Y!RL Spot Workshop on New Markets, New Economics

1. Y!RL Spot Workshop onNew Markets, New Economics • Welcome! • Specific examples of new trends in economics, new types of markets • virtual currency • prediction (“idea”) markets • experimental economics • Interactive, informal • ask questions • rountable discussion wrap-up

2. Distinguished guests (thanks!) • Edward CastronovaProf. Economics, Cal State Fullerton • John LedyardProf. Econ & Social Sciences, CalTech • Justin WolfersProf. Economics, Stanford

3. Schedule 11am-noon Castronova on the Future of Cyberspace Economies noon-1pm Lunch provided 1pm-2pm Ledyard on ~ Information Markets and Experimental Economics 2pm-3pm Wolfers on ~ Prediction Markets, Play Money, & Gambling 3pm-3:30pm Pennock on Dynamic Pari-Mutuel Market for Hedging, Speculating 3:30pm-4pm Roundtable Discussion

4. A Dynamic Pari-Mutuel Market for Hedging, Wagering, and Information Aggregation David M. Pennock paper to appear EC’04, New York

5. Economic mechanisms for speculating, hedging • Financial • Continuous Double Auction (CDA)stocks, options, futures, etc • CDA with market maker (CDAwMM) • Gambling • Pari-mutuel market (PM)horse racing, jai alai • Bookmaker (essentially like CDAwMM) • Socially distinct, logically the same • Increasing crossover

6. Take home message • A dynamic pari-mutuel market (DPM) • New financial mech for speculating on or hedging against an uncertain event; Cross btw PM & CDA • Only mech (to my knowledge) to • involve zero risk to market institution • have infinite (buy-in) liquidity • continuously incorporate new info;allow cash-out to lock in gain, limit loss

7. Outline • Background • Financial “prediction” markets • Pari-mutuel markets • Comparing mechs:PM, CDA, CDAwMM, MSR • Dynamic pari-mutuel mechanism • Basic idea • Three specific variations; Aftermarkets • Open questions/problems

8.  6 = 6 ? = 6 I am entitled to: $1 if $0 if What is a financial“prediction market”? • Take a random variable, e.g. • Turn it into a financial instrument payoff = realized value of variable 2004 CAEarthquake? US’04Pres =Bush?

9. Real-time forecasts • price  expectation of random variable(in theory, in lab, in practice, ...huge literature) • Dynamic information aggregation • incentive to act on info immediately • efficient market  today’s price incorporates all historical information; best estimator • Can cash out before event outcome • BUT, requires bi-lateral agreement

10. Updating on new information

11. Allocate risk (“hedge”) insured transfers risk to insurer, for $$ farmer transfers risk to futures speculators put option buyer hedges against stock drop; seller assumes risk Aggregate information price of insurance prob of catastrophe OJ futures prices yield weather forecasts prices of options encode prob dists over stock movements market-driven lines are unbiased estimates of outcomes IEM political forecasts The flip-side of prediction: HedgingE.g. options, futures, insurance, ...

12. Continuous double auctionCDA • k-double auction repeated continuously • buyers and sellers continually place offers • as soon as a buy offer  a sell offer, a transaction occurs • At any given time, there is no overlap btw highest buy offer & lowest sell offer

13. http://tradesports.com

14. http://www.biz.uiowa.edu/iem http://us.newsfutures.com/

15. Running comparison

16. CDA with market maker • Same as CDA, but with an extremely active, high volume trader (often institutionally affiliated) who is nearly always willing to sell at some price p and buy at price q  p • Market maker essentially sets prices; others take it or leave it • While standard auctioneer takes no risk of its own, market maker takes on considerable risk, has potential for considerable reward

17. http://www.wsex.com/ http://www.hsx.com/

18. Bookmaker • Common in sports betting, e.g. Las Vegas • Bookmaker is like a market maker in a CDA • Bookmaker sets “money line”, or the amount you have to risk to win $100 (favorites), or the amount you win by risking $100 (underdogs) • Bookmaker makes adjustments considering amount bet on each side &/or subjective prob’s • Alternative: bookmaker sets “game line”, or number of points the favored team has to win the game by in order for a bet on the favorite to win; line is set such that the bet is roughly a 50/50 proposition

19. Running comparison

20. A B What is a pari-mutuel market? • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers:

21. What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers: 

22. What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers: 

23. $ on B 8$ on A 4 1+ = 1+ =$3 total $ 12$ on A 4 = = $3 What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • 2 equivalentways to considerpayment rule • refund + share of B • share of total 

24. What is a pari-mutuel market? • Before outcome is revealed, “odds” are reported, or the amount you would win per dollar if the betting ended now • Horse A: $1.2 for $1; Horse B: $25 for $1; … etc. • Strong incentive to wait • payoff determined by final odds; every $ is same • Should wait for best info on outcome, odds •  No continuous information aggregation •  No notion of “buy low, sell high” ; no cash-out

25. Running comparison

26. Dynamic pari-mutuel marketBasic idea • Standard PM: Every $1 bet is the same • DPM: Value of each $1 bet varies depending on the status of wagering at the time of the bet • Encode dynamic value with a price • price is $ to buy 1 share of payoff • price of A is lower when less is bet on A • as shares are bought, price rises; price is for an infinitesimal share; cost is integral

