1. 1 Short Sales and Financial Innovation: How to Take the Good while Avoiding Volatility and Widespread Default Graciela Chichilnisky Columbia University, New York

2. 2 Reading Questions How is a market with short sales defined? Are there necessary and sufficient conditions for a market equilibrium in markets with short sales? How does a market with short sales fail to reach equilibrium? What causes volatility and default in markets with short sales? Can financial innovation cause systemic risks?

3. 3 Reading Questions (cont’d) What are ‘reserves’? How do reserves influence trading patterns? What are ‘graduated reserves’? Explain geometrically the difference between reserves and graduated reserves. Can graduated reserves restore equilibrium, in markets with short sales? How? Do graduated reserves prevent volatility and default – if so, how?

4. 4 Markets with Short Sales Differ from classic Arrow Debreu Markets only in that traders may take short positions of any size Short sales enhance market performance and improve allocation of resources Increased gains means increased risks Risks of added volatility & default

5. 5 Pricing by market clearing conditions  Identify Necessary and Sufficient Conditions for market clearing equilibrium  Chichilnisky (1996, 1998, 2010) Chichilnisky and Heal (1998) Limited Arbitrage is necessary and sufficient for Market Equilibrium

6. Market Equilibrium with Short Sales  Global cones: directions of net trades that always increase a traders’ utility  May depend on traders’ expectations  Limited Arbitrage: the global cones of all traders contained in one half - space 6

7. 7 When Limited Arbitrage Fails Diversity of Traders’ Expectations No market equilibrium Price volatility Default What is the mechanism?

8. 8 Financial Innovation can make things worse Financial Innovation increases individual welfare But causes system-wide risks Cascading effects: Default by one trader leads to default by many Widespread default Chichilnisky and Wu, JME, 2006

9. 9 How to Restore Equilibrium? Introduce Reserves ‘Graduated Reserves’ Restore Limited Arbitrage Restore Market Equilibrium Prevent Widespread default

10. 10 Figure 1. Short Sales without Reserves Short Salesy p x

11. 11 Figure 2. Short Sales with Fixed Reserves Ratio Reserves Short Salesy x

12. 12 Figure 3. Short Sales with Graduated Reserves Short Salesy x

13. 13 Conclusions Markets with Short Sales improve efficiency Limited Arbitrage is necessary and sufficient for market clearing equilibrium However when Limited Arbitrage fails, social diversity, volatility and default Additionally, with financial innovation, systemic risks of widespread default Graduated reserves restore limited arbitrage conditions Graduated reserves thus restore equilibrium and avoid default  Without impeding or limiting short sales