Quantitative trading - page 31

 

Exercise class 4, part 1 (Financial Markets Microstructure)



Exercise class 4, part 1 (Financial Markets Microstructure)

The instructor begins the exercise class by revisiting previous problems from lectures and problem sets. They specifically mention that exercises from lectures 7 and 8 will be covered, which focus on order flow payments and trading costs set by exchanges. The instructor wants to ensure that students have a solid understanding of these concepts.

Next, the instructor shifts the focus to exercise 5 from chapter 6, which delves into the topic of trading fees in the parlors model. This problem explores the different fees charged by trading platforms for market and limit orders and the implications of these fees on trading decisions. The instructor emphasizes the significance of this problem in designing better functioning markets, as the fees charged by trading platforms can significantly impact traders' choices and market dynamics.

To provide some context, the instructor explains the total revenue that an exchange receives per trade, which is derived from the fees collected from both market orders and limit orders. They mention that the model assumes there is one asset with a known value and fixed bid and ask prices. Traders can choose between buy and sell orders, as well as market and limit orders. Private valuations, denoted as Y, are assumed to be uniformly distributed and independent across traders. Notably, the private information does not influence trading decisions. The probabilities of market orders to buy or sell are denoted as P subscript M superscript B or S, respectively.

The instructor acknowledges that they have made certain simplifications and additions to the textbook model of financial markets microstructure. They have enriched the distribution of private valuations and introduced the concept of binary private affiliation (minus y or plus y). Additionally, they assume that market orders can only trade against previously submitted limit orders. They encourage the viewers to think about ways to compute bid and ask quotes in equilibrium, as the textbook model does not assume that if the limit order book is empty, the trade will always be filled by the market maker at the same prices.

Moving forward, the instructor explains the goal of achieving good bid and ask prices in financial markets microstructure. They begin with the basic textbook model, which does not consider trading fees, and aim to find quotes that make traders indifferent between market and limit orders. The speaker illustrates the potential profits of a buy-side trader with a high valuation from both market and limit orders. The trader's objective is to maximize their profit from trading, and the state of indifference arises from this profit maximization.

The concept of submitting a limit order is introduced, which can lead to a better price but also carries some execution risk. The instructor discusses the objective of finding a stationary equilibrium, focusing on identifying a condition that equates the vulgar condition on A and B given fixed values of V ml, which are parameters of the model. The discussion then shifts to how the next trader chooses between market and limit orders. In equilibrium, it is never optimal for a trader at time t + 1 to submit a limit order if they have a market order available. This behavior is the only possible equilibrium, as any other choice would result in a contradiction.

The speaker proceeds to explain the process of determining equilibrium and the price discovery mechanism between market and limit orders in financial markets microstructure. They explain that if one trader chooses to submit a buy order at a slightly lower price (epsilon), they are no longer indifferent between market and limit orders. Another trader can then offer them a slightly better price. It is concluded that one trader must always trade against a limit order when available, and a similar indifference condition must be met by the seller. The speaker further states that spreads and bid-ask prices can be determined based on traders' non-trivial behavior conditioned on this indifference and a uniform distribution of valuations.

The instructor elaborates on how bid-ask spreads in financial markets microstructure are influenced by the cost of limit orders (represented by FL(o)) versus the cost of market orders (represented by F(m)). The goal is to ensure that all traders are indifferent between market and limit orders. If the cost of limit orders increases, it becomes less appealing for traders, resulting in an increase in the bid-ask spread to make limit orders more attractive. Conversely, if market order fees increase, limit orders become more appealing, and the bid-ask spread must decrease to restore the balance of trader preference. The instructor mentions that trading platforms can subsidize limit orders with negative fees and market orders with positive fees, which can help narrow the spread by making limit orders more attractive.

The impact of negative limit orders and cross-subsidizing limit orders with market orders on trading costs is discussed. While these practices may narrow the spread, they do not necessarily decrease trading costs, as the actual amount a trader pays for a market buy order is given by v + 1/3l + f. However, these practices are still considered welfare-enhancing. The discussion then moves on to payments for order flow and explores the consequences of forwarding order flow from unsophisticated investors to dealers. This practice, commonly observed in the real world, prompts the consideration of fundamental values in determining whether a security pays a high or low rate.

Next, the video introduces a model that involves one investor randomly buying or selling an asset without knowledge of its true fundamental values. The investor's probability of being a retail investor or an institutional investor is considered. Institutional investors are further categorized as informed or uninformed, and three dealers participate in the market without any informational advantage. The model assumes no payment for order flow between the broker and dealers, who compete with each other. The broker randomly selects one dealer among those offering the best price for the order. The objective is to compute the bid and ask quotes posted by the dealers, reminiscent of the Glosten-Milgrom model.

The Milgrom model is applied to determine the expected value for the conditional order placed by an informed trader. Market power is not observed despite the presence of a small number of dealers and the possibility of collusion. Dealers are subject to Bertrand competition, which puts them in an oligopoly setting. The formula for the S price is derived using the probability of receiving a buy order from an informed or uninformed institutional investor. Finally, the formula for the bid price is obtained, which is the same as the S price.

The concept of the overflow payment realm is introduced, where Dealer 1 has a payment for order flow arrangement with the broker. In this arrangement, the broker forwards all orders from retail investors to Dealer 1, who agrees to execute these orders at the best available prices set by the other two dealers. The broker acts as a router and decides which dealer to forward the order to. The quotes posted by Dealers 2 and 3 are deduced, revealing that the bid-ask spread is higher in this case compared to when there is no payment for order flow. The probability of a trader being informed is determined to obtain the S price. It is noted that the bid-ask spread is higher when there is payment for order flow. Finally, the largest possible value of P is calculated.

The instructor explains how to determine the largest possible value of P for Dealer 1 and the conditions required for Dealer 1 to be willing to pay P. It is necessary for Dealer 1's profit to be non-negative, and the profit from each order can be derived from the equilibrium in Part B, where Dealer 1 receives Alpha Sigma from any order received. The concept of payment for order flow is discussed, and the question of whether it benefits or harms investors is posed. The answer becomes clear: all investors end up trading at new, worse prices, resulting in unfavorable outcomes for them.

The video concludes by explaining how payment for order flow affects investors. The spread widens, which is detrimental to investors, while Dealer 1 and the broker profit. It is presumed that the broker receives a share of the surplus. However, if brokers are competitive, the profit may be passed on to investors, particularly institutional investors who possess more bargaining power than retail investors. The video ultimately suggests that payments for order flow allow dealers and brokers to thrive at the expense of investors.

  • 00:00:00 The instructor begins an exercise class by revisiting previous problems from lectures and problem sets. In particular, two exercises from lectures 7 and 8 will be covered, which deal with order flow payments and trading costs set by exchanges. The instructor then focuses on exercise 5 from chapter 6, which relates to trading fees in the parlors model. The problem addresses the different fees charged by trading platforms for market versus limit orders and the implications for trading decisions. The instructor clarifies certain aspects of the problem and highlights its importance for designing better functioning markets.

  • 00:05:00 The instructor explains the total revenue that an exchange receives per trade, which comes from fees collected from both the market order and the limit order. The model assumes there is one asset with a known value and exogenously fixed bid and ask prices. Traders choose between buy and sell and limit and market orders. Their private valuations, denoted by Y, are uniformly distributed and independent across traders. Notably, this private information does not affect trading decisions. The probabilities of market orders to buy or sell are denoted as P subscript M superscript B or S, respectively.

  • 00:10:00 The instructor explains that they have made some simplifications and additions to the textbook model of financial markets microstructure. They have enriched the distribution of private valuations and assumed that the private affiliation is binary, either minus y or plus y. They also assume that market orders can only trade against previously submitted limit orders. They are asked to compute the bid and ask quotes in equilibrium, but the instructor presents the question to the viewers and encourages them to think of ways to compute them. They clarify that the textbook model does not make the assumption that if the limit order book is empty, the trade will always be filled by the market maker at the same prices.

  • 00:15:00 The speaker discusses how to get good bid and ask prices for financial markets microstructure. They start with the basic textbook model without trading fees and aim for quotes that make traders indifferent between markets and limit orders. The traders should be able to use both market and limit orders, and the speaker shows the possible profits of the buy-side trader with a high valuation from marketing and limit orders. The trader should maximize their profit from trading, and the indifference comes from profit maximization.

  • 00:20:00 The concept of submitting a limiter is discussed, which can result in a better price but also carries some execution risk. The goal of finding a stationary equilibrium is explained with a focus on finding a condition that equals the vulgar condition on A and B given some fixed values of V ml, which are parameters of the model. The discussion then turns to how the next trader chooses between market and limit orders, which, in equilibrium, can never result in a trader at t +1 submitting a limit order if they have a market order available. This is the only possible equilibrium behavior, as otherwise, it would result in a contradiction.

  • 00:25:00 The speaker explains how to determine equilibrium and find price discovery processes between marketing and limit orders in financial markets microstructure. They explain that if one trader chooses to submit a buy order to the price slightly below epsilon, they're no longer indifferent between submitting a market or limit order, and another trader can offer them a slightly better price. They conclude that one trader must always trade against a limit order when available, and a similar indifference condition must be met by the seller. The speaker then finds that spreads and bid-ask prices can be determined through non-trivial behavior of traders conditionally on this indifference and a uniform distribution of evaluations.

  • 00:30:00 The instructor explains how bid-ask spreads in financial markets microstructure are affected by the cost of limit orders, as represented by FL(o), versus the cost of market orders, represented by F(m). All traders must be indifferent between market and limit orders, so if the cost of limit orders increases, it becomes less appealing for traders, and the bid-ask spread must increase to make limit orders more attractive. Conversely, if market order fees increase, limit orders become more appealing, and the bid-ask spread must decrease to restore the balance of trader preference. Trading platforms may subsidize limit orders with negative fees and market orders with positive fees, which can help narrow the spread by making limit orders more attractive.

  • 00:35:00 The speaker discusses the impact of negative limit orders and cross-subsidizing limit orders with market orders on trading costs. While narrowing the spread nominally, it does not necessarily decrease trading costs as the actual amount a trader pays for a market buy order is given by v + 1/3l + f. However, it is still considered a welfare-enhancing practice. Moving on, the speaker talks about payments for order flow and explores the consequences of forwarding order flow from unsophisticated investors to dealers. This is a widely spread practice in the real world, and the speaker notes that one must consider the fundamental values in determining whether a security pays a high or low rate.

  • 00:40:00 The video introduces a model where there is one investor who either randomly buys or sells an asset with no knowledge of its true fundamental values, based on a probability of being a retail investor or institutional investor. Institutional investors are further divided into informed or uninformed, while there are also three dealers in the market without any informational advantage. The model assumes no payment for order flow between the broker and dealers, who are competing with each other, and the broker randomly selects one dealer among those posting the best price for the order. The goal is to compute the bid and ask quotes posted by the dealers, in a model that is reminiscent of the Glosten-Milgrom model.

  • 00:45:00 The Milgram model is applied to determine the expected value for the conditional order being placed by an informed trader. Market power is not observed despite the existence of few dealers and possible collusion as they are still subjected to Bertrand competition, and price competition puts them in oligopoly. The formula for the S price is derived using the probability of receiving a buy order from an informed or uninformed institutional investor. Finally, the formula for the bit price is obtained, which is the same as the S price.

  • 00:50:00 The concept of overflow payment realm is introduced where it is assumed that Dealer 1 has a payment for order flow arrangement in which the broker gives Dealer 1 all orders from retail investors, and the dealer agrees to execute these orders at the best available prices set by the two remaining dealers. The broker serves as a router and decides to whom to forward the order. The quotes posted by dealers 2 and 3 are deduced, and it is found that the bid-ask spread is higher in this case than when there is no payment for the order flow. The probability of a trader being informed is determined to obtain the s price. The bid-ask spread is higher in this case than when there is no payment for the order flow. Finally, the largest possible value of P is calculated.

