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Understanding Correlations in Modern Portfolio Theory: Implications for Risk Management

This presentation by D. Sykes explores the nuances of correlations in modern portfolio theory (MPT). It delves into how correlations, which often converge towards one during crises, affect expected returns and volatility. It highlights the difference between long-only and long/short strategies in managing risk. With detailed analysis of historical data, the presentation sheds light on market correlations among various asset classes, including equities and bonds, and discusses the implications of rising correlations in times of increased risk.

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Understanding Correlations in Modern Portfolio Theory: Implications for Risk Management

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

  2. 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?

  3. 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?

  4. 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

  5. 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

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

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

  8. 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

  9. 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

  10. 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

  11. 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.

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

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

  14. 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%

  15. 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%

  16. 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%

  17. 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.

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

  19. 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

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

  21. 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

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