Santa Fe Institute March 29, 2005 1 Gambling, Derivatives and Market Inefficiency Edward O. Thorp

Santa Fe Institute March 29, 2005

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Gambling, Derivatives and Market Inefficiency

Edward O. Thorp


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Gambling, Derivatives and Market Inefficiency

ABSTRACTNobel prize-winning economists have claimed for forty years that investors cannot to any significant extent “beat the market” through skill. This is the content of various forms of their “efficient market hypothesis” or EMH. But they are wrong, as shown by the experiences of real world investors, including my own, in the worlds of gambling and the securities markets. I explain the paradox and expect that you will improve your ex ante expected stock market results no matter what type of investor you are.


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• Efficient Market Hypothesis or EMH• 1960s• Cootner (1964), Samuelson (1965), Fama

(1965-70), Roberts (1967) and others• Key consequence no way to “beat the

market,” i.e. excess risk adjusted expected return

• Still no consensus among financial economists, Lo (1997)


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• False theories abound in the history of science

• EMH is false but useful

• Extensive evidence contradicts assumptions

• “Anomalies”

• Behavioral finance


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The Inefficient Market in Action – 3Com Spins Off Palm Pilot

• Thursday, March 2, 2000 6% of palm Pilot was offered in an IPO

• Market valued palm pilot at $53.4 billion

• Therefore 3Com’s 94% of palm Pilot was worth $50 billion

• Yet market valued 3Com at “only” $28 billion


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• “Stub” valued at negative $22 billion!

• Yet analysts valued “stub” between $5 billion and $8.5 billion


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Table 1 Price Disparity COMS and PALM Spin-off

Trading Day COMS PALM PALM Premium

1 Th 3-2-00 81.20 95.06 67 (83%)

2 F 3-3-00 83.06 80.25 45 (55%)

3 M 3-6-00 69.56 63.13 36 (51%)

4 Tu 3-7-00 72.25 66.88 38 (53%)


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• Short PALM and buy 3Com for a 100% profit

• PALM was difficult to borrow to sell short• Any reasonable model of efficient markets

investors always choose more money instead of less money

• EMH: No investments A and B should exist where A dominates B

• Over a month for COMS/PALM disparity to decline to 10% or so


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Table 2 Continuing Disparity COMS and PALM

Trading Day COMS PALM PALM Premium if COMS Stub = 15%

of COMS

5 W 3- 8-00 70.44 64.75 38%

10 W 3-15-00 61.06 55.75 37%

20 W 3-29-00 63.20 49.69 18%

30 W 4-12-00 44.31 33.31 13%

40 Th 4-27-00 38.88 27.06 4%


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The Ideal Efficient Market (You Can’t Beat It)

1. All information instantly available to all participants. COMS/PALM was front page news for weeks.

2. “Sufficiently many” participants are financially rational, always prefer more money to less money, other things being equal.


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3. “Sufficiently many” participants instantly evaluate all relevant information and determine the current fair price of every security.

4. New information: Prices immediately “gap” to new fair price.

Supporters claim this is good approximation

(for large cap stocks in liquid markets).

COM/PALMS example rebuts assumptions 2, 3 and 4


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The Real Inefficient Market (Some of You Can Beat It)

1. Information typically starts out known to limited number, spreads to wider group in stages. People who act earlier gain. Others don’t.

2. Financial rationality of the participants is limited.

3. Participants typically have only some of the relevant information.


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Time and the willingness or ability to analyze information varies among individuals.

4. Buy and sell orders often spread over hours, days or months as academic literature on “Anomalies” documents.


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Replacing EMH

• Positive alpha is a joint function of the market and the observer, further, each observer’s perceptions change over time.

• Two well-known historical examples illustrate this perfectly:


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1. Casino blackjack before and after its mathematical analysis and the discovery of card counting;

2. Derivatives pricing before and after the Black-Scholes formula and the ensuing revolution in quantitative financial analysis.


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• Participants in the “market” only gradually and sporadically used the new information.

• 45 years (1960-2005) for “blackjack market” to return to approximate efficiency.

• Derivatives markets, substantial inefficiencies have persisted for at least 35 years (1967-2002) and perhaps continue.

