Optimum Investment Selection process-Nov 9-2013

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Can Can You Beat the S&P Beat the S&P 500?500?

Prepared byGary Crosbie

A Two Stage Investment Analysis A Two Stage Investment Analysis to maximize the selection of an to maximize the selection of an Optimum Investment Portfolio Optimum Investment Portfolio

that will beat the S&P 500.that will beat the S&P 500.

NNov 2013ov 2013

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Table of ContentsTable of Contents

1.1. -Preface-Preface ……………………………… ……………………………… 332.2. - Analytic Methodology …………… - Analytic Methodology …………… 663.3. -Analytic Results-Analytic Results ………………… ………………… 2121

– Power Coefficient ResultsPower Coefficient Results - Monte Carlo Simulations- Monte Carlo Simulations

44. . RecommendationsRecommendations ………………… ………………… 3131- Proposition 1- Proposition 1

- Proposition 2- Proposition 2

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This Section Defines the Issues:This Section Defines the Issues: Propositions of Interest: Propositions of Interest: Is there a methodology that allows the Is there a methodology that allows the

Investor to beat the S&P 500 ? There are two questions that are Investor to beat the S&P 500 ? There are two questions that are often asked in the investment community:often asked in the investment community:– Proposition 1Proposition 1-- Given previous research completed in 2011, that Given previous research completed in 2011, that

Midcaps(vs large Caps and Small Caps) have the best value per unit of Midcaps(vs large Caps and Small Caps) have the best value per unit of risk , does the results from the periods following the financial crisis risk , does the results from the periods following the financial crisis (2007- 2012) continue to support those results.(2007- 2012) continue to support those results.

– Proposition 2Proposition 2- - IsIs there an alternative investment process (Mix of there an alternative investment process (Mix of Mutual funds in Large Cap, Midcap , Small Cap and Fixed Income Mutual funds in Large Cap, Midcap , Small Cap and Fixed Income Styles) chosen by the highest Power Coef’s that provide better results Styles) chosen by the highest Power Coef’s that provide better results than simply a Mutual fund that duplicates the S&P 500?than simply a Mutual fund that duplicates the S&P 500?

Section-1- Preface:Section-1- Preface:

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Section-1- Section-1- Preface:Preface:

The purpose of this section is to develop an algorithm The purpose of this section is to develop an algorithm that will enumerate the best investments within each that will enumerate the best investments within each style category to maximize performance. style category to maximize performance.

The model developed calculates a Power Coefficient The model developed calculates a Power Coefficient which represents the culmination of weighted which represents the culmination of weighted customer preferences and investment based statistics customer preferences and investment based statistics to rank investment alternatives .to rank investment alternatives .

Those with the highest Coefficients represent the Those with the highest Coefficients represent the Optimum investment alternatives given those Optimum investment alternatives given those weighted preferences.weighted preferences.

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PrPr If there are more than one investment

ranked in a particular style (e.g. Mid Caps) than the allocation process could take one of the following form:

– 100% allocated to the investment with the highest power coefficient

– the % allocated to each investment should be based on the % weighting of the power coefficient

Section-1- Preface:Section-1- Preface:

Section 2- Section 2- Analytical Analytical

MethodologyMethodology

This section will discuss The following:This section will discuss The following:1- Process1- Process

Filtering InvestmentsFiltering Investments2-Modeling2-Modeling

Power CoefficientPower Coefficient3- Monte Carlo Simulations3- Monte Carlo Simulations

Proposition 1- Best StyleProposition 1- Best StyleProposition 2-Diversified PortfolioProposition 2-Diversified Portfolio

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Two Stage Process:Two Stage Process: Step One:Step One:

– Initially filter with Morningstar Fund/ETF screening Initially filter with Morningstar Fund/ETF screening process.process.

– Choose top 3-5 investments in each style..Large Cap, Choose top 3-5 investments in each style..Large Cap, Mid Cap, Small Cap, ..Value, Blend and Growth with the Mid Cap, Small Cap, ..Value, Blend and Growth with the highest Power Coefficientshighest Power Coefficients

– Choose top 3-5 investments in Fixed income-Bonds. Choose top 3-5 investments in Fixed income-Bonds. Step Two:Step Two:

– Use the Power Coefficient defined in the next section to Use the Power Coefficient defined in the next section to rank investments based on personal investor rank investments based on personal investor preferencespreferences

2-Analytic Methodology: 2-Analytic Methodology: Step 1 - Process Step 1 - Process

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Definition: The Power Coefficient: Definition: The Power Coefficient: – A derivative of 10 variables A derivative of 10 variables – Define the short and long run viability of a Define the short and long run viability of a

particular Fund or ETF.particular Fund or ETF.– The variables are weighted based on individual The variables are weighted based on individual

investor preferences to encapsulate :investor preferences to encapsulate : Tolerance for riskTolerance for risk Investment time horizonsInvestment time horizons VolatilityVolatility Rates of Return at different time horizons(1,3,5 yr)Rates of Return at different time horizons(1,3,5 yr)

2-Analytic Methodology: 2-Analytic Methodology:

Step 2 - Modeling Step 2 - Modeling

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Model Algorithm:Model Algorithm:– Generated from the following equation:Generated from the following equation:

