Portfolio Selection

Partial file snippet.

Sheet 1: Two-asset portfolios

	
	
	
	
	
	
		

		

		

		

		

		

		

		

		

		Column1
		

		Column2
		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		Portfolio analysis
		

		

		

		

		Mean
		0.018758333333333
		Mean
		0.009966666666667
	
	
		Month
		Small
		LT Treasuries
		

		

		

		

		

		

		Standard Error
		0.0145506662262
		Standard Error
		0.005459594464534
	
	
		

		Cap
		

		

		w1
		1-w1
		St. Dev
		Mean
		

		Median
		0.0195
		Median
		0.0126
	
	
		

		

		

		

		

		

		

		

		

		Mode
		#N/A
		Mode
		#N/A
	
	
		1
		0.1126
		-0.0324
		

		1.0
		0.0
		0.0504
		0.0188
		

		Standard Deviation
		0.050404986375508
		Standard Deviation
		0.01891259000259
	
	
		2
		0.0452
		0.0051
		

		0.9
		0.1
		0.0448
		0.0179
		

		Sample Variance
		0.002540662651515
		Sample Variance
		0.000357686060606
	
	
		3
		-0.0249
		-0.0094
		

		0.8
		0.2
		0.0393
		0.0170
		

		Kurtosis
		-0.466909670529446
		Kurtosis
		1.23749114745566
	
	
		4
		-0.0403
		0.0016
		

		0.7
		0.3
		0.0339
		0.0161
		

		Skewness
		0.412884277888127
		Skewness
		-0.79910787402517
	
	
		5
		-0.0014
		0.0243
		

		0.6
		0.4
		0.0288
		0.0152
		

		Range
		0.1645
		Range
		0.0722
	
	
		6
		-0.0519
		0.0200
		

		0.5
		0.5
		0.0240
		0.0144
		

		Minimum
		-0.0519
		Minimum
		-0.0324
	
	
		7
		0.0370
		0.0398
		

		0.4
		0.6
		0.0198
		0.0135
		

		Maximum
		0.1126
		Maximum
		0.0398
	
	
		8
		-0.0228
		0.0067
		

		0.3
		0.7
		0.0167
		0.0126
		

		Sum
		0.2251
		Sum
		0.1196
	
	
		9
		0.0131
		0.0185
		

		0.2
		0.8
		0.0153
		0.0117
		

		Count
		12
		Count
		12
	
	
		10
		0.0259
		0.0198
		

		0.1
		0.9
		0.0162
		0.0108
		

		

		

		

		

	
	
		11
		0.0885
		0.0010
		

		0.0
		1.0
		0.0189
		0.0100
		

		

		Column 1
		Column 2
		

	
	
		12
		0.0441
		0.0246
		

		

		

		

		

		

		Column 1
		1
		

		

	
	
		

		

		

		

		

		

		

		

		

		Column 2
		-0.316157793817396
		1
		

	
	
		Mean
		0.0188
		0.0100
		

		

		

		

		

		

		

		

		

		

	
	
		St. Dev.
		0.0504
		0.0189
		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Corr.
		-0.3162
		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	
	
		

		

	

 


Sheet 2: 3-asset portfolios (naive)

	
	
		Three-asset portfolios with known expected return and variance-covariance matrix:
		

		

		

		

		

		

		

		

		
 
		
		
	
		

		

		

		

		

		

		

		

		

		
	
		Mean,  St. Dev
		

		

		

		Correlation Coefficients
		

		
	
		

		

		

		

		

		

		

		

		

		
	
		

		Stock 1
		Stock 2
		Stock 3
		

		

		Stock 1
		Stock 2
		Stock 3
		
	
		Return
		0.14
		0.08
		0.2
		

		Stock 1
		1
		0.5
		0.2
		
	
		St. dev
		0.2
		0.12
		0.3
		

		Stock 2
		 
		1
		0.4
		
	
		

		

		

		

		

		Stock 3
		 
		 
		1
		
	
		

		

		

		

		

		

		

		

		

		
	
		 
		

		Portfolio weight
		

		Portfolio
		Portfolio
		

		

		

		
	
		

		Stock 1
		Stock 2
		Stock 3
		St. Dev
		Return
		

		

		

		
	
		

		0
		0
		1
		0.3
		0.2
		

		

