The document describes using Jensen's alpha and portfolio optimization to evaluate equity performance and allocate investments. It outlines Jensen's performance measure, defines relevant terms, presents sample stock price data, and describes using linear regression to calculate Jensen's alpha for different equities. The document then formulates an optimization model to maximize returns by allocating investments across 34 equities under various constraints, and solves the model using a linear programming solver.

1. PERSONAL FINANCE:
PORTFOLIO OPTIMIZATION
USING JENSEN’S
PERFORMANCE MEASURE
(That uses Least Squares Regression)
Sarang Ananda Rao
anandasg@mail.uc.edu
NOTE
The following project uses confidential data and plenty of independent research.
Please seek permission of author before sharing/reuse

2. PERSONAL FINANCE: PORTFOLIO OPTIMIZATION USING JENSEN’s
PERFORMANCE MEASURE (that uses Least Squares Regression)
NOTE: The following project uses confidential data and plenty of independent research. The
data has been sanitized and therefore dummy variable names and data are used.
INTRODUCTION:
The project uses Linear Optimization and Jensen’s Performance Measure (Alpha) to evaluate the
performance of equities (and risk computation) compared to benchmarks (such as S&P 500 and
Treasury Bills) over time.
LITERATURE:
JENSEN’s PERFORMANCE MEASURE (ALPHA) [1]
Jensen measure (alpha) uses least squares regression to calculate risk-premium for an asset’s
return and market return. A positive alpha means that the asset performed better than the
benchmark (example: S&P 500, Treasury Bills) in risk-adjusted terms. If alpha is zero, the returns
between asset and benchmark.
Jensen’s formula: (ri – rf) = a + b (rm – rf)
Where
(ri – rf) is risk premium for asset i
rf is the risk free rate (For example treasury bills, in this project the average annual return of a
fixed deposit from a trustworthy bank is taken as risk free rate)
rm is the market return (in this project an index such as S&P 500 or SENSEX is taken as market
return)
rf is return on asset i
b is beta co-efficient
a is Jensen’s Performance Measure (alpha)

3. By adjustment, i.e. dividing each asset’s alpha by beta co-efficient (a/b), Jensen’s Alpha can be
used to rank the performance of an asset relative to other assets.
For the linear regression analysis,
Y variable is (ri – rf)
X variable is (rm – rf)
DEFINITIONS:
Table 1: Market Capitalization Definitions
Market Cap:
Lower Limit Upper Limit Market Cap
(in crores) (in crores)
$0.00 $4,999.00 Small Cap
$5,000.00 $20,000.00 Mid Cap
$20,001.00 $350,000.00 Large Cap
Grades:
Through independent research, equities are graded into A, B & C, which represent likelihood of
purchase. For example, Grade A equities are equities that the investor is more likely to purchase than
Grade B (and finally Grade C) Equities.
Average 3 Year Return:
The average return (mean of annual returns) of an equity in the last 3 years 2012-15 (Year on Year)
Expected Returns:
Total One Year expected returns for a particular equity

4. Data Preparation:
A sample of 34 equities from 18 industries were shortlisted through independent research for
the project. The 18 industries used in the project are:
Table 2: Industries considered
1 Appliances
2 Automotive
3 Banking
4 Batteries
5 Conglomerate
6 Cookery
7 Courier
8 Energy
9 Fertilizers
10 FMCG
11 Food Processing
12 IT
13 Media
14 Metals
15 Personal Care
16 Pharmaceuticals
17 Textiles
18 Theatres
Data for the equities such as Grades (calculated through independent research), Market
Capitalization (Market Cap) and 5 year stock price data (first 2 weeks of November) were
collected from reliable financial sources (such as Google Finance).
ASSUMPTION:
Since we are interested in long term risk measure for the equities, it is assumed that stock price
does not fluctuate much in the first 2 weeks of November and therefore stock price during any
day in first 2 weeks of November is considered for ease of data collection (since over a long term
such as 5 years, fluctuation in stock price over 2 weeks is insignificant).
In this project, the value of SENSEX (over a 5 year time period) is considered the market return
(Rm) and the value of interest rate from fixed deposits through a national bank is considered as
a risk free return (Rf).