  • 00:55:00 The instructor explains how to find the largest possible value of P for dealer one and the conditions required for dealer one to be willing to pay P. The profit of dealer one must be non-negative, and their profit from each order can be derived from the equilibrium in Part B, which involves receiving Alpha Sigma from any order received. The payment for order flow is then discussed, and the question is posed as to whether it is beneficial or detrimental to investors. The answer is clear: all investors end up trading at the new, worse prices, resulting in worse outcomes for them.

  • 01:00:00 The video explains how payment for order flow affects investors. The spread widens, which is detrimental to investors, while Dealer 1 and the broker profit. The broker presumably receives some share of the surplus. However, if brokers are competitive, the profit might be transmitted to investors, particularly institutional investors who have more bargaining power than retail investors. The video concludes that payments for order flow allow dealers and brokers to proliferate at the expense of investors.
Exercise class 4, part 1 (Financial Markets Microstructure)
Exercise class 4, part 1 (Financial Markets Microstructure)
  • 2020.04.24
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Exercise class 4, part 1Financial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtube.com/pla...
 

Exercise class 4, part 2 (Financial Markets Microstructure)



Exercise class 4, part 2 (Financial Markets Microstructure)

In the previous lecture, the instructor discussed a complex problem that combined Kyle's model with the Stoll model and introduced a risk-averse dealer with mean-variance preferences. The objective was to find a linear equilibrium where the informed trader's order size is a linear function of the fundamental value, and the dealer sets prices according to a linear schedule. However, the instructor mentions that they will not go through the full solution in this video since it is already available on the course website.

The instructor addresses two challenging aspects that students may be struggling with in the exercise. Part A of the problem requires finding the conditional expectation and variance of firm V based on the observed total order flow queue. This involves calculating the expected value and variability of V given the information about the queue. On the other hand, Part C is considered the centerpiece of the Stoll's model with risk aversion and dealer decision-making. It involves dealers taking the price as given, although in reality, they determine the price schedule based on the order flow. The instructor explains the inconsistency in this logic and how dealers determine how much they are willing to supply at a fixed price.

The video delves into the effects of risk aversion on dealers in financial markets microstructure. When dealers are risk-averse and have concave utility, the concept of indifference with respect to profit per unit traded no longer applies. Each dealer is only willing to buy a limited amount of any risky asset, even if the profit per trade is positive or negative. Risk-averse dealers avoid taking large, risky positions because increasing their buying volume also increases the riskiness of their overall position, leading to a higher variance in their future wealth. As a result, it becomes necessary to determine the maximum amount dealers are willing to buy or sell for any given price. This decision gives rise to the supply curve Q of P and the price schedule P of Q in the financial market.

The instructor explains how the dealer's utility function is utilized to determine the optimal amount to supply, leading to the equation of Y of P, where Y represents the amount that dealers are willing to trade. The competitive nature of dealers is emphasized, and the process of solving the maximization problem is described. The instructor also touches on the algebraic aspects of the problem and then returns to Part A, where the conditional distribution of V, given Q, needs to be found using the RLS equation. The conclusion of RLS (recursive least squares) is used to estimate Y based on the information about X.

The derivation of the distribution of V conditional on Q is explained, with the instructor mentioning that it is described by a probability density function (PDF) that can be calculated using Bayes' rule. The instructor notes that the formula presented is not shown on the slide and emphasizes the importance of keeping track of the expectation of Q and computing the expectation of B. They also discuss a quicker and more efficient way to derive this expression and a longer and more tedious way, particularly for the exact cow model.

The speaker further discusses how to find the joint probability of observing a specific D and Q, which appears in the numerator of the formula, and the probability of observing a particular realization of Q, which is in the denominator. The joint probability can be decomposed into the product of two independent PDFs since U and V are independent variables. The derivation of this formula is explained, with a suggestion for those who are not interested to skip this part.

The properties of the normal distribution are discussed, and the cumulative distribution functions (CDF) of V and U are derived based on the unconditional expectation and variance. The joint PDF for V and U is also determined by invoking the properties of the normal distribution and the independence between the variables. The sum of beta V minus X0 and U is found to be normally distributed, and its mathematical expectation and variance can be computed using the method of mixtures. However, a shorter way to compute this is by directly using the properties of the normal distribution and independence.

The speaker explains how to obtain the conditional probability distribution of Q, assuming that Q has the form beta times the mean of V minus X0 plus the mean of U. The variance of Q is derived as beta squared times the variance of V plus the variance of U. Using these results, the speaker provides an expression for F of Q by combining the PDF of the normal distribution and the joint PDF. Although the resulting expression is complicated, it can be simplified by collecting and summing all the terms. The speaker acknowledges that this distribution is not yet very informative, making it difficult to ascertain whether Q is normally distributed and determine its mean and variance.

Moving forward, the speaker discusses how to find the mean and variance by considering the form of X as normal and rewriting V as a complete square to verify a certain fraction. They simplify the difference into one fraction and confirm that this fraction indeed works as the variance of the conditional on cue.

Finally, the instructor explains how to find the conditional expectation of the conditional queue through algebraic manipulations. They denote the large term as 2V, referred to as mu, and the whole squared as V minus mu squared divided by Sigma squared. This simplification helps find the mean. The instructor concludes by mentioning that there will be more problems covered in lectures 9 and 10, focusing on the value of liquidity and public information in markets, as well as continued discussion on high-frequency trading.

  • 00:00:00 The instructor discusses a difficult problem from the previous lecture that combined Kyle's model with the Stoll model and added a risk-averse dealer with mean-variance preferences. The goal was to find a linear equilibrium where the informed trader's order size is a linear function of the fundamental value and the dealer sets prices according to a linear schedule. The instructor explains that they will not go through the full solution in this video since it was already posted on the course website.

  • 00:05:00 The instructor is addressing two aspects that students may be struggling with in the exercise. Part A requires finding the conditional expectation and variance of firm V based on the observed total order flow queue. Part C is the centerpiece of the Stoll's model with risk aversion and dealer decision-making. It involves dealers taking the price as given, although in reality, they determine the price schedule based on the order flow. The instructor explains the inconsistency in the logic and how dealers determine how much they are willing to supply at a fixed price.

  • 00:10:00 The video discusses the effects of risk aversion on dealers in financial markets microstructure. The concept of indifference with respect to profit per unit traded is no longer applicable when dealers are risk-averse and have concave utility. Each dealer is only willing to buy a limited amount of any risky asset, even if the profit per trade is strictly positive or negative. Risk-averse dealers will not take large, risky positions because the more they buy, the riskier their total position becomes, leading to a larger variance in their future wealth. As a result, for any given price, it is necessary to determine the maximum amount dealers are willing to buy or sell. This decision yields the supply curve Q of P and the price scheduled P of Q in the financial market.

  • 00:15:00 The speaker explains how the dealer's utility function is used to determine the optimal amount to supply and obtain the equation of Y of P, where Y is the amount that dealers are willing to trade. The competitive nature of dealers is highlighted, and the process of solving the maximization problem is explained. The speaker also touches on the algebraic parts of the problem and moves back to Part A, where the conditional distribution of V, conditional on Q, needs to be found using the RLS equation. The conclusion of RLS is used to estimate Y, given the information on X.

  • 00:20:00 The instructor explains how to derive the distribution of V conditional on Q using a probability density function. The instructor states that the distribution is described by a PDF, which can be calculated using Bayes' rule. They also highlight that the formula presented is not shown anywhere on the slide and that the expectation of Q needs to be kept track of, along with computing the expectation of B. Additionally, they explain the quick and fast way to derive this expression and the long and tedious way explicitly for the exact cow model.

  • 00:25:00 The speaker discusses how to find the joint probability of observing a particular D and Q in the numerator of the formula and the probability of observing a particular realization of Q in the denominator. The joint probability can be decomposed into the product of two independent PDFs because U and V are independent variables. The derivation of this formula is explained, with a suggestion for those who are not interested to leave.

  • 00:30:00 The PDF of normal distribution is discussed and the CDF of V and U are derived based on the unconditional expectation and variance. The joint PDF for V and U is also determined by invoking the properties of normal distribution and independently. The sum of beta V minus X0 and U is found to be normally distributed, and the mathematical expectation and variance of this sum can be computed using the method of mixtures. However, a shorter way to compute this is by simply using the properties of normal distribution and independence.

  • 00:35:00 The speaker explains how to obtain the conditional probability distribution of Q, given that we know V and we assume that Q has the form beta times the mean of V nu minus x0 plus the mean of U. The variance of Q is derived as beta squared times the variance of V plus the variance of U. Using these results, the speaker provides an expression for F of Q by combining the PDF of the normal distribution and the joint PDF. The resulting expression is complicated, but it is possible to simplify it by collecting all the terms and adding them up. The speaker notes that this distribution is not very telling yet and that it is difficult to see whether Q is normal and what its mean and variance are.

  • 00:40:00 The speaker discusses how to find the mean and variance given the form of X being normal and how to write V as a full square to confirm that a certain fraction works. They simplify the difference into one fraction and confirm that this fraction actually works as the variance of the conditional on cue.

  • 00:45:00 The instructor talks about how to find the condition expectation of the conditional queue through some algebraic manipulations, denoting the huge term by 2 V as mu and the whole squared as V minus mu squared divided by Sigma squared. This is how to simplify the expression and find the mean. The instructor also mentions that there will be more problems to cover in lecture 9 and 10 on the value of liquidity and public information in markets, as well as continuing to talk about high-frequency trading.
Exercise class 4, part 2 (Financial Markets Microstructure)
Exercise class 4, part 2 (Financial Markets Microstructure)
  • 2020.04.24
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Exercise Class 4, part 2Financial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtube.com/pla...
 

Lecture 13, part 1: High-Frequency Trading; Public Information (Financial Markets Microstructure)



Lecture 13, part 1: High-Frequency Trading; Public Information (Financial Markets Microstructure)

In the lecture, the speaker discusses the effect of high-frequency trading (HFT) on markets and the problem of public information. The presence of HFT in the market creates an imbalance of information between traders, similar to having more informed traders. This information asymmetry harms liquidity, widens the spread, and does not necessarily lead to better price discovery. HFT can be seen as an arms race with wasteful investments made to gain advantages. However, when everyone becomes fast, the situation becomes equivalent to when everyone is slow, except that everyone has invested a significant amount of money to achieve speed.

To address these issues, the speaker proposes replacing the continuous auction with frequent batch auctions. However, HFT generates arbitrary opportunities that do not vanish over time, and this approach fails to foster correlation between identical assets. Even with more HFT traders, the problem of HFT would not be solved solely by implementing a new auction system.

Next, the presenter discusses price efficiency in relation to the S&P 500 spot and future contracts. These assets are correlated as they both track the S&P 500, but the future contract is short-term and reflects the expected value of the S&P 500 in one week. According to the theory, prices should be martingales and efficient for these S&P 500 future contracts. However, when examining price data at shorter intervals, the correlation between the spot and future prices starts to diminish.

The lecture also explores the correlation between price indices and its implications for arbitrage opportunities. The correlation between two price indices increases with longer time intervals. However, as the time interval shrinks to zero, the correlation between the indices becomes zero. This means that the fastest traders, who can operate within milliseconds, will always have access to arbitrage opportunities. A graph illustrating the medium profits per arbitrage over time shows that these profits do not decline. The lecturer presents a simple model with two types of traders: "moist" traders who arrive randomly over time and high-frequency traders who have access to arbitrage opportunities.

Furthermore, the professor explains the role of noise traders and high-frequency traders in the market. Noise traders arrive randomly and want to buy or sell one unit of a stock without any specific intention. High-frequency traders act as liquidity providers, with one of them acting as the market maker and posting quotes for one unit of the asset. Other high-frequency traders act as stale quote snipers, and if they observe public news before the market maker does, they can take advantage of these stale quotes. The professor computes the expected flow profits of the market maker, snipers, and non-snipers in this scenario.

The lecture continues with a discussion on trading opportunities and profits for the market maker and snipers in the case of news arrival. The market maker can profit from trading with informed investors and uninformed noise traders, but incurs losses if sniped by other traders. Snipers have a trading opportunity with a probability defined as lambda jump, and this opportunity is profitable if J (jump) is greater than s over 2. For high-frequency traders to remain indifferent between adopting either rule, the expected profit of the market maker should be equal to the expected profit of a sniper.

