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Unformatted text preview: Trade and Investment St Strategy 45-978 Professor Robert A. Miller October 2009 Teaching assistants: assistants: Chen Li: cli1@andrew.cmu.edu Hao Xue: hxue@andrew.cmu.edu Course objectives This course is about creating gains from trade and strategically exploiting their division. I want you to: 1. Develop a working familiarity with limit order working familiarity with limit order markets as a trader, investor and analyst. 2. Increase your intuition for predicting and your intuition for predicting and evaluating competitive equilibrium outcomes. Learn to optimally respond in a bargaining to optimally respond in bargaining situation, as a contractor and as a bidder in an auction. Design bargaining, contracting and pricing rules. 3. 4. Course materials Course materials The course website is: http://www.comlabgames.com/45-978 At the website you can find: the course syllabus lecture notes games you can download you can download project assignments the on line (draft) textbook on line (draft) textbook other reference materials Lecture 1 Limit Order Markets A limit order market is a real world institution for characterizing the financial sector, and it is also a paradigm for describing almost all trading mechanisms. This lecture defines limit order markets, explains how they work, and gives you some explains how they work, and gives you some experience trading in them. Then we investigate, experimentally, the empirical relevance of arbitrage pricing and the efficient markets hypothesis pricing and the efficient markets hypothesis. Financial Markets Financial Markets Electronic limit order markets are amongst the fastest growing markets within the financial and retail sectors. Whether market makers set the spread (NASDAQ), market makers set the spread (NASDAQ) specialists oversee transactions between investors (NYSE), or the market admits anyone in good standing to submit buy and sell orders (EBAY), these exchanges have a common structure. What can we say about the portfolio management when financial assets are traded on a limit order market? Trading in a generic limit order market Traders submit a market order or a limit order. Each order is for a given quantity, positive (negative) quantities standing for units demanded to buy (for sale). Limit orders specify a transaction price, market orders a reservation price. Market transactions match market orders with limit orders and take place at the limit order price(s) orders, and take place at the limit order price(s). Thus market orders are executed instantaneously, but limit order might never be executed. Precedence Market orders to buy are matched against the lowest price limit order(s) to sell. If two limit orders to buy are submitted at the same price, the order submitted first is matched against a market sell order before the more recently submitted buy order. Similarly lower priced limit orders to sell have a higher priority than higher priced limit sell orders, and if two bidders seeking to sell a unit at the same price the person who bid first will be matched before his rival seller. Trading window The difference between the highest priced limit buy order ask price (the bid price), and the lowest priced limit sell order (the ask price) is called the spread, here 2,000. The trader just placed a sell order for 9 units at price 5,800, reducing the spread from 2,200 by placing an order inside the previous bid ask quotes. th bid Should I place a market order or a limit order? ma limit Market orders transact immediately. Limit orders orders transact immediately Limit orders might never transact, but if they do, yield greater gains. Suppose I value the stock at Value and the ask price is Ask Then the gain from buying the stock price is Ask. Then the gain from buying the stock is: Value - Ask Suppose I place a limit buy order of B’. Denote the place limit buy order of Denote the probability of the ask price falling to B’ by Prob[B’]. Then the gain from placing a limit buy order of B’ is: Prob[B’] *{Value - B’}. Keeping track of limit orders Picking-off risk poses an additional hazard for maintaining unattended limit orders. If I place a limit buy order (below the ask), and then the value of it to everyone: 1. increases due to a favorable announcement, then the spread will shift up and my order won’t fill. 2. decreases due to an unfavorable announcement, then the spread will shift down, my order will fill at the price I selected before the unfavorable announcement was made announcement was made. In other words if I do not keep track of changes in the value of the stock where my orders are placed, then I am more likely to transact