5. Table 3: Sample of stock price over 5 year period (Refer worksheet “5 Year Data_Calculations” for
complete data
Equities - Stock Price during 2011-15
(Values adjusted to splits)
1st Week November 2015 2014 2013 2012 2011
SENSEX $26,265.24 $27,868.63 $21,196.81 $18,683.68 $17,562.61
Equity 21 $284.25 $298.50 $113.85 $83.95 $102.40
Equity 4 $87.80 $47.50 $16.75 $24.25 $27.90
Equity 12 $7,470.00 $6,521.70 $2,800.00 $1,709.60 $1,575.00
Equity 23 $170.00 $220.25 $148.50 $233.00 $226.50
Equity 3 $16,582.00 $12,671.00 $3,999.00 $2,390.00 $1,732.00
For computing the return of assets (Ri), a four year YoY (Year on Year) growth is calculated. The
Y & X variables for linear regression are calculated using the above metrics (Ri, Rm, Rf). An
average 3-year return is computed from the four year YoYs.
Linear Regression Analysis:
To calculate the Jensen’s Performance co-efficient for an equity, a linear regression is run with
Y variable (ri – rf)
X variable (rm – rf)
Table 4: Regression Output for Equity 21
Regression Using Data Analysis Toolpak
Equity
Equity 21
X Y
-14.0% -13.0%
23.3% 154.0%
5.3% 27.4%
-1.8% -26.2%
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.912964
R Square 0.833504

6. Adjusted R
Square 0.750256
Standard Error 0.410716
Observations 4
ANOVA
df SS MS F
Significance
F
Regression 1 1.688954 1.688954 10.0123 0.087036
Residual 2 0.337376 0.168688
Total 3 2.02633
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Uppe
95.0%
Intercept 0.201779 0.211028 0.956171 0.439893 -0.7062 1.109761 -0.7062 1.1097
X 4.821131 1.523639 3.164222 0.087036 -1.73456 11.37682 -1.73456 11.376
R2
is a measure of fit of the line and has values between 0 and 1. Higher R2
means better fit of the line.
Here, the value of R2
is 0.83, which is quite high, which means the curve has a better fit.
For this analysis, we are only interested in the values of slopes and intercept (and not checking p-value
for statistical significance or value of R2
).
The regression equation is (ri – rf) = a + b (rm – rf)
In our case, (ri – rf) = 0.2018 + 4.8211 (rm – rf)
The process is repeated for all the 34 equities and the values of Jensen’s Performance Measure
as well as the Performance Ratio is calculated as shown below:
Table 5: Jensen’s Performance Measure Calculation. Refer Excel worksheet “Regression” for complete
analysis
Y Performance Measure
Ri - Rf
Jensen's
alpha
Jensen's
beta
Jensen's
Ratio
Equities 2015 2014 2013 2012 Slope Y-Intercept alpha/beta
Equity 21 -13.0% 154.0% 27.4% -26.2% 4.8211 0.2018 23.89308089
Equity 4 76.6% 175.4% -39.1% -21.3% 3.0756 0.3810 8.07337654
Equity 12 6.3% 124.7% 55.6% 0.3% 3.4533 0.3573 9.664072978
Equity 23 -31.0% 40.1% -44.5% -5.3% 1.7512 -0.1576
-
11.11264576
Equity 3 22.7% 208.7% 59.1% 29.8% 5.1956 0.6349 8.183522593

