hard · Market Microstructure
A dealer quotes a bid-ask spread using the Glosten-Milgrom framework. The fraction of informed traders is μ, informed traders know the asset's true value V in V_L, V_H with equal priors, and uninformed traders buy or sell with equal probability. The dealer's quotes are set so each is the conditional expectation of V given the order's sign. Now the market maker learns that informed traders, due to a borrowing constraint, can only BUY on good news but cannot short on bad news.
Holding μ fixed, how does this asymmetry change the dealer's quotes relative to the symmetric case?
- The ask rises and the bid rises, because every buy now carries more adverse-selection weight while sells are purely uninformed and thus less informative about low value.
- The ask rises while the bid falls, since the constraint amplifies adverse selection symmetrically on both sides of the market regardless of trade direction.
- The ask falls and the bid rises, narrowing the spread because removing informed selling reduces the total quantity of private information the dealer faces.
- The ask is unchanged while the bid falls, because the constraint affects only the dealer's inference from sell orders and leaves buy-side learning intact.
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