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Santa Fe InstituteMarch 29, 2005 1

Gambling, Derivatives and

Market Inefficiency

Edward O. Thorp


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Gambling, Derivatives and Market Inefficiency

ABSTRACTNobel prize-winning economists have claimedfor forty years that investors cannot to anysignificant extent beat the market through skill.

This is the content of various forms of their efficient market hypothesis or EMH. But theyare wrong, as shown by the experiences of realworld investors, including my own, in the worldsof gambling and the securities markets. I

explain the paradox and expect that you willimprove your ex ante expected stock marketresults 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 themarket, 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 ofscience

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 3Coms 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 moneyinstead of less money

EMH: No investments A and B should

exist where A dominates B Over a month for COMS/PALM disparity todecline to 10% or so


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Table 2 Continuing Disparity

COMS and PALMTrading 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 Cant Beat It)

1. All information instantly available to all

participants. COMS/PALM was frontpage news for weeks.

2. Sufficiently many participants are

financially rational, always prefer moremoney to less money, other things beingequal.


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3. Sufficiently many participants instantly

evaluate all relevant information anddetermine the current fair price of everysecurity.

4. New information: Prices immediatelygap 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 tolimited number, spreads to wider groupin stages. People who act earlier gain.Others dont.

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 toanalyze information varies amongindividuals.

4. Buy and sell orders often spread overhours, days or months as academicliterature on Anomalies documents.


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Replacing EMH

Positive alpha is a joint function of the

market and the observer, further, eachobservers perceptions change over time.

Two well-known historical examples

illustrate this perfectly:


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1. Casino blackjack before and after itsmathematical analysis and the discoveryof card counting;

2. Derivatives pricing before and after theBlack-Scholes formula and the ensuingrevolution 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 35years (1967-2002) and perhaps continue.

Dependence on the observer explains inpart why EMH debate continues.


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Investors

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

1b. No view equals no case for mispricing,

equivalent to his assuming it is properly priced.2. Ex ante, investor believes security not properlypriced, but is wrong.

3. Ex ante, investor believes the security is properly

priced and is correct. (Hedge COMS long andPALM short or swap from PALM to COMS.)


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

2. After costs, the return on the averageactively-managed dollar will be less than

the return on the average passively-managed dollar.


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These assertions hold foranytime period.Moreover, they depend onlyon the laws ofaddition, subtraction, multiplication and

division. Nothing else is required. Active investors as a group incur an

additional 2% per year in trading costs andmanagement fees.

Diminished further through adverse taximpact of trading.


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

They are advised to act as though theEMH is true, and to invest either through

low cost indexing or through buy andhold.


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Examples of Securities WithPositive Alpha

In 1965 I began discovering these; from1967 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, livingexpenses and taxes.

Positive returns in all 38 years.


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Princeton Newport Partners

November 1969 through December 1988compounded net, pretax at 15.1% nolosing years.

Before general partners fee, 18.9%annually.


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Santa Fe InstituteMarch 29, 2005

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Statistical Arbitrage Operation

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

26% annually before general partnersfees.


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Santa Fe InstituteMarch 29, 2005

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References

7. Haugen, Robert A., 1999. The New Finance, The Case Against EfficientMarkets, Second Edition, Prentice Hall, New Jersey.

8. Lo, Andrew W. (Edited by), Market Efficiency: Stock Market Behaviourin Theory and Practice, 1997.

9. Roberts, H., 1967. Statistical versus Clinical Prediction of the StockMarket, unpublished manuscript [28]

10. Samuelson, Paul A., 1965. Proof that Properly Anticipated PricesFluctuate Randomly, industrial Management Review, 6, 41-9. [185]

11. Sewell, Martin, http://www.e-m-h.org/introduction.html

12. Sharpe, W.F., The Arithmetic of Active Management, FinancialAnalysts 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,Winter2003, pp. 39-46.

14. The New York Times, March3, 2000, page A1, Offspring UpstagesParent in Palm Inc.s Initial Trading.

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