7. Using Jensen’s Performance Ratio, the equities are ranked from 1-34 (higher the ratio, lesser rank). A
lesser rank equity has performed better than a higher ranked equity because it has yielded better
returns compared to market (Rm) as well as risk-free returns (Rf).
FINAL DATA:
Table 6: Final Data (Refer “Equities” for complete dataset)
OPTIMIZATION:
We have a limited investment fund for investing in equities and we want to maximize returns from our
investment. The equities are diverse (18 industries) and our best bet would be to diversify our investments
into different sectors and not allocate all our funds into a single equity. This leads us to several constraints.
In our portfolio optimization model,
Objective Function: Maximize returns (over a one year time period) by investing in equities
Decision Variables: Amount (Investment) to be allocated in each asset/equity
Constraints:
1. Non-negativity constraint: All investments made in equities need to be non-negative
2. Equity constraint: No asset should be more than 30% of the portfolio
3. Total investment constraint: Total investment(sum of investments made in all equities) should
be less than or equal to the funds available
4. Industry constraint: For diversifying the portfolio, investments in each industry have an upper
and lower limit
Table 7: Industry constraint
Industry
Lower
Limit
Upper
Limit
Appliances 1% 20%
Automotive 1% 40%
Banking 0% 30%
Batteries 1% 40%
Conglomerate 5% 30%
Cookery 0% 20%
Courier 0% 10%

8. Energy 5% 40%
FMCG 5% 30%
Food Processing 0% 20%
IT 0% 40%
Personal Care 0% 20%
Pharmaceuticals 5% 30%
Textiles 1% 25%
Theatres 0% 10%
5. Market Cap Constraint: In order to diversify, equities should be allocated by all the 3 types of
market cap subject to constraints:
Table 8: Market Cap constraint
Lower Limit Upper Limit
Large Cap 10% 100%
Medium Cap 0% 50%
Small Cap 0% 40%
6. Jensen’s Alpha Constraint: Applies to only B & C Grade Equities: Choose Equities with positive
Jensen's Alpha
7. Jensen’s Ratio Constraint: Applies to only B & C Grade Equities: Choose Equities with Jensen's
Performance Rank<=25
Constraints 6 & 7 are computed by filtering data instead of using constraints in model because of limitation
in number of constraints in Solver (limit of 200 variables) and scaling issues in Premium Solver(in spite of
Automatic scaling).
The objective function, decision variables and constraints are entered in the Solver parameters dialog box
(as shown below). The solving method used is “Simplex LP” since the problem is a linear optimization
problem. We need to check the box “Make unconstrained variables Non-Negative” to include the non-
negativity constraint.

9. Once we click the “Solve” button, we get the Optimal solution for this problem.

10. Understanding Sensitivity Report:
Table 9: Decision Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$F$10 Equity 1 Investment 1000 0 1.341654303 0.362477516 1E+30
$F$11 Equity 2 Investment 0
-
0.364171905 1.427482628 0.364171905 1E+30
$F$12 Equity 3 Investment 30000 0 2.050140486 1E+30 0.258485953
$F$13 Equity 4 Investment 10000 0 1.791654533 0.258485953 0.087522713
$F$14 Equity 5 Investment 0 -0.66387386 1.127780672 0.66387386 1E+30
$F$15 Equity 6 Investment 0
-
0.608528372 1.18312616 0.608528372 1E+30
$F$16 Equity 7 Investment 0 0 1.200120467 0.504011352 1E+30
$F$17 Equity 8 Investment 30000 0 2.995218483 1E+30 1.291086664
$F$18 Equity 9 Investment 5000 0 1.253801048 0.450330772 1E+30
$F$19 Equity 10 Investment 0 0 1.143638805 0.560493014 0.078954092
$F$20 Equity 11 Investment 0
-
0.078954092 1.064684713 0.078954092 1E+30
$F$21 Equity 12 Investment 8000 0 1.704131819 0.087522713 0.060699628
$F$22 Equity 13 Investment 5000 0 1.201004732 0.503127087 1E+30
$F$23 Equity 14 Investment 0
-
0.081486472 1.067733049 0.081486472 1E+30
$F$24 Equity 15 Investment 5000 0 1.149219521 0.554912299 0.081486472
$F$25 Equity 16 Investment 0 0 1.372798676 0.331333144 1E+30
$F$26 Equity 17 Investment 0
-
0.125296976 1.246783057 0.125296976 1E+30
$F$27 Equity 18 Investment 0 0 1.372080033 0.332051787 0.125296976
$F$28 Equity 19 Investment 0 0 1.328606867 0.375524952 1E+30
$F$29 Equity 20 Investment 5000 0 1.368759266 0.335372553 1E+30
$F$30 Equity 21 Investment 1000 0 1.643432191 0.060699628 1E+30
$F$31 Equity 22 Investment 0 0 1.638216929 0.065914891 1E+30
The reduced cost tells us how much the objective co-efficient needs to be reduced in order for a non-
negative variable that is zero in the optimal solution to become positive. Since Equity 1 is already present
in the model, the reduced cost is zero. However, the reduced cost for Equity 2 is 0.3642 i.e. the objective
function of Equity 2 has to increase from 1.42 to 1.78 if investment is to be made in Equity 2 (i.e final value
to be positive).

