From your favorite financial data provider, download the time-series of monthly adjusted closing prices for the period 04/2014-04/2024 for the 10 largest US- listed companies by market capitalization, with tracker IDs: JPM, AVGO, LLY, BRK-A, META, NVDA, AMZN, GOOG, AAPL, MSFT. Moreover, from Ken French’s website, download the monthly Fama-French 3 factors dataset.” As- sume that the current monthly risk-free rate is 1%.
1. Estimate from stock prices the expected monthly return for each of the 10 stocks, as well as the standard deviation of the return.
2. Estimate the variance-covariance matrix Σ, and its inverse -1 (for in- stance, using the excel function MINVERSE)
3. Find the weights of the MVE and MVP portfolios of the 10 stocks. Cal- culate the expected return and standard deviations of these two portfolios and comment on your findings.
4. Use the Mkt-Rf factor to estimate the CAPM ẞ and the intercept a for each of the 10 stocks using an Ordinary least Square regression. Comment on both the point estimates of ẞs and as, as well as their significance. What do your findings suggest about the validity of the CAPM?
5. Use the Mkt-Rf factor to estimate a 1-factor model for each of the 10 stocks, where recall that the factor enters the regression in first differences.
6. Calculate the error-term residuals for each of the 10 stocks, for each month, and estimate their variances-covariances.
7. Now, use all of the three factors to estimate a 3-factor model. Calculate the error-term residuals for each of the 10 stocks, for each month, and estimate their variances-covariances. Finally, compare the error-term covariances of the 1-factor vs. the 3-factor model, and comment on your findings.
8. Using only JPM, LLY, META and GOOG, construct the pure-factor port- folios for each of the 3 Fama-French factors.
9. Use the pure-factor portfolios to track AMZN and AVGO.
“Note that the Factors are in percentage points, so you need to adjust units of measure to compare to the returns you will calculate from stock prices.
On excel, go to Data and then click on Data analysis. Select ‘regression’ from the drop-down list and insert the data on dependent and independent variables.