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WHAT HAPPENS WHEN CORRELATIONS GO TO 1? Presentation by: D. Sykes Wilford wsykes@laudisi.com SPS Holdings

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Modern Portfolio Theory and Correlations: Are they Synonymous? MPT ä Expected Returns ä Volatility in the errors of those expected returns ä Correlation in the errors of those expected returns Correlation ä In markets? ä In your errors in expected returns E (R)s? Key Question: What correlations matter?

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SPS Holdings Correlations Converging Towards Unity Usually refers to market price correlations Implies that E (R)s are market returns May refer to manager style Average nor does it = 1 among managers, but In a crisis – what does this imply?

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SPS Holdings World Equity Market Correlations With The S&P 500 Correlations Time: Periods Ending December, 1984 to December, 1998 Three Year Rolling Correlations of Excess Returns*

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SPS Holdings Three Year Rolling Correlations of Excess Returns* Time: Periods Ending December, 1985 to December, 1998 Correlation of US Treasury Returns to Bunds and JGB's Returns Correlations

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SPS Holdings Correlation of Returns to Various Cross Rates Time: Periods Ending December, 1984 to December, 1998 Three Year Rolling Correlations of Excess Returns* Correlations

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SPS Holdings Cross Market Correlations Time: Periods Ending December, 1985 to December, 1998 Three Year Rolling Correlations of Excess Returns* Correlations

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SPS Holdings Problem Needs to be Sub-divided Correlations Across Markets Bonds, Equities, Currencies Europe Japan Canada U.S. U.K. Equities Bonds Currencies Correlations Within a Market Segment

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SPS Holdings Long Only High Risk Rises Sharply Long/Short Long OnlyMediumRisk Rises Sharply Long/Short Long OnlyLowRisk Rises Sharply Long/Short Slicing the Question Further by Type of Strategy Average Correlation Level Implication of Converging to 1 When Risk is Rising Sharply Strategy

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SPS Holdings Long Only High Risk Rises Sharply Long/ShortHighLittle Risk; May Actually Fall Long OnlyMediumRisk Rises Sharply Long/ShortMediumLittle Implication; Risk Rises a Little Long OnlyLowRisk Rises Sharply Long/ShortLowRisk Rises Sharply in a Similar Manner Slicing the Question Further by Type of Strategy Average Correlation Level Implication of Converging to 1 When Risk is Rising Sharply Strategy

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SPS Holdings Why the Sharp Difference? Long Only vs. Long/Short As average correlation goes from 0 to 1, the long/short strategy can take advantage of correlations to mitigate risk by shorting high correlation, low expected return positions to create Intended Diversification.

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SPS Holdings Asset A 10%10% Asset B4%10% Why? — An Example Expected ReturnExpected Volatility

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SPS Holdings Portfolio Construction: Two Asset Case Assumptions: RETURN OBJECTIVE OF 8% Asset A 10%10% Asset B4%10% Expected ReturnExpected Volatility

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SPS Holdings Weight A Weight B Portfolio Risk Asset A 10%10% Asset B4%10% Corr = 0.980.00%0.00%8.00% Corr = 0.7580.00%0.00%8.00% Corr = 0.580.00%0.00%8.00% Corr = 068.97%27.59%7.43% Portfolio Construction: Two Asset Case Optimal * Weights: Long Only Assumptions: Return Objective of 8% Expected ReturnExpected Volatility

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SPS Holdings Weight A Weight B Portfolio Risk Weight AWeight BPortfolio Risk Asset A 10%10% Asset B4%10% Corr = 0.980.00%0.00%8.00%116.36%-90.91%5.26% Corr = 0.7580.00%0.00%8.00%100.00%-50.00%7.07% Corr = 0.580.00%0.00%8.00%84.21%-10.53%7.95% Corr = 068.97%27.59%7.43%68.97%27.59%7.43% Portfolio Construction: Two Asset Case Optimal * Weights: Long Only Long/Short Assumptions: Return Objective of 8% Expected ReturnExpected Volatility

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SPS Holdings Corr = 0.980.00%0.00%8.00%16.00% Corr = 0.7580.00%0.00%8.00%16.00% Corr = 0.580.00%0.00%8.00%16.00% Corr = 068.97%27.59%7.43%19.31% Weight A Weight BPortfolio Variation Portfolio Variation if Corr 1 and Risk Doubles Corr = 0.9116.36%-90.91%5.26%5.09% Corr = 0.75100.00%-50.00%7.07%10.00% Corr = 0.584.21%-10.53%7.95%14.74% Corr = 068.97%27.59%7.43%19.31% Long Only Weight A Weight BPortfolio Variation Portfolio Variation if Corr 1 and Risk Doubles Long/Short Let Correlation 1 and Risk Doubles (Continued) Table of Optimal Weights

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SPS Holdings Let Correlation 1 and Risk Doubles Summary of Portfolio Risks (Continued) Optimized* Assuming:Long Only Long/Short Corr = 0.916.00%5.09% Corr = 0.7516.00%10.00% Corr = 0.516.00%14.74% Corr = 019.31%19.31% * These calculations assume the weights from the previous table.

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SPS Holdings (Excess Returns) 1998 Average Daily Global Balanced: Volatility by Month **

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SPS Holdings Issues to Consider Long Only vs. Long/Short ä In the real world correlations are usually around.6 to.8 ä Zero correlation could not be a “temporary” phenomenon ä Large deviation in expected returns, given equivalent risk are usually very unusual at.9 correlation, but not necessarily at.6 –.7 correlation Intra-Market Class Correlations ä High correlations are often the norm ä Long/Short dominates

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SPS Holdings Issues to Consider (Continued) Cross-Market Correlations ä Crisis management easier ä Crisis in one sector can creep into another – Yen on October

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SPS Holdings Issues to Consider (Continued) Foreign Exchange is a good diversifier ä On average ä During a crisis ä Especially for Long Only Portfolios Diversifying Managers ä Average Correlations: don’t be fooled ä Crisis Correlations: stress the data Style Diversification Average vs. Crisis Correlations Long/Short

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