– Equation:Equation: Power coefficient generated by the Power coefficient generated by the following:following:

Power CoefPower Coef = = a(1Gr)+b(3 Gr)+c(5 GRa(1Gr)+b(3 Gr)+c(5 GR) x ) x αα (d*(d*ЄЄ )+(e* )+(e* ββ)+)+ (F*(F*σσ))

2-Analytic 2-Analytic Methodology: Methodology:


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– Where:Where: a= Percentage weight for 1 year growth ratea= Percentage weight for 1 year growth rate B= Percentage weight for 3 year growth rateB= Percentage weight for 3 year growth rate c= Percentage weight for 5 year growth ratec= Percentage weight for 5 year growth rate D= Percentage weight for Expense RatioD= Percentage weight for Expense Ratio E= Percentage weight for BetaE= Percentage weight for Beta F= Percentage weight for Standard deviationF= Percentage weight for Standard deviation 1GR= 1 year growth rate1GR= 1 year growth rate 3GR= 3 year growth rate3GR= 3 year growth rate 5GR= 5 year growth rate5GR= 5 year growth rate Є= Expense ratioЄ= Expense ratio

2-Analytic Methodology: 2-Analytic Methodology: Step 2 - Modeling Step 2 - Modeling

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ΒΒ= Beta for the investment indicating correlation = Beta for the investment indicating correlation over time with the general marketover time with the general market

σ σ = Standard Deviation= Standard Deviation α= Measure of performance relative to index of

equivalent investments.

Power Coefficients generated for each fund should be used Power Coefficients generated for each fund should be used to rank funds in ascending order for each Style:to rank funds in ascending order for each Style:– Large Cap Picks:Large Cap Picks:– Mid Cap Picks:Mid Cap Picks:– Small Cap picks:Small Cap picks:– Fixed Income Picks:Fixed Income Picks:



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MethodologyMethodology:: The spread sheet to do the power coefficient calculations and Rank them in The spread sheet to do the power coefficient calculations and Rank them in

order is available by request.order is available by request. Otherwise you may want to look at the following Otherwise you may want to look at the following “Quik Calc” “Quik Calc” method:method:

– Back of the “Match book Cover” Calculation of a power CoefBack of the “Match book Cover” Calculation of a power Coef ( if you don’t wish to have the spreadsheet)( if you don’t wish to have the spreadsheet)

1.1. Pick a desired list of potential investments in each of the Style categories Pick a desired list of potential investments in each of the Style categories discussed previously. (e.g. Morningstar)discussed previously. (e.g. Morningstar)

2.2. Look up the Net Asset value growth for 1 yr, 3yr and 5 yr from Morning Star for Look up the Net Asset value growth for 1 yr, 3yr and 5 yr from Morning Star for each investment in each style under consideration. each investment in each style under consideration.

3.3. Based on preferences weight the 1 yr , 3yr and 5 yr Grwth rate so the sum of the Based on preferences weight the 1 yr , 3yr and 5 yr Grwth rate so the sum of the weights =1 Than do the following calculation; weights =1 Than do the following calculation;

4.4. (1yr wt)*(1 yr Grwth rate) + (3yr wt)*(3 yr Grwth rate) + (5yr wt)* (5 yr Grwth (1yr wt)*(1 yr Grwth rate) + (3yr wt)*(3 yr Grwth rate) + (5yr wt)* (5 yr Grwth rate) =Weighted Avg Grwth Raterate) =Weighted Avg Grwth Rate

5.5. Now…do the same for the Vanguard index fund(VFINX) Now…do the same for the Vanguard index fund(VFINX) Which is the S&P 500 proxy for comparison to the calculationsWhich is the S&P 500 proxy for comparison to the calculations Made above for specific funds..Made above for specific funds..


5. Look up the Standard Deviation (Morningstar) for each Investment. 6. Look up the Standard Deviation (Morningstar) for the Benchmark Investment …. Vanguard index fund(VFINX 7. DIVIDE 4/5 for each Investment 8. DIVIDE 5/6 for the Benchmark- Vanguard Index Fund 9. The result of 4/5 will give you an estimate of the dollar per unit of risk for each investment. 10. The result of 5/6 will give you an estimate of the dollar per unit of risk for the Benchmark- Vanguard Index Fund

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• Methodology : (con)



11. Subtract : 9-8 to get the difference. Rank highest to lowest 11. Subtract : 9-8 to get the difference. Rank highest to lowest differences for each style- LC, MC, SC , FIdifferences for each style- LC, MC, SC , FI 12. The preferred picks are the highest 12. The preferred picks are the highest PositivePositive difference ranking in difference ranking in each styleeach style 13. If you like multiple picks per style, weight the picks as reflected on 13. If you like multiple picks per style, weight the picks as reflected on page 19page 19

14. If you use the above.. make certain you address the 14. If you use the above.. make certain you address the issues of :issues of :- Expense CostsExpense Costs- Beta Beta - AlphaAlpha

15. On growth rates..15. On growth rates..choose investments with time tested (3 & 5 choose investments with time tested (3 & 5 year) returns year) returns . Results in this paper weighted 1yr 3 yr and 5 yr growth . Results in this paper weighted 1yr 3 yr and 5 yr growth rates 30%, 40% 30% respectively.rates 30%, 40% 30% respectively.

