In the spreadsheet, you will find data on the returns of Berkshire Hathaway, the returns of its portfolio of public stocks $($computed via Berkshire$$s $13$F filings to the SEC$),$ and several factor returns.

$1.$

Compute the factor loadings and annualized alpha of Berkshire Hathaway with respect to the following factor models and interpret the results:

a$.$ The $1-$factor market model.

b$.$ The Fama$-$French $3-$factor model with SMB and HML

c$.$ The $5-$factor model consisting of the FF $3-$factor model augmented with BAB and QMJ$.$

$2.$ Do the same for Berkshire$$s portfolio of public stocks $($from its $13$F filings$).$ Make sure the sample of your Y and X are consistent.

$3.$ Compute the annualized average excess returns, volatility, and Sharpe ratio of$,$ respectively, Berkshire and its portfolio of public stocks. Use the time period where data is available for both. Think of the possible sources of differences between Berkshire and its portfolio of public stocks.