		

		
	
		Stocks
		0
		0.2
		0.8
		0.250567356213853
		0.176
		

		

		

		
	
		2 and 3
		0
		0.4
		0.6
		0.204
		0.152
		

		

		

		
	
		

		0
		0.6
		0.4
		0.162775919595006
		0.128
		

		

		

		
	
		

		0
		0.8
		0.2
		0.132
		0.104
		

		

		

		
	
		

		0
		1
		0
		0.12
		0.08
		

		

		

		
	
		

		0
		0
		1
		0.3
		0.2
		

		

		

		
	
		Stocks
		0.2
		0
		0.8
		0.251077677223603
		0.188
		

		

		

		
	
		1 and 3
		0.4
		0
		0.6
		0.21109239683134
		0.176
		

		

		

		
	
		

		0.6
		0
		0.4
		0.185903200617956
		0.164
		

		

		

		
	
		

		0.8
		0
		0.2
		0.181769084280028
		0.152
		

		

		

		
	
		

		1
		0
		0
		0.2
		0.14
		

		

		

		
	
		

		0
		1
		0
		0.12
		0.08
		

		

		

		
	
		Stocks
		0.2
		0.8
		0
		0.121061967603372
		0.092
		

		

		

		
	
		1 and 2
		0.4
		0.6
		0
		0.131696621065235
		0.104
		

		

		

		
	
		

		0.6
		0.4
		0
		0.149879951961562
		0.116
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		0.8
		0.2
		0
		0.173251262621662
		0.128
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		1
		0
		0
		0.2
		0.14
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		0.2
		0.2
		0.6
		0.204626488998859
		0.164
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Mixed
		0.2
		0.4
		0.4
		0.163560386402087
		0.14
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		weights
		0.2
		0.6
		0.2
		0.132966161108757
		0.116
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		0.4
		0.2
		0.4
		0.171580884716218
		0.152
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		0.4
		0.4
		0.2
		0.14271650219929
		0.128
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		0.6
		0.2
		0.2
		0.159649616347801
		0.14
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	



Sheet 3: 3-asset portfolios (Bodie) 

	
	
		A. Inputs on three stocks: mean, standard deviation, and correlation matrix
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		Standard
		Expected
		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Stock
		Deviation
		Return
		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		A
		0.2
		0.14
		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		B
		0.12
		0.08
		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		C
		0.3
		0.2
		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		A
		B
		C
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		St. Dev
		0.2
		0.12
		0.3
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Mean
		0.14
		0.08
		0.2
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		Correlation Matrix
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		A
		B
		C
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		A
		1
		0.5
		0.2
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		B
		0.5
		1
		0.4
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		C
		0.2
		0.4
		1
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		B. Covariance Matrix
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		A
		B
		C
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		A
		0.04
		0.012
		0.012
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		B
		0.012
		0.0144
		0.0144
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		C
		0.012
		0.0144
		0.09
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		C. Equally-Weighted Portfolio
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		A
		B
		C
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Weights
		0.3333
		0.3333
		0.3333
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.3333
		0.004444444444444
		0.001333333333333
		0.001333333333333
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.3333
		0.001333333333333
		0.0016
		0.0016
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.3333
		0.001333333333333
		0.0016
		0.01
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		1.0000
		0.0071
		0.0045
		0.0129
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Variance
		0.0246
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		St. Dev
		0.156773013550731
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		R * weight
		0.046666666666667
		0.026666666666667
		0.066666666666667
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Mean
		0.14
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		D. Minimize Portfolio Variance, Given Portfolio Mean
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Use Excel Solver (under Tools) to minimize portfolio variance, subject to:
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		1. Portfolio weights sum to 1 (a50=1);
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		2. A specified portfolio mean (b54=?);
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		3. Optional: portfolio weights>=0
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Portfolio
		A
		B
		C
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Weight
		-0.7819
		2.4743
		-0.6924
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		-0.78193365079586
		0.024456809369878
		-0.023216862675381
		0.006496616054868
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		2.47430015873159
		-0.023216862675381
		0.088159122367188
		-0.024668964870996
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		-0.692366507935734
		0.006496616054868
		-0.024668964870996
		0.043143424318001
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		1.0000
		0.0077
		0.0403
		0.0250
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Variance
		0.0730
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		St. Dev
		0.270149834484584
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		R * weight
		-0.10947071111142
		0.197944012698528
		-0.138473301587147
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Mean
		-0.05000000000004
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		E. Unrestricted Efficient Frontier
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		