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Power Coefficient Picks: (Using Model on Page 9)Power Coefficient Picks: (Using Model on Page 9)– Large Cap: Large Cap:

1.1. *Sequoia- SEQUX- *Sequoia- SEQUX- (Highest power Coef(Highest power Coef))2.2. YAFFXYAFFX3.3. Wasatch - WGROXWasatch - WGROX

– Mid Cap: Mid Cap: 1.1. *Principal Midcap – PEMGX-*Principal Midcap – PEMGX-(Highest power Coef(Highest power Coef))2.2. Rydex Midcap- RFGRydex Midcap- RFG

– Small Cap: Small Cap: 1.1. *Vulcan Value Partners- VVPSX-*Vulcan Value Partners- VVPSX-(Highest power Coef(Highest power Coef))2.2. Brown Small Cap Mgt- BCSIXBrown Small Cap Mgt- BCSIX

– Fixed income- Bonds- Fixed income- Bonds- 1. *Metropolitan West Total Return – MWTRX-(Highest power Coef(Highest power Coef))2. Aberdeen Global High Income - BJBHX3. Metropolitan West High Yield- MWHYX

2-Analytic Methodology: 2-Analytic Methodology: Step 2 – Modeling Step 2 – Modeling

Using the algorithm identified on page 9 the highest Using the algorithm identified on page 9 the highest coefficients in each style generated the following:coefficients in each style generated the following:– Large Cap= 9.48= Sequoia Large Cap= SEQUXLarge Cap= 9.48= Sequoia Large Cap= SEQUX– Mid Cap= 8.22= Principal Midcap=PEMGXMid Cap= 8.22= Principal Midcap=PEMGX– Small Cap= 8.09=Vulcan Value Partners=VVPSXSmall Cap= 8.09=Vulcan Value Partners=VVPSX

Than weights are derived for each style based on the Than weights are derived for each style based on the power coefficients: Thuspower coefficients: Thus– -Large Cap =Sequoia = SEQUX= weight = 35%-Large Cap =Sequoia = SEQUX= weight = 35%– Mid Cap= Principal Mid CAP= PEMGX…….= 33%Mid Cap= Principal Mid CAP= PEMGX…….= 33%– Small Cap= Vulcan Value Partners=VVPSX=32%Small Cap= Vulcan Value Partners=VVPSX=32%

These weights are used on page 19 to calculate theThese weights are used on page 19 to calculate the Allocation of the base portfolio when comparing Allocation of the base portfolio when comparing

simulation results with the S&P 500 .simulation results with the S&P 500 . 1616

2-Analytic Methodology: 2-Analytic Methodology: Step 2 – Modeling Step 2 – Modeling

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Analytical ComparativesAnalytical Comparatives– Proposition 1Proposition 1:: What is the best investment style What is the best investment style

compared to the S&P 500.(LC, MC,SC)compared to the S&P 500.(LC, MC,SC) Generate a Power Coefficient for the S&P 500Generate a Power Coefficient for the S&P 500 Choose the fund with the highest Power Coefficients for Choose the fund with the highest Power Coefficients for

each style (Large Cap, Mid Cap and Small Cap) and each style (Large Cap, Mid Cap and Small Cap) and compare to the S&P 500.compare to the S&P 500.

Power Coefficient Analytic Comparatives:Power Coefficient Analytic Comparatives:– Run Monte Carlo simulations Run Monte Carlo simulations – Use 1000 iterationsUse 1000 iterations– Compare the results of the :Compare the results of the :

Power Coefficient Style (Large cap, Mid Cap etc)Power Coefficient Style (Large cap, Mid Cap etc) Take the fund with the highest power Coef in each style Take the fund with the highest power Coef in each style vs. the Portfolio that mirrors the S&P 500vs. the Portfolio that mirrors the S&P 500

2-Analytic Methodology: 2-Analytic Methodology: Step 3 – Monte Carlo Step 3 – Monte Carlo

SimulationsSimulations

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Analytical Comparatives: Evaluation ProcessAnalytical Comparatives: Evaluation Process– Proposition 2Proposition 2:: – Utilize Monte Carlo Simulation to develop a diversified portfolio Utilize Monte Carlo Simulation to develop a diversified portfolio

of Large Caps, Midcaps , Small Caps and Fixed Income of Large Caps, Midcaps , Small Caps and Fixed Income investments with the highest Power Coefficients (see investments with the highest Power Coefficients (see Proposition 2Proposition 2 page 34) to maximize returns greater than the page 34) to maximize returns greater than the S&P 500.S&P 500.

1000 interactions were used in the simulation:1000 interactions were used in the simulation:

Given a 60% equity allocation and 40% Fixed Income ,Given a 60% equity allocation and 40% Fixed Income ,

The weights associated with each style LC, MC,SC (Taken The weights associated with each style LC, MC,SC (Taken from page 15)from page 15)



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Given a $1.00 investment, generate a portfolio allocated according to the Given a $1.00 investment, generate a portfolio allocated according to the power coefficients for each style: Large Caps, Midcaps, Small caps & Fixed power coefficients for each style: Large Caps, Midcaps, Small caps & Fixed Income. Income.

