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Volatility Based Volatility-Based Asset Allocation

Scott Lummer, Ph.D., CFA Atlantic Asset Management March 2008

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Volatility-Based Asset Allocation

· · · · · Application of static asset allocation Volatility model y Tests of volatility model Global Alpha Model Historical simulations of Global Alpha Model

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Static Allocations

· Investors are frequently warned by advisors and consultants not to change their asset allocation. · As a result pension plan asset allocations are very result, static. In the 1980's, one well-known consultant joked that

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Static Allocations

· Investors are frequently warned by advisors and consultants not to change their asset allocation. · As a result pension plan asset allocations are very result, static. In the 1980's, one well-known consultant joked that "I don't know what the question is, but the answer is 60%."

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General Concept

· In theory, an institutional investor chooses a volatility theory level that is appropriate for the investment goals and time horizon for the overall fund · The asset allocation SHOULD be dependent on changes in market conditions particularly volatility. · However, we know that in practice that does not happen asset allocations are more static than they should be

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Daily S&P 500 Stock Returns 1986-2006

10% 5% 0% 5% -5% -10%

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86

91

96

01

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Static Allocation A Live Example

How many of you have changed your asset allocation over the past year?

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Static Allocation A Live Example

How many of you have changed your asset allocation over the past year? Last 3 months of MSCI EAFE volatility as of 3/1/07? 10.7% Last 3 months of MSCI EAFE volatility as of 3/1/08?

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Static Allocation A Live Example

How many of you have changed your asset allocation over the past year? Last 3 months of MSCI EAFE volatility as of 3/1/07? 10.7% Last 3 months of MSCI EAFE volatility as of 3/1/08? 24.7%

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Volatility and Risk Reduction

· If volatility shifts over time, it may b optimal to alter l ili hif i i be i l l the asset allocation · Reduce proportion invested in equities during periods when volatility is expected to be high · Increase proportion invested in equities during periods when volatility is expected to be low

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Simulation of Volatility Based Allocation

· Stocks and bonds have zero correlation · Bonds have return of 7% and volatility of 2% · St k h Stocks have return of 12% and volatility of 16% t f d l tilit f · 20 years of data are simulated, 100 trials of simulation · Basic allocation is 50% stocks, 50% bonds · Signal is created suggesting volatility is either increasing or decreasing if increasing, stock allocation drops to 47%, and if decreasing, allocation increased to 53%

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Simulation 1

· V l ili never changes Volatility h · False signal is created with 50% chance of suggesting volatility increase and 50% chance of suggesting volatility decrease

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Results for Simulation 1

Static Allocation Strategy 9.29% 8.08% 64 0.24% Varying Allocation Strategy 9.29% 8.10% 36

Return Standard deviation Number of trials with lower standard deviation Maximum difference in standard deviation

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Simulation 2

· V l ili either increases to 21% or decreases to Volatility i h i d 11% Two signals are created: g gg g y · False signal with 50% chance of suggesting volatility increase and 50% chance of suggesting volatility decrease · Correct signal predicting the volatility change

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Results for Simulation 2

Incorrect Correct Static Varying Varying Allocation Allocation Allocation Strategy Strategy Strategy 9.30% 9.29% 9.29% 8.50% 8.53% 43 3 0.31% 8.22% 99 -0.49%

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Return Standard deviation Trials with lower std dev th d than static t ti Max difference in std dev from static d f t ti

Simulation Implications

· Ch Changing the allocation because of an incorrect i h ll i b f i signal causes an increase in volatility but the g y y g change in volatility is very slight · Changing the allocation because of a correct signal causes a large decrease in volatility

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Quarterly Volatility for the S&P 500 1980-2005

3% 2% 1% 0% 80 85 90 95 00 05

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Quarterly Volatility for the S&P 500 Compared to Volatility in the Succeeding Quarter 1980-2007

3% 2% 1% 0% 0% 1% 2% 3%

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Volatility and Return Enhancement

· Historical data indicate that in periods of low volatility stocks will earn higher returns than in periods of high volatility · Because future volatility is correlated with recent past volatility, volatility it may be advantageous to vary the allocation to stocks to improve overall returns along with lowering risk

