1. EQUILIBRIUM FAST TRADING Tim Lu Sep 09, 2015 Topics in Quantitative Finance Washington University in St. Louis

3. OUTLINE  Introduction  Model Specification  The Equilibrium at Given Level of Fast Trading  Endogenous Fast Trading  Social Optimal Fast Trading and Policy Implication  Conclusion

4. INTRODUCTION Benefit of Fast Trading Enhanced Quotes Search Reduce the cost of delay or partial execution Cost of Fast Trading Access to Advanced Information of Fast Trader Induce adverse selection for traders, which impose negative externalities on economy

5. MODEL SPECIFICATION  Asset  Market  Investors  Valuation  Trading

6. EQUILIBRIUM GIVEN FAST TRADING LEVEL Equilibrium Spread:  Exist  Unique Stable Spread(question)  Increase with the level of fast trading Equilibrium Volume  Fast Institutions trade more because of searching advantage; trade more or less because of information advantage  Under some conditions, fast institutions trade more  An increase in fast trading increase fast institutions, at the same time increase spread

7. ENDOGENOUS FAST TRADING The decision of being fast or slow depends on the relative value of being fast. Being slow has a cost of delayed execution while being fast has both search and speculation value. Equilibrium exists and is higher than 0 under some condition. Strategic Substitute or Strategic Complement depends on the marginal relative benefit with regard to an increase in the level of fast trading. When the level of fast trading increases, spread increases so fast institutions’ profit decreases, however, slow institutions’ profit may decrease more

8. SOCIAL OPTIMAL FAST TRADING Compare Social Cost with Social Benefit  Social cost includes tech cost and negative externality cost  Social benefit comes from fast execution There Exists Overinvestment, Especially under Complementary in Institutions’ Decisions Solutions:  Pigovian Tax  Separate Markets  Banning Fast Trading

9. CONCLUSION  Fast trading has value  Fast trading has private cost and social cost(negative externality)  Overinvestment is more acute when institutions’ investment decisions are strategic complements  Pigovian tax can lead fast trading to social optimal level  The tax should be carefully devised to tax easily observable investments(colocation, fiber-optic cables)

10. MY QUESTION The author assumes the market makers are risk neutral with no private information, and the market for market maker is competitive or monopolistic competition(with 0 profit). In reality, the market maker(broker-dealer firm) is most likely also a high frequency firm; while there is significant barriers to entry both from up-front investment as well as regulation.

11. YOUR QUESTIONS?

12. THANK YOU FOR YOUR TIME!