excess returns.
   2. Repeat the tests of part 3 using this dataset. Compare the out of sample Sharpe ratio of the MVE approach and the 1/N approach. How did increasing N change the performance of the 1/N and the MVE portfolios?

[1]  You can use the matrix approach or the regression approach. They both produce similar results.