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dyck/files/File/Toronto Dealer Markets Empirical.ppt

  1. 1. Empirical Market Microstructure Rotman School Distinguished Lecture Series March 2008 Ingrid M. Werner Martin and Andrew Murrer Professor of Finance Fisher College of Business, The Ohio State University
  2. 2. Empirical tests of MM models <ul><li>Dealer markets </li></ul><ul><ul><li>Theory of Dealer Markets </li></ul></ul><ul><ul><li>Cross-sectional spreads </li></ul></ul><ul><ul><li>Inventory management </li></ul></ul><ul><ul><li>Interdealer trading </li></ul></ul><ul><li>Asymmetric Information/Strategic Trading </li></ul><ul><ul><li>Transaction Costs </li></ul></ul><ul><ul><li>Intraday patterns </li></ul></ul><ul><li>Spread decomposition </li></ul><ul><ul><li>Order processing </li></ul></ul><ul><ul><li>Inventory </li></ul></ul><ul><ul><li>Asymmetric information </li></ul></ul><ul><li>Price process </li></ul>
  3. 3. The Inventory Control Hypothesis <ul><li>Objective: </li></ul><ul><ul><li>To understand how market prices arise given the nature of order flow and the market-clearing protocol. </li></ul></ul><ul><li>Focus: </li></ul><ul><ul><li>The “liquidity provider” </li></ul></ul><ul><ul><ul><li>Specialist </li></ul></ul></ul><ul><ul><ul><li>Dealer </li></ul></ul></ul><ul><ul><ul><li>Market Maker (MM) </li></ul></ul></ul>
  4. 4. Garman (1976) Bankruptcy Risk <ul><li>Can a market maker who posts bid and ask prices and faces random asynchronous arrival of buy and sell orders avoid bankruptcy? </li></ul><ul><li>That is, can he/she avoid running out of cash and/or stock? </li></ul><ul><li>How should he/she set bid and ask prices to maximize the chances of avoiding bankruptcy? </li></ul><ul><li>Gambler’s ruin problem… </li></ul><ul><li>Key insight: A positive spread is necessary to avoid going bankrupt with probability one </li></ul>
  5. 5. Garman (1976) Bankruptcy Risk <ul><li>Key assumptions </li></ul><ul><ul><li>Single risk-neutral monopolistic dealer </li></ul></ul><ul><ul><ul><li>sets the bid price, p b , and ask price, p a (only once) </li></ul></ul></ul><ul><ul><ul><li>receives orders </li></ul></ul></ul><ul><ul><ul><li>clears trades </li></ul></ul></ul><ul><ul><ul><li>holds stock and cash </li></ul></ul></ul><ul><ul><li>Maximizes expected profits, tries to avoid bankruptcy </li></ul></ul><ul><ul><li>Order-arrival processes </li></ul></ul><ul><ul><ul><li>± o ne unit of stock </li></ul></ul></ul><ul><ul><ul><li>Poisson arrivals </li></ul></ul></ul><ul><ul><ul><ul><li>Sells ( λ a (p a ), λ ’ a (p a ) ≤ 0) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Buys ( λ b (p b ), λ ’ b (p b ) ≥ 0) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Waiting time between order arrivals is exponentially distributed </li></ul></ul></ul></ul><ul><ul><ul><li>Buy and sell orders are driven by independent processes </li></ul></ul></ul><ul><ul><ul><ul><li>No herding or information driven trading </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Black-box, only depends on price, p </li></ul></ul></ul></ul>
  6. 6. Garman (1976) Bankruptcy Risk <ul><li>Key insights </li></ul><ul><ul><li>Order arrivals will affect both the inventory of stock and cash </li></ul></ul><ul><ul><ul><li>Let I c (0) be the initial inventory of cash and I s (0) be the inventory of stock. </li></ul></ul></ul><ul><ul><ul><li>Let R(t) (Q(t)) be the probability that the dealer will run out of stock (cash). </li></ul></ul></ul><ul><ul><li>Note that p a > p b is required for λ a p a > λ b p b and λ a < λ b to hold </li></ul></ul><ul><ul><li>The dealer has to post a positive spread to avoid failure with probability equals one. </li></ul></ul><ul><ul><li>No matter what prices the dealer sets, he will fail with probability > 0. </li></ul></ul>
  7. 7. Garman (1976) Bankruptcy Risk <ul><li>How are prices set? </li></ul><ul><ul><li>Raise ask and buy orders slow down </li></ul></ul><ul><ul><li>Raise bid and sell orders arrive more rapidly </li></ul></ul><ul><ul><li>To achieve zero-drift in inventories of cash and stock, the dealer needs to set prices such that arrival rates are equated </li></ul></ul><ul><ul><li>Λ a (p e )= λ b (p e )= λ e => profits = 0 </li></ul></ul><ul><ul><li>λ a = λ b = λ * => profits > 0 </li></ul></ul><ul><li>Shortcomings </li></ul><ul><ul><li>Dealer cannot change prices over time </li></ul></ul><ul><ul><li>No link between prices and the inventory position of the dealer </li></ul></ul>λ * p a p b λ b (p b ) λ a (p a ) Dealer seeks to maximize shaded area… Arrival rate λ e p e
