A Risk Adjusted Analysis A Risk Adjusted Analysis of the Marginal of the Marginal

Efficiency of Investment Efficiency of Investment (MEI)(MEI)

What investment style provides the best What investment style provides the best Risk adjusted Rate of return in Bull and Risk adjusted Rate of return in Bull and Bear Markets.Bear Markets.

- Preface- Preface

- Hypothesis- Hypothesis

- Purpose- Purpose

- Methodology- Methodology

- Updated Results- Updated Results Investment OptimizationInvestment Optimization Recessions/Bear MarketsRecessions/Bear Markets Monte Carlo SimulationMonte Carlo Simulation

- Updated Conclusions- Updated Conclusions

Gary Crosbie

An Update – Feb 2011An Update – Feb 2011

Preface:Preface:

There is no shortage of analysis and commentary on the There is no shortage of analysis and commentary on the timing and benefits of investment allocation and timing and benefits of investment allocation and weighting on Small Caps, Mega Caps, Large Caps, weighting on Small Caps, Mega Caps, Large Caps, Technology , international and fixed income alternatives Technology , international and fixed income alternatives

However, in comparison, much less attention has been However, in comparison, much less attention has been given to Mid Cap styles. That is those companies with given to Mid Cap styles. That is those companies with capitalizations between 5 and 10 billion dollars. capitalizations between 5 and 10 billion dollars.

While there has been some attention given to the relative While there has been some attention given to the relative ROR, hardly any attention is given to the efficiency of the ROR, hardly any attention is given to the efficiency of the investment…That is ..what is the intrinsic value of the investment…That is ..what is the intrinsic value of the investment …investment …– The return per unit of risk and how that Marginal Efficiency The return per unit of risk and how that Marginal Efficiency

of Investment (MEI) compares to alternative forms of of Investment (MEI) compares to alternative forms of investment.investment.

Preface:Preface:

Finally…given the risk profile of alternative investments what is the rate of return that achieves that risk assessment.

The risk profile was 90%. Thus Monte Carlo simulations of 1000 iterations were conducted to determine a rate of return that would yield a 90 % probability.

Hypothesis:Hypothesis:

In my work in Wealth management, it has been my hypothesis In my work in Wealth management, it has been my hypothesis that Mid Cap investments offer more than a higher ROR on NAV that Mid Cap investments offer more than a higher ROR on NAV but additionally have a higher net return per unit of risk than but additionally have a higher net return per unit of risk than other investment alternatives,other investment alternatives,

Therefore given the appropriate individual risk reward profile, Mid Therefore given the appropriate individual risk reward profile, Mid caps warrant review for higher weighted allocations in the caps warrant review for higher weighted allocations in the investors overall portfolio mix investors overall portfolio mix

Further, there was additional interest in whether that hypothesis Further, there was additional interest in whether that hypothesis would “prevail” or “fail” equally in Bull or Bear markets.would “prevail” or “fail” equally in Bull or Bear markets.

This paper is an update to the initial investigation conducted in This paper is an update to the initial investigation conducted in 2008….. in essense verifying that hypothesis.2008….. in essense verifying that hypothesis.

The Update is to further validate previous conclusions particuarily The Update is to further validate previous conclusions particuarily in light of the extensive length of the past recession (technically in light of the extensive length of the past recession (technically ending 7/2009) and the persistence of stagnant growth and ending 7/2009) and the persistence of stagnant growth and unemployment though the end of 2010.unemployment though the end of 2010.

Thus…in summary this analysis will evaluate:Thus…in summary this analysis will evaluate:

Purpose:

What is the Optimum Risk Adjusted Investment What is the Optimum Risk Adjusted Investment Alternative in Growth and Recession Markets;Alternative in Growth and Recession Markets;– Analysis was initiated at the end of 2008 to Analysis was initiated at the end of 2008 to

evaluate the best style of investment (Mega, evaluate the best style of investment (Mega, Large Cap, Mid Cap , Small Cap, Technology Large Cap, Mid Cap , Small Cap, Technology per unit of Risk as measured by the calculated per unit of Risk as measured by the calculated Standard Deviation.Standard Deviation.

