How optimal is the market portfolio

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How optimal is the market portfolio?

• William C. Wojciechowski Rice University
• CoFES Symposium
• September 20, 2004

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Outline

• Previous Approaches
• Simulation Approach
• Performance Measures
• Results and Conclusions

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Challenges with market observations

• Previous reseach can produce misleading and
  incorrect conculsions
• Outlier removal, OLS, Normality assumptions
• Limited time periods, limited market segments,
  single trading strategy

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Robust approach

• Observe the market through simulated portfolios
• No distribution assumptions
• Outliers included
• Market and time segments only limited by
  available data
• Observe all possible strategies at once

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Simulation
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Performance Measures
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Compare to Capital Market Line
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Other Simulation Details

• Time period 1970 to 2002
• Largest 1000 Market Cap companies as of January
  1st of each year
• Generate 50,000 portfolios for each year
• Market portfolio consists of all stocks on
  NASDAQ, AMEX, NYSE weighted by market cap
• 1 year treasury bill is the riskless instrument

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Results
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Bull vs. Bear Market Outperformance
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Returns and Volatility
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Returns and Volatility
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Returns and Volatility
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Returns and Volatility

• 10 years have positive relation
• 13 years have no relation
• 10 years have negative relations

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Conclusions

• Market is not theoretically efficient
• Market portfolio is far from optimal
• Further research would be to cluster/classify the
  random portfolios for commonality