Bid-Ask Spreads and Volume: The Role of Trade Timing

Transcription

1 Bid-Ask Spreads and Volume: The Role of Trade Timing Toronto, Northern Finance 2007 Andreas Park University of Toronto October 3, 2007 Andreas Park (UofT) The Timing of Trades October 3, / 25

2 Patterns in Financial Market Variables There are persistent patterns of key market variables: 1 Volume TSX, NYSE and Nasdaq: U- or reverse J-shaped. London Stock Exchange: reverse L-shaped, with two small humps, one in the morning and the other in the early afternoon. Taiwan and Singapore: reverse L-shaped. Japan: bum-shaped (word stolen from Vikas Mehrota). 2 Bid-ask-spreads NYSE: U-shape (early evidence), L-shape (after decimalization). Most other markets are L-shaped (Nasdaq, LSE, Taiwan, Singapore). 3 Volatility and returns also display persistent patterns. Thus far, there is no satisfactory theory that remotely explains these patterns. My claim: One of the most standard models of sequential trading would generate patterns once one allows strategic trade-timing. Andreas Park (UofT) The Timing of Trades October 3, / 25

3 Questions with Timing of Financial Market Trades People receive information of different quality. When will people trade? How does timing affect prices and bid-ask spreads? How does timing affect volume? How does timing affect volatility? Andreas Park (UofT) The Timing of Trades October 3, / 25

4 Results Compare two cases: 1 Strategic timing is allowed. 2 People act myopically ( now or never ). Analytical results: 1 Early movers have better/higher quality information with timing. 2 Bid-ask-spreads naturally decrease over time but timing spreads compared to myopic spreads are smaller early and larger later. 3 Price volatility is lower with timing. 4 Total volume is lower. Numerical Results: 1 With timing volume is low early and high late. Without timing it is the reverse. 2 Intertemporally, spreads are stable with timing but display a large drop without timing. 3 PIN (the probability of informed trading) is low early and large later with timing and the reverse without timing. Andreas Park (UofT) The Timing of Trades October 3, / 25

5 Simulation Insights for Spreads Numerical Observation (Spreads) Without timing the change in the size of the spreads is larger than with timing. Timing Spreads Myopic Spreads Andreas Park (UofT) The Timing of Trades October 3, / 25

6 Simulated Volume Numerical Observation (Early vs. Late Volume) In the myopic case volume decreases from Period 1 to 2, whereas with timing volume rises from Period 1 to 2. Timing Volume Myopic Volume Andreas Park (UofT) The Timing of Trades October 3, / 25

7 Probability of Informed Trading Definition PIN := probability of informed trade. probability of a trade Numerical Observation (PIN) In the myopic case, PIN decreases from Period 1 to Period 2; with timing, PIN increases from Period 1 to 2. Timing PIN Myopic PIN Andreas Park (UofT) The Timing of Trades October 3, / 25

8 What s new? Of course, I am not the first to look at the timing of trades! E.g. Kyle (EMA, 1985) studies timing. BUT: the model is for batch auctions, not sequential trading different microstructure/market organization. Admati & Pfleiderer (RFS 1988) also study trade timing. But in an REE model (again, different microstructure). Also: Gul & Lundholm (JPE 1994), Chamley & Gale (EMA 1994), Chari & Kehoe (JET 2004), and the list goes on. Yet there is no paper that explicitly models continuous trading and spreads. I fill this gap. Andreas Park (UofT) The Timing of Trades October 3, / 25

9 What s new? This paper s contribution My focus is on the impact of trade-trading on prices and overall trading volume: what lessons can be learned? Most measures of market liquidity use some component of the bid-ask-spread it is important to fully understand the theoretical impact of trading behavior on spreads. Models that explain spread and volume pattern usually assume exogenous fluctuations/cycles in noise trading. E.g. in Admati & Pfleiderer there are with exogenous fluctuations of noise trading any pattern can be explained. My contribution: Tweak the most standard model to allow timing. Lessons learned confirm parts of observed patterns. Andreas Park (UofT) The Timing of Trades October 3, / 25