11. Table 10: Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$34 Total Investment Investment $100,000.00 1.704131819 100000 2000 8000
$U$10 Appliances % of Portfolio 0.01 0 0.2 1E+30 0.19
$U$11 Automotive % of Portfolio 0.4 8752.271324 0.4 0.08 0.02
$U$12 Banking % of Portfolio 0 0 0.3 1E+30 0.3
$U$13 Batteries % of Portfolio 0.3 0 0.4 1E+30 0.1
$U$14 Conglomerate % of Portfolio 0.05 0 0.3 1E+30 0.25
$U$15 Cookery % of Portfolio 0 0 0.2 1E+30 0.2
$U$16 Courier % of Portfolio 0.08 0 0.1 1E+30 0.02
$U$17 Energy % of Portfolio 0.05 0 0.4 1E+30 0.35
$U$18 FMCG % of Portfolio 0.05 0 0.3 1E+30 0.25
$U$19 Food Processing % of Portfolio 0 0 0.2 1E+30 0.2
$U$20 IT % of Portfolio 0 0 0.4 1E+30 0.4
$U$21 Personal Care % of Portfolio 0 0 0.2 1E+30 0.2
$U$22 Pharmaceuticals % of Portfolio 0.05 0 0.3 1E+30 0.25
$U$23 Textiles % of Portfolio 0.01 0 0.25 1E+30 0.24
$U$24 Theatres % of Portfolio 0 0 0.1 1E+30 0.1
$U$10 Appliances % of Portfolio 0.01
-
36247.75165 0.01 0.08 0.01
$U$11 Automotive % of Portfolio 0.4 0 0.01 0.39 1E+30
$U$12 Banking % of Portfolio 0 -50401.1352 0 0.08 0
$U$13 Batteries % of Portfolio 0.3 0 0.01 0.29 1E+30
$U$14 Conglomerate % of Portfolio 0.05
-
45033.07718 0.05 0.08 0.02
$U$15 Cookery % of Portfolio 0
-
56049.30143 0 0.08 0
$U$16 Courier % of Portfolio 0.08 0 0 0.08 1E+30
$U$17 Energy % of Portfolio 0.05
-
50312.70873 0.05 0.08 0.02
$U$18 FMCG % of Portfolio 0.05
-
55491.22986 0.05 0.08 0.02
$U$19 Food Processing % of Portfolio 0
-
33133.31438 0 0.08 0
$U$20 IT % of Portfolio 0
-
33205.17865 0 0.08 0
$U$21 Personal Care % of Portfolio 0
-
37552.49519 0 0.08 0
$U$22 Pharmaceuticals % of Portfolio 0.05 -33537.2553 0.05 0.08 0.02
$U$23 Textiles % of Portfolio 0.01
-
6069.962836 0.01 0.08 0.01

