A Two stage Investment A Two stage Investment Analysis to maximize the Analysis to maximize the selection of an Optimum selection of an Optimum

Investment PortfolioInvestment Portfolio

How to maximize the asset allocation How to maximize the asset allocation selection of investments within each style. selection of investments within each style. (Large Cap, Mid cap , Small Cap, (Large Cap, Mid cap , Small Cap, International ) to optimize the total return International ) to optimize the total return profile of the Overall Portfolio. profile of the Overall Portfolio.

- - PrefacePreface

- Purpose- Purpose

- Analytic Methodology- Analytic Methodology

- Power Coefficient Results- Power Coefficient Results

- Monte Carlo Simulations- Monte Carlo Simulations

- Recommendations- RecommendationsPrepared by

Gary Crosbie

Feb 2011Feb 2011

Preface:Preface:

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

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

Preface:Preface:

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 coeff

– the % allocated to each investment should be based on the % breakout of the power coeff.

Analytic Methodology: Analytic Methodology: 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 Choose top 3-5 investments in each style..Large

Cap, Mid Cap, Small Cap, International ..Value, Cap, Mid Cap, Small Cap, International ..Value, Blend and GrowthBlend and Growth

Step Two:Step Two:– Use the Power Coefficient to rank investments Use the Power Coefficient to rank investments

based on personal investor preferencesbased on personal investor preferences

Analytic Methodology: Analytic Methodology: Step 2 Step 2

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)

Analytic Methodology: Analytic Methodology: Step 2 Step 2

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

((ЄЄ + + ββ++ σ σ))

Analytic Methodology:Analytic Methodology: Step 2 Step 2

– 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 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 ΒΒ= Beta for the investment indicating correlation over time = Beta for the investment indicating correlation over time

with the general marketwith the general market σ σ = Standard Deviation= Standard Deviation α= Measure of performance relative to index of equivalent

investments.

Analytic Methodology: Analytic Methodology: Step 2 Step 2

Power Coefficients generated for each fund and Power Coefficients generated for each fund and ranked in ascending order:ranked in ascending order:– Large Cap Picks:Large Cap Picks:– Mid Cap Picks:Mid Cap Picks:– Small Cap picks:Small Cap picks:– International Picks:International Picks:

Given the Power Coefficients for each style:Given the Power Coefficients for each style:– Take the Investment with the largest Power Coefficient(PC) Take the Investment with the largest Power Coefficient(PC)

for each style.for each style.– Allocate to an investment portfolioAllocate to an investment portfolio– Use the mehodology defined in the next section to compare Use the mehodology defined in the next section to compare

the value of the selection process with a baseline the value of the selection process with a baseline

Portfolio defined by the S&P 500….Vanguard Index-VFINXPortfolio defined by the S&P 500….Vanguard Index-VFINX

Analytic Methodology: Analytic Methodology: Comparative AnalyticsComparative Analytics

– Define a portfolioDefine a portfolio Use the highest power coefficients in each style:Use the highest power coefficients in each style: Large CapsLarge Caps Mid CapsMid Caps Small CapsSmall Caps International International

Re-Calculate a power coefficient based on a $1.00 investment using Re-Calculate a power coefficient based on a $1.00 investment using following Asset Allocation:following Asset Allocation:– Large Caps- 30%Large Caps- 30%– Mid Caps- 40%Mid Caps- 40%– Small Caps- 20%Small Caps- 20%– International -10%International -10%

Compare to an equivalent $1.00 investment in a Fund that duplicates the Compare to an equivalent $1.00 investment in a Fund that duplicates the S&P 500- Vanguard Index- VFINXS&P 500- Vanguard Index- VFINX– Calculate a power coefficientCalculate a power coefficient

Analytic Methodology: Analytic Methodology:

Power Coefficient Analytic Power Coefficient Analytic Comparatives: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 Allocated Power Coefficient Style Allocated Portfolio(Large cap, Mid Cap etc)Portfolio(Large cap, Mid Cap etc)

vs. the Portfolio that mirrors the S&P vs. the Portfolio that mirrors the S&P 500500

Results: Power Coefficient Picks:Power Coefficient Picks:

– Large Cap:Large Cap: Brown Advisory Growth Equity-BIAGXBrown Advisory Growth Equity-BIAGX Monetta Young Investor- MYIFXMonetta Young Investor- MYIFX

– Mid Cap:Mid Cap: First hand Commerce-TEFQXFirst hand Commerce-TEFQX Meredian Growth- MERDXMeredian Growth- MERDX

– Small Cap:Small Cap: Brown Small Cap Mgt- BCSIXBrown Small Cap Mgt- BCSIX Ridgefield Small Cap-SCETXRidgefield Small Cap-SCETX

– InternationalInternational Matthews Asia Growth- MACSX I Shares Latin America-ILF Currency Shares –Australia-FXA

Results:Results:

Analytical ComparativesAnalytical Comparatives

– Generate a Power Coefficient for the Generate a Power Coefficient for the S&P 500S&P 500

– Compare the Power Coefficients for Compare the Power Coefficients for the highest style (Large Cap, Mid Cap the highest style (Large Cap, Mid Cap etc) investments with that of the etc) investments with that of the S&P 500.S&P 500.

Monte Carlo Monte Carlo Simulations:Simulations: Methodology Methodology

Utilize Monte Carlo Simulation to compare the Utilize Monte Carlo Simulation to compare the power Coefficients for the best investment power Coefficients for the best investment choices by style with the S&P 500.choices by style with the S&P 500.