  8. 8. Amihud and Mendelson (1980) Inventory Management <ul><li>Generalizes Garman (1976) by modeling a profit maximizing, risk neutral monopolistic dealer who changes prices over time . </li></ul><ul><li>Punt on the bankruptcy problem by assuming that inventory, I, is finite and bounded from below I in (-K, L), L < ∞ . </li></ul><ul><li>Translate the Poisson arrival process of Garman (1976) into a “birth and death” process </li></ul><ul><li>This is a semi-Markov decision process where the state variable is the inventory of stock, I j , at hand. </li></ul><ul><li>The decisions are to set bid, p b (I j ), and ask, p a (I j ), prices. </li></ul><ul><li>Dealer controls the arrival rates directly as a function of the state variable, I j . </li></ul><ul><li>Key insights: A positive spread arises due to dealer market power. Market prices will fluctuate in part due to dealer inventory control. </li></ul>
  9. 9. Amihud and Mendelson (1980) Inventory Management <ul><li>Optimal bid and ask prices are monotone decreasing functions of the dealer’s inventory position </li></ul><ul><li>The dealer has a preferred inventory position, -K < I* < L </li></ul><ul><ul><li>The preferred inventory position is a function of the variability of order arrival rates (cushion) </li></ul></ul><ul><li>Positive spread arises because of market power </li></ul><ul><ul><li>The spread is increasing in the distance between the dealers current inventory and his desired inventory </li></ul></ul><ul><ul><li>The mid-quote is not always equal to the true value of the stock! </li></ul></ul><ul><ul><li>The spread is wider than the spread that the Garman specialist would set. </li></ul></ul><ul><li>Competition would drive this spread to zero </li></ul><ul><li>Empirically testable predictions: Market prices will fluctuate in part because of inventory control Price effects of inventory imbalances are transient </li></ul>B 1 B 2 A 2 A 1 I 1 > I 2
  10. 10. Amihud and Mendelson (1980) Inventory Management I* Inventory level p a p a p b p b Δ Δ
  11. 11. Stoll (1978) Inventory Risk <ul><li>Dealer as a supplier of immediacy. </li></ul><ul><li>Dealers are regular risk-averse traders . </li></ul><ul><li>A dealer is a trader who voluntarily alters his portfolio away from the optimal portfolio to accommodate other traders’ demands. </li></ul><ul><li>Dealers require compensation for doing so. </li></ul><ul><li>The compensation for risk is the bid-ask spread. </li></ul><ul><li>Earlier work modeled risk-neutral traders (Amihud and Mendelson (1980) and Garman (1976)) and the spread was the result of monopoly power. </li></ul><ul><li>Key insight: The spread is compensation for the risk the dealer takes on by tilting his portfolio away from the optimal portfolio </li></ul>
  12. 12. Stoll (1978) Inventory Risk <ul><li>Costs for providing immediacy </li></ul><ul><ul><li>Holding costs associated with suboptimal portfolio. </li></ul></ul><ul><ul><li>Order-processing costs. </li></ul></ul><ul><ul><li>Asymmetric information costs. </li></ul></ul><ul><li>Dealer is assumed to have exogenous beliefs about the true price of the asset, and its true rate of return. </li></ul><ul><li>Returns are normally distributed. </li></ul><ul><li>Utility is negative exponential => CARA </li></ul><ul><li>Dealer maximized terminal wealth. </li></ul><ul><li>Sets prices for one transaction (buy or sell). </li></ul><ul><li>Inventory is financed by borrowing/lending at the risk-free rate. </li></ul><ul><li>Market for supplying liquidity services is competitive . </li></ul>
  13. 13. Stoll (1978) Inventory Risk <ul><li>Let Q i be the true value of a trade in stock i and C i be the present dollar cost to the dealer of trading Q i </li></ul><ul><li>Expanding both sides (Taylor series expansion), dropping terms of order higher than two, setting R f = 0, and simplifying the resulting expression for the cost to the dealer of trading per unit of Q is </li></ul>
