Market Microstructure Bid-Ask Spreads and PIN Daniel Sungyeon Kim

Bid-Ask spread The bid-ask spread can be decomposed into what two components? Adverse selection component Transaction cost component

Four-way Decomposition of the spread Adverse selection component Transaction cost component can be further decomposed into three pieces: Inventory risk component – compensates dealers for bearing price risk their inventory Order processing cost component – compensates dealers for their normal cost of doing business Monopoly profits component – extra profits that can be extracted by monopoly power

Four-way Decomposition of the spread Recent estimate by Henker and Martens: Adverse selection = 15% of spread = 1.0 cents Inventory risk = 17% of spread = 1.2 cents Order processing = 65% of spread = 4.5 cents Monopoly profits = 3% of spread = 0.2 cents Total spread = 6.9 cents

Explanations for Adverse Selection Comp. What are the two explanations for adverse selection component? Information perspective Accounting perspective

Figure 14-1 Ask0 = V0 + (1/2) Adv Selection + (1/2) Transaction Cost Bid0 = V0 – (1/2) Adv Selection – (1/2) Transaction Cost Figure directly shows information perspective: If buy trade, value increases from If sell trade, value decreases from

Figure 14-2 Suppose there is a buy trade, value increases from This becomes the new midpoint: Ask1 = V1 + (1/2) Adv Selection + (1/2) Transaction Cost Bid1 = V1 – (1/2) Adv Selection – (1/2) Transaction Cost If next trade = buy, value increases from If next trade = sell, value decreases from Change in value = V1 –V0 = (1/2) Adv Selection Adverse Selection = Permanent Component of the spread Vs. Transaction Cost=Transitory Component of the spread That is, Ask0 - went away  did not become part of change in value If the market is Efficient = reflects all available info, then value changes are unpredictable = Random Walk

“Most Important Lesson in this Book for Most Readers” Uninformed traders lose to informed trader regardless of whether they use a limit order or market order Example: Ask = 30.10, Bid = 30.00, informed have good news that stock is worth 35.00 (1) Uninformed submits limit sell at 30.10  informed buys at 30.10, price rises to 35.00  uninformed sold at 30.10 & missed price rise (2) Uninformed submits limit buy at 30.00 informed submits limit buy at 30.01 (or buys at 30.10) price rises to 35.00 uninformed limit buy doesn’t execute & misses price rise (3) Uninformed submits market buy or market sell  pays the spread, which is wider due to adv select comp

Easley, Keifer, O’Hara, and Paperman Develop a simple, classic model of adverse selection Can estimate how much informed trading in any stock  PIN = Probability of INformed trade = % of traders that are informed

PIN Computation Chance of Informed Sell = Chance of Informed Buy = Chance of Informed Trade = Chance of Uninformed Trade= PIN = % of traders that are informed

A PIN example Day Buys Sells 1 53 49 2 74 51 3 48 78 4 50 Best guess of α? Two events out of four trading days = 0.50. Best guess of δ? One good event, one bad event; 0.50 Best guess of ε? 50 Best guess of μ? 25 Best guess of PIN? .5x50 / (.5x50 + 2x50) = 25 / 125 = 20%

PIN Model Dynamics Some traders are informed and others are uninformed Trading is anonymous  Market makers don’t know which trader is informed vs. uninformed  Every trade causes a price reaction Every sell causes a lower bid and ask Every buy causes a higher bid and ask

= PIN

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