10 Weapons in the arsenal to analyze Bid-Ask-Spreads Focus here: asymmetric information portion of spreads. Weapon of choice for spreads: Glosten-Milgrom (JFE 1986). The most common, stylized form: 1 Competitive market maker sets zero-profit bid- and ask-price. 2 Unit lot trades. 3 Informed and uninformed investors. 4 Informed = receive private signal 5 Uninformed = trade at random for reasons outside the model. 6 Traders arrive in exogenous, random sequence, one at a time. 7 Trade only at arrival time. 8 Common setup: high/low state and binary private signals. Andreas Park (UofT) The Timing of Trades October 3, / 25

11 Andreas Customization 2 periods, 2 traders, 2 possible signals. Signal has continuum of qualities (high quality high type). All arrive at time 0. Can trade only once, either at t = 1 or t = 2. Equilibrium = marginal trading type. Continuous types nice measure of spreads etc. Andreas Park (UofT) The Timing of Trades October 3, / 25

12 Some Parts of the Model 1 Security V {0, 1} 2 Private signal S {H, L} 3 Informed with probability µ, uninformed with 1 µ; 4 If uninformed, buy/sell with equal probability. 5 Private signal s quality: Pr(S = H V = 1) = Pr(S = L V = 0) = q i [1/2, 1]. 6 Qualities have a continuous distribution. 7 Signal + quality private belief π = Pr(V = 1 S, q). Andreas Park (UofT) The Timing of Trades October 3, / 25

13 Insider s Private Information V qi signal = H µ informed g( ) g( ) signal quality qi qi 1 qi signal = L signal = H V qi signal = L buy in µ 1 2 V buy in 2 sell in 2 uninformed 1 4 sell in 1 buy in buy in 2 V sell in 2 sell in 1 Andreas Park (UofT) The Timing of Trades October 3, / 25

14 Trading Investors submit unit trade orders: buy or sell; or abstain from trading ( hold ). Prices bid-price = highest price to sell a security, ask-price = lowest price to buy a security. Usually bid-ask-spread > 0 because 1 Inventory costs (for which market makers require compensation). 2 Adverse selection (market maker may trade with better informed insider). I focus on asymmetric information. Thus bid-price t = p B t = E[V H t, a sale at p B t ] ask-price t = p A t = E[V H t, a buy at p A t ]. For liquidity: larger spread lower liquidity. Focus on symmetric Bayesian Nash Equilibria, with monotone decision rules. Andreas Park (UofT) The Timing of Trades October 3, / 25

15 Some Early Insights for the Equilibrium Suppose everyone delays in Period 1 1 Time t = 1 ask-bid = 0 because trading is uninformative. 2 Time t = 2 ask-bid > 0 better to trade early. Informed must trade in both periods! Sub-martingale property of favorable opinions: high signal believe that buys are more likely believe that public belief will increase. Question: Why delay? Doesn t the above imply that every informed trader should believe that tomorrow s/he gets a worse deal? Answer: No! Bid- and ask-prices are decisive and these change depending on the extent of information asymmetries! In equilibrium, marginal trader has balanced expectation of rising price and decreasing spread. Andreas Park (UofT) The Timing of Trades October 3, / 25

16 Intuition for the result A trader buys today if 1 (Individual Rationality): E[V S] p A > 0 2 (Incentive Compatibility): E[V S] p A > E[E[V S] p A S] By law of iterated expectations E[E[V S] S] = E[V S]. Thus (IC) E[p A S] > p A. Between today and tomorrow, one of three things happens: 1 a buy price increases 2 a sale price decreases 3 a hold price decreases or increases. Tentatively, (for the purposes of the intuition) When high types trade, spreads are wide, when low types trade, spreads are tight. Thus two effects when delaying: 1 negative: buys more likely than sales prices rise. 2 positive: spreads tighten. Marginal trading type is indifferent between trading and delaying. Andreas Park (UofT) The Timing of Trades October 3, / 25

17 Myopic/Static Equilibrium Look for thresholds π b and π s such that buy if private belief π π b, sell if private belief π π s, abstain from trading otherwise. Threshold type π b must be indifferent between trading and abstaining: E[V H 1, π b ] = p A 1 (π b ). blue: p A (π b ) red: E[V π b ] Andreas Park (UofT) The Timing of Trades October 3, / 25