• Dependence on the observer explains in part why EMH debate continues.


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Investors

1a. Investor believes the security (or bet) is properly priced.

1b. No view equals no case for mispricing, equivalent to his assuming it is properly priced.

2. Ex ante, investor believes security not properly priced, but is wrong.

3. Ex ante, investor believes the security is properly priced and is correct. (Hedge COMS long and PALM short or swap from PALM to COMS.)


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Limitations on the Exploitation of Market Inefficiency

William Sharpe (1991)

“The Arithmetic of Active Management: (Sharpe’s Principle):

If active and passive management styles are defined in sensible ways, it must be the case that:


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1. Before costs, the return on the average actively-managed dollar will equal the return on the average passively-managed dollar; and

2. After costs, the return on the average actively-managed dollar will be less than the return on the average passively-managed dollar.


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• These assertions hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required.”

• Active investors as a group incur an additional 2% per year in trading costs and management fees.

• Diminished further through adverse tax impact of trading.


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• Reason for persistence of EMH: Most investors do not (and cannot) unequivocally identify positive (after cost) alpha.

• They are advised to act as though the EMH is true, and to invest either through low cost indexing or through “buy and hold.”


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Examples of Securities With Positive Alpha

• In 1965 I began discovering these; from 1967 until now I have invested in them.

• How have I done?

• Modest 1967 net worth is in 2005 6,680 times as large, annual compound rate of 26%. Net after costs, gifts, living expenses and taxes.

• Positive returns in all 38 years.


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Princeton Newport Partners

• November 1969 through December 1988 compounded net, pretax at 15.1% no losing years.

• Before general partners’ fee, 18.9% annually.


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Statistical Arbitrage Operation

• August 1992 to October 2002 pretax 20% annually to limited partners.

• 26% annually before general partners’ fees.


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References1. Cootner, P. (ed.), 1964. The Random Character of Stock Market

Prices [326]2. Fama, Eugene F., 1965. “The Behavior of Stock Market Prices,”

Journal of Business, Volume 38, Issue 1 (Jan., 1965), 34-105. [395]3. Fama, Eugene F., and Marshall E. Blume, 1966. “Filter Rules and

Stock Market Trading,” The Journal of Business, Volume 39, Issue 1, Part 2: Supplement on Security Prices (Jan., 1966), 226-241. [105]

4. Fama, Eugene F., et al., 1969. “The Adjustment of Stock Prices to New Information,” International Economic Review, Volume 10, Issue 1. (Feb., 1969), 1-21. [328]

5. Fama, Eugene F., 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance, Volume 25, Issue 2, Papers and Proceedings of the Twenty-Eighth Annual Meeting of the American Finance Association New York, N.Y. December, 28-30, 1969 (May, 1970), 383-417. [777]

6. Fama, Eugene F., 1998. “Market Efficiency, Long-Term Returns, and Behavioral Finance,” Journal of Financial Economics, 49 (1998) 283-306 [496]


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References7. Haugen, Robert A., 1999. The New Finance, The Case Against Efficient

Markets, Second Edition, Prentice Hall, New Jersey. 8. Lo, Andrew W. (Edited by), Market Efficiency: Stock Market Behaviour

in Theory and Practice, 1997.9. Roberts, H., 1967. Statistical versus Clinical Prediction of the Stock

Market, unpublished manuscript [28]10. Samuelson, Paul A., 1965. “Proof that Properly Anticipated Prices

Fluctuate Randomly,” industrial Management Review, 6, 41-9. [185]11. Sewell, Martin, http://www.e-m-h.org/introduction.html12. Sharpe, W.F., “The Arithmetic of Active Management,” Financial

Analysts Journal, January/February 1991, pp. 7-9.13. Stein, David M., “Active and Passive Arguments: In Search of an

Optimal Investment Experience,” Journal of Wealth Management, Winter 2003, pp. 39-46.

14. The New York Times, March 3, 2000, page A1, “Offspring Upstages Parent in Palm Inc.’s Initial Trading.”

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Santa Fe Institute March 29, 2005 1 Gambling, Derivatives and Market Inefficiency Edward O. Thorp