– Given the population is representative, Given the population is representative, Simulations of Rates of return were replicated Simulations of Rates of return were replicated generating the probability of meeting and/or generating the probability of meeting and/or exceeding those RORs. exceeding those RORs.

The following is an update to that analysis to The following is an update to that analysis to include two more years of data thru 2010include two more years of data thru 2010

Methodolgy:Methodolgy:

Two phases of the analysis were Two phases of the analysis were conducted:conducted:1.1. Phase-1Phase-1- All inclusive historical time series of data for - All inclusive historical time series of data for

all styles.all styles.- Initially studied thru 2008 and now updated thru 2010- Initially studied thru 2008 and now updated thru 2010

1.1. Phase-2-Phase-2- Recession Analysis: Recession Analysis:– Analysis and conclusions were initiated to evaluate if the Analysis and conclusions were initiated to evaluate if the

conclusions reached in 1 - above changed significantly conclusions reached in 1 - above changed significantly when recessions were evaluated .when recessions were evaluated .

– Initially studied thru 2008 and now updated thru 2010Initially studied thru 2008 and now updated thru 2010

Because of data availability only 3 recessions Because of data availability only 3 recessions were evaluated:were evaluated:

1.1. 199019902.2. 200120013.3. 20072007

Methodolgy:Methodolgy:

Styles Analyzed for both Analysis:Styles Analyzed for both Analysis:

– Mega-CapMega-Cap– Large CapLarge Cap– Mid CapMid Cap– Small CapSmall Cap– NASDQNASDQ– InternationalInternational– Fixed IncomeFixed Income

Methodolgy: Methodolgy: Investment Data BaseInvestment Data Base

Analysis based on historical analysis Analysis based on historical analysis retrieved from Yahoo Data baseretrieved from Yahoo Data base

Styles Analyzed for both Analysis:Styles Analyzed for both Analysis:

– Mega Cap-Mega Cap- DOW DOW– Large Cap Index-Large Cap Index- S&P 50 S&P 50– Mid Cap Index-Mid Cap Index- S&P Mid Cap 400 S&P Mid Cap 400– Small Cap Index-Small Cap Index- Russell 2000 Russell 2000– Large Cap-Large Cap- Technology Technology– International- International- BRICBRIC– Fixed Investments- Fixed Investments- BondsBonds

Methodolgy: Methodolgy: Investment Data BaseInvestment Data Base

Years Analyzed:Years Analyzed:

– Dow-Dow- From 1929 From 1929– S&P-S&P- From 1950 From 1950– Mid Cap-Mid Cap- 1990 1990– Russell 2000-Russell 2000- 1988 1988– NASDQ-NASDQ-19701970– Bonds-Bonds- 19991999– International-International- 1999 1999

Methodolgy: Methodolgy: Bear Markets:Bear Markets:

Recessions Analyzed:Recessions Analyzed:

– 19901990– 20012001– 20072007

In the initial analysis the time series ended year In the initial analysis the time series ended year end 2008.end 2008.

This Up-dated analysis extends the time series This Up-dated analysis extends the time series to cover the documented end of the 2007 to cover the documented end of the 2007 recession (7-2009) and additional data through recession (7-2009) and additional data through 12-201012-2010

Methodolgy: Methodolgy: Analytics:Analytics:

Marginal of Efficiency of Investment Marginal of Efficiency of Investment EquationEquation

MEI MEI == Avg NAV RORAvg NAV ROR Stnd DevStnd Dev

Where:Where:- - Avg NAV RORAvg NAV ROR= Average Net Asset Value = Average Net Asset Value

Rate of ReturnRate of Return

- Stnd Dev= Standard Deviation of the Monthly - Stnd Dev= Standard Deviation of the Monthly Net Asset Value’s over the Planning horizonNet Asset Value’s over the Planning horizon

Updated Results:Updated Results:

Best Overall Investment Alternative is :Best Overall Investment Alternative is : – Growth Markets:Growth Markets: Mid Caps & International Mid Caps & International– Recessions:Recessions: Across all three recessions- Mid Across all three recessions- Mid

Caps and Mega CapsCaps and Mega Caps– Update Differences: Update Differences: Decision Rules & Decision Rules & Results did Results did

not change between the analysis .not change between the analysis .