The speaker then shifts the focus to the equilibrium spread in trading and how it is unaffected by the number of high-frequency traders in the market. This means that having more high-frequency traders does not necessarily improve the market in terms of spread, liquidity, or price narrowing. The lecture also explores the proposal of a frequent batch auction as a potential solution to the market failure caused by continuous trading. In a frequent batch auction, traders can submit their orders at different intervals based on their latency. Uninformed, slow traders submit their orders earlier, while informed, fast traders can submit later but at larger time intervals.

The lecture explains that implementing a batch auction system introduces delays, which can be inefficient as they allow the possibility of asymmetric information, enabling fast traders to trade on stale quotes that arrive during this time. However, if the delay time (tau) is sufficiently large, the relative length of the interval where informed trading occurs becomes small enough to mitigate the problem of informed trading and reduce the sniping of stale quotes. This suggests that transitioning from a continuous market to relatively frequent batch auctions can be a solution to address the race for minimized latency among high-frequency traders.

The discussion then shifts to the impact of public information on markets. The lecturer highlights that most models have primarily focused on the effects of asymmetric information and private signals, while the influence of overall volatility and global uncertainty on prices and trade has been less explored. The concept of higher-order beliefs is introduced, which has gained traction in explaining empirical phenomena. The lecture presents a model that attempts to explain the high trading volume observed after public announcements through the lens of higher-order beliefs.

Next, the concept of second-order beliefs in game theory is explored within the framework of a simple model known as the Lost Milgram Model. This model incorporates two components, theta one and theta two, which are equiprobable and independent, and collectively determine the asset's value. Both traders observe the public signal theta one, but only the informed trader has access to theta two. The public signal impacts outcomes in terms of spread but not mid-price. Understanding second-order beliefs is crucial in comprehending player behavior in games, although most games reduce them to first-order beliefs due to the complexity and inconvenience associated with infinite loops.

The speaker explains that theta two, the private signal available only to the informed trader, should be expected based on the public information accessible to all traders. The dealer, who has access to public information, knows that if the signal is theta one and the order comes from a noise trader, the expected value conditioned on this information is simply theta one. The bid price, which can be higher or lower, is also determined by the same information. As a result, the spread does not depend on theta one and remains constant. In this closed Milgram model, all agents simultaneously update their opinions about the asset's valuation in response to the public signal, but no actual trades occur. The model assumes that all agents only consider the fundamental value of the asset and does not incorporate resale.

Additionally, the lecture introduces a model of trading with asymmetric information involving two generations of traders with different trading times and locations. Short-term traders in London offload their positions to traders in New York at the end of the London trading day, as New York traders are willing to carry inventory overnight. London traders primarily focus on the resale value of their positions to New York traders, thus forming conjectures about how much New York traders would be willing to pay for their positions upon purchasing assets. The speaker demonstrates that more precise public information leads to increased disagreement among traders regarding the asset's value. This disagreement generates trading volume and diverging beliefs based on private information. The speaker also addresses a question regarding how currency traders close their positions, which can be done by either holding cash in a safe currency or repaying borrowed money in the same currency.

  • 00:00:00 The lecturer discusses the effect of high-frequency trading (HFT) on markets and the problem of public information. The existence of HFT in the market leads to informational asymmetry between traders, just like having more informed traders, harming liquidity and widening the spread, and not necessarily leading to better price discovery. High-frequency trading is like an arms race with wasteful investment in gaining advantages, but when everyone is fast, it is the same as when everyone is slow, except everyone has invested a lot of money into getting fast. The lecturer proposes to replace the continuous auction with frequent batch auctions but HFT generates these arbitrary opportunities that do not vanish over time and will not foster the correlation between identical assets, even with more HFT traders, meaning that the problem of HFT would not be solved solely by a new auction system.

  • 00:05:00 The presenter discusses price efficiency and how it pertains to the S&P 500 spot and future contracts. The prices of these assets are correlated as they both follow the S&P 500, but the future contract is short-term and reflects the expected value of the S&P 500 in one week. Prices are martingales and should be efficient for these S&P 500 future contracts. Price data from a trading day shows that the two prices are closely correlated, but when examined at shorter intervals, the correlation between the two begins to vanish.

  • 00:10:00 The correlation between price indices is discussed, with a focus on the opportunities for arbitrage. The correlation between two price indices increases with time intervals, but as the time interval shrinks to zero, the correlation is always zero, meaning that the fastest traders who can operate on a few milliseconds notice will always have access to arbitrage opportunities. The same point is illustrated by a graph that shows medium profits per arbitrage over time, which does not decline. A simple model that explains this phenomenon is also presented, where there are two types of traders in the market, the moist traders who arrive randomly over time and high-frequency traders who have access to arbitrage opportunities.

  • 00:15:00 The professor explains the role of noise traders and high-frequency traders in the market. Noise traders arrive randomly and want to buy or sell one unit of a stock with no specific intention. High-frequency traders, on the other hand, act as liquidity providers, and one of them takes up the role of the market maker posting quotes for one unit of the asset. Other high-frequency traders act as stale quote snipers, and if they observe public news before the market maker does, they can snipe these stale quotes. The professor computes the expected flow profits of the market maker, the snipers, and the non-snipers in this scenario.

  • 00:20:00 The lecturer discusses the different trading opportunities and profits that arise for the market maker and the snipers in the case of an arrival of news. The market maker makes profits through trading with informed investors, uninformed noise traders, and losses if sniped by other traders. The snipers, on the other hand, get to trade with probability lambda jump and have a profitable trading opportunity if J is greater than s over 2. The expected profit of the market maker should be equal to the expected profit of a sniper for high-frequency traders to remain indifferent between adopting either of the two rules.

  • 00:25:00 The speaker discusses the equilibrium spread in trading and how it is not affected by the number of high-frequency traders in the market. This means that having more high-frequency traders does not necessarily benefit the market as it does not change the spread or improve liquidity or narrow down the prices. The speaker also talks about the proposal of a frequent batch auction to counter this market failure caused by continuous trading, which allows traders to submit their orders at different intervals depending on their latency. The uninformed, slow traders submit their orders earlier than the informed, fast traders who can submit later but at a larger time interval.

  • 00:30:00 The speaker explains that the delay caused by a batch auction system can be inefficient as it allows the possibility of asymmetric information where fast traders can trade on stale quotes that arrive during this time. However, if the delay time (tau) is big enough, the relative length of the interval where informed trading happens becomes small enough that the informed trading problem vanishes, reducing the sniping of stale quotes. This means that moving from a continuous market to relatively frequent batch auctions can be a solution to high-frequency traders' race to minimize their latency.

  • 00:35:00 The focus shifts to the effect of public information on markets. The lecturer explains that most of the models seen so far have mostly looked at the effects of asymmetric information and private signals. However, the effect of overall volatility of global uncertainty on prices and trade on the markets in general has rarely been looked at. The lecturer then introduces the concept of higher-order beliefs, which are theoretical but have gained traction in explaining empirical phenomena. The lecture looks at a model that tries to explain the high trading volume after public announcements through higher-order beliefs.

  • 00:40:00 The concept of second-order beliefs in game theory is explored in the context of a simple model called the Lost Milgram Model. The model involves two components that form an asset's value, theta one and theta two, both being equiprobable and independent. The two traders observe public signal theta one, but only the informed trader observes theta two. The public signal affects the outcomes, but only in terms of the spread and not the mid-price. The concept of second-order beliefs is crucial in understanding the behavior of players in games, but these are often reduced to first-order beliefs in most games due to the complexity and inconvenience of working with infinite loops.

  • 00:45:00 The speaker explains that theta 2, which is the private signal that only the informed trader receives, should be expected given the public information available to traders. The dealer has access to public information and knows that if the signal was theta 1 and the order comes from a noise trader, the expected value condition on this information that the dealer receives is just theta 1. However, the same applies to the bid price, which will be higher or lower, and therefore, the spread does not depend on theta 1, meaning it is constant. In this closed Milgram model, all agents in the market simultaneously update their opinion about the valuation of the asset in response to the public signal, but no trade actually happens. The model assumes that all agents only care about the fundamental value of the asset and does not feature any resale.

  • 00:50:00 The speaker introduces a model of trading with asymmetric information in which there are two generations of traders with different trading times and locations. Short-term traders in London offload their position to traders in New York at the end of the London trading day, as the New York traders are willing to carry inventory overnight. London traders only care about the resale value of their position to New York traders, and therefore form conjectures about how much New York traders will be willing to pay for their positions when they buy assets. The speaker shows that more precise public information leads to more disagreement among traders about the asset's value, generating trading volume and diverging beliefs depending on private information. The speaker also answers a question about how currency traders close their positions, which can be done by either holding cash in a safe currency or repaying borrowed money in the same currency.
Lecture 13, part 1: High-Frequency Trading; Public Information (Financial Markets Microstructure)
Lecture 13, part 1: High-Frequency Trading; Public Information (Financial Markets Microstructure)
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Lecture 13, part 1: High-Frequency Trading; Public InformationFinancial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course...
 

Lecture 13, part 2: Public Information (Financial Markets Microstructure)



Lecture 13, part 2: Public Information (Financial Markets Microstructure)

The lecturer dives into the Contour model, starting with a simple example that illustrates the divergence of second-order beliefs between two groups of traders, labeled I and J. In this example, the fundamental value of the asset has two components, theta I and theta J. Traders in Group I possess some information about theta I, while traders in Group J have a signal about theta J. However, there is no public signal, and the assumptions of mutual independence and zero mean are made. As a result, trader I and trader J have no knowledge about each other's theta, leading to a second-order belief of zero.

Moving forward, the lecture delves into the influence of public information and assumes the existence of a public signal Y that provides information about the total theta. Trader I's opinion about trader J's asset valuation does not rely on trader I's private signal but is based on both traders' observations of the public signal Y. It is found that the second-order expectation decreases in X I, indicating that the higher a trader's private signal is, the lower their valuation of the other player's asset. This result can be understood intuitively as a trader with a high private signal and a positive valuation of the asset assuming that the other player, who lacks the same private signal, values the asset less.

The lecturer discusses the significance of second-order beliefs in financial markets' microstructure and highlights the heterogeneity of information possessed by different players regarding the various components of the total asset value (theta). When public information is more precise, private signals of different players diverge, leading to increased trade volumes. This explains why there is typically higher trading activity around public announcements that generate new public information. Most models in this field assume that all signals pertain to the same thing, but accounting for heterogeneity can result in more informative models.

To illustrate the role of second-order beliefs in driving trade, the speaker introduces the framework of the Contour model. This model consists of two groups of traders, I and J, operating over three periods. In the second period, traders from Group I exit the market, while traders from Group J receive value theta from holding the asset in the third period. All traders are competitive and can condition their demand on the price, behaving similarly to dealers in the Kyle model. Traders in the model have exponential utility with constant absolute risk aversion, and their wealth is determined by di times p2 minus p1 for traders in Group I and value theta minus p2 for traders in Group J.

The model assumes a normal aggregate supply of assets in both periods, with a zero mean and some variance. In the first period, the asset supply must equal the demand from Group I traders who exercise their demand function. In the second period, asset demand must equal the total demand from Group J traders, including Group I traders who sell their holdings from the first period, plus an additional aggregate supply X. Due to the randomness of this supply, prices will not be perfectly informative, resulting in imperfect informational efficiency. The maximization problem for Group I traders involves maximizing their expected utility from wealth given their private and public signals, with the only choice being their demand DI.

The speaker explains the problem setup with two traders, where trader I possesses an asset and trader J needs it, and the uncertainty lies in the price at which they are willing to transact. Equilibrium is assumed to have a linear relationship between P2 and P1, U1 and U2, resulting in a normal distribution of trader I's wealth. By applying mean-variance preferences, the speaker shows that agents who maximize their carry utility are identical to agents with mean-variance preferences. Trader J's problem is solved using the same approach as trader I. The resulting maximization problem considers the expectation and variance of their wealth given the conditioning variables.

