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Y!RL Spot Workshop on New 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.

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y rl spot workshop on new markets new economics
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
distinguished guests thanks
Distinguished guests (thanks!)
  • Edward CastronovaProf. Economics, Cal State Fullerton
  • John LedyardProf. Econ & Social Sciences, CalTech
  • Justin WolfersProf. Economics, Stanford

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

a dynamic pari mutuel market for hedging wagering and information aggregation

A Dynamic Pari-Mutuel Market for Hedging, Wagering, and Information Aggregation

David M. Pennock

paper to appear EC’04, New York

economic mechanisms for speculating hedging
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
take home message
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
  • 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
what is a financial prediction market

 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?

real time forecasts
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
the flip side of prediction hedging e g options futures insurance
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, ...
continuous double auction cda
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



cda with market maker
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



  • 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
what is a pari mutuel market



What is a pari-mutuel market?
  • E.g. horse racetrack style wagering
  • Two outcomes: A B
  • Wagers:
what is a pari mutuel market21
What is a pari-mutuel market?



  • E.g. horse racetrack style wagering
  • Two outcomes: A B
  • Wagers:

what is a pari mutuel market22
What is a pari-mutuel market?



  • E.g. horse racetrack style wagering
  • Two outcomes: A B
  • Wagers:

what is a pari mutuel market23

$ on B 8$ on A 4

1+ = 1+ =$3

total $ 12$ on A 4

= = $3

What is a pari-mutuel market?



  • E.g. horse racetrack style wagering
  • Two outcomes: A B
  • 2 equivalentways to considerpayment rule
    • refund + share of B
    • share of total

what is a pari mutuel market24
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
dynamic pari mutuel market basic idea
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
dynamic pari mutuel market example interface
Dynamic pari-mutuel marketExample Interface





  • Outcomes: A B
  • Current payoff/shr: $5.20 $0.97








sell 100@


sell 100@

market maker


sell 100@

sell 100@





sell 35@

sell 3@



buy 4@

buy 200@

buy 52@


dynamic pari mutuel market setup notation
Dynamic pari-mutuel marketSetup & Notation





  • 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
how are prices set
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
redistribution rule
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
losing money redistributed


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)
market probability
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)
price function i
Price function I
  • Suppose: pri1 = Pay2 pri2=Pay1natural, reasonable, reduces dimens., supports random walk hypothesis
  • Implies

MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2

deriving the price function
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
interface issues
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
    • ...
price function ii
Price function II
  • Suppose: pri1/pri2 = Mon1/Mon2also natural, reasonable
  • Implies

MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2

deriving the price function37
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 =

all money redistributed
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
price function iii
Price function III
  • Suppose: pri1/pri2 = Mon1/Mon2
  • Implies
    • MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2
    • pri1(m) = cost1(m) =
  • 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
  • Losing money redistributed: Each share is different. Composed of:
    • Original price refundedpriI(A)where I(A) is indicator fn
    • PayoffPayI(A)
  • 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))
alternative psuedo aftermarket
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
running comparison44
Running comparison

[Hanson 2002]

pros cons of dpms generally
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
open questions problems
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