  14. 14. Stoll (1978) Inventory Risk <ul><li>Where z is the dealer’s coefficient of relative risk aversion, Q p is the true dollar value of the dealer’s optimal inventory, σ ip is the covariance between the rate of return on stock i and the optimal portfolio and σ i 2 is the variance of stock i’s return. </li></ul><ul><li>So, the cost function depends on: </li></ul><ul><ul><li>Dealer wealth and risk preferences </li></ul></ul><ul><ul><li>The level of the dealer’s “optimal” inventory </li></ul></ul><ul><ul><li>The size of the trade in stock i </li></ul></ul><ul><ul><li>The variance of the stock and its covariance with the dealer’s “optimal” inventory. </li></ul></ul>
  15. 15. Stoll (1978) Inventory Risk <ul><li>If the dealer quotes symmetric quantities on the bid and the offer, Q i , it is easy to show that the spread relative to the true price will be </li></ul><ul><li>The spread is thus linear in trade size. </li></ul><ul><li>The dealer’s inventory will affect where the bid and ask prices are placed, but not the spread. </li></ul><ul><li>Empirically testable prediction: Spread is linearly increasing in trade size and in the volatility of the stock </li></ul>
  16. 16. Ho and Stoll (1981) Dynamic Model… <ul><li>Extends the intuition of Stoll (1978) to a multi-period framework in which both order flow (Poisson) and returns are stochastic. </li></ul><ul><li>Dealers are risk-averse and maximize utility of terminal wealth. </li></ul><ul><li>Model is solved using finite horizon dynamic programming to characterize the dealer’s optimal pricing policy. </li></ul><ul><li>Characteristics of the solution: </li></ul><ul><ul><li>The spread includes an adjustment for risk that depends on dealer risk aversion, the size of the transaction, and the risk of the stock. </li></ul></ul><ul><ul><ul><li>Transactions uncertainty per se does not affect the spread. </li></ul></ul></ul><ul><ul><ul><li>In the limit there is only a risk-neutral (monopoly) spread. </li></ul></ul></ul><ul><ul><li>Dealer’s optimal pricing depends on the time horizon (dealer becomes less risk averse over time). </li></ul></ul><ul><ul><li>The spread is independent of the inventory level. </li></ul></ul><ul><li>Key insight: The spread arises due to market power plus an adjustment for inventory risk plus an adjustment for the risk from a suboptimal asset allocation. </li></ul>
  17. 17. Ho and Stoll (1983) Multiple Dealers <ul><li>How do dealers decide on optimal prices in a setting with competition (e.g., Nasdaq, Forex, OTC markets)? </li></ul><ul><li>Extension of Ho and Stoll (1981) to a setting with multiple competitive dealers that can trade with the public as well as with each other (interdealer trading). </li></ul><ul><li>Public orders go to dealer with the best price, and are randomly allocated if several dealers quote the best price. </li></ul><ul><li>The order size is fixed. </li></ul><ul><li>Dealer wealth and inventories are public information. </li></ul><ul><li>Inventory is more risky than if the dealer had an exclusive franchise. </li></ul><ul><li>Each dealer’s strategy depends on the strategies of all other dealers. Need symmetry to facilitate solution. </li></ul><ul><li>Key insight (English auction): Optimal strategy is for the dealer who is the most eager to sell (buy) to place his ask ε above (bid ε below) the second most eager dealer to sell (buy). The market spread depends on risk aversion, order size, and riskiness of the stock and on the distribution of inventories. </li></ul>
  18. 18. Ho and Stoll (1983) Multiple Dealers <ul><li>As in previous models, the inventory will play a key role. </li></ul><ul><li>Inventories dictate the reservation values for each dealer, i.e., they determine the prices (p a =1+a r , p b =1-b r ) at which the dealer is indifferent between trading and not trading. </li></ul><ul><li>Since inventories are public information, everyone knows each others’ reservation values. </li></ul><ul><li>It is possible to order dealers in terms of their eagerness to buy (lowest inventory) and to sell (highest inventory). </li></ul>
  19. 19. Ho and Stoll (1983) Multiple Dealers <ul><li>It is not necessarily optimal to quote reservation values. </li></ul><ul><li>Suppose we order inventory levels (public information) from the lowest to the highest: I 1 < I 2 < … < I N-1 < I N </li></ul><ul><li>It follows from our reservation quotes: b 1 < b 2 < … < b N-1 < b N a N < a N-1 < … < a 2 < a 1 </li></ul>1+a 1 1+a N 1+a N-1 1+a 2 1-b 1 1-b 2 1-b N-1 1-b N 1-b 2 + ε 1+a N-1 - ε Dealer one shades his bid by b 2 -b 1 - ε Dealer N shades her ask by a N-1 -a N - ε If you are the marginal dealer on either side, set prices ε away from the reservation quotes of the second most desperate dealer..