The lecturer explains the computation of the model's equilibrium. Prices are assumed to be linear functions of relevant factors, including the public signal Y, the supply and demand of both periods, and the asset value. P1 is a linear function of theta, the public signal Y, and the supply U1, while P2 is a linear function of theta J, the public signal Y, and the supply Y to U2. The price signal of period 1, q1, depends on the local supply and demand. The agents' optimal demands are determined by the variance of P2 and the precision of their information about P2 and theta. To compute the equilibrium, the speaker explains how to obtain the expectations of P2 conditioned on market demands and supplies.

The speaker discusses the information available to traders in Group J compared to those in Group I, particularly the information about theta that traders extract from the previously established market price. This advantage allows Group J traders to have an edge in the market over Group I traders. The speaker explains that prices will be linear functions with different coefficients, although these coefficients are not identified at this point. The process of finding q1, which represents the conditional expectation of theta I given price p1 and Y, is explained, along with its relation to the prices in the market. The purpose of determining these expectations and prices is to understand how they factor into the agents' optimal strategies.

The lecturer explains how to express the conditional expectation of P2 and theta as linear combinations of signals, including X, Y, q1, q2, and other variables. These expressions are then plugged back into the optimal strategies to obtain equilibrium demands for both players. Market clearing conditions are used to connect the equilibrium prices to the signals, resulting in linear prices for P1 and P2. By matching the coefficients, the optimal demands can be calculated as a function of the signals. This process provides one equilibrium of the model, although there may exist other equilibria with nonlinear prices.

The speaker discusses how trading is driven by disagreement among agents and how player 1's optimal demand in period 1 depends on their second-order expectation of theta. A higher private signal received by agents in period 1 leads to a lower expectation of second-order beliefs held by agents in period 2, resulting in lower prices in period 2. The paper also considers a slightly more general model that includes theta K.

The lecture also addresses the impact of public information on trading volume, noting that more precise signals lead to higher trading volume. The model considers the effects of short and long-horizon traders on market integration and shows that high market integration leads to low trading volume. An empirical paper is referenced to support these results, which demonstrate that public announcements have a strong effect on trading volumes when there is lower market integration. However, the lecturer cautions that standard models may not accurately represent the impact of public information on trading volume.

Continuing the lecture, the speaker emphasizes the need for more accurate models that capture the impact of public information on trading volume. Standard models often overlook the heterogeneity of signals and fail to account for the complex dynamics that arise from different players possessing varying levels of information. By incorporating these factors into the models, researchers can gain deeper insights into market behaviors and outcomes.

Next, the lecturer explores the broader implications of the Contour model and its relevance to financial markets. The model provides a framework for understanding how second-order beliefs drive trading activities and price formation. It highlights the importance of considering not only the direct beliefs and signals of individual traders but also their beliefs about the beliefs of others. These higher-order expectations can have a significant impact on market dynamics, influencing trading decisions, price levels, and trading volumes.

Furthermore, the Contour model sheds light on the interplay between public information, private signals, and market integration. The precision of public information affects the divergence of private signals among traders, which, in turn, impacts trading volumes. When public announcements contain highly informative signals, they lead to greater heterogeneity in private signals, resulting in increased trading activity. However, the degree of market integration also plays a role, as high integration dampens trading volume due to a convergence of signals and reduced heterogeneity.

To support these findings, the lecturer references an empirical paper that provides empirical evidence for the relationship between public announcements, market integration, and trading volumes. The study shows that when market integration is lower, public announcements have a more pronounced effect on trading volumes. This highlights the importance of considering the interaction between public information, market structure, and trading behavior in empirical research.

The lecture on the Contour model explores the divergence of second-order beliefs among traders, the impact of public information on trading dynamics, and the role of market integration. By incorporating heterogeneity in signals and beliefs into models, researchers can better understand and predict market behaviors. The lecture highlights the need for more accurate models that capture the complex dynamics of financial markets and provides insights into the factors that drive trading volume and price formation.

  • 00:00:00 The lecturer delves into the Contour model, starting with a simple example that showcases the divergence of second-order beliefs of two groups of traders, labeled I and J, with the fundamental value of the asset having two components theta I and theta J. Traders in Group I will have some information about theta I, while traders in the second group have signal about theta J. However, there is no public signal, and mutual independence and being 0 mean are assumed. From the model, it is seen that trader I and trader J will have no idea about each other's theta, leading to a second-order belief of zero.

  • 00:05:00 The lecture continues to discuss public information and assumes the existence of a public signal Y that is informative about the total theta. Trader I's opinion about trader J's asset valuation does not depend on trader I's private signal but is based on both traders' observations of the public signal Y. The second-order expectation is found to be decreasing in X I, meaning that the higher a trader's private signal is, the lower they value the other player's asset. The intuition behind this result is that if a player has a high private signal and values the asset highly, they assume that the other player, who does not have the same private signal, values the asset less.

  • 00:10:00 The lecturer discusses the intuition behind why second-order beliefs matter in financial markets microstructure. The key factor is the heterogeneity of information that different players possess about the various components of the total value of the asset being traded (theta). The more precise the public information is, the more the private signals of different players diverge, leading to increased trade volumes. This explains why there is typically more trading around public announcements that generate new public information. The standard assumption in most models of this kind is that all signals are about the same thing, but the lecturer argues that accounting for this heterogeneity can yield more informative models.

  • 00:15:00 The speaker discusses the framework of a condor model to demonstrate how second-order beliefs drive agents to trade. The model consists of two groups of traders, I and J, who operate over three periods, with the I traders leaving the market in period two and the J traders receiving value theta from having the asset in period three. All traders are competitive, and they can condition their demand on the price, with traders behaving like dealers in the Kyle model. The traders have exponential utility with constant absolute risk aversion, and their wealth is given by di times p2 minus p1 for traders I and value theta minus p2 for traders J.

  • 00:20:00 The model of the financial market microstructure assumes a normal aggregate supply of assets in both periods, with zero mean and some variance. In period 1, the asset supply must equal demand from I traders who exercise their demand function, while in period 2, asset demand must equal the total demand from J agents, including I traders who sell their U1 holdings, plus some extra aggregate supply X. The randomness of this supply means that prices will not be perfectly informative, resulting in imperfect informational efficiency. I traders' maximization problem is to maximize their expected utility from wealth given their private and public signals, with the only choice being their demand DI.

  • 00:25:00 The speaker explains the setup of the problem with two traders, where trader I has an asset and trader J needs it, and the uncertainty lies in the price they are willing to pay for it. The equilibrium is assumed to have a linear relationship between P2 and P1, U1, and U2, resulting in a normal distribution of agent I's wealth. By applying mean variance preferences, the speaker shows that agents who maximize their carry utility are identical to agents who have mean variance preferences. Similarly, trader J's problem is solved using the same approach as that of trader I. The resulting maximization problem takes into account the expectation and variance of their wealth given the conditioning variables.

  • 00:30:00 The speaker discusses computing the equilibrium of the model. The prices are assumed to be linear functions of everything relevant, including the public signal Y, the supply and demand of both periods, and the asset value. P1 is a linear function of theta, the public signal Y, and the supply U1, while P2 is a linear function of theta J, the public signal Y, and the supply Y to U2. The price signal of period 1, q1, depends on the local supply and demand. The agents' optimal demands are determined by the variance of P2 and the precision of their information about P2 and theta. To compute the equilibrium, the speaker goes on to explain how to arrive at the expectations of P2 conditioned on market demands and supplies.

  • 00:35:00 The speaker discusses the information that J traders have compared to I traders, specifically information about theta the time that traders extract from the price that was established in the market before they arrived. This allows J traders to have an advantage in the market over I traders. The speaker explains that prices will be linear functions and that there will be different coefficients, however, at this point, they cannot identify these coefficients. They go on to explain the process of finding q1, which is the conditional expectation of theta I given price p1 and Y, and how it relates to the prices in the market. The purpose of finding these expectations and prices is to understand how they factor into the agents' optimal strategies.

  • 00:40:00 The lecturer explains how to express the conditional expectation of p2 and θ as linear combinations of signals, including X, Y, q1, q2, and other variables. These expressions are then plugged back into the optimal strategies to obtain equilibrium demands for both players. Market clearing conditions are used to connect the equilibrium prices to the signals, resulting in linear prices for P1 and P2. By matching the coefficients, the optimal demands can be calculated as a function of the signals. This process gives us one equilibrium of the model, but there may be other equilibria with nonlinear prices.

  • 00:45:00 The speaker discusses how trading is driven by disagreement between agents and how the optimal demand of player 1 in period 1 depends on their second-order expectation of theta. The higher the private signal received by agents in period 1, the lower they expect the second-order beliefs of period 2 agents to be, resulting in lower prices in period 2. The paper also considers a slightly more general model that includes theta K.

  • 00:50:00 The lecturer discusses the impact of public information on trading volume, where more precise signals lead to higher trading volume. The model considers the effects of short and long-horizon traders on market integration, which shows that high-market integration leads to low trading volume. An empirical paper is also used to support the results, which shows that public announcements have a strong effect on trading volumes when there is lower market integration. However, the lecturer cautions that standard models may not accurately represent the impact of public information on trading volume.
Lecture 13, part 2: Public Information (Financial Markets Microstructure)
Lecture 13, part 2: Public Information (Financial Markets Microstructure)
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Lecture 13, part 2: Public InformationFinancial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.y...
 

Exercise class 5, part 1 (Financial Markets Microstructure)



Exercise class 5, part 1 (Financial Markets Microstructure)

The lecturer dives into the Contour model, starting with a simple example that illustrates the divergence of second-order beliefs between two groups of traders, labeled I and J. In this example, the fundamental value of the asset has two components, theta I and theta J. Traders in Group I possess some information about theta I, while traders in Group J have a signal about theta J. However, there is no public signal, and the assumptions of mutual independence and zero mean are made. As a result, trader I and trader J have no knowledge about each other's theta, leading to a second-order belief of zero.

Moving forward, the lecture delves into the influence of public information and assumes the existence of a public signal Y that provides information about the total theta. Trader I's opinion about trader J's asset valuation does not rely on trader I's private signal but is based on both traders' observations of the public signal Y. It is found that the second-order expectation decreases in X I, indicating that the higher a trader's private signal is, the lower their valuation of the other player's asset. This result can be understood intuitively as a trader with a high private signal and a positive valuation of the asset assuming that the other player, who lacks the same private signal, values the asset less.

The lecturer discusses the significance of second-order beliefs in financial markets' microstructure and highlights the heterogeneity of information possessed by different players regarding the various components of the total asset value (theta). When public information is more precise, private signals of different players diverge, leading to increased trade volumes. This explains why there is typically higher trading activity around public announcements that generate new public information. Most models in this field assume that all signals pertain to the same thing, but accounting for heterogeneity can result in more informative models.

To illustrate the role of second-order beliefs in driving trade, the speaker introduces the framework of the Contour model. This model consists of two groups of traders, I and J, operating over three periods. In the second period, traders from Group I exit the market, while traders from Group J receive value theta from holding the asset in the third period. All traders are competitive and can condition their demand on the price, behaving similarly to dealers in the Kyle model. Traders in the model have exponential utility with constant absolute risk aversion, and their wealth is determined by di times p2 minus p1 for traders in Group I and value theta minus p2 for traders in Group J.

The model assumes a normal aggregate supply of assets in both periods, with a zero mean and some variance. In the first period, the asset supply must equal the demand from Group I traders who exercise their demand function. In the second period, asset demand must equal the total demand from Group J traders, including Group I traders who sell their holdings from the first period, plus an additional aggregate supply X. Due to the randomness of this supply, prices will not be perfectly informative, resulting in imperfect informational efficiency. The maximization problem for Group I traders involves maximizing their expected utility from wealth given their private and public signals, with the only choice being their demand DI.

