Considering the attached set of securities and portfolio returns:

1. Find the combination of the weights that minimizes CV of the portfolio.

   1. How does the CV of the optimal portfolio compare with the CVs of its constituents?

2. 1. 

Individual Portfolio Assets Tickers WMT KO PFE Allocation Percentage Name 20.00% Walmart Inc 10.00% Coca-Cola Co 5.00% Pfizer Inc. 25.00% CVS Health Corp 40.00% Berkshire Hathaway Inc. Class A Allocation (w) 0.20 0.10 0.05 0.25 0.40 Mean Returns (u) 6.24% 4.06% 0.33% 7.33% 9.53% Annualized Std Dev (Volatility o) 15.65% 14.89% 15.33% 24.75% 16.05% Sharpe Ratio 0.44 0.31 0.06 0.32 0.63 CVS BRK.A # Assets Portfolio Calculations (Annualized) StdDev Allocation Expected Returns (Volatility o) 100.00% 7.32% 13.74% Sharpe Ratio 5 0.58 Portfolio Coorelation Matrix KO CVS WMT KO WMT 1.000 0.240 0.085 0.348 0.318 PFE 0.085 0.140 0.968 0.198 0.168 0.240 0.985 0.140 0.350 0.567 PFE CVS BRK.A BRK.A 0.318 0.567 0.168 0.457 0.994 0.348 0.350 0.198 0.999 0.457 Portfolio Annualized Covariance Matrix WMT KO PFE CVS BRK.A WMT 0.027 0.007 0.004 0.014 0.009 KO 0.007 0.028 0.006 0.014 0.016 PFE 0.004 0.006 0.068 0.013 0.007 CVS 0.014 0.014 0.013 0.059 0.018 BRKA 0.009 0.016 0.007 0.018 0.027 Individual Portfolio Assets Tickers WMT KO PFE Allocation Percentage Name 20.00% Walmart Inc 10.00% Coca-Cola Co 5.00% Pfizer Inc. 25.00% CVS Health Corp 40.00% Berkshire Hathaway Inc. Class A Allocation (w) 0.20 0.10 0.05 0.25 0.40 Mean Returns (u) 6.24% 4.06% 0.33% 7.33% 9.53% Annualized Std Dev (Volatility o) 15.65% 14.89% 15.33% 24.75% 16.05% Sharpe Ratio 0.44 0.31 0.06 0.32 0.63 CVS BRK.A # Assets Portfolio Calculations (Annualized) StdDev Allocation Expected Returns (Volatility o) 100.00% 7.32% 13.74% Sharpe Ratio 5 0.58 Portfolio Coorelation Matrix KO CVS WMT KO WMT 1.000 0.240 0.085 0.348 0.318 PFE 0.085 0.140 0.968 0.198 0.168 0.240 0.985 0.140 0.350 0.567 PFE CVS BRK.A BRK.A 0.318 0.567 0.168 0.457 0.994 0.348 0.350 0.198 0.999 0.457 Portfolio Annualized Covariance Matrix WMT KO PFE CVS BRK.A WMT 0.027 0.007 0.004 0.014 0.009 KO 0.007 0.028 0.006 0.014 0.016 PFE 0.004 0.006 0.068 0.013 0.007 CVS 0.014 0.014 0.013 0.059 0.018 BRKA 0.009 0.016 0.007 0.018 0.027