  20. 20. Ho and Stoll (1983) Multiple Dealers <ul><li>There is no guarantee that the optimal policy we just derived will result in a market ask price that exceeds the bid! </li></ul><ul><li>It depends on the support of the inventory distribution, and on the other parameters (A, σ 2 , Q) </li></ul><ul><li>Introduce a round of interdealer trading prior to customer order arrival… </li></ul>1+a 1 1+a N 1+a N-1 1+a 2 1-b 1 1-b 2 1-b N-1 1-b N 1-b 2 + ε 1+a N-1 - ε Dealer one shades his bid by b 2 -b 1 - ε Dealer N shades her ask by a N-1 -a N - ε Absent interdealer trading, optimal spread would be negative, leaving room for arbitrage by customers...
  21. 21. Ho and Stoll (1983) Multiple Dealers <ul><li>Implications (Empirically testable): </li></ul><ul><ul><li>As long as there are more than 2 dealers, interdealer trading may occur. </li></ul></ul><ul><ul><li>Dealers will use interdealer trades to reduce some of the discrepancies in inventories by trading with each other. </li></ul></ul><ul><ul><li>They will then compete with each other for the arriving customer orders (second price auction) </li></ul></ul><ul><ul><li>Quotes will be less “spread” out in the public market than if we do not allow interdealer trading </li></ul></ul><ul><ul><li>Market spread is declining in the number of dealers </li></ul></ul><ul><li>Problems: </li></ul><ul><ul><li>The assumption of full transparency of inventories is unrealistic! </li></ul></ul><ul><ul><li>Dealers also need to know A, subjective σ 2 , etc </li></ul></ul><ul><ul><li>Model is static and order flow is naïve… </li></ul></ul>
  22. 22. Biais (1993) Incomplete Transparency/Fragmentation <ul><li>In practice, we cannot easily track dealer trades or when a particular dealer quotes get hit (fragmentation). </li></ul><ul><li>Can the model of Ho and Stoll (1983) be relaxed to deal with incomplete transparency? </li></ul><ul><li>How would dealers optimally set their quotes if they do not know each others’ inventories? </li></ul><ul><li>Biais (1993) assumes that dealers do not know each others’ inventories, but they do know the distribution from which each dealer’s inventory is drawn. </li></ul><ul><li>Quotes are “sealed-bid” Dutch auction… </li></ul><ul><li>Key insights: Dealers will act strategically and shade their prices. The spread is wider than under full transparency. Competition will reduce the “room” for strategic behavior => spreads narrow when there are more dealers. </li></ul>
  23. 23. Biais (1993) Incomplete Transparency/Fragmentation <ul><li>Game </li></ul><ul><ul><li>Traders decide whether or not to become a dealer </li></ul></ul><ul><ul><li>Dealers receive inventories I in [-R, R], iid </li></ul></ul><ul><ul><li>Market order arrives, B/S with equal probability, </li></ul></ul><ul><ul><li>Best quotes gets the order </li></ul></ul><ul><ul><li>Final value of the asset is realized </li></ul></ul><ul><li>Solution is by backwards induction </li></ul><ul><ul><li>Lucky for us, it starts with Ho and Stoll (1981, 1983) solution for reservation quotes. </li></ul></ul><ul><ul><li>Difference is that the dealer does not know the reservation values of his/her competitors (since inventories are not public information) </li></ul></ul><ul><ul><li>Dealer needs to figure out the probability that his ask (bid) price is lower (higher) than that of all other dealers (could get the trade) </li></ul></ul><ul><ul><li>Bayes-Nash equilibrium concept </li></ul></ul>
  24. 24. Biais (1993) Incomplete Transparency/Fragmentation <ul><li>Assume that the inventory distribution is uniform. </li></ul><ul><li>Optimal bid (1-b i ) and ask (1+a i ) quotes are: </li></ul>-R R 1/2R I i 0 I’ i Dealer will post an ask price as if his inventory is I’ i < I i (I i -(-R)) divided by N determines shading… Dealers shade their quotes Shading is increasing in A, σ 2 , R Shading is decreasing in the number of dealers… Dealer spreads are decreasing in the number of dealers