The speaker explains the problem setup with two traders, where trader I possesses an asset and trader J needs it, and the uncertainty lies in the price at which they are willing to transact. Equilibrium is assumed to have a linear relationship between P2 and P1, U1 and U2, resulting in a normal distribution of trader I's wealth. By applying mean-variance preferences, the speaker shows that agents who maximize their carry utility are identical to agents with mean-variance preferences. Trader J's problem is solved using the same approach as trader I. The resulting maximization problem considers the expectation and variance of their wealth given the conditioning variables.

The lecturer explains the computation of the model's equilibrium. Prices are assumed to be linear functions of relevant factors, including the public signal Y, the supply and demand of both periods, and the asset value. P1 is a linear function of theta, the public signal Y, and the supply U1, while P2 is a linear function of theta J, the public signal Y, and the supply Y to U2. The price signal of period 1, q1, depends on the local supply and demand. The agents' optimal demands are determined by the variance of P2 and the precision of their information about P2 and theta. To compute the equilibrium, the speaker explains how to obtain the expectations of P2 conditioned on market demands and supplies.

The speaker discusses the information available to traders in Group J compared to those in Group I, particularly the information about theta that traders extract from the previously established market price. This advantage allows Group J traders to have an edge in the market over Group I traders. The speaker explains that prices will be linear functions with different coefficients, although these coefficients are not identified at this point. The process of finding q1, which represents the conditional expectation of theta I given price p1 and Y, is explained, along with its relation to the prices in the market. The purpose of determining these expectations and prices is to understand how they factor into the agents' optimal strategies.

The lecturer explains how to express the conditional expectation of P2 and theta as linear combinations of signals, including X, Y, q1, q2, and other variables. These expressions are then plugged back into the optimal strategies to obtain equilibrium demands for both players. Market clearing conditions are used to connect the equilibrium prices to the signals, resulting in linear prices for P1 and P2. By matching the coefficients, the optimal demands can be calculated as a function of the signals. This process provides one equilibrium of the model, although there may exist other equilibria with nonlinear prices.

The speaker discusses how trading is driven by disagreement among agents and how player 1's optimal demand in period 1 depends on their second-order expectation of theta. A higher private signal received by agents in period 1 leads to a lower expectation of second-order beliefs held by agents in period 2, resulting in lower prices in period 2. The paper also considers a slightly more general model that includes theta K.

The lecture also addresses the impact of public information on trading volume, noting that more precise signals lead to higher trading volume. The model considers the effects of short and long-horizon traders on market integration and shows that high market integration leads to low trading volume. An empirical paper is referenced to support these results, which demonstrate that public announcements have a strong effect on trading volumes when there is lower market integration. However, the lecturer cautions that standard models may not accurately represent the impact of public information on trading volume.

Continuing the lecture, the speaker emphasizes the need for more accurate models that capture the impact of public information on trading volume. Standard models often overlook the heterogeneity of signals and fail to account for the complex dynamics that arise from different players possessing varying levels of information. By incorporating these factors into the models, researchers can gain deeper insights into market behaviors and outcomes.

Next, the lecturer explores the broader implications of the Contour model and its relevance to financial markets. The model provides a framework for understanding how second-order beliefs drive trading activities and price formation. It highlights the importance of considering not only the direct beliefs and signals of individual traders but also their beliefs about the beliefs of others. These higher-order expectations can have a significant impact on market dynamics, influencing trading decisions, price levels, and trading volumes.

Furthermore, the Contour model sheds light on the interplay between public information, private signals, and market integration. The precision of public information affects the divergence of private signals among traders, which, in turn, impacts trading volumes. When public announcements contain highly informative signals, they lead to greater heterogeneity in private signals, resulting in increased trading activity. However, the degree of market integration also plays a role, as high integration dampens trading volume due to a convergence of signals and reduced heterogeneity.

To support these findings, the lecturer references an empirical paper that provides empirical evidence for the relationship between public announcements, market integration, and trading volumes. The study shows that when market integration is lower, public announcements have a more pronounced effect on trading volumes. This highlights the importance of considering the interaction between public information, market structure, and trading behavior in empirical research.

The lecture on the Contour model explores the divergence of second-order beliefs among traders, the impact of public information on trading dynamics, and the role of market integration. By incorporating heterogeneity in signals and beliefs into models, researchers can better understand and predict market behaviors. The lecture highlights the need for more accurate models that capture the complex dynamics of financial markets and provides insights into the factors that drive trading volume and price formation.

  • 00:00:00 The speaker introduces the exercises for the day, which includes cleaning up exercises from previous classes and revisiting some questions from lecture nine and ten regarding transparency and liquidity in financial markets microstructure. The class mainly focuses on the model of post-trade transparency and the measurement of average price discovery, which will be used to show the efficiency of price discovery in a transparent market. The class will also be limited to the case where there are enough informed traders. The video outlines the model of the transparency and the different notations that will be used in the class.

  • 00:05:00 The speaker explains a model used to illustrate the different ways in which markets can operate, with a focus on transparent and opaque markets. The model assumes a particular distribution of how traders arrive at a market, with both informed and uninformed traders. In a transparent market, all dealers in the second period can see the first order and can identify the informed trader based on the correlation in order flow. In the opaque market, only the dealer who executed the first order knows what it was, making pricing more involved. The transparent market uses standard loss-on-Milgram pricing, while in the opaque market, dealers will have to guess whether the first trader was informed or not to price accordingly.

  • 00:10:00 The speaker discusses the market microstructure in a financial market and how dealers set their prices to make a profit. The uninformed dealer's price is based on the expected value, but the informed dealer sets their price lower than the uninformed dealer's quote. The uninformed dealers then quote the widest spread possible to avoid trading at a loss. Dealer I trades at a profit by offering unappealing prices to uninformed traders. The profits from information generate a quote war in period one as both dealers want to attract order flow to make a profit in period two.

  • 00:15:00 The speaker discusses the profit per trade that informed dealers get in the second period of trading and how it leads to half spreads being reduced to a certain value. The speaker explains how the model assumes pi to be greater than half and why it is uncomfortable to have half spreads that are negative. They also discuss how price discovery works in this model, including the computation of the residual variance expression and the possible events that occur in the model. The section concludes by explaining the behavior of informed and uninformed traders in different scenarios.

  • 00:20:00 The speaker discusses the computation of the transaction price and the replication process to ensure the accuracy of the calculations. The probability of selling and buying an asset is divided equally, which determines the transaction price either as a1t or b1t. The speaker replicates the computation of the sell order probability for an informed trader and an uninformed trader, with the probability of pi and 1-pi/2, respectively. Using the model's symmetry, the speaker simplifies the expression for the squared expectation of p1t - v, showing that both the upper and lower brackets are equal. Additionally, the resulting first bracket simplifies to 1 + pi/2 over two.

  • 00:25:00 The speaker explains how to compute the residual variance for prices in two periods under two scenarios, focusing on the second period under transparency. With probability pi, traders are informed and the residual variance is zero, while with probability one minus pi, the residual variance is equal to sigma, meaning the price reverts down to mu. By taking the average of the two terms over time, the expression for the residual variance under transparency is derived.

  • 00:30:00 The speaker discusses the computation of the expected price variance in the first period under opaqueness, which is equal to the same amount as that under transparency. The expected price variance is derived through algebraic manipulation of the half spreads and involves two cases, one where there is a high value of the asset and both traders want to buy and the other where there is a high value of the assets and the traders are willing to sell. The final equation includes terms such as pi, sigma, mu, and four pi squared sigma squared, which are slowly simplified to determine the expected price variance.

  • 00:35:00 The speaker discusses the comparison between residual price variances under opaqueness and transparency. Using algebraic computations, they reveal that the residual price variance under transparency is lower than under opaqueness, indicating that price discovery under transparency is better. While this may seem like an intuitive result, the calculations required to arrive at this conclusion are not entirely trivial and involve complex mathematical equations. The speaker concludes by stating that this completes their exploration of this exercise and that the remaining two problems will be discussed later.

  • 00:40:00 The instructor discusses the length of time it will take to cover the next two exercises and mentions that they may finish early. He suggests taking a break before moving on and offers to answer any questions about the previous problem once they return from the break.
Exercise class 5, part 1 (Financial Markets Microstructure)
Exercise class 5, part 1 (Financial Markets Microstructure)
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Exercise class 5, part 1Financial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtube.com/pla...
 

Exercise class 5, part 2 (Financial Markets Microstructure)



Exercise class 5, part 2 (Financial Markets Microstructure)

The lecture begins with the introduction of the day's exercises, which involve revisiting and cleaning up previous class exercises. The focus is on questions from lectures nine and ten, specifically related to transparency and liquidity in financial markets microstructure. The lecturer explains that the class will mainly concentrate on the model of post-trade transparency and the measurement of average price discovery. The analysis will be limited to the case where there are sufficient informed traders. The video provides an overview of the transparency model and introduces the different notations that will be used throughout the class.

Moving on, the speaker delves into a model designed to illustrate the various ways in which markets can operate, with particular emphasis on transparent and opaque markets. The model assumes a specific distribution of how traders enter the market, including both informed and uninformed traders. In a transparent market, all dealers in the second period have access to the first-order information and can identify the informed trader based on the correlation in order flow. In contrast, in an opaque market, only the dealer who executed the first order knows its content, making pricing more complex. In the transparent market, standard loss-on-Milgram pricing is used, while in the opaque market, dealers must make educated guesses about the informed trader to price accordingly.

Next, the lecturer discusses the market microstructure in a financial market and how dealers set their prices to generate profits. The price quoted by uninformed dealers is based on the expected value, while informed dealers set their price lower than the quote of uninformed dealers. Uninformed dealers widen their spreads to avoid trading at a loss. Dealer I, who possesses information, aims to make a profit by offering unattractive prices to uninformed traders. The profits generated from information trigger a quote war in the first period as both dealers compete to attract order flow and earn profits in the second period.

The speaker further explains the profit per trade that informed dealers receive in the second period and how it leads to a reduction in half spreads to a specific value. The model assumes that the profit (pi) is greater than half and discusses the discomfort associated with negative half spreads. Price discovery in this model is explored, including the computation of the residual variance expression and the potential events within the model. The lecture concludes this section by examining the behavior of informed and uninformed traders in different scenarios.

Continuing, the speaker addresses the computation of the transaction price and the replication process to ensure accuracy in calculations. The probability of selling and buying an asset is divided equally, determining whether the transaction price is a1t or b1t. The computation of the sell order probability for informed and uninformed traders is replicated, considering the probabilities pi and 1-pi/2, respectively. By utilizing the symmetry of the model, the expression for the squared expectation of p1t - v is simplified, demonstrating that the upper and lower brackets are equal. The resulting first bracket further simplifies to (1 + pi)/2.

The lecture then proceeds to explain the computation of the residual variance for prices in two periods, focusing on the second period under transparency. In scenarios where traders are informed with probability pi, the residual variance is zero, while in cases where traders are uninformed (with probability one minus pi), the residual variance is equal to sigma, signifying a reversion of price to mu. By averaging the two terms over time, the expression for the residual variance under transparency is derived.

Furthermore, the computation of the expected price variance in the first period under opaqueness is discussed. It is determined to be equal to the expected price variance under transparency. The computation involves algebraic manipulation of the half spreads and considers two cases: one where the asset has a high value and both traders want to buy, and the other where the asset has a high value and traders are willing to sell. The final equation includes terms such as pi, sigma, mu, and four pi squared sigma squared, which are gradually simplified to determine the expected price variance.

The speaker proceeds to compare the residual price variances under opaqueness and transparency. By performing algebraic computations, they demonstrate that the residual price variance under transparency is lower than under opaqueness, indicating better price discovery under transparency. While this result may seem intuitive, the calculations involved in reaching this conclusion are not entirely straightforward and involve complex mathematical equations. The lecture concludes by stating that this completes the exploration of the exercise and mentions that the remaining two problems will be discussed later.

Towards the end, the instructor addresses the timing for covering the next two exercises, suggesting that they may finish earlier than expected. They recommend taking a break before proceeding and offer to answer any questions regarding the previous problem once the break concludes.

