WHAT HAPPENS WHEN CORRELATIONS GO TO 1?

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

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

Correlations Converging Towards Unity • Usually refers to market price correlations • Implies that E (R)s are market returns • May refer to manager style • Average r ¹ 0 nor does it = 1 among managers, but • In a crisis r Þ 1 – what does this imply?

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

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

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

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

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

Slicing the Question Further by Type of Strategy • Long Only High Risk Rises Sharply • Long/Short • Long Only Medium Risk Rises Sharply • Long/Short • Long Only Low Risk Rises Sharply • Long/Short Implication of Converging to 1 When Risk is Rising Sharply Average Correlation Level Strategy

Slicing the Question Further by Type of Strategy • Long Only High Risk Rises Sharply • Long/Short High Little Risk; May Actually Fall • Long Only Medium Risk Rises Sharply • Long/Short Medium Little Implication; Risk Rises a Little • Long Only Low Risk Rises Sharply • Long/Short Low Risk Rises Sharply in a Similar Manner Implication of Converging to 1 When Risk is Rising Sharply Average Correlation Level Strategy

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.

Why? — An Example • Asset A 10% 10% • Asset B 4% 10% Expected Return Expected Volatility

Portfolio Construction: Two Asset Case • Assumptions: Expected Return Expected Volatility • Asset A 10% 10% • Asset B 4% 10% RETURN OBJECTIVE OF 8%

Portfolio Construction: Two Asset Case • Assumptions: Expected Return Expected Volatility • Asset A 10% 10% • Asset B 4% 10% Return Objective of 8% Optimal* Weights: Long Only Weight A Weight B Portfolio Risk Corr = 0.9 80.00% 0.00% 8.00% Corr = 0.75 80.00% 0.00% 8.00% Corr = 0.5 80.00% 0.00% 8.00% Corr = 0 68.97% 27.59% 7.43%

Portfolio Construction: Two Asset Case • Assumptions: Expected Return Expected Volatility • Asset A 10% 10% • Asset B 4% 10% Return Objective of 8% Optimal* Weights: Long Only Long/Short Weight A Weight B Portfolio Risk Weight A Weight B Portfolio Risk Corr = 0.9 80.00% 0.00% 8.00% 116.36% -90.91% 5.26% Corr = 0.75 80.00% 0.00% 8.00% 100.00% -50.00% 7.07% Corr = 0.5 80.00% 0.00% 8.00% 84.21% -10.53% 7.95% Corr = 0 68.97% 27.59% 7.43% 68.97% 27.59% 7.43%

Let Correlation Þ 1 and Risk Doubles (Continued) • Table of Optimal Weights Long Only Portfolio Variation if Corr r Þ1 and Risk Doubles Weight B Portfolio Variation Weight A Corr = 0.9 80.00% 0.00% 8.00% 16.00% Corr = 0.75 80.00% 0.00% 8.00% 16.00% Corr = 0.5 80.00% 0.00% 8.00% 16.00% Corr = 0 68.97% 27.59% 7.43% 19.31% Long/Short Portfolio Variation if Corr r Þ1 and Risk Doubles Weight A Weight B Portfolio Variation Corr = 0.9 116.36% -90.91% 5.26% 5.09% Corr = 0.75 100.00% -50.00% 7.07% 10.00% Corr = 0.5 84.21% -10.53% 7.95% 14.74% Corr = 0 68.97% 27.59% 7.43% 19.31%

Summary of Portfolio Risks (Continued) • Let Correlation Þ 1 and Risk Doubles • Optimized* • Assuming: Long Only Long/Short • Corr = 0.9 16.00% 5.09% • Corr = 0.75 16.00% 10.00% • Corr = 0.5 16.00% 14.74% • Corr = 0 19.31% 19.31% • * These calculations assume the weights from the previous table.

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

Issues to Consider • Long Only vs. Long/Short • In the real world correlations are usually around .6 to .8 • Zero correlation could not be a “temporary” phenomenon • 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 • High correlations are often the norm • Long/Short dominates

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

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

WHAT HAPPENS WHEN CORRELATIONS GO TO 1?