  25. 25. Empirical Predictions: Inventories <ul><li>Predictions from theory: </li></ul><ul><ul><li>Arrival rate of orders is price elastic </li></ul></ul><ul><ul><li>Quotes should reflect inventory position of dealers. </li></ul></ul><ul><ul><li>The rate at which dealer trade inventory imbalances depends on </li></ul></ul><ul><ul><ul><li>risk aversion </li></ul></ul></ul><ul><ul><ul><li>the number of dealers </li></ul></ul></ul><ul><ul><ul><li>risk of the stock </li></ul></ul></ul><ul><ul><ul><li>time </li></ul></ul></ul><ul><ul><li>There is a target inventory level and spreads widen as we move away from this target inventory level. </li></ul></ul><ul><ul><li>The market spread should be increasing in the size of the customer trade </li></ul></ul><ul><ul><li>The market spread should be increasing in the volatility of the stock </li></ul></ul><ul><ul><li>The market spread should be decreasing in the number of dealers </li></ul></ul>
  26. 26. Stoll (1978) Cost of Trading on Nasdaq <ul><li>Sample of 2,508 stocks for 6 trading days… </li></ul><ul><ul><li>Median # dealers is 5 </li></ul></ul><ul><ul><li>Median % spread is 3-4 % </li></ul></ul><ul><li>The number of dealers is increasing in liquidity </li></ul><ul><li>Not all registered dealers are actively trading </li></ul><ul><li>Empirical model for % spreads (log-linear) </li></ul><ul><li>Spreads are declining in #dealers and liquidity! </li></ul><ul><li>Spreads are increasing in proxy for adverse selection! </li></ul>%spread Wealth Risk Volume Risk-aversion Turnover #Dealers Order Processing Costs Avg. daily inventory change Concentration ratio CAPM MM Residual
  27. 27. Stoll (1976) Nasdaq Dealer Inventory <ul><li>Start with our model of dealer spreads (Ho and Stoll (1978)) </li></ul><ul><li>Add order processing and information costs (ad hoq) </li></ul><ul><li>Assume a lot of symmetry and perfect competition </li></ul><ul><li>Let Δ Q be the change in aggregate inventory ( proxy: order imbalance ) </li></ul><ul><li>Let P be the midquote and r the midquote return </li></ul><ul><li>Use data on 5 days for 2,052 stocks… </li></ul><0 Suggests passive inventory adjustment r>0 => Δ Q < 0 “ stabilizing” Dealers get taken by informed traders <0 Suggests mean Reversion => 8-10 days to reverse Q => Inventory risk…
  28. 28. Hasbrouck and Sofianos (1993) Trades of NYSE Specialists <ul><li>Inventory is sometimes negative (short positions) </li></ul><ul><li>There is no obvious drift or divergence </li></ul><ul><li>Patterns suggests rather tight inventory management </li></ul><ul><li>The mean inventory is near zero </li></ul><ul><li>Overnight positions are small: Dealers tend to go home flat </li></ul><ul><li>Liquid stock </li></ul><ul><li>Large market capitalization </li></ul>
  29. 29. Hasbrouck and Sofianos (1993) Trades of NYSE Specialists <ul><li>Discrete jump </li></ul><ul><ul><li>Offsetting position in other stock? Options/derivatives? </li></ul></ul><ul><ul><li>Overseas traded? </li></ul></ul><ul><ul><li>Illiquid stock </li></ul></ul><ul><ul><li>Small capitalization </li></ul></ul><ul><li>Wandering inventory </li></ul><ul><ul><li>Offsetting position in other stock? Options/derivatives? </li></ul></ul><ul><ul><li>Overseas traded? </li></ul></ul><ul><ul><li>Illiquid stock Small capitalization </li></ul></ul>