  • 00:00:00 The video discusses the value of liquidity in financial markets and focuses on the Gordon model and its implications when dividends are added. The model assumes that investors come to the market and buy a stock, hold it for one period, and then sell it at a constant relative spread. The investors have a required rate of return, denoted as small R, which is typically given by some outside option. The video then explores how the growth of transaction cost return is defined and looks to determine the effect on the liquidity premium when a stock gives out dividends.

  • 00:05:00 The instructor explains how to incorporate dividends into the nominal rate of return, defined as one plus R, that an investor receives from a stock. The investor receives both dividends and a change in the stock price, which can be viewed as two sources of returns. The instructor defines R with dividends as R = (μT + 1 + D) / μT, where μT represents the old fundamental value of the stock and D is the dividend paid to the investor at time T + 1. There are other interpretations as well, including one where dividends are scaled with the stock price, which also yields a higher dividend due to the growth in the stock price. However, this nominal rate of return, as seen from the data, is not exactly what the investor earns due to other factors such as spreads when buying and selling the asset and illiquidity premiums.

  • 00:10:00 The speaker explains the concept of equilibrium gross return by examining the connection between the spread, the required rate of return, and the dividend rate. The investor buys the asset at the price of mu T times the spread of 1 plus s over 2, whereas the selling price is mu t plus 1 times 1 minus s over 2. By plugging in asset prices and conducting some algebra, the speaker arrives at the expression 1 plus capital R equals 1 plus small R plus the fraction of the spread times D minus D divided by 1 plus s over 2. The speaker concludes that rearranging this expression places 1 plus capital R on the left and the remaining variables on the right side.

  • 00:15:00 The instructor explains the algebraic solution to part B of the problem followed by answering part C, which deals with determining how liquidity premium responds to an increase in dividend yield (D) and its intuition. Liquidity premium is the difference between the nominal rate of return and the risk-adjusted rate of return. The liquidity premium is decreasing in D, meaning that an increased dividend yield lowers the liquidity premium as dividends are not subject to stock liquidity. Therefore, as the share of dividends in investor returns increases, the investor suffered less from liquidity, decreasing the required liquidity premium.

  • 00:20:00 The instructor discusses Exercise #2 from Problem Set #2 which covers the data kernel Patterson Model and its reaction to Phi, which is the probability of meeting a dealer. The model features a single asset that lacks a fundamental value and instead pays dividends that different traders value differently. Traders can hold either one or zero units of the asset, but they cannot sell short or stockpile it. The required rate of return is R, and traders can go to a bank that pays interest as an outside option. Traders randomly switch between being high and low value investors with a probability of sigh in each period and must search for dealers to buy or sell assets with a probability of Phi. Dealers do not hold inventory and bargain with traders over prices.

  • 00:25:00 The presenter explores the impact of the probability of finding a dealer (Phi) on the spread generated in the model. The spread is mainly influenced by dealers' market power, as there was no private information or adverse selection in the model. The effect of Phi on the spread is non-monotonic, depending on the probability of value switching (sy). If sy is high and traders expect to trade frequently, to not hold the asset for long periods, and to not stay without the asset for long periods, a higher probability of finding a dealer increases the spread. However, if sy is low, a higher probability of finding a dealer will lower the spread. The presenter discusses the potential positive and negative effects that dominate for different values of sy.

  • 00:30:00 The instructor discusses how traders value assets higher as liquidity increases. This is due to the fact that higher liquidity allows traders to find dealers more frequently, allowing them to trade faster and suffer less from switching to low valuations for dividends. As a result, traders are willing to pay more for assets when liquidity is high, leading to an increase in the asset's value. The instructor further explains that the dealer's bargaining power can also play a significant role in inefficiencies in the market.

  • 00:35:00 The video discusses how the dealer's profit is measured by S and why the spread can possibly increase as Phi increases, as traders are more willing to buy assets and pay more for them. However, dealers appropriate a fixed share of the surplus, and when Phi increases, the dealer's market power decreases, causing the spread to decrease as traders become more competitive. These are two countervailing effects that operate depending on whether Phi is high or low, meaning that one of them dominates in each case, although it is unclear why.

  • 00:40:00 The instructor concludes the exercise class and summarizes the main points discussed. They mention the importance of meeting the dealers when switching values, and how this relates to dealing with both informational and inventory effects. The class ends with a preview of the next topic on bubbles in financial markets, which the instructor promises will be insightful and entertaining.
Exercise class 5, part 2 (Financial Markets Microstructure)
Exercise class 5, part 2 (Financial Markets Microstructure)
  • 2020.05.01
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Exercise class 5, part 2Financial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtube.com/pla...
 

Lecture 14, part 1: Herding and Bubbles (Financial Markets Microstructure)



Lecture 14, part 1: Herding and Bubbles (Financial Markets Microstructure)

The lecture begins with the professor introducing the topic of bubbles in financial markets and highlighting that bubbles pose a puzzle for classical economics. The class then focuses on herding models, which suggest that agents can ignore their private information and trade solely based on public information, leading to everyone doing the same thing and generating herding, which can result in bubbles.

The speaker introduces another model that deals with higher-order beliefs and the lack of aggregation of private information, which can also lead to bubbles. Different definitions of bubbles are provided, including one from Webster Dictionary and Wikipedia. The lecturer discusses three types of definitions of bubbles in financial markets.

The first definition is from the University of Chicago's Wikipedia page, which defines bubbles as a deviation of prices from fundamental values. The second definition is from Investopedia, which refers to a bubble as a surge in equity prices more than warranted by fundamentals in a particular sector, followed by a drastic drop in prices as a massive sell-off occurs. The third definition, from the Chicago Fed, states that bubbles exist when the market price of an asset exceeds its price determined by fundamental factors by a significant amount for a prolonged period.

The lecturer emphasizes that none of these definitions include the behavioral aspect of how traders behave in these markets. The section concludes with examples of bubbles, including Enron, the US housing bubble, and the Bitcoin/cryptocurrency bubble, illustrating both common and exotic cases.

Moving on, the speaker delves into the concept of herding and its role in bubbles within financial markets' microstructure. They reference a previous uranium bubble in early 2006, which may have been initiated by a flooded mine in Canada containing the largest known and developed reserves of uranium. This incident led to a perceived supply shortage and excessive demand, resulting in a bubble in the market for a short period.

The lecture then explores theories on herding, where the idea is to rely on public information and how it can be seen as an efficient response to new information. Herding is described as a rational but inefficient decision-making process in which investors ignore private information in favor of public information, following the dominant force in the market. The momentum trading strategy is presented as an example, where investors buy stocks that are trending up and sell those that are trending down.

The herding model assumes that agents arrive at the market sequentially, receiving private signals and observing the decisions of previous agents but not the private information that led to those decisions. The lecture explains that the ideal outcome would be to pool everyone's private information to achieve the optimal decision and price. However, this is unrealistic, as agents have an incentive to exploit their private information. Due to sequential decision-making, those who arrive earlier have less information to work with, leading to suboptimal outcomes.

The video discusses a model where people start disregarding their private information and rely solely on public information, resulting in herding behavior and informational cascades. The uncertainty in the model is captured by a fundamental value that can be low or high. Agents arrive at the market with a prior belief, which is updated based on private signals. Another belief, which is the same as market valuation, is updated based on the decisions of all past agents. The model demonstrates the inefficiencies that occur when people rely too heavily on public information and ignore their private signals.

The lecture further explores the concept of herding and its relationship with bubbles in financial markets. It is explained that private signals and imperfect prior beliefs can lead to herding behavior, where agents ignore their private signals and behave based on the public belief. The video argues that this behavior can result in a lack of new information being added to the public belief, causing it to remain the same over time.

The speaker presents a model where traders arrive with prior knowledge of an asset's value and are rational. However, noise traders, who have no prior knowledge, buy, sell, or abstain with equal probability, along with the profit-maximizing traders. Initially, the speaker suggests that herding is not possible in this model due to the random nature of the noise traders. However, a more complex model presented by Avery and Zemsky indicates that herding might be possible, considering varying degrees of access to perfect information and the absence of noise traders.

The lecture discusses the uncertainty in the market maker's model, which includes uncertainty about news events and their nature (good or bad). The market maker lacks knowledge about trading with informed or less informed traders and doesn't know the number of informed traders in the economy. Herds can occur in this model, and non-speculative bubbles can arise if all traders know that an asset is fundamentally undervalued while the market maker does not. This creates a speculative bubble where every trader overweighs public information compared to their private signal.

The lecturer briefly touches on non-speculative bubbles and explains that they can also occur through herding. The Gloucester Milgram model is mentioned before the speaker takes a break and provides a preview of the next section, which will cover the Bro Bruna Maya model.

  • 00:00:00 The professor introduces the topic of bubbles in financial markets and explains that bubbles are a puzzle for classical economics. The class then looks at herding models that suggest that agents can ignore their private information and trade solely based on public information, which leads to everyone doing the same thing and generating herding, which can lead to bubbles. The lecture also introduces another model that deals with higher-order beliefs and lack of aggregation of private information, which can also result in bubbles. The professor provides different definitions of bubbles, including one from Webster Dictionary and Wikipedia.

  • 00:05:00 The lecturer discusses three types of definitions of bubbles in financial markets. The first is from the University of Chicago's Wikipedia definition that defines bubbles as a deviation of prices from fundamental values; the second is Investopedia's definition of a bubble, which refers to a surge in equity prices more than warranted by fundamentals in a particular sector, followed by a drastic drop in prices as a massive sell-off occurs; while the third definition from the Chicago Fed states that bubbles exist when the market price of an asset exceeds its price determined by fundamental factors by a significant amount for a prolonged period. The lecturer also highlights that none of these definitions include the behavioral aspect of how traders behave in these markets. The section concludes with examples of bubbles, both common and exotic, including Enron, the US housing bubble, and the Bitcoin/cryptocurrency bubble.

  • 00:10:00 The speaker discusses the concept of herding and bubbles in financial markets microstructure. They reference a previous uranium bubble that occurred in early 2006, which may have been jump-started by a mine in Canada being flooded and containing the largest known and developed reserves of uranium. This led to a perceived shortage of supply and excessive demand, resulting in a bubble in the market for a short while. The lecture then delves into theories on herding, where the idea is to rely on public information, and how it can be an efficient response to new information.

  • 00:15:00 The concept of herding in financial markets is discussed as a potential explanation for bubbles and suboptimal outcomes. Herding is seen as a result of a rational but inefficient decision-making process, where investors ignore private information in favor of public information to follow the dominant force in the market. An example of this is the momentum trading strategy, where investors buy stocks that are trending up and sell those that are trending down. The herding model assumes that agents arrive at the market sequentially, receiving private signals and observing the decisions of previous agents, but not the private information that led to those decisions. The ideal outcome would be to pull everyone's private information to achieve the optimal decision and price, but this is unrealistic, as agents have an incentive to exploit their private information. As a result of sequential decision-making, those who arrive earlier have less information to work with, which can lead to suboptimal outcomes.

  • 00:20:00 The video discusses a model in which people start disregarding their private information and rely solely on public information. This results in herding behavior and informational cascades, where everyone makes decisions based on a few pieces of private information that may be incorrect. The uncertainty in the model is captured by a fundamental value that is either low or high, and agents arrive at the market with a prior belief, PT, which is updated based on private signals. Another belief, QT, is the same as market valuation and is updated based on the decisions of all past agents. Overall, the model shows the inefficiencies that occur when people rely too heavily on public information and ignore their private signals.

  • 00:25:00 The section discusses the concept of herding and bubbles in financial markets microstructure by analyzing the behavior of agents who decide whether or not to invest in an asset based on both public and private information. The agent's private signal and past agents' decisions are combined to form a posterior belief, which is then used to calculate a threshold belief. The agent will only invest if their expected utility from doing so is high enough, meaning if they assign a large enough weight to the asset value actually being high. The threshold belief is decreasing in public belief, indicating that the more favorable information inferred from other agents' decisions, the less confidence the agent needs to invest. If public information is good enough, the private information can be bad enough and vice versa. This discussion highlights the importance of understanding how information and beliefs are combined in financial decision-making.

