Efficient Frontier Spreadsheet Panel A Expected excess returns (risk premiums) of each country index U.S. U.K. 0.060 0.053 France 0.070 Germany 0.080 Australia 0.058 Japan 0.045 Canada 0.059 Panel B Bordered Covariance Matrix Portfolio weights 1.0000 0.0000 0.0000 U.S. U.K. France 0.0000 Germany 0.0000 0.0000 0.0000 Australia Japan Canada 1.0000 U.S. 0.0224 0.0184 0.0250 0.0288 0.0195 0.0121 0.0205 0.0000 U.K. 0.0184 0.0223 0.0275 0.0299 0.0204 0.0124 0.0206 0.0000 France 0.0250 0.0275 0.0403 0.0438 0.0259 0.0177 0.0273 0.0000 Germany 0.0288 0.0299 0.0438 0.0515 0.0301 0.0183 0.0305 0.0000 Australia 0.0195 0.0204 0.0259 0.0301 0.0261 0.0147 0.0234 0.0000 Japan 0.0121 0.0124 0.0177 0.0183 0.0147 0.0353 0.0158 0.0000 Canada 0.0205 0.0206 0.0273 0.0305 0.0234 0.0158 0.0298 1.0000 0.0224 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Risk Prem 0.0600 Std Dev 0.1495 Sharpe 0.4013 Formulas used in key cells Cell A17 - A23 Cell C15 Cell A24 Cell C24 Cell D24 through 124 Cell C25 Cell C26 Cell C27 Panel C These are portfolio weights. You can set initial value arbitrarily as long as sum = 1 =A17, and so on. The portfolio weights in column A are copied to row 17. =SUM(A17:A23) =C15*SUMPRODUCT($A17:$A23,C17:C23) Copied from C24 (note the use of absolute addresses) =SUMPRODUCT(A17:A23,$B5:$B11) =SUM(C24:124)^0.5 =C25/C26 Various points along the efficient frontier. Optimal Min var (tangency) portfolio portfolio Risk Prem: 0.0350 0.0383 0.0400 0.0450 0.0500 0.0550 0.0564 0.0575 0.0600 0.0700 0.0800 Std Dev: 0.1141 0.1132 0.1135 0.1168 0.1238 0.1340 0.1374 0.1401 0.1466 0.1771 0.2119 Sharpe: 0.3066 0.3386 0.3525 0.3853 0.4037 0.4104 0.4107 0.4106 0.4092 0.3953 0.3774 U.S. 0.5944 0.6112 0.6195 0.6446 0.6696 0.6947 0.7018 0.7073 0.7198 0.7699 0.8201 U.K. 1.0175 0.8778 0.8083 0.5992 0.3900 0.1809 0.1214 0.0758 -0.0283 -0.4465 -0.8648 France -0.2365 -0.2140 -0.2029 -0.1693 -0.1357 -0.1021 -0.0926 -0.0852 -0.0685 -0.0014 0.0658 Germany -0.6077 -0.5097 -0.4610 -0.3144 -0.1679 -0.0213 0.0205 0.0524 0.1253 0.4185 0.7117 Australia 0.0588 0.0695 0.0748 0.0907 0.1067 0.1226 0.1271 0.1306 0.1385 0.1704 0.2023 Japan 0.2192 0.2055 0.1987 0.1781 0.1575 0.1369 0.1311 0.1266 0.1164 0.0752 0.0341 Canada -0.0459 -0.0402 -0.0374 -0.0288 -0.0203 -0.0118 -0.0093 -0.0075 -0.0032 0.0139 0.0309