27. Dynamic pari-mutuel marketExample Interface A B A B • Outcomes: A B • Current payoff/shr: $5.20 $0.97 $3.27 $3.27 $3.27 $3.27 $3.27 $3.27 $3.25 sell 100@ $0.85 sell 100@ market maker traders sell 100@ sell 100@ $3.00 $0.75 $1.50 $0.50 sell 35@ sell 3@ $1.25 $0.25 buy 4@ buy 200@ buy 52@ $1.00

28. Dynamic pari-mutuel marketSetup & Notation A B A B • Two outcomes: A B • Price per share: pri1 pri2 • Payoff per share: Pay1 Pay2 • Money wagered: Mon1 Mon2 (Tot=Mon1+Mon2) • # shares bought: Num1 Num2

29. How are prices set? • A price function pri(n) gives the instantaneous price of an infinitesimal additional share beyond the nth • Cost of buying n shares: • Different assumptions lead to different price functions, each reasonable

30. Redistribution rule • Two alternatives • Losing money redistributed. Winners get: original money refunded + equal share of losers’ money • All money redistributed. Winners get equal share of all money • For standard PM, they’re equivalent • For DPM, they’re significantly different

31. ! Losing money redistributed • Payoffs: Pay1=Mon2/Num1 Pay2=. • Trader’s exp pay/shr for e shares: Pr(A) E[Pay1|A] + (1-Pr(A)) (-pri1) • Assume: E[Pay1|A]=Pay1 Pr(A) Pay1 + (1-Pr(A)) (-pri1)

32. Market probability • Market probability MPr(A) • Probability at which the expected value of buying a share of A is zero • “Market’s” opinion of the probability • MPr(A) = pri1 / (pri1 + Pay1)

33. Price function I • Suppose: pri1 = Pay2 pri2=Pay1natural, reasonable, reduces dimens., supports random walk hypothesis • Implies MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2

34. Deriving the price function • Solve the differential equationdm/dn = pri1(n) = Pay2 = (Mon1+m)/Num2where m is dollars spent on n shares • cost1(n) = m(n) = Mon1[en/Num2-1] • pri1(n) = dm/dn = Mon1/Num2 en/Num2

35. Interface issues • In practice, traders may find costs as the sol. to an integral cumbersome • Market maker can place a series of discrete ask orders on the queue, e.g. • sell 100 @ cost(100)/100 • sell 100 @ [cost(200)-cost(100)]/100 • sell 100 @ [cost(300)-cost(200)]/100 • ...

36. Price function II • Suppose: pri1/pri2 = Mon1/Mon2also natural, reasonable • Implies MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2

37. Deriving the price function • First solve for instantaneous pricepri1=Mon1/Num1 Num2 • Solve the differential equationdm/dn = pri1(n) = Mon1+m(Num1+n)Num2 cost1(n) = m = pri1(n) = dm/dn =

38. All money redistributed • Payoffs: Pay1=Tot/Num1 Pay2=. • Trader’s expected pay/shr for e shares:Pr(A) (Pay1-pri1) + (1-Pr(A)) (-pri1) • Market probabilityMPr(A) = pri1 / Pay1

39. Price function III • Suppose: pri1/pri2 = Mon1/Mon2 • Implies • MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2 • pri1(m) = cost1(m) =

40. Aftermarkets • A key advantage of DPM is the ability to cash out to lock gains / limit losses • Accomplished through aftermarkets • All money redistributed: A share is a share is a share. Traders simply place ask orders on the same queue as the market maker

41. Aftermarkets • Losing money redistributed: Each share is different. Composed of: • Original price refundedpriI(A)where I(A) is indicator fn • PayoffPayI(A)

42. Aftermarkets • Can sell two parts in two aftermarkets • The two aftermarkets can be automatically bundled, hiding the complexity from traders • New buyer buys priI(A)+PayI(A) for pri dollars • Seller of priI(A) gets $ priMPr(A) • Seller of PayI(A) gets $ pri(1-MPr(A))

43. Alternative “psuedo” aftermarket • E.g. trader bought 1 share for $5 • Suppose price moves from $5 to $10 • Trader can sell 1/2 share for $5 • Retains 1/2 share w/ non-negative value, positive expected value • Suppose price moves from $5 to $2 • Trader can sell share for $2 • Retains $3I(A) ; limits loss to $3 or $0

44. Running comparison [Hanson 2002]

45. Pros & cons of DPM types

46. Pros & cons of DPMs generally • Pros • No risk to mechanism • Infinite (buying) liquidity • Dynamic pricing / information aggregationAbility to cash out • Cons • Payoff vector indeterminate at time of bet • More complex interface, strategies • One sided liquidity (though can “hedge-sell”) • Untested

47. Open questions / problems • Is E[Pay1|A]=Pay1 reasonable? Derivable from eff market assumptions? • DPM call market • Combinatorial DPM • Empirical testingWhat dist rule & price fn are “best”? • >2 discrete outcomes (trivial?)Real-valued outcomes