		

		

		Portfolio Weights
		

		

		

		

		

		

		

		

		

		

		

		

		

	
	
		Mean
		St. Dev
		A
		B
		C
		

		
 
		
		
	
		

		

		

		

		

		

		
	
		-0.05
		0.270149834484584
		-0.78194726166354
		2.47430696416543
		-0.692359702501894
		

		
	
		-0.02
		0.222987278946538
		-0.590263686941401
		2.1284651768037
		-0.538201489862302
		

		
	
		0
		0.193534436453269
		-0.462474645030171
		1.89790398918142
		-0.43542934415125
		

		
	
		0.02
		0.166665138772147
		-0.334679207790395
		1.66733127056186
		-0.332652062771469
		

		
	
		0.04
		0.143837983580411
		-0.206890162271805
		1.4367700811359
		-0.229879918864097
		

		
	
		0.06
		0.127245120028976
		-0.079101113665536
		1.2062088901661
		-0.127107776500565
		

		
	
		0.08
		0.119512193102635
		0.048681541588545
		0.975659229205396
		-0.024340770793941
		

		
	
		0.1
		0.122330314649954
		0.17647058933309
		0.745098038666457
		0.078431372000453
		

		
	
		0.12
		0.135041125131134
		0.304259634888692
		0.51453684922199
		0.181203515889318
		

		
	
		0.14
		0.155233253793053
		0.432048681541836
		0.283975659228751
		0.283975659229413
		

		
	
		0.16
		0.18041196939739
		0.559837728194979
		0.053414469235513
		0.386747802569508
		

		
	
		0.18
		0.208780871567971
		0.687626774848123
		-0.177146720757726
		0.489519945909603
		

		
	
		0.2
		0.239207616884766
		0.815415819167406
		-0.407707909584034
		0.592292090416628
		

		
	
		0.22
		0.270999951348458
		0.943204868155365
		-0.63826910074468
		0.695064232589315
		

		
	
		0.25
		0.320357709303102
		1.13489482758621
		-0.984122413793103
		0.849227586206897
		

		
	
		

		

		

		

		

		

		
	
		F. Restricted Efficient Frontier (No short sales)
		

		

		

		

		

		
	
		

		

		

		

		

		

		
	
		

		

		

		Portfolio Weights
		

		

		
	
		Mean
		St. Dev
		A
		B
		C
		

		
	
		

		

		

		

		

		

		
	
		0.08
		0.119999989131562
		5.43423724285592E-07
		0.999999456576276
		0
		

		
	
		0.09
		0.119583455565413
		0.112565787696112
		0.86038377281828
		0.027050439485609
		

		
	
		0.1
		0.122330314649954
		0.176470588235548
		0.745098039215228
		0.078431372549224
		

		
	
		0.11
		0.127580066734574
		0.240365110446049
		0.629817444776645
		0.129817444777307
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.12
		0.135041125131134
		0.304259634888692
		0.51453684922199
		0.181203515889318
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.13
		0.144371056754494
		0.368154158215263
		0.399256254225371
		0.232589587559366
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.14
		0.155233253793053
		0.432048681541836
		0.283975659228751
		0.283975659229413
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.15
		0.1673295808905
		0.495943204868408
		0.168695064232132
		0.33536173089946
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.16
		0.180411969397283
		0.559837725827047
		0.053414470420141
		0.386747803752812
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.17
		0.19621416870357
		0.499999999999337
		0
		0.500000000000663
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.18
		0.223109340409213
		0.333333333332671
		0
		0.666666666667329
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.19
		0.258736244937821
		0.166666666666005
		0
		0.833333333333995
		

		

		

		

		

		

		

		

		

		

		

		

	
	
		0.2
		0.3
		0
		0
		1

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...Sheet twoasset portfolios column portfolio analysis mean month small lt treasuries standard error cap w st dev median mode na deviation sample variance kurtosis skewness range minimum maximum sum count corr asset naive threeasset with known expected return and variancecovariance matrix correlation coefficients stock weight stocks mixed weights bodie a inputs on three b c covariance equallyweighted r d minimize given use excel solver under tools to subject specified optional gt...