But relative magnitude increase in the MEI for Mid But relative magnitude increase in the MEI for Mid caps increased significantly in both analysis.caps increased significantly in both analysis.

From 1.69 to 2.42 in the Total Growth Market From 1.69 to 2.42 in the Total Growth Market scenarioscenario

From -.08 to .68 in the Recession AnalysisFrom -.08 to .68 in the Recession Analysis

Updated ResultsUpdated Results::

Part-1-Part-1- Through out the Total Times Series analysis Through out the Total Times Series analysis the Best Return per unit of Risk(MEI) were Mid Caps the Best Return per unit of Risk(MEI) were Mid Caps and International .and International .

Reserved Opinion on International:Reserved Opinion on International:- International was based on a significantly - International was based on a significantly smaller sample size of 10 years of data… smaller sample size of 10 years of data…- This warrants caution because while current & - This warrants caution because while current & potential growth is significant , in BRIC countries in potential growth is significant , in BRIC countries in particular , that growth is highly dependant on particular , that growth is highly dependant on reasonable commodity access and pricing, political reasonable commodity access and pricing, political and monetary stability and in particular a floating and monetary stability and in particular a floating stable currency . Note…the International returns in stable currency . Note…the International returns in the update diminished somewhat as a result of this the update diminished somewhat as a result of this reality.reality.- -

Part-1-Marginal Part-1-Marginal Efficiency of Investment- Efficiency of Investment-

Dec 2008 AnalysisDec 2008 AnalysisIndexIndex Growth RateGrowth Rate Std DevStd Dev MEIMEI

DOWDOW 6.88%6.88% 5.3%5.3% 1.29 1.29

S&P 500S&P 500 8.85%8.85% 6.2%6.2% 1.42 1.42

Midcap 400Midcap 400 9.44%9.44% 5.6%5.6% 1.69 1.69

Russ 2000Russ 2000 8.29%8.29% 8.0%8.0% 1.04 1.04

NasdqNasdq 10.21%10.21% 9.6%9.6% 1.07 1.07

Bonds/otherBonds/other 3.80%3.80% 4.0%4.0% 0.96 0.96

InternationaInternationall 20.00%20.00% 8.3%8.3% 2.40 2.40

Part-1- UPDATED: Marginal Part-1- UPDATED: Marginal Efficiency of Investment- Efficiency of Investment-

Jan 2010 AnalysisJan 2010 Analysis

IndexIndex Growth RateGrowth Rate Std DevStd Dev MEIMEI

DOWDOW 7.15%7.15% 5.3%5.3% 1.341.34

S&P 500S&P 500 9.28%9.28% 6.1%6.1% 1.53 1.53

Midcap 400Midcap 400 12.0%12.0% 5.0%5.0% 2.402.40

Russ 2000Russ 2000 10.3%10.3% 7.7%7.7% 1.34 1.34

NasdqNasdq 11.38%11.38% 9.3%9.3% 1.221.22

Bonds/otherBonds/other 3.80%3.80% 4.0%4.0% 0.96 0.96

InternationaInternationall 17.00%17.00% 9.0%9.0% 1.171.17

MEIOptimums

MEI- Updated Analysis-12/2010

MEI- Original Analysis-11/2009

Part-2 Recession Part-2 Recession AnalysisAnalysis Updated Results Updated Results There was not sufficient data to evaluate International There was not sufficient data to evaluate International

results for the recession periods under evaluation.results for the recession periods under evaluation.

Results:Results:– Best returns In the following:Best returns In the following:

19901990……The best returns per unit of risk was Mega Cap and Mid The best returns per unit of risk was Mega Cap and Mid Caps.Caps.

2001…2001…The best returns per unit of risk was Mid Cap and The best returns per unit of risk was Mid Cap and MegaCaps.MegaCaps.

2007…2007…The best returns per unit of risk was Mid Cap. Tech and The best returns per unit of risk was Mid Cap. Tech and Small Caps were approx equal.Small Caps were approx equal.

