Maximizing Information, Optimizing Risk, and Leveraging Forecasts in Securities Markets

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Maximizing Information, Optimizing Risk, and
Leveraging Forecasts in Securities Markets

• David M. PennockNEC Research Institute

Contributors Michael P. Wellman, University
of Michigan Steve Lawrence, NEC Research
Institute C. Lee Giles, Pennsylvania State
University
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Securities marketsstocks, options, futures,
insurance, ..., sports bets, ...

• Allocate risk
• insured transfers risk to insurer, for
• farmer transfers risk to futures speculators
• put option buyer hedges against stock drop
  seller assumes risk
• sports bet may hedge against other stakes in
  outcome

• 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

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Example IEM
http//www.biz.uiowa.edu/iem
1 if Hillary Clinton wins
1 if Rick Lazio wins
1 if Rudy Giuliani wins
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Talk overview

• (1) Compact securities markets
• (2) Web market games

• Maximizing Information
• Optimizing Risk
• Leveragingforecasts

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Talk overview

• (1) Compact securities markets
• (2) Web market games

• Maximizing Information
• Optimizing Risk
• Leveragingforecasts

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Classical theoryAtomic securities

• Events
• e.g house floods 100ltNEClt110 Bush wins
• Security
• pays off 1 if E1 occurs, nothing otherwise
• 1 iff flood iff 100ltNEClt110 iff Bush wins
• Conditional security
• pays off 1 if E1 E2 occur
• lose price paid if E1 E2 bet called off if
  E2
• 1 iff 100ltNEClt110 given that Bush wins

E2
E1
E3
1 if E1
1 if E1E2
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Classical theoryOptimal risk sharing maximal
information

• Requires ?-1 linearly indep securities, where ?
  E1?E2?E3? all world states
• Benefits
• Pareto optimal allocation of risk
• max info collective probability forecasts
  available for all ??? (state prices)
• Major practical hurdle
• ?2events intractable!

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Compact securities markets

• Classical complete market
• enough secs to span joint space of events
• Pareto optimal reallocation of risk
• market probabilities defined over full joint

• New compact market
• structured as a Bayesian network
• exponentially fewer securities may suffice
• still Pareto optimal
• market probabilities still defined over full
  joint
• P W, UAI 2000

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Compact securities markets Intuition
classical
Interestrate ?
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI
Dow avg ?
1 if YNDI
1 if YNDI
1 if YNDI
1 if YNDI

• Y is cond indep of D,I, given N(and everyone
  agrees, and more )

Nasdaq avg ?
Yahoo ?
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Extended exampleDrug development process

• Cost of one new drug to market 359M avg, up to
  500M
• 5 in 5000 drugs pass pre-clinical testing
• 1 in 5000 approved by FDA
• Huge risk

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Extended exampleDrug development process
1 if FDA approves drug X
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Extended exampleDrug development process
1 if drug passes pre-clinical testing
1 if drug passes Phase I testing pre
1 if drug passes Phase II testing PI
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if drug passes pre-clinical testing
1 if drug passes Phase I testing pre
1 if drug passes Phase II testing PI
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if drug passes pre-clinical testing
1 if drug passes Phase I testing pre
1 if drug passes Phase II testing PI
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if lab testing ?
1 if animal testing ?
1 if drug passes pre-clinical testing l, a
1 if drug passes Phase I testing pre
1 if drug passes Phase II testing PI
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if lab testing ?
1 if animal testing ?
1 if drug passes pre-clinical testing l, a
1 if safe in humans pre
1 if drug passes Phase I testing pre, safe
1 if drug passes Phase II testing PI
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if lab testing ?
1 if animal testing ?
1 if drug passes pre-clinical testing l, a
1 if safe in humans pre
1 if drug passes Phase I testing pre, safe
1 if effective in small trials PI
1 if drug passes Phase II testing PI, eff
1 if drug passes Phase III testing PII
1 if NDA approved PIII
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Extended exampleDrug development process
1 if lab testing ?
1 if animal testing ?
1 if drug passes pre-clinical testing l, a
1 if safe in humans pre
1 if drug passes Phase I testing pre, safe
1 if effective in small trials PI
1 if drug passes Phase II testing PI, eff
1 if safe effectivein large trials PII
1 if drug passes Phase III testing PII, se
1 if NDA approved PIII
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Extended exampleDrug development process
1 if lab testing ?
1 if animal testing ?
1 if drug passes pre-clinical testing l, a
1 if safe in humans pre
1 if drug passes Phase I testing pre, safe
1 if effective in small trials PI
1 if drug passes Phase II testing PI, eff
1 if safe effectivein large trials PII
1 if drug passes Phase III testing PII, se
1 if NDA approved PIII, IND
1 if IND approved life
compact 31 vs classical 639
1 if treats life-threatening illness
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Bayesian networks
Bayesiannetwork
DecomposableBayesian network
Pr(E6E3E5) Pr(E6E3E5) Pr(E6E3E5) Pr(E6E3E5)
(moralized, triangulated)
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Structured markets

• Securities markets can be structured analogously
  to a BN
• One (conditional) security for each CPT entry
• Fully connected BN ? complete market

E1
E2
E4
E5
E3
1 if E6E3E5
E6
Pr(E6E3E5) Pr(E6E3E5) Pr(E6E3E5) Pr(E6E3E5)
1 if E6E3E5
1 if E6E3E5
1 if E6E3E5
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Compact markets Take one

• Natural structure market according to
  unanimously agreed-upon independencies

E5
E4
E6
E1
E2
E3

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Example GLU

E1
E2
CIE1,Ø,E2
1 if E1
1000?
1 if E2
-800?
u(y) ln(y b) Generalized Logarithmic Utility
for money
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Risk-Neutral Probability

• Behavior is the product of Pr and u
• maxa ?? Pr(?) ? u(a, ?)
• An observer cannot determine Pr or u
• Agent A with Pr ? f(?) and u/f(?) is equivalent
  to agent A with Pr and u
• PrRN ? ? Pr u?
• uRN ??u/u?