18 Some results Theorem (Malinova-Park 2006) A unique symmetric equilibrium of the static problem exists. Actually, MP s theorem covers a wider problem (for an arbitrary, random number of agents etc), but I can just use the same proof. Lemma (Maximization) The equilibrium π b maximizes p A (π b ), equilibrium π s minimizes p B (π s ). Let π 1,m b, πs 1,m be the equilibrium thresholds for a static Period 1 problem. Andreas Park (UofT) The Timing of Trades October 3, / 25

19 Solution to the Timing Problem: Period 2 I now proceed by backward induction: fix Period 1 thresholds π 1 b, π1 s and assume symmetry, π 1 b = 1 π1 s. Theorem Given symmetric Period 1 thresholds π 1 b, π1 s, there exists a unique symmetric equilibrium of the static problem π 2 b, π2 s. Marginal types found in a similar manner as the static ones. Note: Whether or not the Period 1 thresholds involve strategic trade-timing, the Period 2 marginal types are always found as the solution to a myopic problem. Since markets do close at some point, this end period is a justified assumption. Andreas Park (UofT) The Timing of Trades October 3, / 25

20 Solution to the Timing Problem: Period 1 Now I need to find πb 1 such that Massaging this equation I get ( β 1 β 0 + β 1 π 2 b = p A 1 (π 1 b) = E[p A 2 (π 1 b, π 2 b) π 1 b]. π 2 b β 1 β 1 π 2 b + β 0(1 π 2 b ) π 2 b β 0 β 0 π 2 b + β 1(1 π 2 b ) ) (π 1 b π 2 b)(β 1 β 0 ) LHS = difference of today s and tomorrow s ask price both with neutral priors. This can be thought of as an average benefit of delaying through tightened spreads. RHS, first term: difference worst case price minus best case price. RHS, second term: excess confidence of the Period 1 over the Period 2 marginal buyer. RHS, third term: probability of a type II error (not buying a valuable asset). Andreas Park (UofT) The Timing of Trades October 3, / 25

21 Solution to the Timing Problem and Properties Theorem There exist symmetric thresholds π T,1 b, πs T,1 that solve the dynamic problem. Proposition (Timing Marginal Trading Types are Larger) Compared to the myopic scenario, with timing, (a) the Period 1 buying-threshold is larger, π 1,T b π 1,m b, (b) the Period 2 buying-threshold is larger, π 2,T b π 2,m b. The myopic marginal type strictly prefers to delay. average informed trade in Period 1 has better information. Average information quality in Period 2 is also larger. Andreas Park (UofT) The Timing of Trades October 3, / 25

22 Solution to the Timing Problem and Properties private expectation signal&quality myopic ask 1 timing ask 1 ask 1 marginal quality marginal myopic buyer marginal timing buyer signal quality Andreas Park (UofT) The Timing of Trades October 3, / 25

23 Impact on Spreads Proposition (Bid-Ask-Spreads and Price Variability) (a) Timing bid-ask-spreads relative to myopic bid-ask-spreads are smaller in Period 1 and larger in Period 2. (b) Bid-ask-spreads decline from Period 1 to Period 2. (c) Price variability is smaller with timing. ask 1 ask 1 ask 2 ask 2 bid 2 bid 2 bid 1 bid 1 Period 1 Period 2 Period 1 Period 2 Myopic Spreads Timing Spreads Andreas Park (UofT) The Timing of Trades October 3, / 25

24 Volume Proposition (Total Volume) Compared to the myopic scenario, with timing, (a) Period 1 volume is lower and (b) total average volume measured across both periods is lower. Total volume and Period 1 volume is smaller with timing because the marginal trading type is larger. There is no analytical result for patterns but intuition is With timing, spread average quality probability of quality. At t = 1 average quality is but rare, at t = 2 average quality is low but common Volume low early high late. Without timing volume equal fraction of remaining in each period smaller and smaller share of total. Andreas Park (UofT) The Timing of Trades October 3, / 25

25 Conclusion I tweaked one of the most standard models to allow trade-timing. Patterns of spreads and volume arise naturally without silly assumptions such as exogenous cycles of uninformed trader arrival. The observed patterns are in line with observed data (with some reservations). While stylized, the intuition derived in the standard model should carry through to more general settings: 1 Better informed move early, 2 despite higher transaction costs. 3 They are fewer high types thus higher volume later. Bottom line: the standard model can tell us something. Andreas Park (UofT) The Timing of Trades October 3, / 25