Total…Total…When looking at the sum of three recessions the results When looking at the sum of three recessions the results show MEGA Cap and Midcaps provide the best return per unit of show MEGA Cap and Midcaps provide the best return per unit of Risk…They are approx equal:Risk…They are approx equal:

– NOTE:NOTE: In two of the three recessions analyzed Midcaps give the In two of the three recessions analyzed Midcaps give the better risk adjusted return.better risk adjusted return.

MEI Optimum

Part-3- Monte Carlo Part-3- Monte Carlo Simulation :Probabilistic Simulation :Probabilistic Rate of Return-UpdatedRate of Return-Updated

A series of Probability distributions reflects A series of Probability distributions reflects rates of Return by asset allocation Mixrates of Return by asset allocation Mix

– The simulation was based on 1000 iterationsThe simulation was based on 1000 iterations

– Analysis of:Analysis of: 100% allocated to Mega Cap stocks100% allocated to Mega Cap stocks 100% asset allocation to S&P 500 stocks100% asset allocation to S&P 500 stocks 100% asset allocation to Mid Cap stocks100% asset allocation to Mid Cap stocks 100% asset allocation to Small Cap stocks100% asset allocation to Small Cap stocks 100% asset allocation to Technology stocks100% asset allocation to Technology stocks

Mega Cap Stock-DOWMega Cap Stock-DOW

100% in the Mega 100% in the Mega Cap- DOWCap- DOW

90% Probability 100% 90% Probability 100% asset allocation in asset allocation in Mega Cap-DOW stocks Mega Cap-DOW stocks will yield 7.16% rate will yield 7.16% rate of Return –Std dev- of Return –Std dev- 5.3%5.3%

Implication:Implication: Lower rates of return..but lower standard deviation indicating safer returns particularly in recessions. Heavier weighting of Mega Cap in recessions provides a 3-4% floor return due to dividends.

Large Cap- S&P 500Large Cap- S&P 500

100% in the Large 100% in the Large Cap- S&P 500 indexCap- S&P 500 index

90% Probability 100% 90% Probability 100% asset allocation in asset allocation in Large Cap- S&P 500 Large Cap- S&P 500 index of stocks will index of stocks will yield 9.26% rate of yield 9.26% rate of Return –Std dev- Return –Std dev- 6.2%6.2%Implication: Solid returns with higher volatility and standard deviation. Similar to Mega Caps…as growth markets age in the business cycle Large Caps outperform due to 3-5% dividend payout. This justifies heavier weighting in recessions.

Mid Cap-S&P 400 Mid Cap-S&P 400 IndexIndex

100% in the Mid Cap- 100% in the Mid Cap- S&P 400 IndexS&P 400 Index

90% Probability 100% 90% Probability 100% asset allocation in Mid asset allocation in Mid Cap S&P 400 index of Cap S&P 400 index of stocks will yield stocks will yield 11.97% rate of Return 11.97% rate of Return –Std dev- 5.7–Std dev- 5.7

Implication: Highest combination of returns with lower standard deviation except in the diversified case. Suggests a heavier weighting within the diversified portfolio . Heavier weighting in Midcaps and Small caps coming out of a recession yields higher returns.

Small Cap-Russell Small Cap-Russell 2000 Index2000 Index

100% in the Small 100% in the Small Cap-Russell 2000IndexCap-Russell 2000Index

90% Probability 100% 90% Probability 100% asset allocation in asset allocation in Small Cap- Russell Small Cap- Russell 2000 will yield 2000 will yield 10.46% rate of Return 10.46% rate of Return –Std dev- 8%–Std dev- 8%

Implication: Overall returns and risk aren’t the highest but small caps perform best leading out of a bear market or recession and generate generous returns in that environment.

Technology –NASDQ Technology –NASDQ IndexIndex

100% in the 100% in the Technology- NASDQ Technology- NASDQ IndexIndex

90% Probability 100% 90% Probability 100% asset allocation in asset allocation in Technology Index-Technology Index-NASDQ will yield NASDQ will yield 11.4% rate of Return –11.4% rate of Return –Std dev- 9.6%Std dev- 9.6%

Implication: High returns with higher than average risk. However technology should be a part of every portfolio the weighting dependant on tolerance for risk..(5-15%)..Overweight coming out of a bear or recessionary cycle.