when prices move against me. Market makers and specialists Market makers (at NASDAQ) and specialists (at NYSE) play an intermediary role to facilitate the speed with play an intermediary role to facilitate the speed with which transactions take place. Market makers compete with each other (about 14 for each type of security) by posting a spread, a bid and an ask, that investors can trade at. as ca at Specialists (just one per share) can post a spread at which they must transact at but must process orders which they must transact at, but must process orders coming from investors in the exact order they are received without interfering with orders that cross. Flash orders and high frequency trading Flash orders give designated insiders (associated with the exchange) an opportunity to react to an outside limit order, before everyone else can. Flash orders are likely to be banned soon. High frequency trading refers to computer programs for placing orders. They are typically based on data analysis designed to identify favorable trading opportunities. The algorithms react very quickly to changes in the book algorithms react very quickly to changes in the book and market conditions. Front Running Specialists on stocks only listed on the NYSE do not compete with each other but only with outside traders for determining trading volume and pricing determining trading volume and pricing. If permitted specialists could make substantial monopoly rents by breaking the precedence rule preventing buy rents by breaking the precedence rule, preventing buy and sell limit orders to cross, and extracting the difference between the buy and sell limit prices. In this illegal maneuver the specialist, rather than the buyer, purchases directly from the seller at the ask price, buyer, purchases directly from the seller at the ask price, and then sells the stock to the buyer at the bid price. This illegal practice is punished with jail time. illegal practice is punished with jail time Insider Trading Insider trading laws discourage managers and other associates from using privy information about the fi firm to their advantage when trading stock. th The FTC enforces these laws by reviewing evidence of whether a large volume of shares traded hands just before a financial event, (and in the case of a negative event where there would be short sale negative event where there would be a short sale before just after as well) They check to see whether the people who profited th might have known one another, who there source might be, and typically use wire tapping procedures for self incriminating statements. Inside information and performance pay Although insider trading is illegal, my research with Prof Gayle on the S&P 1500 composite shows that: 1. Changes in the stock components of the manager’s compensation is a significant predictor of future financial returns, executives opting for more stock and less cash and bonus when the firms they manage subsequently do well manage subsequently do well. 2. Retrospectively replicating the manager’s compensation strategies and forming a simple ti investment strategy, we would have earned 20 percent return per year over the 9 year panel for the 1500 firms, instead of the market return of about 9 percent. How efficient are limit order markets? With two other researchers, Prof Hollifield and I conducted an empirical investigation into three stocks previously traded on the Vancouver exchange th to see how much of the potential gains from trade are realized in limit order markets. Published in the Journal of Finance, ours is the first study to do this. We chose this exchange for two main reasons: 1. Data Availability of all limit orders rather than just transaction data. 2. This exchange had a “wild west” reputation, so was a good test of how well this market mechanism works. Types of inefficiency Limit order markets for financial securities might not realize all the potential gains from trade for four reasons: 1. Limit orders are not executed when they should be (that is to maximize the total gains from trade) (that is to maximize the total gains from trade). 2. Traders do not submit orders when they should (deterred by the order submission cost and the low (deterred by the order submission cost and the low probability of execution). order rather than a sell order (to profit from stale limit sells after value of stock has fallen). (because of order submission costs) . 