32 Portolio theory with an investment universe that does not include the World Index 83 34 Auxiliary Data 35 Annualized Covariance Matrix (excluding World) 36 37 38 89 40 41 42 43 0,031139831 0,02509615 0,02706237 0,01415945 0,01722748 0,025096153 0,03818486 0,03842346 0,01928867 0,02329977 0,02706237 0,03842346 0,044271488 0,02180679 0,02550643 0,01415945 0,01928867 0,021806788 0,02014873 0,01498457 0,017227482 0,02329977 0,025506426 0,01498457 0,02144234 44 Auxiliary 45 A 46 B 47 C Expected return Vec of 1s den 0,12216893 1 fra 0,05794865 1 7,551286951 ger 0,04090876 1 1,661646685 jap 0,04041407 1 69,64483697 usa 0,11368103 1 1 1 1 1 1 48 Vector of ones (transposed) 49 50 Minimum Variance Portfolio 51 weights 52 mean 53 variance 0,26849214 0,11303426 -0,57769625 0,59064702 0,60552283 0,10842565 0,01435857 0,10842565 0,01435857 54 standard deviation 55 56 57 The mean-variance frontier with a risk-free asset (using as risk-free rate the historical average) 58 risk-free rate 59 50 A-Crf 0,009695513 6,876044542 51 52 63 Weights of P 64 mean of P 65 variance of P 0,032186266 66 standard deviation of P 0,179405313 57 58 69 Risk-aversion parameter 70 Mean 71 Standard Deviation 72 Variance 73 74 75 76 77 Weights on the risky assets. 78 79 0,74956752 -0,01886747 -1,22282127 -0,28563231 1,77775353 0,231009714 weights 0,26849214 0,11303426 -0,57769625 0,59064702 0,60552283 Inverse Annualized Covariance Matrix (excluding World) 72,39528817 -20,7407611 -17,57393375 -2,188078382 -13,19342369 -20,7407611 221,6335229 -161,1472273 2,008723863 -33,88200593 -34,01047817 -41,1583507 -41,86273338 -17,57393375 -161,147227 213,6564289 -2,188078382 2,008723863 -34,01047817 117,1880817 -13,19342369 -33,8820059 -41,1583507 -41,86273338 172,2680524 riskfree premium 0,11247342 weights p 0,04825313 0,03121325 0,03071855 0,74956752 -0,01886747 -1,22282127 -0,28563231 1 0,10398552 1,77775353 09 08 0,7 40 0,5 1 1,5 2 2.5 3 3,5 3,176866171 2,46719785 6,08706523 1,58843309 1,05895539 1,23359892 0,822399283 0,79421654 0,61679946 0,63537323 0,49343957 6,87604454 0,5294777 0,45383802 0,39710827 0,01588433 0,23100971 0,41119964 0,35245684 0,30839973 0,01233599 0,17940531 4 100 1,52176631 0,676340581 0,38044158 0,24348261 0,16908515 0,12422582 0,09511039 0,00015218 0,03218627 0,6 30 Weight on rf 31 32 Confirming that we obtain the same result by using y* 83 y* 34 mean 35 standard deviation Expected Return 0,5 04 0,3