Updated ConclusionsUpdated Conclusions

Growth Rate differences in the Update: Growth Rate differences in the Update: Growth rates Growth rates increased in all investment categories except Fixed increased in all investment categories except Fixed income and International:income and International:– Largest increases occurred in Midcaps and Small Caps.Largest increases occurred in Midcaps and Small Caps.– Decreases in InternationalDecreases in International

Increases in Mid Caps and Small Caps Increases in Mid Caps and Small Caps are due to are due to traditional cyclical higher growth rates in these styles traditional cyclical higher growth rates in these styles coming out of a recession.coming out of a recession.

Lower growth in International Lower growth in International was due to European was due to European and Mideast instability , European Financial contagion and Mideast instability , European Financial contagion and Inflation in the BRIC countries .and Inflation in the BRIC countries .– The above resulted in the EU contractionary monetary and The above resulted in the EU contractionary monetary and

fiscal policy and its impact on the Euro.fiscal policy and its impact on the Euro.

Updated ConclusionsUpdated Conclusions Asset Allocation:Asset Allocation: This analysis does not suggest a This analysis does not suggest a

100% allocation in any one particular index style. In 100% allocation in any one particular index style. In fact the results show a diversified asset allocation fact the results show a diversified asset allocation provides the best results.provides the best results.

Style Weighting:Style Weighting: Most of the investment literature Most of the investment literature concentrates on Mega, Small Cap or Large Cap styles. concentrates on Mega, Small Cap or Large Cap styles. Little attention is given to Mid CapsLittle attention is given to Mid Caps. . – This analysis suggests that within a diversification This analysis suggests that within a diversification

scheme, a heavier weighting in Mid caps in good scheme, a heavier weighting in Mid caps in good and bad times gives you a solid core of higher Risk and bad times gives you a solid core of higher Risk adjusted rates of return that will contribute to adjusted rates of return that will contribute to maximum portfolio performance. maximum portfolio performance.

– Additionally Additionally overweighting Midcaps coming out of a overweighting Midcaps coming out of a bear or recession market provides higher returns.bear or recession market provides higher returns.

Updated ConclusionsUpdated Conclusions

This is reflected in this updated analysis: This is reflected in this updated analysis: Due to the additional 2 years of Due to the additional 2 years of data….Note the 27% increase in Midcap data….Note the 27% increase in Midcap growth rates in the updated analysis vs growth rates in the updated analysis vs the original..9.4% to 12%. the original..9.4% to 12%.

This also applies to a lessor extent This also applies to a lessor extent to to Small Caps..8.3% to 10.3 %.Small Caps..8.3% to 10.3 %.

The MEI for MidcapsThe MEI for Midcaps..that is the Marginal ..that is the Marginal return for each unit of risk is still return for each unit of risk is still significantly higher for Midcaps at 2.4 vs significantly higher for Midcaps at 2.4 vs Small Caps at 1.34 Small Caps at 1.34

Updated ConclusionsUpdated Conclusions

Reservations:Reservations: Higher risk adjusted Higher risk adjusted rates of return in International rates of return in International reflect the significant growth in reflect the significant growth in Global economies (particularly the Global economies (particularly the last 10 years) and specifically in the last 10 years) and specifically in the BRIC markets. The question of BRIC markets. The question of volatility and sustainability warrants volatility and sustainability warrants more investigation due to the small more investigation due to the small sample size.sample size.

Updated ConclusionsUpdated Conclusions

International Investments:International Investments: Results of Results of International investments suggest an International investments suggest an appropriate weighting in diversified appropriate weighting in diversified portfolio is warranted (5-15%) portfolio is warranted (5-15%) depending on Geo-Econo-politics and depending on Geo-Econo-politics and tolerance for risk…which is tolerance for risk…which is significantly higher than the average.significantly higher than the average.

Data Access:Data Access: The detailed analysis The detailed analysis including the data used in this analysis including the data used in this analysis is readily available on request in is readily available on request in Microsoft Excel format.Microsoft Excel format.