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PORTFOLIO OPTIMIZATIONPORTFOLIO OPTIMIZATION Shawn M Saran
INPUTS EXPECTED STANDARD 1+ Exp. Rate
RETURN DEVIATION
Riskless Rate ® 5.00% 0.00% 105.00%
LB Aggregate Bond 9.25% 6.34% 109.25% 100.00%
IA Monthly Convertible Bond 11.81% 12.96% 111.81% 100.00%
IA All Value 14.55% 16.23% 114.55% 100.00%
S&P 500 14.72% 17.49% 114.72% 100.00%
IA Small Stock 15.25% 20.75% 115.25% 100.00%
MSCI EAFE 13.97% 25.50% 113.97% 100.00%
CORRELATIONS
1 2 3 4 5 6
1 100.00% 58.00% 93.00% 56.00% 82.00% 32.00%
2 58.00% 100.00% 72.00% 34.00% 74.00% 11.00%
3 93.00% 72.00% 100.00% 55.00% 79.00% 40.00%
4 56.00% 34.00% 55.00% 100.00% 64.00% 20.00%
5 82.00% 74.00% 79.00% 64.00% 100.00% 24.00%
6 32.00% 11.00% 40.00% 20.00% 24.00% 100.00%
STANDARD DEVIATION (RISK FACTOR)
RISKY ASSETS 1 2 3 4 5 6
6.34% 12.96% 16.23% 17.49% 20.75% 25.50%
VARIANCES & CO-VARIANCES
1 2 3 4 5 6
1 0.40% 0.48% 0.96% 0.62% 1.08% 0.52%
2 0.48% 1.68% 1.51% 0.77% 1.99% 0.36%
3 0.96% 1.51% 2.63% 1.56% 2.66% 1.66%
4 0.62% 0.77% 1.56% 3.06% 2.32% 0.89%
5 1.08% 1.99% 2.66% 2.32% 4.31% 1.27%
6 0.52% 0.36% 1.66% 0.89% 1.27% 6.50%
Statistical non-rounded results from excel:Statistical non-rounded results from excel:
A 2315.6626691
B 2472.9538545
C 2641.2551757
DELTA 755.24320452
GAMMA 0.0240917112
Graphing Data
STANDARD
DEVIATION
EFFICIENT FRONTIER
CURVE
INDIVIDUAL
ASSET
OPTIMAL COMBO
(RISKIEST ASSETS IN
TANGENT PORTFOLIO)
LB Aggregate Bond 6.34% 9.25% 113.04%
IA Monthly Convertible Bond 12.96% 11.81% 30.46%
IA All Value 16.23% 14.55% -39.89%
S&P 500 17.49% 14.72% 10.46%
IA Small Stock 20.75% 15.25% -19.16%
MSCI EAFE 25.50% 13.97% 5.09%
INDEX Exp. Return
0 25.00% -7.44%
1 22.52% -6.01%
2 20.04% -4.59%
3 17.56% -3.17%
4 15.09% -1.74%
5 12.63% -0.32%
6 10.18% 1.10%
7 7.76% 2.52%
8 5.40% 3.95%
9 3.24% 5.37%
10 2.08% 6.79%
11 3.24% 8.22%
12 5.40% 9.64%
13 7.76% 11.06%
14 10.18% 12.48%
15 12.63% 13.91%
16 15.09% 15.33%
17 17.56% 16.75%
18 20.04% 18.17%
19 22.52% 19.60%
20 25.00% 21.02% EFFICIENT TRADE OFF LINEEFFICIENT TRADE OFF LINE
OPTIMAL COMBINATION 2.49% 7.58%
EFFICIENT TRADE OFF LINE 0.00% 0.00% 5.00%
100.00% 2.49% 7.58%
200.00% 4.98% 10.16%
Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
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0.0634 0.0634 0.0634 0.0925
0.1296 0.1296 0.1296 0.1181
0.1623 0.1623 0.1623 0.1455
0.1749 0.1749 0.1749 0.1472
0.2075 0.2075 0.2075 0.1525
0.255 0.255 0.255 0.1397
0.25 -0.0743538874 0.25 0.25
0.2251822594 -0.0601260074 0.2251822594 0.2251822594
0.2003882807 -0.0458981273 0.2003882807 0.2003882807
0.175628128 -0.0316702473 0.175628128 0.175628128
0.1509184507 -0.0174423672 0.1509184507 0.1509184507
0.1262888806 -0.0032144872 0.1262888806 0.1262888806
0.1017975792 0.0110133929 0.1017975792 0.1017975792
