1. A Two stage Investment Analysis to
maximize the selection of an Optimum
Investment Portfolio
How to maximize the asset allocation selection
of investments within each style. (Large Cap,
Mid cap , Small Cap, International ) to optimize
the total return profile of the Overall Portfolio.
- Preface
- Purpose
- Analytic Methodology
- Power Coefficient Results
- Monte Carlo Simulations
- Recommendations
Prepared by
Gary Crosbie
Feb 2011

2. Preface:
 The purpose of this analysis is to develop an algorithum
that will enumerate the best investments within each
style category to maximize performance.
 The model developed calculates a Power Coefficent
which represents the culmination of weighted
customer preferences and investment based statistics to
rank investment alternatives .
 Those with the highest Coefficients represent the
Optimum investment alternatives given those
weighted preferences.

3. 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.

4. Analytic Methodology:
 Two Stage Process:
 Step One:
– Initially filter with Morningstar Fund/ETF
screening process.
– Choose top 3-5 investments in each style..Large
Cap, Mid Cap, Small Cap, International ..Value,
Blend and Growth
 Step Two:
– Use the Power Coefficient to rank investments
based on personal investor preferences

5. Analytic Methodology:
Step 2
 Definition: The Power Coefficient:
– A derivative of 10 variables
– Define the short and long run viability of a
particular Fund or ETF.
– The variables are weighted based on individual
investor preferences to encapsulate :
 Tolerance for risk
 Investment time horizons
 Volatility
 Rates of Return at different time horizons(1,3,5 yr)

6. Analytic Methodology:
Step 2
Model Algorithm:
– Generated from the following equation:
– Equation: Power coefficient generated by the
following:
Power Coef = a(1Gr)+b(3 Gr)+c(5 GR) x α
(Є + β+ σ)

7. Analytic Methodology:
Step 2
– Where:
 a= Percentage weight for 1 year growth rate
 B= Percentage weight for 3 year growth rate
 c= Percentage weight for 5 year growth rate
 1GR= 1 year growth rate
 3GR= 3 year growth rate
 5GR= 5 year growth rate
 Є= Expense ratio
 Β= Beta for the investment indicating correlation
over time with the general market
 σ = Standard Deviation
 α= Measure of performance relative to index of
equivalent investments.

8. Analytic Methodology:
Step 2
 Power Coefficients generated for each fund and
ranked in ascending order:
– Large Cap Picks:
– Mid Cap Picks:
– Small Cap picks:
– International Picks:
 Given the Power Coefficients for each style:
– Take the Investment with the largest Power
Coefficient(PC) for each style.
– Allocate to an investment portfolio
– Use the mehodology defined in the next section to
compare the value of the selection process with a baseline
Portfolio defined by the S&P 500….Vanguard Index-VFINX

9. Analytic Methodology:
 Comparative Analytics
– Define a portfolio
 Use the highest power coefficients in each style:
 Large Caps
 Mid Caps
 Small Caps
 International
 Re-Calculate a power coefficient based on a $1.00 investment
using following Asset Allocation:
– Large Caps- 30%
– Mid Caps- 40%
– Small Caps- 20%
– International -10%
 Compare to an equivalent $1.00 investment in a Fund that duplicates
the S&P 500- Vanguard Index- VFINX
– Calculate a power coefficient

10. Analytic Methodology:
 Power Coefficient Analytic
Comparatives:
– Run Monte Carlo simulations
– Use 1000 iterations
– Compare the results of the :
Power Coefficient Style Allocated
Portfolio(Large cap, Mid Cap etc)
 vs. the Portfolio that mirrors the S&P 500

11. Results:
 Power Coefficient Picks:
– Large Cap:
 Brown Advisory Growth Equity-BIAGX
 Monetta Young Investor- MYIFX
– Mid Cap:
 First hand Commerce-TEFQX
 Meredian Growth- MERDX
– Small Cap:
 Brown Small Cap Mgt- BCSIX
 Ridgefield Small Cap-SCETX
– International
 Matthews Asia Growth- MACSX
 I Shares Latin America-ILF
 Currency Shares –Australia-FXA

12. Results:
 Analytical Comparatives
– Generate a Power Coefficient for the
S&P 500
– Compare the Power Coefficients for the
highest style (Large Cap, Mid Cap etc)
investments with that of the S&P 500.

13. Monte Carlo Simulations:
Methodology
 Utilize Monte Carlo Simulation to compare the
power Coefficients for the best investment
choices by style with the S&P 500.
 1000 interactions were used in the simulation:
 Allocation Comparisons:
– 30 % in Large Cap with Highest Power Coef
– 40 % in Mid Caps with Highest Power Coef
– 20% in Small Cap with Highest Power Coef
– 10% in International with Highest Power Coef

14. Monte Carlo Simulations:
Methodology
 Given a $1.00 investment generate a portfolio
allocated according to the power coefficients:
1. Large Caps- 30%
 Brown Advisory Growth-BIAGX- $.1
 Monetta Young Investor-MYIFX-$.2
2. Mid Caps- 40%
 First Hand Commerce- TEFQX-$.2
 Meredian Growth-MERDX- $.2
3. Small Caps- 20%
 Brown Small Cap Mgt-BCSIX- $.1
 Ridgefield Small Cap-SCETX- $.1

15. Monte Carlo Simulations:
Methodology
4- International- 10%
 Currency Shares-Australia-FXA-$.05
 Matthews Asia Growth-MACSX-$ .05
Total $1.00
S&P500 baseline
– Vanguard Index Fund-VFINX-$1.00
– This fund replicates the S&P 500
Total $1.00
NOTE: The 1 dollar investment amount was used
To simplify the comparatives.

16. Monte Carlo Simulations:
Methodology
 The two $1.00 portfolios are compared
after a 1000 iteration Monte Carlo
Simulation.
– The $1.00 S&P Index fund
Vs
– The $1.00 Power Coefficient portfolio
 Investments selected based on highest
calculated power Coefficients

17. Analytic Results:
Baseline –S&P Portfolio
 Baseline S&P Portfolio-
VFINX
 $1.00 Investment
 100% Invested in S&P
Fund- VFINX
 Mean Value from the
simulation was $1.42
 Standard deviation was
4.22
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.

18. Analytic Results:
Power Coefficient Portfolio
 Power Coefficient
Portfolio
 $1.00 Investment
 30% Large Cap, 40% Mid
Cap, 20% Small Cap,
10% International
 Mean Value from the
simulation was $2.51
vs $1.42 for the S&P 500
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 .

19. Analytic Results:
Simulation Comparatives
 The mean difference
between the Power
Coefficient generated
portfolio and the S&P 500
is $1.14
 86% Probability the
Power Coefficient
generated portfolio will
exceed the S&P 500
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

20. Recommendations:
icks 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-

21. 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 equity
Portion of a portfolio