  • 00:30:00 The video discusses how private signals and imperfect prior beliefs can lead to herding behavior in financial markets. The assumption is that private signals cannot perfectly infer the true state of the market and that prior beliefs are bounded within some interval. Based on this, a public belief is arrived at that determines optimal investment behavior regardless of private signals. This can lead to a herd where agents ignore their private signals and behave based on the public belief. The video argues that this behavior can lead to a lack of new information being added to the public belief, causing it to remain the same over time.

  • 00:35:00 The concept of herding in financial markets is explored. It is demonstrated that once again, the public information is shown to overpower private information, leading to a herd. The key challenge is to arrive at the belief that sets off the herd, which can be incorrect with some probability. Additionally, it is possible for the threshold value to lie within the upper and lower bound, allowing for private information to matter. A more general model is also considered, which shows the possibility of everyone completely ignoring public information and using only their private information to make decisions, leading to inefficiency.

  • 00:40:00 The instructor discusses a model in which rational agents fail to aggregate available information due to their actions not containing enough information or being too noisy to convey private signals. These incorrect herds, which occur when the distribution of private signals is bounded, can be prevented by allowing some people to trade who have a lot of information. The instructor also notes the subtle difference between the terms "herd" and "cascade" and explains that the distinction is not critical for the purposes of the lecture. Finally, the instructor considers the impact of allowing the price to be flexible in the model.

  • 00:45:00 The speaker discusses a model where traders arrive with prior knowledge of an asset's value, and with probability 1, are rational. Noise traders, who have no prior knowledge, buy, sell or abstain with equal probability along with the profit-maximizing traders. The speaker then posits a question to the audience, asking if herding is possible in such a model, to which the answer is no due to the random nature of the noise traders. However, the speaker goes on to explain that a more complex model presented by Avery and Zemsky indicates that herding might be possible. In this model, traders have varying degrees of access to perfect information and noise traders are absent.

  • 00:50:00 The lecturer discusses the uncertainty in the market maker's model, which includes the uncertainty of whether there was a news event and whether it was good or bad news. The market maker doesn't know if they're trading with informed or less informed traders, and they don't know how many informed traders there are in the economy. Herds can happen in this model, and it's possible for there to be non-speculative bubbles if all traders know that an asset is fundamentally undervalued, but the market maker does not. This can lead to a kind of speculative bubble where every trader overweighs public information compared to their private signal.

  • 00:55:00 The speaker briefly discusses non-speculative bubbles and explains that they can also occur through herding. He mentions the Gloucester Milgram model before taking a break and previewing the topic of the next section, the Bro Bruna Maya model.
Lecture 14, part 1: Herding and Bubbles (Financial Markets Microstructure)
Lecture 14, part 1: Herding and Bubbles (Financial Markets Microstructure)
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i had a brief internet outage at 9:50; you can safely skip to 11:05Lecture 14, part 1: Herding and BubblesFinancial Markets Microstructure course (Masters in...
 

Lecture 14, part 2: Herding and Bubbles (Financial Markets Microstructure)



Lecture 14, part 2: Herding and Bubbles (Financial Markets Microstructure)

The lecturer emphasizes that despite the complexity and challenges associated with herding behavior, mispricing, and bubbles in financial markets, there are mechanisms in place that can help mitigate these issues to some extent. The price mechanism, for instance, plays a crucial role in bringing the asset's price back to its fundamental value through market adjustments. However, it is important to note that if uncertainty is particularly high or coordination becomes difficult, herding and mispricing can still occur, leading to the formation of bubbles.

Furthermore, the lecture highlights the concept of momentum trading as a rational strategy. This strategy involves buying an asset when its price is trending upwards and selling it when the price is trending downwards. The lecturer explains that momentum trading can be interpreted as a rational response to the observed market behavior, indicating that traders often make decisions based on the perceived trend rather than solely relying on fundamental analysis.

The lecturer shifts the focus to a specific model that addresses the dynamics of herding and bubbles in financial markets. The model introduces the notion of value growth and its subsequent slowdown, leading to the potential occurrence of an exogenous correction or an endogenous collapse. Rational and behavioral traders are incorporated into the model, where rational traders possess knowledge about mispricing, while behavioral traders exhibit overoptimistic beliefs about the asset's value. The distribution of when rational traders become informed about the mispricing is assumed to be uniform, adding an element of uncertainty regarding the duration of the bubble and the timing of the exogenous correction.

In this context, the lecturer highlights the importance of rational traders' decision-making process. While rational traders are aware that the high price growth is temporary, they lack precise information about when the bubble will burst. This uncertainty poses a challenge for rational traders in determining the optimal time to sell their assets, as they must strike a balance between maximizing profits by selling at a later stage and avoiding potential losses by selling before the collapse. The lecturer underscores the intricate trade-off faced by rational traders and the significance of timing their actions effectively.

Throughout the lecture, the lecturer continuously emphasizes the role of information, coordination, uncertainty, and decision-making in the formation and collapse of bubbles in financial markets. By delving into various models and concepts, the lecturer provides a comprehensive understanding of the factors contributing to herding behavior, mispricing, and the emergence of bubbles, shedding light on the intricacies and challenges inherent in these phenomena.

The lecture concludes by noting that the covered material will be reviewed before moving on to the next topic—auction models. This comprehensive review will ensure a solid foundation of knowledge and understanding before exploring the dynamics of auctions in financial markets.

In the subsequent part of the lecture, the speaker delves into the concept of reputation concerns and contracting incentives, which can further fuel herding behavior in financial markets. Managers, in particular, may feel compelled to follow the actions of others to protect their reputation or secure a safe payoff. This behavior arises when private information cannot be easily aggregated, making it difficult for managers to rely solely on their own signals. Consequently, they may choose to imitate the actions of their peers, even if it goes against their own judgment.

The lecturer underscores that reputation concerns and contracting incentives can promote herding, especially in situations where there is a lack of common knowledge or coordination among market participants. While the price mechanism can partially alleviate the problem by facilitating market adjustments, herding can still persist in cases where uncertainty is pervasive or coordination becomes challenging.

The lecture then delves into a model that explores the relationship between herding, bubbles, and coordination. The model challenges the classical economics argument that bubbles are impossible by introducing the notion that common knowledge about the peak of a bubble may not exist. In such cases, coordination becomes essential in order to facilitate a price adjustment and restore the asset's value to its fundamental level.

The model highlights the significance of higher-order beliefs and their influence on market coordination. It demonstrates that a trader's beliefs about the actions of other traders can impact the overall market dynamics. The speaker emphasizes the interplay between traders' beliefs, coordination, and market outcomes, shedding light on the complex dynamics that can contribute to the formation and persistence of bubbles.

Moving on, the lecturer introduces the audience to a more intricate model that incorporates various factors and scenarios related to asset pricing. This model considers the growth rate of an asset until a random time, at which point it experiences a slowdown. The asset's price continues to grow at a slower rate until an exogenous correction or an endogenous collapse occurs. Rational and behavioral traders are included in the model, with the assumption that rational traders become informed about mispricing at different points in time.

The distribution of when rational traders acquire information about mispricing further adds to the uncertainty surrounding the duration of the bubble and the timing of the correction. The lecturer highlights the importance of rational traders' decision-making under such uncertainty, as they must assess how long to ride the bubble and estimate the remaining time before an exogenous correction takes place.

The lecture provides a comprehensive exploration of herding behavior, mispricing, and the formation of bubbles in financial markets. It covers various models, concepts, and factors that contribute to these phenomena, including reputation concerns, contracting incentives, coordination, higher-order beliefs, and the interplay between rational and behavioral traders. By delving into the intricacies of these dynamics, the lecture equips the audience with a deeper understanding of the complexities involved in financial market dynamics and the challenges associated with predicting and managing bubbles.

  • 00:00:00 Thus, they choose to follow the first manager's lead and invest, even if it goes against their own signal. This leads to herding behavior, which can result in bubbles. Another factor that can lead to bubbles is the market maker's underestimation of the informativeness of the order flow, which results in slow price adjustment and potentially a bubble in the opposite direction. It's important to note the difference between speculative and non-speculative bubbles, and that bubbles can arise due to informational asymmetries and failure of information aggregation. Reputation concerns can also contribute to herding behavior.

  • 00:05:00 The lecturer discusses how reputation concerns and contracting incentives can lead to herding in financial markets, as managers may be incentivized to follow the actions of others to save their reputation or guarantee a safe payoff. The lecturer notes that these factors can promote herding when private information cannot be easily aggregated and that the price mechanism can alleviate the problem to some extent. However, if uncertainty is complicated, herding can still occur. Lastly, the lecturer mentions that momentum trading, buying when the asset is trending upwards and selling when it is trending downwards, can be interpreted as a rational strategy.

  • 00:10:00 The video discusses a model that deals with herding and bubbles in financial markets. The model starts by addressing the classical economics argument that bubbles are impossible due to the backwards induction argument. However, if there is no common knowledge about when the bubble will peak, it is possible for there to be a bubble. The model shows that coordination is needed to cause a price adjustment and bring the price back to the fundamental value of the asset. Higher order beliefs play a role in the coordination, and it is shown that what one trader believes about other traders' actions can have an impact on the market.

  • 00:15:00 The speaker discusses a model of asset pricing where the value of the asset grows at a rate G until some random time T0 where it slows down to a rate R. However, the asset price continues to grow at rate G until either an exogenous correction at time Tau bar or an endogenous collapse due to rational traders deciding to sell occurs. The model has both rational and behavioral traders, and the distribution of the times at which rational traders become informed about mispricing is assumed to be uniform between T0 and T0 plus some beta. This leads to uncertainty for rational traders in terms of how long to write the bubble and how much time is left before the exogenous correction.

  • 00:20:00 The lecture discusses two types of traders: rational and behavioral. Rational traders are informed about the market and understand the mispricing of an asset, while behavioral traders believe that the price surge will last forever and overvalue the asset. When rational traders are willing to sell the asset at a slightly lower price, behavioral traders are willing to buy, believing that the growth will continue. However, there is a limited number of behavioral traders, and they can only absorb a share of the total supply from rational traders. Rational traders are aware that the high price growth is temporary but do not know when it will stop.

  • 00:25:00 The lecturer discusses how traders may not be sure when they are informed about news in the market and what other traders believe. He explains how the distribution of informativeness is uniform, meaning traders have an equal chance of being informed at any time point. If a trader is informed later, they may not know when other traders received the news, causing uncertainty and mistakes about the asset's value. This uncertainty can lead to a mispricing of the asset.

  • 00:30:00 The lecturer explains the tradeoff that traders face when trying to sell an asset before a bubble collapses. They want to sell as late as possible to make a higher profit, but not too late that they miss the opportunity to sell before the bubble bursts. The lecturer also discusses the common knowledge of mispricing layers and how it makes it difficult to predict when to sell the asset. A model is presented in the paper showing the distribution of informativeness times of awareness, and traders' awareness of the bubble before it collapses. The lecturer notes that there is a mistake in the graph presented in the paper, which he challenges the audience to identify.

  • 00:35:00 The lecturer discusses the factors that can lead to the creation of bubbles in financial markets and how to define them. Due to the difficulty of coordination between traders and their limited knowledge about what others know and think, mispricing can endure for a long time even when traders realize a market will crash. A bubble is defined as the persistence of mispricing after enough traders are aware of it to burst it, and if traders take either the maximum loan or short position, where all traders can hold 0 or 1 units of the asset, and rational traders begin with one unit while behavioral traders begin with zero units.

  • 00:40:00 The lecturer explains a more complex model in which the rational seller sells an asset and models allow for other long and short positions, as well as other initial positions. The model shows that when a trader goes short, all other traders who had learned about the mispricing before this trader would have already gone short, meaning that reaction times are monotone. The lecturer then discusses two types of equilibria in this model, which are called exogenous crash and endogenous crash. Exogenous crash occurs when there is a lot of profit to write in the bubble and the risk is low, and endogenous crash happens when the price adjustment is triggered by enough of the rational traders sell in the asset.