0.0775756151 0.0252412729 0.0775756151 0.0775756151
0.0539867405 0.039469153 0.0539867405 0.0539867405
0.0324426172 0.053697033 0.0324426172 0.0324426172
0.0207808043 0.067924913 0.0207808043 0.0207808043
0.0324426172 0.0821527931 0.0324426172 0.0324426172
0.0539867405 0.0963806731 0.0539867405 0.0539867405
0.0775756151 0.1106085532 0.0775756151 0.0775756151
0.1017975792 0.1248364332 0.1017975792 0.1017975792
0.1262888806 0.1390643133 0.1262888806 0.1262888806
0.1509184507 0.1532921933 0.1509184507 0.1509184507
0.175628128 0.1675200734 0.175628128 0.175628128
0.2003882807 0.1817479534 0.2003882807 0.2003882807
0.2251822594 0.1959758335 0.2251822594 0.2251822594
0.25 0.2102037135 0.25 0.25
0.024922684 0.024922684 0.0757823188 0.024922684
0 0 0.05 0
0.024922684 0.024922684 0.0757823188 0.024922684
0.049845368 0.049845368 0.1015646376 0.049845368
-0.150
-0.075
0
0.075
0.150
0.225
0.300
0 0.075 0.150 0.225 0.300
EFFICIENT TRADE OFF LINE & EFFICIENT FRONTIER CURVE
Series 1
Series 2
Series 3
Standard Deviation
Expected
Return
Shawn M Saran
-1.25
0
1.25
2.50
3.75
5.00
1 2 3 4 5 6
PORTFOLIO WEIGHTS IN OPTIMAL “TANGENT” PORTFOLIO
Series 1
Asset Number
Portfolio
Weights

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Statistics for optimization project pdf file

  • 1. PORTFOLIO OPTIMIZATIONPORTFOLIO OPTIMIZATION Shawn M Saran INPUTS EXPECTED STANDARD 1+ Exp. Rate RETURN DEVIATION Riskless Rate ® 5.00% 0.00% 105.00% LB Aggregate Bond 9.25% 6.34% 109.25% 100.00% IA Monthly Convertible Bond 11.81% 12.96% 111.81% 100.00% IA All Value 14.55% 16.23% 114.55% 100.00% S&P 500 14.72% 17.49% 114.72% 100.00% IA Small Stock 15.25% 20.75% 115.25% 100.00% MSCI EAFE 13.97% 25.50% 113.97% 100.00% CORRELATIONS 1 2 3 4 5 6 1 100.00% 58.00% 93.00% 56.00% 82.00% 32.00% 2 58.00% 100.00% 72.00% 34.00% 74.00% 11.00% 3 93.00% 72.00% 100.00% 55.00% 79.00% 40.00% 4 56.00% 34.00% 55.00% 100.00% 64.00% 20.00% 5 82.00% 74.00% 79.00% 64.00% 100.00% 24.00% 6 32.00% 11.00% 40.00% 20.00% 24.00% 100.00% STANDARD DEVIATION (RISK FACTOR) RISKY ASSETS 1 2 3 4 5 6 6.34% 12.96% 16.23% 17.49% 20.75% 25.50% VARIANCES & CO-VARIANCES 1 2 3 4 5 6 1 0.40% 0.48% 0.96% 0.62% 1.08% 0.52% 2 0.48% 1.68% 1.51% 0.77% 1.99% 0.36% 3 0.96% 1.51% 2.63% 1.56% 2.66% 1.66% 4 0.62% 0.77% 1.56% 3.06% 2.32% 0.89% 5 1.08% 1.99% 2.66% 2.32% 4.31% 1.27% 6 0.52% 0.36% 1.66% 0.89% 1.27% 6.50% Statistical non-rounded results from excel:Statistical non-rounded results from excel: A 2315.6626691 B 2472.9538545 C 2641.2551757 DELTA 755.24320452 GAMMA 0.0240917112 Graphing Data STANDARD DEVIATION EFFICIENT FRONTIER CURVE INDIVIDUAL ASSET OPTIMAL COMBO (RISKIEST ASSETS IN TANGENT PORTFOLIO) LB Aggregate Bond 6.34% 9.25% 113.04% IA Monthly Convertible Bond 12.96% 11.81% 30.46% IA All