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							Column1		Column2

			Portfolio analysis				Mean	0.018758333333333	Mean	0.009966666666667
Month	Small	LT Treasuries					Standard Error	0.0145506662262	Standard Error	0.005459594464534
	Cap		w1	1-w1	St. Dev	Mean	Median	0.0195	Median	0.0126
							Mode	#N/A	Mode	#N/A
1	0.1126	-0.0324	1.0	0.0	0.0504	0.0188	Standard Deviation	0.050404986375508	Standard Deviation	0.01891259000259
2	0.0452	0.0051	0.9	0.1	0.0448	0.0179	Sample Variance	0.002540662651515	Sample Variance	0.000357686060606
3	-0.0249	-0.0094	0.8	0.2	0.0393	0.0170	Kurtosis	-0.466909670529446	Kurtosis	1.23749114745566
4	-0.0403	0.0016	0.7	0.3	0.0339	0.0161	Skewness	0.412884277888127	Skewness	-0.79910787402517
5	-0.0014	0.0243	0.6	0.4	0.0288	0.0152	Range	0.1645	Range	0.0722
6	-0.0519	0.0200	0.5	0.5	0.0240	0.0144	Minimum	-0.0519	Minimum	-0.0324
7	0.0370	0.0398	0.4	0.6	0.0198	0.0135	Maximum	0.1126	Maximum	0.0398
8	-0.0228	0.0067	0.3	0.7	0.0167	0.0126	Sum	0.2251	Sum	0.1196
9	0.0131	0.0185	0.2	0.8	0.0153	0.0117	Count	12	Count	12
10	0.0259	0.0198	0.1	0.9	0.0162	0.0108
11	0.0885	0.0010	0.0	1.0	0.0189	0.0100		Column 1	Column 2
12	0.0441	0.0246					Column 1	1
							Column 2	-0.316157793817396	1
Mean	0.0188	0.0100
St. Dev.	0.0504	0.0189

Corr.	-0.3162

Three-asset portfolios with known expected return and variance-covariance matrix:

Mean, St. Dev					Correlation Coefficients

	Stock 1	Stock 2	Stock 3			Stock 1	Stock 2	Stock 3
Return	0.14	0.08	0.2		Stock 1	1	0.5	0.2
St. dev	0.2	0.12	0.3		Stock 2		1	0.4
					Stock 3			1

		Portfolio weight		Portfolio	Portfolio
	Stock 1	Stock 2	Stock 3	St. Dev	Return
	0	0	1	0.3	0.2
Stocks	0	0.2	0.8	0.250567356213853	0.176
2 and 3	0	0.4	0.6	0.204	0.152
	0	0.6	0.4	0.162775919595006	0.128
	0	0.8	0.2	0.132	0.104
	0	1	0	0.12	0.08
	0	0	1	0.3	0.2
Stocks	0.2	0	0.8	0.251077677223603	0.188
1 and 3	0.4	0	0.6	0.21109239683134	0.176
	0.6	0	0.4	0.185903200617956	0.164
	0.8	0	0.2	0.181769084280028	0.152
	1	0	0	0.2	0.14
	0	1	0	0.12	0.08
Stocks	0.2	0.8	0	0.121061967603372	0.092
1 and 2	0.4	0.6	0	0.131696621065235	0.104
	0.6	0.4	0	0.149879951961562	0.116
	0.8	0.2	0	0.173251262621662	0.128
	1	0	0	0.2	0.14
	0.2	0.2	0.6	0.204626488998859	0.164
Mixed	0.2	0.4	0.4	0.163560386402087	0.14
weights	0.2	0.6	0.2	0.132966161108757	0.116
	0.4	0.2	0.4	0.171580884716218	0.152
	0.4	0.4	0.2	0.14271650219929	0.128
	0.6	0.2	0.2	0.159649616347801	0.14