  30. 30. Hasbrouck and Sofianos (1993) Trades of NYSE Specialist <ul><li>Stationary? They have to be (at least mean reverting) … </li></ul><ul><ul><li>Noisy data </li></ul></ul><ul><ul><li>Misinterpreted </li></ul></ul><ul><ul><li>Horizon not long enough </li></ul></ul><ul><li>How fast do specialists get rid of inventory positions? Slow… </li></ul>
  31. 31. Madhavan and Sofianos (1993) Trades of NYSE Specialists <ul><li>Why is the mean reversion so slow? </li></ul><ul><ul><li>Measurement issues? </li></ul></ul><ul><ul><li>Study days with extreme price changes </li></ul></ul><ul><ul><ul><li>Evidence shows that specialists reverts large inventory shocks quickly </li></ul></ul></ul><ul><ul><ul><li>24/40 cases one day </li></ul></ul></ul><ul><ul><ul><li>36/49 cases by fourth day </li></ul></ul></ul><ul><ul><li>Hedging </li></ul></ul><ul><ul><ul><li>Evidence suggests not commonly used </li></ul></ul></ul><ul><ul><li>Correlated securities </li></ul></ul><ul><ul><ul><li>Correlation of inventories across stocks is on average positive for 41 out of the 50 specialists units </li></ul></ul></ul><ul><ul><li>Speculation </li></ul></ul><ul><ul><ul><li>Would mess up our estimates? </li></ul></ul></ul>
  32. 32. Hasbrouck and Sofianos (1993) Trades of NYSE Specialists <ul><li>Are NYSE specialists profitable? </li></ul><ul><ul><li>On average, profits are negative </li></ul></ul><ul><ul><ul><li>Short and medium term profits are positive </li></ul></ul></ul><ul><ul><ul><li>Long term profits are negative and very noisy </li></ul></ul></ul><ul><ul><li>Specialists make profits from the spread, but there is also some evidence of profitable speculation (informed trading) </li></ul></ul><ul><li>Prices, trades, and inventories </li></ul><ul><ul><li>Most of the quote dynamics are attributable to trades, with inventories contributing little explanatory power. </li></ul></ul><ul><ul><li>Positions are not managed by adjustment of publicly quoted bids and offers. </li></ul></ul><ul><li>But, how is then inventory management done? </li></ul><ul><ul><li>Selective nonpublic quoting </li></ul></ul><ul><ul><li>Interdealer trading </li></ul></ul><ul><ul><li>Market specific rules that allow dealers to participate in trades without publicly signaling through their quotes (NYSE). </li></ul></ul>
  33. 33. Madhavan and Smidt (1993) Inventories and Quotes of NYSE Specialists <ul><li>Develop a structural model to estimate </li></ul><ul><ul><li>Mean reversion of inventories, β </li></ul></ul><ul><ul><li>β = -1 implies inventories reversed in one day </li></ul></ul><ul><ul><li>Desired inventory level, I d </li></ul></ul><ul><li>Results </li></ul><ul><ul><li>β is negative and significant for 8 out of 16 stocks </li></ul></ul><ul><ul><li>β is on average -0.05 which implies a half life of 49 days (even slower than H&S (1993)) </li></ul></ul><ul><ul><li>Desired inventory is positive and significant for 12 out of 16 stocks! </li></ul></ul><ul><li>Bad news </li></ul><ul><ul><li>Structural model did not manage to eliminate the slow mean reversion… </li></ul></ul><ul><li>Allow for shifts in desired inventory </li></ul><ul><ul><li>β is negative and significant for 13 out of 16 stocks </li></ul></ul><ul><ul><li>β is on average -0.134 which implies a half life of 7.3 </li></ul></ul>
  34. 34. Madhavan and Smidt (1993) Quotes and Inventories of NYSE Specialists <ul><li>Half lives vary significantly across stocks. </li></ul><ul><li>Midquote-updates are modeled as a function of </li></ul><ul><ul><li>Shocks to order imbalances (+) </li></ul></ul><ul><ul><li>Inventory adjustment (-) </li></ul></ul><ul><ul><li>If there is a positive shock to (buy) order imbalances, midquotes increases => Information? </li></ul></ul><ul><ul><li>If inventory levels increase, midquotes decrease </li></ul></ul><ul><ul><li>Thus, M&S (1993) find a strong link between quotes and inventories </li></ul></ul>