An average portfolio allocation is 55-65% Equity ,35% to 45% Fixed Income. An average portfolio allocation is 55-65% Equity ,35% to 45% Fixed Income. For the purpose of this analysis a Mid point allocation was assumed. That is For the purpose of this analysis a Mid point allocation was assumed. That is 60% equity, 40% Fixed Income . Further per the discussion under 60% equity, 40% Fixed Income . Further per the discussion under proposition 1 (page 28) in the previous section Power Coef of Large Caps proposition 1 (page 28) in the previous section Power Coef of Large Caps (LC’s) had a slight advantage over Mid Cap’(MC)s and SC’s (SC) (LC’s) had a slight advantage over Mid Cap’(MC)s and SC’s (SC)

The Diversified Portfolio is:The Diversified Portfolio is: Large Caps= 35 % Power Coef weighting * 60% =21 %=SEQUXLarge Caps= 35 % Power Coef weighting * 60% =21 %=SEQUX Mid Caps = 33% Power Coef weighting * 60% = 20%=PEMBXMid Caps = 33% Power Coef weighting * 60% = 20%=PEMBX Small Caps= 32% Power Coef weighting* 60% =19%=VVPSXSmall Caps= 32% Power Coef weighting* 60% =19%=VVPSX Fixed Income =40% in Fixed Income-Bonds- MWTRXFixed Income =40% in Fixed Income-Bonds- MWTRX



– The sum of the weights =100%The sum of the weights =100%– For simplicity assume a portfolio of $ 1.OO thereforeFor simplicity assume a portfolio of $ 1.OO therefore– The $1.00 Diversified Portfolio becomes:The $1.00 Diversified Portfolio becomes:

$.21 to SEQUX- large Cap$.21 to SEQUX- large Cap .$.2 to PEMBX -Midcap.$.2 to PEMBX -Midcap $.19 to VVPSX- Small Cap$.19 to VVPSX- Small Cap $.4 0 to MWTRX- Fixed Income$.4 0 to MWTRX- Fixed Income Total $ 1.00Total $ 1.00

Thus in summary:Thus in summary:1.1. Large Caps- Large Caps- 21%21%

The best of the Large caps =Sequoia- SEQUX= The best of the Large caps =Sequoia- SEQUX= $.21$.212.2. Mid Caps- Mid Caps- 20%20%

The best of the midcaps =Principal Midcap- PEMGX=$.27The best of the midcaps =Principal Midcap- PEMGX=$.273.3. Small Caps- Small Caps- 19%19%

The best of the small caps= Vulcan Value Partner -SCETX-=$.12The best of the small caps= Vulcan Value Partner -SCETX-=$.12

2020



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4- 4- Fixed Income- Bonds- 40%Fixed Income- Bonds- 40% Metropolitan West Total Return – MWTRX-$.40

Total of Large Caps +Midcaps +Small Caps + Fixed Income =$1.00Total of Large Caps +Midcaps +Small Caps + Fixed Income =$1.00S&P 500 baseline S&P 500 baseline

– Vanguard Index Fund-VFINX-$1.00Vanguard Index Fund-VFINX-$1.00– This fund replicates the S&P 500This fund replicates the S&P 500

Total $1.00Total $1.00NOTE:NOTE: The 1 dollar investment amount was usedThe 1 dollar investment amount was used To simplify the comparatives.To simplify the comparatives.



Section-3 Section-3 Results Results

This section This section discusses the results of the discusses the results of the methodology discussed in section 2 to methodology discussed in section 2 to the two propositions:the two propositions:

– Proposition 1-Proposition 1- Given previous research Given previous research completed in 2011, that Midcaps(vs large Caps completed in 2011, that Midcaps(vs large Caps and Small Caps) have the best value per unit of and Small Caps) have the best value per unit of risk , does the results from the periods following risk , does the results from the periods following the financial crisis (2007- 2012) continue to the financial crisis (2007- 2012) continue to support those results.support those results.

– Proposition 2-Proposition 2- Is there an alternative investment Is there an alternative investment process (Mix of Mutual funds in Large Cap, process (Mix of Mutual funds in Large Cap, Midcap , Small Cap and Fixed Income Styles) Midcap , Small Cap and Fixed Income Styles) chosen by the highest Power Coef’s that provide chosen by the highest Power Coef’s that provide better results than simply a Mutual fund that better results than simply a Mutual fund that duplicates the S&P 500?duplicates the S&P 500?

