WTZIMI

Great investors and hedge fund managers: their methods and evaluation

Prof William T ZiembaAlumni Professor of Financial Modeling and Stochastic Optimization (Emeritus)

Mathematical Institute, Oxford UniversityICMA Centre, University of Reading

William T Ziemba Investment Management Inc, Vancouver, BCDr 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

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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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• 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

The symmetric downside Sharpe ratio performance measure

• 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

Buffett: still does not beat the Ford Foundation - and Harvard is also better than Buffett but not Ford with the quarterly data

higher, rest all lower

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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 $110,000/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