The Limits of Arbitrage

1. The Limits of Arbitrage ANDREI SHLEIFER and ROBERT W.VISHNY 商学院 周 美 & 杜慧卿

2. ABSTRACT • In reality，almost all arbitrage requires capital, and is typically risky. • Professional arbitrage is conducted by a relatively small number of highly speciali-zed investors using other’s capital. • Arbitrage becomes ineffective in extreme circumstances. • Anomalies in financial markets.

3. “The simultaneous purchase and sale of the same, or essentially similar, security in two different markets for advantage-ously different prices.” No risk and need no capital. Fundamental concepts “The simultaneous purchase and sale of the same, or essentially similar, security in two different markets for advantage-ously different prices.” No risk and need no capital.

4. Require capital good faith money • In short run, one may lose money • Different trading hours, settlement dates, and delivery terms. • If prices are moving rapidly, the value may differ additional risks Realistic arbitrage are more complex • Require capital good faith money • In short run, one may lose money • Different trading hours, settlement dates, and delivery terms. • If prices are moving rapidly, the value may differ additional risks

5. PBA( performance-based arbitrage) • More commonly, conducted by relatively few professional, highly specialized investors; • Outside resources • Brains and resources are separated • Allocate funds based on past returns

6. Assume： • Three types: noise traders, arbitrageurs, and investors in arbitrage funds • Fundamental value is V; • Three time periods • , , An agency model of limited arbitrage • Assume： • Three types: noise traders, arbitrageurs, and investors in arbitrage funds • Fundamental value is V; • Three time periods

7. Arbitrageurs‘ demand • Aggregate demand equals the unit supply: • Arbitrageurs‘ demand • Aggregate demand equals the unit supply: • Not fully invest, • Arbitrageurs‘ demand • Aggregate demand equals the unit supply: • Not fully invest, • , • Arbitrageurs‘ demand • Aggregate demand equals the unit supply: • Not fully invest, • , • Market segment, T investors with $1, so • Arbitrageurs‘ demand • Aggregate demand equals the unit supply: • Not fully invest, • , • Market segment, T investors with $1, so An agency model of limited arbitrage • Arbitrageurs‘ demand

8. Compete in the price the charge; • Assume marginal cost constant, so competition drives price to marginal cost • Bayesians, allocate funds according to past performance( PBA ); • An increasing function: An agency model of limited arbitrage • Compete in the price the charge; • Assume marginal cost constant, so competition drives price to marginal cost • Bayesians, allocate funds according to past performance( PBA ); • An increasing function:

9. Benchmark: zero return • A linear function: ,with • Benchmark: zero return • A linear function: ,with • Then • Benchmark: zero return • A linear function: ,with • Then • If , gain funds; or ,lose funds • The higher is , the more sensitive to past performance An agency model of limited arbitrage • Benchmark: zero return • A linear function:

10. An arbitrageur’s optimization problem: q ; 1-q An arbitrageur’s optimization problem: q ; 1-q , An arbitrageur’s optimization problem: q ; 1-q , . Maximize: An arbitrageur’s optimization problem: q ; 1-q , . Maximize: An agency model of limited arbitrage An arbitrageur’s optimization problem: q

11. The case of first order condition: • The case of first order condition: Inequality： • The case of first order condition: Inequality： ； Equality： • The case of first order condition: Inequality： ； Equality： . The initial displacement is large and will recover with a high probability; if they fall, it can’t be large. • The case of first order condition: Inequality： ； Equality： . The initial displacement is large and will recover with a high probability; if they fall, it can’t be large. fully invested at 1 Performance-based Arbitrage and Market Efficiency • The case of

12. Proposition 1:For a given , , , ; and , there is a such that, for , , and for , . Proposition 2: At the corner solution( ), , , and . At theinterior solution, , , and . It shows that arbitrageurs ability to bear mispricing is limited, larger shocks, less efficient. Performance-based Arbitrage and Market Efficiency

13. Performance-based Arbitrage and Market Efficiency Uncertainty of the effect: • a higher a could make market less efficient, by withdrawing funds; • A higher a will make prices adjust quickly by giving more funds after a partial reversal of the noise shock.

14. Consider about the extreme circumstances: two ways: ？ ？ Proposition 3：If arbitrageurs are fully invested at , and noise trader mispe-rceptions deepen at , then, for , , and . Fully invested arbitrageurs may face equity withdrawals and liquidate. Performance-based Arbitrage and Market Efficiency Consider about the extreme circumstances: two ways:

15. Proposition 4: At the fully invested equili-brium, and . • This shows: prices fall more than one for one with the noise trader shock at time 2,when fully invested at time 1. • A market driven by PBA can be quite in-effective in extreme circumstances. Performance-based Arbitrage and Market Efficiency • Proposition 4: At the fully invested equili-brium, and .

16. Discussion of Performance-based Arbitrage • We are uncertain about the significance of PBA • Funds decline with a lag • Contractual restrictions expose more risk • Agency problem inside • Arbitrageurs are risk-averse So the efficiency of arbitrage will be limited.

17. Discussion of Performance-based Arbitrage • PBA supposes that all arbitrageurs have the same sensitivity, and will invest all funds when asset mispriced. • In reality, they differ. resources indepen-dent and invest more when price diverge further; not need to liquidate. • Big shock need more to eliminate, if not, mispricing gets deeper. • Little fresh capital available to stabilize. So PBA is likely to be important .

18. Empirical Implications • A. Which markets attract arbitrage reso-urces? large funds concentrated in a few markets, bond markets & foreign exch-ange market; the ability to ascertain value; specialized arbitrageurs avoid volatile; short horizons may be more relevant

19. Empirical Implications • B. Anomalies • higher historical returns. • EMH: compensation for higher risk impl-ausible: large number of diversified arbitrageurs. • few specialized arbitrageurs care about total risk fundamental or idiosyncratic. • failing to recognize price-revisal .

20. Empirical Implications • In extreme circumstances, lose enough money and liquidate; • Investors become knowledgeable about the strategies, diminish withdrawals; but it will be slowly for investors take action.

21. Conclusion • PBA may not be fully effective in bringing prices to fundamental values; • Specialized professional arbitrageurs may avoid extremely volatility; • The avoidance suggests a different approach to understanding persistent excess returns.

22. Thank you !