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Power Coefficient PortfolioPower Coefficient Portfolio 100% Small Caps100% Small Caps

– Vulcan Value Partners- Vulcan Value Partners- VVPSXVVPSX

$1.00 Investment$1.00 Investment Mean Value from the Mean Value from the

simulation was $7.01 a 30% simulation was $7.01 a 30% increase vs $5.4 for the S&P increase vs $5.4 for the S&P 500 Index portfolio 500 Index portfolio

The 100% SC portfolio has a The 100% SC portfolio has a 63 % probability of exceeding 63 % probability of exceeding the S&P 500 the S&P 500 Implication: The above 100% Small Cap portfolio

generated a 30% higher Power Coefficient result of $7.01 vs. $5.40 for the S&P 500.. The 100% SC portfolio has a 63% probability of exceeding the S&P 500 Index Portfolio

3-Proposition-1- Analytic 3-Proposition-1- Analytic Results:Results:

What is the Best Investment Style What is the Best Investment Style (SC, MC,LC) Compared to the S&P (SC, MC,LC) Compared to the S&P

50500 0

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The mean difference between The mean difference between the the Small Cap Small Cap (VVPSX)Power (VVPSX)Power Coefficient Coefficient generated portfolio and the generated portfolio and the S&P 500 is $1.20S&P 500 is $1.20

57 % Probability the Mean 57 % Probability the Mean Difference Power Coefficient Difference Power Coefficient generated portfolio will exceed generated portfolio will exceed 0.0.Implication: The Power Coefficient generated portfolio

yields a higher mean return of $1.20 (30% higher )and lower Standard Deviation 7.57 vs 9.75 (7% lower) than the Fund mirroring the S&P. The simulations yields a 64.4% probability that the Power Coefficient generated portfolio will exceed the S&P 500 portfolio


What is the Best Investment What is the Best Investment Style (SC, MC,LC) Compared to Style (SC, MC,LC) Compared to

the S&P 50the S&P 500 0

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Power Coefficient Mid Cap Power Coefficient Mid Cap PortfolioPortfolio

100% Midcaps100% Midcaps– Principal Midcap-PEMGXPrincipal Midcap-PEMGX

$1.00 Investment$1.00 Investment Mean Value from the Mean Value from the

simulation was $6.95 a 29% simulation was $6.95 a 29% increase vs $5.40 for the S&P increase vs $5.40 for the S&P 500 Index portfolio 500 Index portfolio

Implication: The 100% Mid Cap portfolio with a dollar invested generated a 29% higher Power Coefficient result of $6.95. versus $5.4 of the S&P 500 portfolio. The 100% Midcap portfolio had a 63% probability exceeding the S&P 500 port of 5.46




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The Mean Difference The Mean Difference between the between the Mid Cap Mid Cap (VVPSX)(VVPSX)Power Coefficient Power Coefficient generated portfolio and the generated portfolio and the S&P 500 is $1.59S&P 500 is $1.59

60% Probability the Mean 60% Probability the Mean Difference Mid Cap Power Difference Mid Cap Power Coefficient generated Coefficient generated portfolio will exceed 0.portfolio will exceed 0.Implication: The Mean Mid Cap Power Coefficient yielded

a higher mean differential return of $1.59 (24% higher )and lower differential Standard Deviation of 7.76 than the Fund mirroring the S&P. The simulations yields a 60% probability that the Mean Mid Cap Power Coefficient generated portfolio will exceed 0.

3-Proposition-1- Analytic Results:3-Proposition-1- Analytic Results:What is the Best Investment Style (SC, MC,LC) Compared to What is the Best Investment Style (SC, MC,LC) Compared to


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Power Coefficient Mid Cap Power Coefficient Mid Cap PortfolioPortfolio

100% Large caps100% Large caps– Sequoia-SEQUXSequoia-SEQUX

$1.00 Investment$1.00 Investment Mean Value from the simu-Mean Value from the simu-lation was $7.96 a 47% increase lation was $7.96 a 47% increase

vs $5.4 for the S&P 500 Index vs $5.4 for the S&P 500 Index portfolio portfolio

Implication: The 100% Large Cap portfolio with a dollar invested generated a 47% higher Power Coefficient result of $7.96 vs 6.64 for the S&P portfolio.The Large Cap portfolio had a 72% prob of exceeding the S&P 500 index Portfoluio

3-Proposition-1- Analytic Results:3-Proposition-1- Analytic Results:What is the Best Investment Style What is the Best Investment Style (SC, MC,LC) Compared to the S&P (SC, MC,LC) Compared to the S&P

50500 0

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The mean difference The mean difference between between the Large Cap the Large Cap (SEQUX)(SEQUX)Power Coefficient Power Coefficient generated portfolio and generated portfolio and the S&P 500 is $2.46 the S&P 500 is $2.46 (45%higher)(45%higher)

65% Probability that the 65% Probability that the mean difference ($2.46) of mean difference ($2.46) of the Large Cap portfolio the Large Cap portfolio will be greater than 0.will be greater than 0.

Implication: The Mean Large Cap Power Coefficient generated a higher differential of 2.46 (45% higher) than the Fund mirroring the S&P. The simulations yields a 65.% probability that the Mean difference Large Cap Power Coefficient of $2.46 will be greater than 0.




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Baseline S&P Portfolio-Baseline S&P Portfolio-VFINXVFINX

$1.00 Investment$1.00 Investment 100% Invested in S&P Fund- 100% Invested in S&P Fund-

VFINXVFINX Mean Value from the Mean Value from the

simulation was $5. 40simulation was $5. 40 The measure of Risk or The measure of Risk or

Standard deviation was Standard deviation was 9.759.75

Implication: The above $1.00 investment in The S&P 500 Fund yielded a Mean Power Coefficient of $5.4 with a standard deviation of 9.75.

