Adverse Selection Model I - PowerPoint PPT Presentation

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Adverse Selection Model I

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Adverse Selection Model I A simple model Assumptions True value (v) follows a uniform distribution over [-1, 1]. Everybody knows the distribution, but the informed ... – PowerPoint PPT presentation

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Title: Adverse Selection Model I


1
Adverse Selection Model I
  • A simple model

2
Assumptions
  • True value (v) follows a uniform distribution
    over -1, 1.
  • Everybody knows the distribution, but the
    informed trade knows the actual v also.
  • There are N traders, of which ZN are informed
    traders and (1 Z)N are uninformed traders.
  • The market maker (MM) sets the ask price (spread)
    (S) to break even.

3
Price-Setting by Market Maker
  • To liquidity traders, MM sells at S where the
    expected value of v is still zero (i.e., no
    information is conveyed by liquidity trading). MM
    makes
  • S E(v) S 0 S per share.
  • Informed trades will buy only if v is greater
    than S. Thus the conditional expected value of
    v,
  • E(v/Buy) (S 1)/2.
  • Thus, to informed traders, MM loses
  • (S 1)/2 S (1 S)/2 per share.

4
Equilibrium
  • MM sets S to break even
  • Expected profit from liquidity traders Expected
    loss to informed traders
  • (I Z)NS ZN(1 S)/2
  • Hence the equilibrium spread S Z/(2 Z)
  • If Z 0, then S 0
  • If Z 1, then S 1
  • If Z 0.5, then S 1/3
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