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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

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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
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
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
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
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
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
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
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
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 strategy10
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
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
Why? — An Example
  • Asset A 10% 10%
  • Asset B 4% 10%

Expected Return

Expected Volatility

portfolio construction two asset case
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 case14
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 case15
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 1 and risk doubles continued
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
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.
issues to consider
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
Issues to Consider (Continued)
  • Cross-Market Correlations
    • Crisis management easier
    • Crisis in one sector can creep into another – Yen on October
issues to consider continued21
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