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Risk-Neutral Probability

• A RN agent would buy if pltEgt lt Pr(E)
• Any agent would buy if pltEgt lt PrRN(E)
• Any agent would sell if pltEgt gt PrRN(E)
• If PriRN(E) ? PrjRN(E) then i and j would desire
  to trade
• At equilibrium, all agents risk-neutral
  probabilities agree, equal prices

1 if E
1 if E
1 if E
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Compact markets take twoRisk-neutral
independency markets

• Instead structure market according to agreed
  upon risk-neutral independencies
• If, in equil, all RN indep agree with market
  structure ? mkt is operationally complete
• Pareto optimal allocation of risk
• probabilities for all states (state prices)
  inferable
• But RN independencies change out of equilibrium
  perhaps more arguable basis for agreement on true
  independencies

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Example CARA

E1
E2
CIE1,Ø,E2
1 if E1
1000?
1 if E2
-800?
u(y) -e-cy Constant Absolute Risk Aversion
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Example CARA

1 if E2E1
1 if E3E2
1 if E1
u(y) -e-cy Constant Absolute Risk Aversion
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Example CARA

1 if E3E1E2
1 if E2
1 if E1
u(y) -e-cy Constant Absolute Risk Aversion
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Example CARA

1 if E6E3E5
moralized,triangulated graph
1 if E5E3E4

u(y) -e-cy Constant Absolute Risk Aversion
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Compact marketsTake three Independency markets

• CARA Markov indep ? risk-neutral indep
• If all agents have CARA, then market structured
  as TRIANGULATE?ni1 MORALIZE(Di) is op complete
• Can yield exponential savings
• This example 19 vs. 63

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Inherent limitations

• CARA, non-Markov structure ? not op complete
• GLU, Markov structure ? not op complete
• Impossibility theorems severely restrict
  independence preserving functionsGenest
  Wagner 86Pennock and Wellman UAI-99
• Market aggregation function subject to same
• Structured markets may yield approximately
  optimal allocations in more general settings

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Computational complexityarbitrage

• If redundant securities are inconsistently
  priced, arbitrage is possible
• In a risk-neutral independency market, correct
  prices of redundant securities are computable
  given other prices and market structure
• Correct pricing ? Bayesian inference
• P-complete

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Compact markets summary

• Under certain conditions, structured markets are
  optimal, with exponentially fewer securities than
  would otherwise be required
• Applications new derivatives markets that allow
  agents to hedge more of their risks, w/o combin.
  explosion of fin. instruments
• drug development
• energy
• financials, etc

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Talk Overview

• Maximizing Information
• Optimizing Risk
• Leveragingforecasts

• (1) Compact securities markets
• (2) Web market games

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Example IEM
http//www.biz.uiowa.edu/iem
1 if Hillary Clinton wins
1 if Rick Lazio wins
1 if Rudy Giuliani wins
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Play-money market gamesHollywood Stock Exchange
http//www.hsx.com/
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Play-money market gamesForesight Exchange
http//www.ideosphere.com/
1 iff Cancer curedby 2010
Canada breaks upby 2020
Machine Go championby 2020
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EfficiencyHollywood Stock Exchange

• Prices of movie stocks and options adhere to
  put-call parity, as in real markets
• Arbitrage loopholes disappear over time, as in
  real markets

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EfficiencyIowa electronic market

• Qualitatively similar to HSX, though
  quantitatively more efficient

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Information incorporationHollywood Stock Exchange

• Market probabilities can be evaluated according
  to log score compared w experts
• Log score - surprise in info-theoretic sense
• Can be considered info rate in bits

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Information incorporationIowa electronic market

• Qualitatively similar to HSX

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Forecast accuracyHSX movie box office predictions

• 0.94 correlation
• Comparable to expert forecasts at Box Office Mojo

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Probabilistic forecastsEntertainment awards

• Bins of similarly-priced options
• Observed frequency? average price
• Analysis similar for horse racing markets
• Error bars 95 confidence intervals assuming
  events are indep Bernoulli trials

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Probabilistic forecastsFX science and
technology outcomes

• Prices 30 days before expiration
• Similar results
• 60 days before
• specific date

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Market games summary

• Market games are easier to set up(few
  regulations)
• Web market games popular and growing
• Q Are incentives strong enough?A Yes (to a
  degree)
• Even play-money markets can hold valuable
  information
• http//artificialmarkets.com
• Science 291 987-988, February 9 2001
• KDD 2001

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Applications

• Harvest information from existing games
• Build new games in areas of interest
• Otherwise difficult economic experiments
• Use game data as baseline boost with proprietary
  data and algorithms for improved predictions
• box office prediction(market chat, news,
  experts, web, ...)
• weather forecasting(futures, derivatives
  experts, satellite images,...)

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Homepage

• http//www.neci.nec.com/homepages/dpennock