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Volatility and Return Enhancement

Average return for 20 groups of days ranked by volatility

3% 2% 1%

Re eturn

0% -1% -2% 2% 0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

Standard Deviation

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Tests of Volatility Model

· C Create benchmark 60/40 model b h k d l · During periods of high volatility, decrease allocation to equities by 3% -- during periods of low volatility, increase allocation to equities by 3% · Determine increase in return and decrease in risk caused by varying allocation · Tests conducted on 19 markets (18 developed countries plus U.S. small cap) for which data is US available from 1986-present

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Test: U.S. Large Cap Example T t US L C E l 1986-2006

Varying Allocation ll (63%-57% equity) Average Return Standard Deviation Excess Return Decrease in Risk 10.33% 10.16% 10 16% Fixed Allocation d ll (60% equity) 10.17% 10.36% 10 36%

16 basis points 20 basis points

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Decrease in Risk Caused by Varying Allocations Based on Recent Volatility: 1986-2006

0.3% 0.2% 0.1%

UK USS HK

0.0%

Can Den Aus Aut Fra Ger

Ire

Ita

Sin

Swe

-0 1% 0.1% -0.2%

USL

Jap

Nor

Net

Swi

Bel

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Increase in Return Caused by Varying Allocations Based on Recent Volatility: 1986-2006 y

0.3% 0.2% 0.1% 0.0% 0 0%

HK UK

-0.1%

USS

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Ire

Ita

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USL

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Volatility Model Test: Summary Results for 1986-2006

Proportion of markets with decreased risk Proportion of markets with increased return Average decline in risk Average increase in return Average increase in return per change in allocation 79% 89% 9 basis points 14 basis points 2.26%

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How Can Return Enhancement Exist?

Inefficiencies created by: I ffi i i db · Country preference biases · Static allocations · Static volatility assumptions

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The Global Alpha Model

Combine volatility with three other factors: · Market valuation · Economic conditions · Price momentum Net result of model is a favorable (bullish) or unfavorable (bearish) signal of market conditions When favorable, invest 100% in stocks -- when unfavorable, invest 100% in bonds ,

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Returns in Markets Identified by Global Alpha Model as Favorable and Unfavorable by Model: 1986-2006

30% 20% 10% 0% Aus Aut Bel Can Den Fra Ger HK -10%

Favorable Unfavorable

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Ire

Ita

Returns in Markets Identified by Global Alpha Model as Favorable and Unfavorable by Model: 1986-2006

30% 20% 10% 0% Jap -10%

Favorable Unfavorable

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Net

Nor

Sin Swe Swi

U K USL U SS

Excess Return of Global Alpha Model over 60/40 Benchmark by Country: 1986-2006 y y

8% 6% 4% 2%

HK UK USS

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Ire

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0%

Hypothetical Portfolios with f Global Alpha Model

· Model can be applied as an overlay or used to develop a fund · In a fund, we create 22 separate positions in a portfolio · Proportion of portfolio invested in equity is the proportion of countries identified as favorable · Constrained optimization determines the relative weights of the countries in the portfolio

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Global Alpha Model Hypothetical Portfolio Returns: 1986-2006

Return Global Alpha Model MSCI World 15.1% 10.5% Standard deviation 7.7% 14.6% Sharpe ratio 1.2 0.3

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Global Alpha Model Hypothetical Annual Portfolio Returns

40% 30% 20% 10% 0% -10% 86 -20% 91 96 01

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Global Alpha Fund Actual Returns: , y , December 1, 2006 - February 29, 2008

Global Alpha Model MSCI World 6.8% 1.7%

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Conclusion

· Th There i no j ifi i for maintaining static asset is justification f i i i i allocation weights in the face of dynamic capital markets · Varying the allocation consistent with recent volatility shifts has added return and decreased risk · Tactical models based on the volatility variable provided good hypothetical and actual performance

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Volatility Based Asset Allocation

Scott Lummer, Ph.D., CFA Atlantic Asset Management March 2008

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