Value 16.23% 14.55% -39.89% S&P 500 17.49% 14.72% 10.46% IA Small Stock 20.75% 15.25% -19.16% MSCI EAFE 25.50% 13.97% 5.09% INDEX Exp. Return 0 25.00% -7.44% 1 22.52% -6.01% 2 20.04% -4.59% 3 17.56% -3.17% 4 15.09% -1.74% 5 12.63% -0.32% 6 10.18% 1.10% 7 7.76% 2.52% 8 5.40% 3.95% 9 3.24% 5.37% 10 2.08% 6.79% 11 3.24% 8.22% 12 5.40% 9.64% 13 7.76% 11.06% 14 10.18% 12.48% 15 12.63% 13.91% 16 15.09% 15.33% 17 17.56% 16.75% 18 20.04% 18.17% 19 22.52% 19.60% 20 25.00% 21.02% EFFICIENT TRADE OFF LINEEFFICIENT TRADE OFF LINE OPTIMAL COMBINATION 2.49% 7.58% EFFICIENT TRADE OFF LINE 0.00% 0.00% 5.00% 100.00% 2.49% 7.58% 200.00% 4.98% 10.16%
  • 2. Series 1 Series 2 Series 3 Series 4 Series 5 Series 6 Untitled 1 Untitled 2 Untitled 3 Untitled 4 Untitled 5 Untitled 6 Untitled 7 Untitled 8 Untitled 9 Untitled 10 Untitled 11 Untitled 12 Untitled 13 Untitled 14 Untitled 15 Untitled 16 Untitled 17 Untitled 18 Untitled 19 Untitled 20 Untitled 21 Untitled 22 Untitled 23 Untitled 24 Untitled 25 Untitled 26 Untitled 27 Untitled 28 Untitled 29 Untitled 30 Untitled 31 Untitled 32 0.0634 0.0634 0.0634 0.0925 0.1296 0.1296 0.1296 0.1181 0.1623 0.1623 0.1623 0.1455 0.1749 0.1749 0.1749 0.1472 0.2075 0.2075 0.2075 0.1525 0.255 0.255 0.255 0.1397 0.25 -0.0743538874 0.25 0.25 0.2251822594 -0.0601260074 0.2251822594 0.2251822594 0.2003882807 -0.0458981273 0.2003882807 0.2003882807 0.175628128 -0.0316702473 0.175628128 0.175628128 0.1509184507 -0.0174423672 0.1509184507 0.1509184507 0.1262888806 -0.0032144872 0.1262888806 0.1262888806 0.1017975792 0.0110133929 0.1017975792 0.1017975792 0.0775756151 0.0252412729 0.0775756151 0.0775756151 0.0539867405 0.039469153 0.0539867405 0.0539867405 0.0324426172 0.053697033 0.0324426172 0.0324426172 0.0207808043 0.067924913 0.0207808043 0.0207808043 0.0324426172 0.0821527931 0.0324426172 0.0324426172 0.0539867405 0.0963806731 0.0539867405 0.0539867405 0.0775756151 0.1106085532 0.0775756151 0.0775756151 0.1017975792 0.1248364332 0.1017975792 0.1017975792 0.1262888806 0.1390643133 0.1262888806 0.1262888806 0.1509184507 0.1532921933 0.1509184507 0.1509184507 0.175628128 0.1675200734 0.175628128 0.175628128 0.2003882807 0.1817479534 0.2003882807 0.2003882807 0.2251822594 0.1959758335 0.2251822594 0.2251822594 0.25 0.2102037135 0.25 0.25 0.024922684 0.024922684 0.0757823188 0.024922684 0 0 0.05 0 0.024922684 0.024922684 0.0757823188 0.024922684 0.049845368 0.049845368 0.1015646376 0.049845368 -0.150 -0.075 0 0.075 0.150 0.225 0.300 0 0.075 0.150 0.225 0.300 EFFICIENT TRADE OFF LINE & EFFICIENT FRONTIER CURVE Series 1 Series 2 Series 3 Standard Deviation Expected Return Shawn M Saran
  • 3. -1.25 0 1.25 2.50 3.75 5.00 1 2 3 4 5 6 PORTFOLIO WEIGHTS IN OPTIMAL “TANGENT” PORTFOLIO Series 1 Asset Number Portfolio Weights