Great investors and hedge fund managers: their methods and evaluation

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Great investors and hedge fund managers their
methods and evaluation
Prof William T Ziemba Alumni Professor of
Financial Modeling and Stochastic Optimization
(Emeritus) Mathematical Institute Oxford
University ICMA Centre University of
Reading William T Ziemba Investment Management
Inc Vancouver BC Dr Z Investments Inc San Luis
Obispo CA and Private International Wealth
Management BC Capital Group Nassau CARISMA
Seminar June 25 2007
Session 4 Measuring the performance of
investors and hedge fund managers
WTZIMI
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15. Using the Sharpe ratio
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16. Using a modified Sharpe ratio that does not
penalize gains
Summary over funds of negative observations and
arithmetic and geometric means
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The symmetric downside Sharpe ratio performance
measure

• we want to determine if Warren Buffett really is
  a better investor than the rather good but lesser
  funds mentioned here especially the Ford
  Foundation and the Harvard endowment in some
  fair way.
• The idea is presented in a Figure below where we
  have plotted the Berkshire Hathaway and Ford
  Foundation monthly returns as a histogram and
  show the losing months and the winning months in
  a smooth curve. We want to penalize Warren for
  losing but not for winning. So define the
  downside risk as

• This is the downside variance measured from zero
  not the mean so it is more precisely the
  downside risk.
• To get the total variance we use twice the
  downside variance

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17. Is Buffett a better investor than the Ford
Foundation or the Harvard Endowment
Comparison of ordinary and symmetric downside
Sharpe yearly performance measures
higher rest all lower
Buffett still does not beat the Ford Foundation
- and Harvard is also better than Buffett but not
Ford with the quarterly data
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We all know that Buffett is better but we need
another way to show it
That is long run wealth growth of the Kelly
criterion Why Tails still too fat Thorp (2006)
shows that Buffett is essentially a full Kelly
bettor. Thorp dinner in 1969 someday that man
(Buffett) will be the richest person in the world
he told his wife. He bought Berkshire stock at
100 now worth about 110000/share.
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Berkshire Hathaway versus Ford Foundation
monthly returns distribution January 1977 to
April 2000
Bh has bigger gains yes but also bigger losses
than the Ford Foundation
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Return distributions of all the funds quarterly
returns distribution December 1985 to March 2000
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Summary of the means both arithmetic and
geometric and the Sharpe and symmetric downside
Sharpe ratios for the monthly quarterly and
yearly data all annualized
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18 Incentives in hedge funds effect of
incentive fees and managers investment in the fun
(eating your own cooking)

• Kouwenberg-Ziemba (2007) paper on this
• Call option on investors money is worth 0 to 18
• When fund manager has 30 in the fund risk
  taking behavior is greatly reduced

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19. Performance of hedge funds and funds of funds

• Most funds do not make back their fees
• Fund of funds do better