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

Allocation Comparisons:Allocation Comparisons:– 30 % in Large Cap with Highest Power Coef30 % in Large Cap with Highest Power Coef– 40 % in Mid Caps with Highest Power Coef40 % in Mid Caps with Highest Power Coef– 20% in Small Cap with Highest Power Coef20% in Small Cap with Highest Power Coef– 10% in International with Highest Power Coef10% in International with Highest Power Coef

Monte Carlo Monte Carlo Simulations:Simulations: Methodology Methodology Given a $1.00 investment generate a portfolio Given a $1.00 investment generate a portfolio

allocated according to the power coefficients:allocated according to the power coefficients:

1.1. Large Caps- 30%Large Caps- 30% Brown Advisory Growth-BIAGX- $.1Brown Advisory Growth-BIAGX- $.1 Monetta Young Investor-MYIFX-$.2Monetta Young Investor-MYIFX-$.2

2.2. Mid Caps- 40%Mid Caps- 40% First Hand Commerce- TEFQX-$.2First Hand Commerce- TEFQX-$.2 Meredian Growth-MERDX- $.2Meredian Growth-MERDX- $.2

3.3. Small Caps- 20%Small Caps- 20% Brown Small Cap Mgt-BCSIX- $.1Brown Small Cap Mgt-BCSIX- $.1 Ridgefield Small Cap-SCETX- $.1Ridgefield Small Cap-SCETX- $.1

Monte Carlo Monte Carlo Simulations:Simulations: Methodology Methodology 4- 4- International- 10%International- 10%

Currency Shares-Australia-FXA-$.05Currency Shares-Australia-FXA-$.05 Matthews Asia Growth-MACSX-$ .05Matthews Asia Growth-MACSX-$ .05

Total $1.00Total $1.00

S&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 $1.00

NOTE: NOTE: The 1 dollar investment amount was usedThe 1 dollar investment amount was used

To simplify the comparatives.To simplify the comparatives.

Monte Carlo Monte Carlo Simulations:Simulations: Methodology Methodology The two $1.00 portfolios are The two $1.00 portfolios are

compared after a 1000 iteration compared after a 1000 iteration Monte Carlo Simulation.Monte Carlo Simulation.

– The $1.00 S&P Index fundThe $1.00 S&P Index fund

VsVs

– The $1.00 Power Coefficient portfolioThe $1.00 Power Coefficient portfolio Investments selected based on highest Investments selected based on highest

calculated power Coefficientscalculated power Coefficients

Analytic Results:Analytic Results:Baseline –S&P PortfolioBaseline –S&P Portfolio

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

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

Fund- VFINXFund- VFINX Mean Value from the Mean Value from the

simulation was $1.42simulation was $1.42 Standard deviation Standard deviation

was was

4.224.22

Implication: The above $1.00 investment in The S&P 500 Fund yielded a Power Coefficient of $1.42 with a standard deviation of 4.22.

Analytic Results:Analytic Results:Power Coefficient Power Coefficient PortfolioPortfolio Power Coefficient Power Coefficient

PortfolioPortfolio $1.00 Investment$1.00 Investment 30% Large Cap, 40% 30% Large Cap, 40%

Mid Cap, 20% Small Mid Cap, 20% Small Cap, 10% InternationalCap, 10% International

Mean Value from the Mean Value from the simulation was $2.51simulation was $2.51

vs $1.42 for the S&P vs $1.42 for the S&P 500500

Index portfolio Index portfolio Implication: The above Power Coefficient of the diversified portfolio with a dollar invested generated a higher Power Coefficient result of $2.51 with a lower Std Deviation of 3.55 .

The mean difference The mean difference between the Power between the Power Coefficient generated Coefficient generated portfolio and the S&P portfolio and the S&P 500 is $1.14500 is $1.14

86% Probability the 86% Probability the Power Coefficient Power Coefficient generated portfolio will generated portfolio will exceed the S&P 500 exceed the S&P 500 Portfolio.Portfolio.

Implication: The Power Coefficient generated portfolio yields a higher mean return and lower Standard Deviation than the Fund mirroring the S&P. The simulations yield an 86% probability that the Power Coefficient generated portfolio will exceed the S&P 500 portfolio

Analytic Results:Analytic Results:Simulation Simulation ComparativesComparatives

Recommendations:Recommendations: • Picks and Allocations: From

current and previous power coefficient analysis

1. Large Caps- 25%*• Brown Advisory Growth-BIAGX- • Monetta Young Investor-MYIFX-• Fairhome- FAIRX• Yacktman- YAFFX

2. Midcaps- 35%• First Hand Commerce- TEFQX-• Meredian Growth-MERDX- • Rydex S&P Midcap 400 Growth-RFG

3. Small Caps- 20%• Brown Small Cap Mgt-BCSIX- • Ridgefield Small Cap-SCETX-

Recommendations:Recommendations:• Picks: From current and previous power coefficient

analysis (Con)

4. International- 10%• Currency Shares-Australia-FXA-• Matthews Asia Growth-MACSX-• I Shares S&P Latin America 40 Index-ILF• Columbia Acorn International- ACINX

5. Commodities:10%• Gold- GLD• Silver- SLV• Paladium-Pall• Powershare Dynamic Energy Sector-PXI

*The percentage allocations represent the equityPortion of a portfolio

•