  35. 35. Madhavan and Sofianos (1998) NYSE Specialist Trades <ul><li>How does dealer activity vary across stocks? </li></ul><ul><ul><li>Liquidity </li></ul></ul><ul><ul><li>Off-exchange competition </li></ul></ul><ul><ul><li>Tick size (tick/P high => more specialist trading?) </li></ul></ul><ul><ul><li>Specialist participation rate (SP) is defined as specialist purchases and sales, divided by total purchases and sales. </li></ul></ul><ul><ul><li>Level SP(Liquidity (-), Off-exchange competition (-), Tick/P (-), …) </li></ul></ul><ul><li>What affects specialist trading over time in an individual stock? </li></ul><ul><ul><li>Inventory </li></ul></ul><ul><ul><li>Spread </li></ul></ul><ul><ul><li>Trade size </li></ul></ul><ul><ul><li>Momentum </li></ul></ul><ul><ul><li>Signed SP(Inventory(-), Spread (-), Trade Size (+), Momentum (-), …) </li></ul></ul>
  36. 36. Madhavan and Sofianos (1998) NYSE Specialist Trades
  37. 37. Madhavan and Sofianos (1998) NYSE Specialist Trades
  38. 38. Hansch, Naik, and Viswanathan (1998) Dealer Inventories in London <ul><li>Study normalized inventories </li></ul><ul><li>Over 50% of large trades are taken by dealer with extreme inventory </li></ul><ul><li>Dealers posting at the BBO attract more than their expected share of order flow </li></ul><ul><li>There is a strong (?) link between quotes and inventories </li></ul>
  39. 39. Hansch, Naik, and Viswanathan (1998) Dealer Inventories in London <ul><li>Model mean reversion as a piece-wise linear regression </li></ul><ul><li>There is considerable variation in the speed of mean reversion depending on how extreme the position is in the first place. </li></ul><ul><li>Mean reversion is still relatively slow! </li></ul><ul><ul><li>One sigma shock </li></ul></ul><ul><ul><ul><li>Half-life 5 days (All) </li></ul></ul></ul><ul><ul><ul><li>Half-life 3.5 days (Non-ADR) </li></ul></ul></ul><ul><ul><li>Five sigma shock </li></ul></ul><ul><ul><ul><li>Half-life 1.3 days (All) </li></ul></ul></ul><ul><ul><ul><li>Half-life 1.2 days (Non-ADR) </li></ul></ul></ul><ul><li>Problems </li></ul><ul><ul><li>Variable transformation… </li></ul></ul><ul><ul><li>Pre-arranged trades… </li></ul></ul>
  40. 40. Reiss and Werner (1998) London Interdealer Trading
  41. 41. Reiss and Werner (1998) London Interdealer Trading
  42. 42. Reiss and Werner (1998) London Interdealer Trading <ul><li>Does risk-sharing motivate interdealer trading (Ho and Stoll (1983))? </li></ul><ul><ul><li>Methodology </li></ul></ul><ul><ul><li>Inventory cycles </li></ul></ul><ul><ul><li>Prepositioned/Anticipated trades </li></ul></ul><ul><li>ID trading represents roughly 25 percent of volume </li></ul><ul><li>Active inventory management compared to HN&V (1998) </li></ul><ul><ul><li>One (FTSE) to two days (non-FTSE) </li></ul></ul><ul><li>ID trading conforms to Ho and Stoll’s (1983) hypotheses </li></ul><ul><ul><li>ID are used to reduce inventory imbalances </li></ul></ul><ul><ul><li>Roughly 80% of ID trades are in the “unwinding” direction </li></ul></ul><ul><ul><li>Roughly 65% of ID trades have both dealers “unwinding” </li></ul></ul><ul><ul><li>Dealers in ID trades have extreme inventories </li></ul></ul><ul><li>Position taking is profitable, and profits are larger if customer trades are used to unwind the inventory </li></ul>