A. Inputs on three stocks: mean, standard deviation, and correlation matrix

	Standard	Expected
Stock	Deviation	Return
A	0.2	0.14
B	0.12	0.08
C	0.3	0.2

	A	B	C
St. Dev	0.2	0.12	0.3
Mean	0.14	0.08	0.2

	Correlation Matrix
	A	B	C
A	1	0.5	0.2
B	0.5	1	0.4
C	0.2	0.4	1

B. Covariance Matrix

	A	B	C
A	0.04	0.012	0.012
B	0.012	0.0144	0.0144
C	0.012	0.0144	0.09

C. Equally-Weighted Portfolio

	A	B	C
Weights	0.3333	0.3333	0.3333
0.3333	0.004444444444444	0.001333333333333	0.001333333333333
0.3333	0.001333333333333	0.0016	0.0016
0.3333	0.001333333333333	0.0016	0.01
1.0000	0.0071	0.0045	0.0129
Variance	0.0246
St. Dev	0.156773013550731
*R weight**	0.046666666666667	0.026666666666667	0.066666666666667
Mean	0.14

D. Minimize Portfolio Variance, Given Portfolio Mean

Use Excel Solver (under Tools) to minimize portfolio variance, subject to:
	1. Portfolio weights sum to 1 (a50=1);
	2. A specified portfolio mean (b54=?);
	3. Optional: portfolio weights>=0

Portfolio	A	B	C
Weight	-0.7819	2.4743	-0.6924
-0.78193365079586	0.024456809369878	-0.023216862675381	0.006496616054868
2.47430015873159	-0.023216862675381	0.088159122367188	-0.024668964870996
-0.692366507935734	0.006496616054868	-0.024668964870996	0.043143424318001
1.0000	0.0077	0.0403	0.0250
Variance	0.0730
St. Dev	0.270149834484584
*R weight**	-0.10947071111142	0.197944012698528	-0.138473301587147
Mean	-0.05000000000004

E. Unrestricted Efficient Frontier

			Portfolio Weights
Mean	St. Dev	A	B	C

-0.05	0.270149834484584	-0.78194726166354	2.47430696416543	-0.692359702501894
-0.02	0.222987278946538	-0.590263686941401	2.1284651768037	-0.538201489862302
0	0.193534436453269	-0.462474645030171	1.89790398918142	-0.43542934415125
0.02	0.166665138772147	-0.334679207790395	1.66733127056186	-0.332652062771469
0.04	0.143837983580411	-0.206890162271805	1.4367700811359	-0.229879918864097
0.06	0.127245120028976	-0.079101113665536	1.2062088901661	-0.127107776500565
0.08	0.119512193102635	0.048681541588545	0.975659229205396	-0.024340770793941
0.1	0.122330314649954	0.17647058933309	0.745098038666457	0.078431372000453
0.12	0.135041125131134	0.304259634888692	0.51453684922199	0.181203515889318
0.14	0.155233253793053	0.432048681541836	0.283975659228751	0.283975659229413
0.16	0.18041196939739	0.559837728194979	0.053414469235513	0.386747802569508
0.18	0.208780871567971	0.687626774848123	-0.177146720757726	0.489519945909603
0.2	0.239207616884766	0.815415819167406	-0.407707909584034	0.592292090416628
0.22	0.270999951348458	0.943204868155365	-0.63826910074468	0.695064232589315
0.25	0.320357709303102	1.13489482758621	-0.984122413793103	0.849227586206897

F. Restricted Efficient Frontier (No short sales)

			Portfolio Weights
Mean	St. Dev	A	B	C

0.08	0.119999989131562	5.43423724285592E-07	0.999999456576276	0
0.09	0.119583455565413	0.112565787696112	0.86038377281828	0.027050439485609
0.1	0.122330314649954	0.176470588235548	0.745098039215228	0.078431372549224
0.11	0.127580066734574	0.240365110446049	0.629817444776645	0.129817444777307
0.12	0.135041125131134	0.304259634888692	0.51453684922199	0.181203515889318
0.13	0.144371056754494	0.368154158215263	0.399256254225371	0.232589587559366
0.14	0.155233253793053	0.432048681541836	0.283975659228751	0.283975659229413
0.15	0.1673295808905	0.495943204868408	0.168695064232132	0.33536173089946
0.16	0.180411969397283	0.559837725827047	0.053414470420141	0.386747803752812
0.17	0.19621416870357	0.499999999999337	0	0.500000000000663
0.18	0.223109340409213	0.333333333332671	0	0.666666666667329
0.19	0.258736244937821	0.166666666666005	0	0.833333333333995
0.2	0.3	0	0	1

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