3-Proposition-2-3-Proposition-2-Analytic Analytic Results:Results:

Diversified Portfolio vs Diversified Portfolio vs S&P 500S&P 500

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Power Coefficient PortfolioPower Coefficient Portfolio $1.00 Investment$1.00 Investment 21% Large Cap, 20% 21% Large Cap, 20%

Mid Cap, 19% Small Mid Cap, 19% Small Cap, 40% Fixed IncomeCap, 40% Fixed Income

The Mean Value from The The Mean Value from The Diversified Portfolio Diversified Portfolio simulation was $6.55simulation was $6.55

vs $5.4 for the S&P 500 vs $5.4 for the S&P 500 PortPort

69% probability the Div 69% probability the Div PortPort

> Than the S&P 500 > Than the S&P 500 Implication: The above Power Coefficient of the diversified portfolio with a dollar invested generated a higher Power Coefficient of $6.55 (21% higher) vs $5.4 for the S&P 500 with a 7% lower Std Deviation of 8.76% vs 9.75 for the S&P 500. The Diversified Port has a 69% prob of exceeding the S&P 500 Index portfolio



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The Mean Difference The Mean Difference between the Power between the Power Coefficient generated Coefficient generated portfolio and the S&P 500 is portfolio and the S&P 500 is $1.16(21% higher)$1.16(21% higher)

59.4% Probability the Mean 59.4% Probability the Mean Diff Power Coefficient Diff Power Coefficient generated portfolio will generated portfolio will exceed 0 .exceed 0 .

Implication: The Mean Difference (Diversified Portfolio vs. the S&P 500)Power Coefficient generated portfolio yields a higher mean difference return of $1.16 (21% higher )and lower Standard Deviation of 7.57 than the Fund mirroring the S&P of 9.75 . The simulations yields a 57% probability that the Mean Difference Power Coefficient generated portfolio will exceed 0.



CChapter 4- hapter 4- RecommendationsRecommendations

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This section outlines conclusions:

– Proposition 1- Best Styles(LC.MC,SC, FI)

–Additional Comments:

– Proposition 2- Optimum Diversified Portfolio:

– Recommended Model Portfolio:

– Other Recommendations with High Power Coef”s:

–Additional Remarks

Proposition -1Proposition -1-- What is the Best Investment Style (SC, MC,LC) What is the Best Investment Style (SC, MC,LC) Compared to the S&P 50Compared to the S&P 500 0

Based on the power Coefficient and Monte Carlo simulation Based on the power Coefficient and Monte Carlo simulation analysis analysis all the styles reflected a power coefficient higher all the styles reflected a power coefficient higher than the S&P.than the S&P.

The resulting simulation The resulting simulation breakout allocation of the power breakout allocation of the power Coefficients came out fairly even between the 3 styles.. Coefficients came out fairly even between the 3 styles.. 35% large Cap., 33% Mid Cap and ,32%% Small Cap.35% large Cap., 33% Mid Cap and ,32%% Small Cap.

Allocating your investment portfolio with the above allocation of Allocating your investment portfolio with the above allocation of the equity segment of the portfolio will give you The optimum the equity segment of the portfolio will give you The optimum efficient segmentation.efficient segmentation.

This allocation was used to develop the portfolio used in the 2 This allocation was used to develop the portfolio used in the 2 proposition.proposition.

ChapterChapter 4- 4- Recommendations:Recommendations:

Additional Remarks :Additional Remarks :Research completed in 2011 suggested that of the three styles Research completed in 2011 suggested that of the three styles LC,MC,SC …LC,MC,SC …that midcap investments over 50 years of data that midcap investments over 50 years of data provided the best value return per unit of risk. Including 2011 provided the best value return per unit of risk. Including 2011 thru 2013 into the historical timeline does NOT change the thru 2013 into the historical timeline does NOT change the long term results.long term results.However, Given the 5 years 2007 thru 2012 , following the financial However, Given the 5 years 2007 thru 2012 , following the financial crisis , it is of interest to verify the validity of this hypothesis given crisis , it is of interest to verify the validity of this hypothesis given significant changes in exogenous variables such as extremely low significant changes in exogenous variables such as extremely low interest rates and simulative Fed Policy that have a significant effect interest rates and simulative Fed Policy that have a significant effect on savings and investment.on savings and investment.The results indicate that, The results indicate that, during this period of very low interest during this period of very low interest rates, Large Caps had a marginally better return value per rates, Large Caps had a marginally better return value per unit of risk over Mid Caps and Small Caps as evidenced by the unit of risk over Mid Caps and Small Caps as evidenced by the higher power coefficients.higher power coefficients.

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ChapterChapter 4- 4- RecommendationsRecommendations::

Small caps and Midcaps were approx. equivalent in value per unit Small caps and Midcaps were approx. equivalent in value per unit of risk given the relative parity of the Power Coefficientsof risk given the relative parity of the Power Coefficients..