  43. 43. Additional Research on Dealer Inventories… <ul><li>Naik and Yadav (2003) study London dealers trading multiple stocks and find that dealers do not seem to take a portfolio approach to their risk exposure. </li></ul><ul><li>Lyons (1995) study one FOREX dealer and finds strong evidence of inventory control. </li></ul><ul><li>Manaster and Mann (1996) study futures markets and find patterns consistent with inventory control. </li></ul><ul><li>Chakravarty and Li (2003) study futures markets and find rapid mean reversion in the personal inventory of dual traders. </li></ul><ul><li>Kavajez and Odders-White (2001) study NYSE specialists and find no evidence that specialists revise their price schedules in response to changes in their inventory. </li></ul>
  44. 44. Inventory Empirics: Conclusion <ul><li>Spreads do seem to be consistent with models of dealer markets in the cross-section </li></ul><ul><li>Mean reversion of inventories seems surprisingly slow in many markets </li></ul><ul><li>Link between quotes and inventories is surprisingly weak </li></ul><ul><li>Why is dealer inventory management so difficult to measure? </li></ul><ul><ul><li>Dealers have complex objectives </li></ul></ul><ul><ul><li>Off-exchange trading </li></ul></ul><ul><ul><li>Order preferencing, payment for order flow, soft dollars, etc… </li></ul></ul>
  45. 45. Dealer Market References <ul><li>Theory </li></ul><ul><ul><li>O;Hara, M., 1995, Market Microstructure Theory , Chapter 2. </li></ul></ul><ul><ul><li>Hasbrouck, J., 2007, Empirical Market Microstructure, Chapter 11. </li></ul></ul><ul><ul><li>Amihud, Y., and H. Mendelson, 1980, Dealership markets: Market making with inventory, Journal of Financial Economics 8, 31-53. </li></ul></ul><ul><ul><li>Biais, B., 1993, Price formation and equilibrium liquidity in fragmented and centralized markets, Journal of Finance 48, 157-185. </li></ul></ul><ul><ul><li>Garman, M., 1976, Market microstructure, Journal of Financial Economics 3, 257-275. </li></ul></ul><ul><ul><li>Ho, T., and H. Stoll, 1981, Optimal dealer pricing under transactions and return uncertainty, Journal of Financial Economics 9. 47-73. </li></ul></ul><ul><ul><li>Ho, T., and H. Stoll, 1983, The dynamics of dealer markets under competition, Journal of Finance 38, 1053-1074. </li></ul></ul><ul><ul><li>O’Hara, M., and G. Oldfield, 1980, The microeconomics of market making, Journal of Financial and Quantitative Analysis 21, 361-376. </li></ul></ul><ul><ul><li>Stoll, H., 1978, The supply of dealer services in securities markets, Journal of Finance 33, 1133-1151. </li></ul></ul>
  46. 46. Dealer Market References <ul><li>Empirical </li></ul><ul><ul><li>Bacidore, J. and G. Sofianos, 2002, Liquidity provision and specialist trading in NYSE-listed non-U.S. stocks, Journal of Financial Economics 63, 133-158. </li></ul></ul><ul><ul><li>Hansch, O., Naik, N., and S. Viswanathan, 1998, Do inventories matter in dealership markets? Evidence from the London Stock Exchange, Journal of Finance 53, 1623-1656. </li></ul></ul><ul><ul><li>Hasbrouck, J., and G. Sofianos, 1993, The trades of market makers: An empirical analysis of NYSE specialists, Journal of Finance 48, 1565-1593. </li></ul></ul><ul><ul><li>Madhavan, A., and S. Smidt, 1993, An intraday analysis of daily changes in specialist inventories and quotations, Journal of Finance 48, 1595-1628. </li></ul></ul><ul><ul><li>Manaster, S., and S. Mann, 1996, Life in the pits: competitive market making and inventory control, Review of Financial Studies 6, 953-975. </li></ul></ul><ul><ul><li>Lyons, R., 1993, Test of microstructure hypotheses in the foreign exchange market, Journal of Financial Economics 39, 321-351. </li></ul></ul><ul><ul><li>Reiss, P., and I.M. Werner, 1998, Does risk sharing motivate interdealer trading? Journal of Finance 53, 1657-1703. </li></ul></ul><ul><ul><li>Stoll, H., 1976, Dealer inventory behavior: An empirical investigation of Nasdaq stocks, Journal of Financial and Quantitative Analysis 11, 359-380. </li></ul></ul>