12. $U$24 Theatres % of Portfolio 0
-
6591.489051 0 0.08 0
$I$10 Equity 1 % of portfolio 0.01 0 0.3 1E+30 0.29
$I$11 Equity 2 % of portfolio 0 0 0.3 1E+30 0.3
$I$12 Equity 3 % of portfolio 0.3 25848.59532 0.3 0.1 0.2
$I$13 Equity 4 % of portfolio 0.1 0 0.3 1E+30 0.2
$I$14 Equity 5 % of portfolio 0 0 0.3 1E+30 0.3
$I$15 Equity 6 % of portfolio 0 0 0.3 1E+30 0.3
$I$16 Equity 7 % of portfolio 0 0 0.3 1E+30 0.3
$I$17 Equity 8 % of portfolio 0.3 129108.6664 0.3 0.08 0.02
$I$18 Equity 9 % of portfolio 0.05 0 0.3 1E+30 0.25
$I$19 Equity 10 % of portfolio 0 0 0.3 1E+30 0.3
$I$20 Equity 11 % of portfolio 0 0 0.3 1E+30 0.3
$I$21 Equity 12 % of portfolio 0.08 0 0.3 1E+30 0.22
$I$22 Equity 13 % of portfolio 0.05 0 0.3 1E+30 0.25
$I$23 Equity 14 % of portfolio 0 0 0.3 1E+30 0.3
$I$24 Equity 15 % of portfolio 0.05 0 0.3 1E+30 0.25
$I$25 Equity 16 % of portfolio 0 0 0.3 1E+30 0.3
$I$26 Equity 17 % of portfolio 0 0 0.3 1E+30 0.3
$I$27 Equity 18 % of portfolio 0 0 0.3 1E+30 0.3
$I$28 Equity 19 % of portfolio 0 0 0.3 1E+30 0.3
$I$29 Equity 20 % of portfolio 0.05 0 0.3 1E+30 0.25
$I$30 Equity 21 % of portfolio 0.01 0 0.3 1E+30 0.29
$I$31 Equity 22 % of portfolio 0 0 0.3 1E+30 0.3
$U$32 Large Cap % of portfolio 0.55 0 1 1E+30 0.45
$U$33 Mid Cap % of portfolio 0.15 0 0.5 1E+30 0.35
$U$34 Small Cap % of portfolio 0.3 0 0.4 1E+30 0.1
$U$32 Large Cap % of portfolio 0.55 0 0.1 0.45 1E+30
$U$33 Mid Cap % of portfolio 0.15 0 0 0.15 1E+30
$U$34 Small Cap % of portfolio 0.3 0 0 0.3 1E+30
The shadow price tells how much the value of the objective function will change as the right hand side of
the constraint is increased by 1. For example, if we consider the total investment constraint, the RHS of
constraint is $100,000. If we increase the total funds by $1, our objective function will increase by 1.704
i.e. our returns will increase by $1.704. However, the allowable increase for the RHS is $2000 for our
optimal solution to be the same. If we increase the total funds by $2001, then we need to resolve the
model to get the optimal solution.