3. Traders submit “wrong sided” orders, such as a buy buy 4. Traders submit orders when they should not 2790 The Journal of Finance Table X Estimates of the Gains from Trade The first row of the top panel reports the estimates of the maximum gains from trade, measured as a percent of the common value. The next three rows report the estimates of the lower and upper bounds and the average current gains from trade; details are provided in Appendix E. The next six rows report the lower and upper bounds and the average for the difference between the maximum and the current gains from trade, and the current gains from trade as a percentage of the maximum gains from trade. The middle panel reports the average percentage of the efficiency loss associated with no execution, no submission, wrong direction, and extramarginal submissions computed for the average current gains from trade. The bottom panel reports the monopoly gains from trade as a percentage of the common value, and the current gains as a percentage of the monopoly gains. We verify that the second-order conditions hold at the computed monopoly bid and ask quotes at each observation. The three sample stocks are Barkhor Resources (BHO), Eurus Resources (ERR), and War Eagle Mining Company (WEM). BHO ERR WEM Lower bound Upper bound Average Lower bound Upper bound Average Lower bound Upper bound Average Gains Maximum gains as a % of the common value 9.07 8.61 Current gains as a % of the common value 7.88 8.09 8.45 8.31 8.16 8.20 Maximum gains minus current gains 0.62 0.30 1.20 0.52 0.91 0.41 Current gains as a % of maximum gains 86.79 93.97 93.13 96.57 89.96 95.27 Decomposition of Losses No execution as a % of total losses 32.32 31.20 40.10 39.01 72.42 70.21 No submission as a % of total losses 2.24 0.62 1.98 0.15 4.22 0.77 Wrong direction as a % of total losses 0.86 0.02 0.20 0.05 1.06 0.07 Extramarginal submissions as a % of total losses 9.81 11.87 12.49 17.07 22.30 28.94 100.00 100.00 Monopoly Gains Monopoly gains as a % of the common value 5.02 5.57 Monopoly gains as a % of maximum gains 55.31 64.71 Current gains as a % of monopoly gains 162.65 147.23 6.75 6.08 6.40 6.24 0.35 0.67 0.51 90.07 94.81 92.44 Sell side Buy side Subtotal Sell side Buy side Subtotal Sell side Buy side Subtotal Sell side Buy side Subtotal Total 33.05 41.85 74.90 0.41 0.71 1.12 0.39 0.63 1.02 10.30 12.66 22.96 100.00 4.18 61.87 149.41 Payoff equivalence Some features of the solution to a market game are evident without explicitly solving the game. Perhaps the most important one comes from the notion of arbitrage, which is based on payoff equivalence payoff equivalence. Two bundles of securities are payoff equivalent if they have the same probability distribution determining the payoffs at the end of the game. of the game. Arbitrage pricing The optimal exploitation of arbitrage opportunities puts bounds on the best prices th quoted in the limit order book of payoff equivalent portfolios. Loosely speaking, arbitrage compels payoff equivalent securities to trade at the same price equivalent securities to trade at the same price. More precisely, it should not be possible, by means of market orders alone, to sell one bundle of securities and purchase another payoff equivalent bundle and make a net profit. Arbitrage Pricing in Limit Order Markets A general formulation Suppose there are J assets labeled as j 2 f1, 2, . . . , J g. Let qj denote the amount of asset j traded by an investor. If qj > 0 then the investor is buying qj of j . If qj < 0 then the investor is selling qj of j . Let pj > 0 denote the market price(s) of the j th asset where: pj Aj if qj > 0 Bj if qj < 0 Finally let vj > 0 denote the expected present value of the dividend stream plus the liquidation value of the j th asset. The Arbitrage Pricing Theory (APT) says: j =1 () ∑ ( vj J pj ) qj 0 October 26, 2009 1 / 10 Arbitrage Pricing in Limit Order Markets An example: Telecommunications providers Imagine there are three market segments in the telecommunications sector. Some consumers want wireless only, others just cable, while a third segment demands a wireless/cable combination service. A …rm provides: q1 quantity of wireless service, q2 quantity of cable service, q3 quantity of wireless/cable combination service. Suppose scale economies in marketing are realized from emphasizing any one segment. The …rm’ value is: s j 2f1 ,2 ,3 g max fvj qj g + j =1 ∑ vj qj 3 where: v1 is a demand factor for wireless, v2 is a demand factor for cable, v3 = 2v1 + v2 () October 26, 2009 2 / 10 Arbitrage Pricing in Limit Order Markets Arbitrage conditions in the telecommunications sector The only way to achieve production e¢ ciency in this sector is for every …rm to specialize in just one of the three market segments. We assume this happens, and analyze the resulting arbitrage conditions. Arbitrage pricing in the …rst two segments requires that for j 2 f1, 2g: 2vj Bj For the third sector we require: 4v1 + 2v2 B3 A3 4v1 + 2v2 Aj 2vj Putting the four sets of