So what changed to mitigate the previous results. Primarily it has to do So what changed to mitigate the previous results. Primarily it has to do with the Federal Reserves manipulation of the yield curve to with the Federal Reserves manipulation of the yield curve to uncharacteristically low rates . The result has caused a predictable uncharacteristically low rates . The result has caused a predictable misallocation of investor resources to Large Cap stocks. The reason is with misallocation of investor resources to Large Cap stocks. The reason is with the short end of the yield curve at uncharacteristically low levels(10 year the short end of the yield curve at uncharacteristically low levels(10 year bond rate at 2.5-2.65 percent) investors who need a monthly return to bond rate at 2.5-2.65 percent) investors who need a monthly return to maintain there standard of living moved to proxy bond investments with maintain there standard of living moved to proxy bond investments with dividend paying large Cap Value stocks. So with a dividend rate of 3-4% dividend paying large Cap Value stocks. So with a dividend rate of 3-4% and a growth factor of 1-2% , investors sold their bonds for proxy Large and a growth factor of 1-2% , investors sold their bonds for proxy Large Cap Value stocks and forced a large volume move in in this vehicle. The Cap Value stocks and forced a large volume move in in this vehicle. The primary driver to this mass movement to proxy bonds thru the purchase of primary driver to this mass movement to proxy bonds thru the purchase of Large Cap dividend paying value investments was further exacerbated by Large Cap dividend paying value investments was further exacerbated by the simultaneous Federal reserve policy to implement the massive buying the simultaneous Federal reserve policy to implement the massive buying of mortgage back securities (QE1,2,3) . of mortgage back securities (QE1,2,3) .

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To the tune of 85 billion a month..This forced Bond prices up and yields down at the To the tune of 85 billion a month..This forced Bond prices up and yields down at the shorter end of the yield curve driving even more investors to stocks.shorter end of the yield curve driving even more investors to stocks.This was the main contributing factor to the temporary 5 year (2007-2012)slight This was the main contributing factor to the temporary 5 year (2007-2012)slight advantage of large Caps over Midcaps. Once the yield curve assumes a more advantage of large Caps over Midcaps. Once the yield curve assumes a more normal trajectory (10 year at 4.- 5%) , income based risk averse investors will normal trajectory (10 year at 4.- 5%) , income based risk averse investors will return the balance of there portfolio’s to fixed income investments . return the balance of there portfolio’s to fixed income investments . The key will be when(timing) the bond vigilantes decide that there is not enough The key will be when(timing) the bond vigilantes decide that there is not enough risk built into the yield curve, and the markets or the federal reserve begins to risk built into the yield curve, and the markets or the federal reserve begins to increase the discount rate . At that time the result should yield a transference of increase the discount rate . At that time the result should yield a transference of Large Caps back to bonds and the historical relationship will favor investing in Large Caps back to bonds and the historical relationship will favor investing in midcaps.midcaps.When this will happen remains to be seen given the high unemployment and very When this will happen remains to be seen given the high unemployment and very low growth in GDP between 1.5 -1.9% %low growth in GDP between 1.5 -1.9% % NOTE: The % allocation is marginally higher for Large Caps than Mid Caps and NOTE: The % allocation is marginally higher for Large Caps than Mid Caps and

Small caps based on research done previously and documented in Section-2Small caps based on research done previously and documented in Section-2

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ChapterChapter 4- 4-

RecommendationsRecommendations::


Propositin -2Propositin -2 Is there a diversified Portfolio that will Is there a diversified Portfolio that will

beat the S&P 500beat the S&P 500.. Yes…Using the allocation from the results of proposition Yes…Using the allocation from the results of proposition

1 , the following portfolio is defined as the optimum 1 , the following portfolio is defined as the optimum allocation (see page 19 and 20) allocation (see page 19 and 20) 1.1. Large Caps- Large Caps- 21%21%

1.1. The best of the Large caps =Sequoia- SEQUX= The best of the Large caps =Sequoia- SEQUX= $.21$.212.2. Mid Caps- Mid Caps- 20%20%

1.1. The best of the midcaps =Principal Midcap- PEMGX=$.27The best of the midcaps =Principal Midcap- PEMGX=$.273.3. Small Caps- Small Caps- 19%19%

1.1. The best of the small caps= Vulcan Value Partner -SCETX-The best of the small caps= Vulcan Value Partner -SCETX-

4-4-Fixed Income- Bonds- Fixed Income- Bonds- 40%40%– Metropolitan West Total Return – MWTRX-$.40

Total of Large Caps +Midcaps +Small Caps + Fixed Total of Large Caps +Midcaps +Small Caps + Fixed Income Income =$1.00=$1.00

55- S&P 500 baseline - S&P 500 baseline - Vanguard Index Fund-VFINX-$1.00- Vanguard Index Fund-VFINX-$1.00

– This fund replicates the S&P 500This fund replicates the S&P 500 - Total= $1.00- Total= $1.00

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The above Power Coefficient of the diversified portfolio with a The above Power Coefficient of the diversified portfolio with a dollar invested generated a higher Power Coefficient of $6.55 dollar invested generated a higher Power Coefficient of $6.55 (21% higher) vs $5.4 for the S&P 500 (21% higher) vs $5.4 for the S&P 500

Additionally there was a 7% lower Std Deviation of 8.76% Additionally there was a 7% lower Std Deviation of 8.76% vs 9.75 for the S&P 500. vs 9.75 for the S&P 500.