13. Table 11: Binding Constraints
Cell Name Cell Value Formula Status
$F$34 Total Investment Investment $100,000.00 $F$34<=$F$36 Binding
$U$10 Appliances % of Portfolio 1.0% $U$10<=$W$10
Not
Binding
$U$11 Automotive % of Portfolio 40.0% $U$11<=$W$11 Binding
$U$12 Banking % of Portfolio 0.0% $U$12<=$W$12
Not
Binding
$U$13 Batteries % of Portfolio 30.0% $U$13<=$W$13
Not
Binding
$U$14 Conglomerate % of Portfolio 5.0% $U$14<=$W$14
Not
Binding
$U$15 Cookery % of Portfolio 0.0% $U$15<=$W$15
Not
Binding
$U$16 Courier % of Portfolio 8.0% $U$16<=$W$16
Not
Binding
$U$17 Energy % of Portfolio 5.0% $U$17<=$W$17
Not
Binding
$U$18 FMCG % of Portfolio 5.0% $U$18<=$W$18
Not
Binding
$U$19 Food Processing % of Portfolio 0.0% $U$19<=$W$19
Not
Binding
$U$20 IT % of Portfolio 0.0% $U$20<=$W$20
Not
Binding
$U$21 Personal Care % of Portfolio 0.0% $U$21<=$W$21
Not
Binding
$U$22 Pharmaceuticals % of Portfolio 5.0% $U$22<=$W$22
Not
Binding
$U$23 Textiles % of Portfolio 1.0% $U$23<=$W$23
Not
Binding
$U$24 Theatres % of Portfolio 0.0% $U$24<=$W$24
Not
Binding
$U$10 Appliances % of Portfolio 1.0% $U$10>=$V$10 Binding
$U$11 Automotive % of Portfolio 40.0% $U$11>=$V$11
Not
Binding
$U$12 Banking % of Portfolio 0.0% $U$12>=$V$12 Binding
$U$13 Batteries % of Portfolio 30.0% $U$13>=$V$13
Not
Binding
$U$14 Conglomerate % of Portfolio 5.0% $U$14>=$V$14 Binding
$U$15 Cookery % of Portfolio 0.0% $U$15>=$V$15 Binding
$U$16 Courier % of Portfolio 8.0% $U$16>=$V$16
Not
Binding
$U$17 Energy % of Portfolio 5.0% $U$17>=$V$17 Binding

14. $U$18 FMCG % of Portfolio 5.0% $U$18>=$V$18 Binding
$U$19 Food Processing % of Portfolio 0.0% $U$19>=$V$19 Binding
$U$20 IT % of Portfolio 0.0% $U$20>=$V$20 Binding
$U$21 Personal Care % of Portfolio 0.0% $U$21>=$V$21 Binding
$U$22 Pharmaceuticals % of Portfolio 5.0% $U$22>=$V$22 Binding
$U$23 Textiles % of Portfolio 1.0% $U$23>=$V$23 Binding
$U$24 Theatres % of Portfolio 0.0% $U$24>=$V$24 Binding
$I$10 Equity 1 % of portfolio 1.00% $I$10<=$K$10
Not
Binding
$I$11 Equity 2 % of portfolio 0.00% $I$11<=$K$11
Not
Binding
$I$12 Equity 3 % of portfolio 30.00% $I$12<=$K$12 Binding
$I$13 Equity 4 % of portfolio 10.00% $I$13<=$K$13
Not
Binding
$I$14 Equity 5 % of portfolio 0.00% $I$14<=$K$14
Not
Binding
$I$15 Equity 6 % of portfolio 0.00% $I$15<=$K$15
Not
Binding
$I$16 Equity 7 % of portfolio 0.00% $I$16<=$K$16
Not
Binding
$I$17 Equity 8 % of portfolio 30.00% $I$17<=$K$17 Binding
$I$18 Equity 9 % of portfolio 5.00% $I$18<=$K$18
Not
Binding
$I$19 Equity 10 % of portfolio 0.00% $I$19<=$K$19
Not
Binding
$I$20 Equity 11 % of portfolio 0.00% $I$20<=$K$20
Not
Binding
$I$21 Equity 12 % of portfolio 8.00% $I$21<=$K$21
Not
Binding
$I$22 Equity 13 % of portfolio 5.00% $I$22<=$K$22
Not
Binding
$I$23 Equity 14 % of portfolio 0.00% $I$23<=$K$23
Not
Binding
$I$24 Equity 15 % of portfolio 5.00% $I$24<=$K$24
Not
Binding
$I$25 Equity 16 % of portfolio 0.00% $I$25<=$K$25
Not
Binding
$I$26 Equity 17 % of portfolio 0.00% $I$26<=$K$26
Not
Binding
$I$27 Equity 18 % of portfolio 0.00% $I$27<=$K$27
Not
Binding
$I$28 Equity 19 % of portfolio 0.00% $I$28<=$K$28
Not
Binding
$I$29 Equity 20 % of portfolio 5.00% $I$29<=$K$29
Not
Binding