inequalities together we obtain two inequalities in terms of prices alone, namely: 2B1 + B2 B3 () A3 October 26, 2009 3 / 10 2A1 + A2 E¢ cient Markets Hypothesis in Limit Order Markets A general formulation For an expected value maximizer, who by de…nition only occurs about the mean of a payo¤ distribution, the E¢ cient Markets Hypothesis (EMH) is essentially a corollary of APT. Suppose the j th asset only pays out upon liquidation and let Ajt denote its ask price at time t , and Bjt its bid price. We also write E [ jIt ] for the expected value of a random variable when know It about it. The EMH says: E [Bj ,t +1 jIt ] Bjt Ajt Using the law of iterated expectations it is easy to generalize these inequalities to: E [Bj ,t +s jIt ] Ajt Ajt E [Bj ,t +s jIt ] () October 26, 2009 4 / 10 E [Aj ,t +1 jIt ] E¢ cient Markets Hypothesis in Limit Order Markets Perfectly liquid markets In a perfectly liquid market, the spread collapses and Ajt = Bjt . Then the EMH simpli…es to: E [Bj ,t +1 jIt ] or: Ajt = Bjt = E [Aj ,t +1 jIt ] = E [Bj ,t +1 jIt ] In words, transaction prices follow a random walk. Ajt = Bjt E [Aj ,t +1 jIt ] () October 26, 2009 5 / 10 E¢ cient Markets Hypothesis in Limit Order Markets Currency Exchange Suppose U.S. export companies sporadically receive euro injections from sales in the E.U. Similarly European (Chinese) exporters earn yuan (dollars) for sales in China (the U.S.). Export …rms can also on the foreign exchange market between date 0 and T, but at date T all export companies are liquidated and no further value is placed on holding foreign currency. We assume the U.S. dollar is a dominant currency, meaning all currency prices are quoted in dollars. We assume each export …rm maximizes its expected accumulated domestic reserves before the liquidation date T. () October 26, 2009 6 / 10 E¢ cient Markets Hypothesis in Limit Order Markets Market Liquidity The hypothesis that asset prices follow a random walk might be regarded as a test of liquidity. In the previous example we may assume without loss of generality that there is continuous trading in the asset up until a common liquidation date T when the capitalized value of all the …rms are recognized. How would prices behave if consumers had limited opportunities to enter and exit the market, e¤ectively segmenting the market into di¤erent time markets? () October 26, 2009 7 / 10 E¢ cient Markets Hypothesis in Limit Order Markets Illiquid markets Suppose exporters face the threat of their foreign earnings being con…scated, or there are incomplete markets that limit savings and borrowing opportunities in domestic markets. Then exporters might immediately capitalize their foreign earnings by converting them to domestic dividends and distributing them as dividends. In this case successive prices in the foreign exchange market would exhibit mean reversion. At the other extreme to the random walk observed in perfectly liquid market, prices in disconnected markets are independently distributed, and in a stationary environment, have the same conditional mean. () October 26, 2009 8 / 10 Summary A recapitulation We de…ned and discussed the main features of limit order markets, including limit orders, market orders, and picking o¤ risk. We explained some issues of concern to regulators, such as ‡ash trading, inside trading and front running. We showed how arbitrage pricing theory (APT) can be rehabilitated quite simply within limit order markets, inequalities rather than equalities de…ning how asset bid-ask prices are linked across assets formed from di¤erent combinations of latent factors. Similarly the E¢ cient Markets Hypothesis (EMH) was restated within a limit order market, again in the weaker form of inequalities rather than equalities. When markets are perfectly liquid, EMH predicts that prices will follow a random walk when traders are risk neutral, but the result does not hold when markets are not liquid. We might observe mean reversion. () October 26, 2009 9 / 10 Summary Food for thought The role of liquidity emerges very naturally in limit order markets: Why did …nancial markets melt down last year? Were markets illiquid? Did we misallocate resources to housing and construction? How did the bad bets of …nancial …rms play a role? Could a di¤erent public policy averted the steep decline in stock markets and the recession triggered in the housing and construction sectors? How does our analysis today shed light on this issue? () October 26, 2009 10 / 10 ...
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This note was uploaded on 09/21/2010 for the course BUS 1142 taught by Professor Miller during the Spring '10 term at Carnegie Mellon.

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