Bottom line is:Bottom line is:– The Diversified Port has a 69% probability of The Diversified Port has a 69% probability of

exceeding the S&P 500 Index portfolioexceeding the S&P 500 Index portfolio– With 7% lower risk.With 7% lower risk.– The ALPHA’s for the recommended portfolio have The ALPHA’s for the recommended portfolio have

high multiples( 2.7 to 7.2) compared to the S&P 500high multiples( 2.7 to 7.2) compared to the S&P 500

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1- Recommended Model Portfolio:•Large Caps:

Sequoia-SEQUXPresent % allocation- 21%Future Allocation: 21%

•Mid Caps:Principal Midcap- PEMGX% allocation- 20%Future Allocation; As Fed tightens…increase allocation to 27%

•Small Caps:Vucan Value Partners-VVPSX% allocation- 19%Future Allocation; - as Fed tightens…decrease allocation to 12%

Fixed IncomeFixed Income– Metropolitan West Total Return-MWTWXMetropolitan West Total Return-MWTWX– % Allocation- 40%...Bond durations should be < = 5 Years% Allocation- 40%...Bond durations should be < = 5 Years– Monitor…for every 100 basis point increase in 10 year results Monitor…for every 100 basis point increase in 10 year results in 5% decrease in yield(value)in 5% decrease in yield(value)

2-Other Recommendations with high Power Coef:2-Other Recommendations with high Power Coef: Large CapsLarge Caps

– Yackman- YAFFXYackman- YAFFX– Wasatch-WGROXWasatch-WGROX

Midcaps:Midcaps:– Artisian Midcap- ARTQXArtisian Midcap- ARTQX

Small Caps:Small Caps:– Brown Capital Mgt-BCSIXBrown Capital Mgt-BCSIX

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Fixed IncomeFixed Income– Aberdeen Global High-BJBHXAberdeen Global High-BJBHX– Fidelity Strategic Income-FSICXFidelity Strategic Income-FSICX

Sector – Sector – Analysis- High to LowAnalysis- High to Low- - The only Sector ETF that warrants consideration based on The only Sector ETF that warrants consideration based on

Power Coef‘s is Industrials-PRN .Power Coef‘s is Industrials-PRN .– Industrials-PRN- Highest Power CoefficientIndustrials-PRN- Highest Power Coefficient– Finance-PFIFinance-PFI– Technology-PTFTechnology-PTF– Energy- PXIEnergy- PXI– Basic materials- PYZBasic materials- PYZ– Consumer Staples-PSLConsumer Staples-PSL

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Additional Remarks::Additional Remarks::– Note: TNote: There are no international investment recommendations.here are no international investment recommendations.– The reason is……….. international investments reflect lower power The reason is……….. international investments reflect lower power

coefficients relative to domestic opportunities. This is primarily coefficients relative to domestic opportunities. This is primarily because growth in Europe(less than 1%) and the BRICS is lower because growth in Europe(less than 1%) and the BRICS is lower (tending toward deflation) than the States exacerbated by tight (tending toward deflation) than the States exacerbated by tight monetary policy. The ECB in particular needs to loosen significantly monetary policy. The ECB in particular needs to loosen significantly by lowering rates to provide much needed monetary stimulus .by lowering rates to provide much needed monetary stimulus .

– The results of this excessively tight monetary policy leads to The results of this excessively tight monetary policy leads to foreign investments re-allocated to higher growth opportunities in foreign investments re-allocated to higher growth opportunities in the states which adds to higher asset pricing and more growth in the states which adds to higher asset pricing and more growth in earnings and markets.earnings and markets.

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This is another reason for short to middle term optimism about Stocks. This is another reason for short to middle term optimism about Stocks. Until the economic climate changes , overseas investors see more Until the economic climate changes , overseas investors see more opportunity here. opportunity here.

Note further when the fed decides to tighten…or even implications Note further when the fed decides to tighten…or even implications thru interpretation of release transcripts of fed meeting minutes, the thru interpretation of release transcripts of fed meeting minutes, the market is likely to drop , in the short run 5-15%. The driver to market is likely to drop , in the short run 5-15%. The driver to tightening would be an unemployment rate of 6-6.5%. The best guess tightening would be an unemployment rate of 6-6.5%. The best guess to Fed Tightening either thru tapering of MBS purchases or increasing to Fed Tightening either thru tapering of MBS purchases or increasing interest rates is sometime late 2015 to 2016.interest rates is sometime late 2015 to 2016.

Finally….when choosing an investment or group of investments, it is Finally….when choosing an investment or group of investments, it is important to select that which invests in growth sectors. One of the important to select that which invests in growth sectors. One of the reasons this portfolio has positive results(per high Alpha’s discussed reasons this portfolio has positive results(per high Alpha’s discussed earlier) earlier) is the correct sector diversification in Financials, is the correct sector diversification in Financials, Cyclicals, Industrials and energy. Cyclicals, Industrials and energy.

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Optimum Investment Selection process-Nov 9-2013