15. $I$30 Equity 21 % of portfolio 1.00% $I$30<=$K$30
Not
Binding
$I$31 Equity 22 % of portfolio 0.00% $I$31<=$K$31
Not
Binding
$U$32 Large Cap % of portfolio 55.0% $U$32<=$W$32
Not
Binding
$U$33 Mid Cap % of portfolio 15.0% $U$33<=$W$33
Not
Binding
$U$34 Small Cap % of portfolio 30.0% $U$34<=$W$34
Not
Binding
$U$32 Large Cap % of portfolio 55.0% $U$32>=$V$32
Not
Binding
$U$33 Mid Cap % of portfolio 15.0% $U$33>=$V$33
Not
Binding
$U$34 Small Cap % of portfolio 30.0% $U$34>=$V$34
Not
Binding
When the LHS of constraint is equal to RHS, the constraint in binding. In our example in the total
investment constraint, we utilize all the allocated funds. Therefore, the LHS of the constraint is equal to
the RHS of the constraint and the constraint is binding. In the Small Cap % of portfolio constraint, we
require at max 40% of our portfolio to be small cap. However, our allocation is only 30% which means LHS
is not equal to RHS and therefore the constraint is not binding.
Table 12: Slack for constraints
Slack is the difference between the LHS and RHS of constraint. For example, in Appliances % of portfolio
constraint, we have at max 20% as the RHS of the constraint. However, our allocation in Appliances in only
1%, which means that there is a slack of 19%.

16. CONCLUSION:
Our optimal solution from the model after applying Linear Optimization is:
Equity Investment Average 3 Year Return
Expected Returns
(After one year)
% of
portfolio
Equity 1 $1,000.00 34.17% $1,341.65 1.00%
Equity 2 $0.00 42.75% $0.00 0.00%
Equity 3 $30,000.00 105.01% $61,504.21 30.00%
Equity 4 $10,000.00 79.17% $17,916.55 10.00%
Equity 5 $0.00 12.78% $0.00 0.00%
Equity 6 $0.00 18.31% $0.00 0.00%
Equity 7 $0.00 20.01% $0.00 0.00%
Equity 8 $30,000.00 199.52% $89,856.55 30.00%
Equity 9 $5,000.00 25.38% $6,269.01 5.00%
Equity 10 $0.00 14.36% $0.00 0.00%
Equity 11 $0.00 6.47% $0.00 0.00%
Equity 12 $8,000.00 70.41% $13,633.05 8.00%
Equity 13 $5,000.00 20.10% $6,005.02 5.00%
Equity 14 $0.00 6.77% $0.00 0.00%
Equity 15 $5,000.00 14.92% $5,746.10 5.00%
Equity 16 $0.00 37.28% $0.00 0.00%
Equity 17 $0.00 24.68% $0.00 0.00%
Equity 18 $0.00 37.21% $0.00 0.00%
Equity 19 $0.00 32.86% $0.00 0.00%
Equity 20 $5,000.00 36.88% $6,843.80 5.00%
Equity 21 $1,000.00 64.34% $1,643.43 1.00%
Equity 22 $0.00 63.82% $0.00 0.00%
Total Investment $100,000.00 Total Expected Returns $210,759.38
<=
$100,000.00
(Max. Investment)
As we can observe, we allocated funds worth $100,000 and after adopting Linear Optimization and using
Jensen’s Performance Measure, our Expected returns in one year is $210,759.38 which is a 111% increase.
Reference:
[1] Jenson’s Performance Measure p148-150, “101 Investment Tools for Buying Low and Selling High”, Jae
K. Shim and Jonathan Lansner, 2001