  • 00:45:00 The lecturer discusses the incentive for traders to sell their stocks before the bubble bursts, but not too early to miss out on potential profits. The timing of the sale depends on the value of Kappa, which represents the proportion of traders that need to sell before the bubble bursts. When Kappa is high, traders want to delay their sale to be closer to the last trader who sold before the bubble bursts, whereas when Kappa is low, traders want to sell quickly to avoid missing out. This creates a coordination game among traders where they all want to sell around the same time, just before the bubble bursts.

  • 00:50:00 The lecturer discusses sunspot equilibria and how random events can serve as coordination devices. These events, also known as "sunspots," were shown in examples where trade data had a big market impact in the 1980s and statements from Alan Greenspan were more influential in the 1990s. The lecturer concludes that higher-order uncertainty about common knowledge between agents can cause interesting results in some models such as global games. Although the course will not focus on global games this year, the lecturer will review everything covered so far before discussing auction models in the next lecture.
Lecture 14, part 2: Herding and Bubbles (Financial Markets Microstructure)
Lecture 14, part 2: Herding and Bubbles (Financial Markets Microstructure)
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Lecture 14, part 2: Herding and BubblesFinancial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www....
 

Lecture 15, part 1: Auction Models (Financial Markets Microstructure)



Lecture 15, part 1: Auction Models (Financial Markets Microstructure)

Continuing from the previous lecture on herding and bubbles in financial markets, the current lecture shifts the focus to auction models in financial market microstructure. The professor highlights the relevance of auctions in various contexts, including financial markets and production theory. While auction models are not exclusive to financial markets, their universality and applicability make them widely used and studied.

The lecture begins by providing an overview of the three main ways in which trade can be organized: dealer markets, continuous auction models with limit or electronic books, and batch auction models. However, the primary emphasis is on auction models and their characteristics.

The professor introduces auction models by discussing their purpose of capturing the dynamics of imperfect competition between traders or bidders when the number of agents in the market is finite. Auction models are instrumental in studying a range of questions, including market efficiency, market allocation, trading volumes, and price responses.

Several auction formats are presented, including sealed and open bids, first and second price auctions, as well as variations in auction types such as private or common evaluations, one-unit or multi-unit auctions, and single or double-sided auctions. The lecture highlights the significance of these variations in understanding different aspects of market dynamics and trading strategies.

The lecture then delves into specific auction models, starting with the private value first-price auction, which serves as a fundamental and straightforward model. In this auction, there is one item for sale, multiple potential buyers with private valuations, and rational, risk-neutral bidders. The auction proceeds with each bidder submitting a bid, and the highest bidder wins and pays their bid, while the other bidders pay nothing. The lecture explores how bidders' bidding strategies and expected profits are influenced by their desire to win the auction and maximize their expected profit.

Next, the speaker explains the optimization process of maximizing profit in an auction by taking the first derivative with respect to the bidding variable. They demonstrate how the bidding strategy can be derived by considering the inverse function of the bidding function and transforming the probability distribution of bidders' valuations. The lecture emphasizes the importance of finding the equilibrium bid that aligns with the bidding strategy.

Furthermore, the lecturer explores the derivative of valuation with respect to bid, emphasizing the equilibrium condition and the optimal bid that aligns with the bidding strategy. They discuss the role of information asymmetry and the impact it has on the shading of bids compared to valuations.

To illustrate the concepts, the lecture provides a simple example using a distribution and demonstrates how it can be employed to determine the equilibrium strategy. The example highlights the influence of the number of bidders on the degree of shading in bids and the resulting profitability of traders.

The lecturer also touches upon other auction formats, including the English auction and the Dutch auction, discussing their equivalence to the first-price auction in specific contexts. The lecture briefly introduces the concept of common value auctions and explores the differences between single-unit and multi-unit auctions, highlighting the concept of being the "cave highest bid" in multi-unit auctions.

Towards the end of the lecture, the speaker mentions that there are extensions and variations to auction models, but the general approach to solving auction-related problems remains the same. The lecture concludes with an invitation for questions and clarifications regarding the previously discussed private value first-price auction.

The lecture provides a comprehensive introduction to auction models in financial market microstructure, exploring various auction formats, bidding strategies, equilibrium conditions, and their implications for market dynamics and trading outcomes.

  • 00:00:00 The professor discusses auction models in financial markets microstructure. The previous week's lecture covered models of herding and bubbles in financial markets, with an emphasis on public information overpowering private signals and the potential for bubbles to burst due to endogenous market correction. Now, the focus is on the three main ways in which trade can be organized: dealer markets, continuous auction models with limit or e-books, and batch auction models. The professor provides an overview of these models and their characteristics.

  • 00:05:00 The lecturer discusses call auction formats and how they are used in some markets, such as the electricity market, for clearing the market. The lecturer introduces auction models and explains that while auction models are not specific to financial markets, they are widely used because of their universality. The lecturer goes on to mention some of the most relevant models, such as auctioneering and contextual ad options. The lecturer also highlights the two primary applications of auction theory: contextual ad options and spectrum auctions.

  • 00:10:00 The professor discusses how auctions are relevant in financial markets and production theory. The main point of auction models is to capture the imperfect competition between traders or bidders in the presence of a finite number of agents in the market. The models can be applied to study questions such as market efficiency, market allocation, trading volumes, and price responses. The professor lists several auction formats such as sealed and open bids, first and second price auctions, as well as different auction types including private or common evaluations, one-unit or multi-unit auctions, and single or double-sided auctions.

  • 00:15:00 We learn about auction models and how they can be combined in various ways due to the many different variations available. The lecture starts with the simplest model, a private value first price auction, where there is one item for sale, n potential buyers, and each has a private valuation. The auction is such that everyone submits a bid, and the highest bid is drawn to determine the winner who pays their bid, while the other bidders pay nothing. The bidders are rational, meaning they maximize their expected profit and are risk-neutral. The lecture explores how submitting higher bids balances the agent's desire to win with their expected profit, ultimately leading to optimal bidding strategies and symmetric equilibrium.

  • 00:20:00 The speaker discusses auction models in financial market microstructure and how agents can find the optimal bid. They assume that all other agents use some strategy beta effects, and the bidding strategy is strictly increasing in X, meaning there is a maximal bid that one can expect from their opponent. The speaker rules out some possible bids, including bids strictly above beta of X bar, which are strictly dominated by being exactly beta of X bar, and the agent whose private valuation is zero would bid zero and either lose or win and get the useless assets for zero price because they would not be willing to pay anything for the passage. They then explore the probability of winning using probability theory and rewrite the expected profit given some b2b and valuation X.

  • 00:25:00 The speaker explains how to maximize profit in an auction using the first derivative with respect to the variable B. By taking the inverse function of beta on both sides of an inequality, and transforming the probability distribution of a bidder's valuation, the mechanical way to derive this function is found. However, for a simpler and more intuitive understanding, it is stated that by bidding Bi, the bidder wins if the highest valuation of the competitor falls below the valuation of the highest bidder using the strategy beta, and once the profit function is written in this form, it is possible to maximize it by taking the first derivative with respect to B.

  • 00:30:00 The speaker discusses how to find the derivative of valuation with respect to bid according to the bidding function beta. They explain that the equilibrium condition requires the optimal bid to be the same as the bidding strategy, and this strategy is dependent on the distribution of private values. The equilibrium strategy is ultimately equal to the expectation of y1 given that y1 is smaller than X, where bidding much more or less than this optimal bid leads to overpayment or losing to a more aggressive competitor.

  • 00:35:00 The lecturer gives a simple example of a distribution and how it can be used to find the equilibrium strategy. The example uses the assumption of a small number of bidders who are not perfectly competitive, so they get positive profits. The degree of shading in bids depends on the number of players, with larger numbers leading to less shading. The main takeaway from the first price option is that bids are shaded compared to valuation because traders want to have some profit, and the degree of shading does depend on the number of bidders.

  • 00:40:00 The lecturer explains auction models and private value auctions. He discusses the role of asymmetric information in the market and how it affects trading strategies. The model used does not involve adverse selection as the asymmetric information only concerns each player's valuation for the asset. The lecturer also emphasizes that the process for any auction model is similar and universal, but the details may differ. The first price private value auction is not a perfect model as it involves sealed bids, which is not always the case in real-world markets. Other auction formats include the English auction, which is shown to be exactly playoff equivalent to the first price auction.

  • 00:45:00 The lecturer discusses different auction models and how they compare in terms of efficiency. The first-price auction, English auction, and Dutch auction all lead to the highest private valuation bidder obtaining the item, making them efficient. The lecturer then considers whether private value is the right setting for auctions, and introduces the common value model. The lecture also looks at single and multi-unit auctions, where multi-unit auctions are almost equivalent to single-unit auctions with linear profits in quantity. Finally, the lecture discusses the concept of being the cave highest bid in multi-unit auctions, which means bidding just enough to win but not overpaying.

  • 00:50:00 The speaker introduces several extensions to auction models and explains that the general approach to solving the problem is the same. The lecture then focuses on the common value first price auction and second price options, before briefly touching on double options. The speaker takes a break and invites any questions about the first price private value option discussed so far.
Lecture 15, part 1: Auction Models (Financial Markets Microstructure)
Lecture 15, part 1: Auction Models (Financial Markets Microstructure)
  • 2020.05.13
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Lecture 15, part 1: Auction ModelsFinancial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtu...
 

Lecture 15, part 2: Auction Models (Financial Markets Microstructure)



Lecture 15, part 2: Auction Models (Financial Markets Microstructure)

Continuing the lecture, the focus shifts towards common value first-price auctions. In this type of auction, there is a single item for sale with a fundamental value that is the same for all bidders. However, each bidder receives a private signal that provides a noisy estimate of the true value. Based on their signals, the bidders make bids, and the highest bidder wins the item. However, the concept of the "winner's curse" arises when the highest bidder realizes that they likely overestimated the worth of the item since their bid is based on the highest private signal.

The lecture proceeds to explain how to address the winner's curse in common value first-price auctions using a similar approach to the private value first-price auction. The video emphasizes that the distributions of y1, denoted as G's, are still present but are now conditional on the private signal received by each bidder. It introduces a convoluted method of mimicking the private value case, where player I chooses whom to mimic instead of selecting B_di. By framing the problem in terms of the choice of Z, the expected profits from bidding like type Z become the expectation over all possible values of y that are lower than Z. The lecture demonstrates taking the first-order condition to maximize profits with respect to Z.

The lecturer discusses the optimal type to mimic in an auction and introduces the first-order condition that gives the optimal type after incorporating the equilibrium condition. It is emphasized that it is crucial to make a bid high enough to win the asset but low enough to limit the amount paid. Additionally, a differential equation and its resultant expression are presented, representing the expectation of the devaluation of the person's signal integrated over the newly constructed measure L, although further elaboration is not provided.

The concept of the winner's curse is further explored in auctions, highlighting that the valuation of the asset, conditioned on the bids of traders who did not win the auction and had signals below the winner, is even lower than the valuation based solely on the winner's private signal. This is due to the winner taking into account the expected value of other traders' valuations, which are significantly lower than the winner's valuation. The lecture then delves into second-price auctions, noting that the expression for expected profit remains similar to that of private and common value auctions, except for the fact that the winner pays the second-highest bid. It is demonstrated that bidding your own valuation is a weakly dominant strategy in second-price auctions, making them an optimal choice.

The speaker examines the impact of bidding above one's true valuation in a second-price auction with private values. By considering different scenarios based on the location of the highest losing bid relative to the bidder's valuation, they show that bidding strictly above one's valuation is strictly worse if there is a positive probability that someone bids within that interval. Similarly, bidding below one's valuation is also suboptimal, as it can lead to losing the auction and missing out on positive expected profit. Ultimately, the strategy of bidding one's own valuation is weakly dominant in a private value second-price auction, and this result can be extended to other assumptions as long as the second-price auction framework is applicable.

The concept of a symmetric equilibrium in auction models is then discussed, particularly in common value second-price auctions. A comparison is made to private value second-price auctions, explaining why it is optimal to bid at exactly one's valuation in the latter. In common value second-price auctions, the optimal strategy is to win against a bid if the asset's valuation is higher than the bid, and to lose if it is lower. The equilibrium bidding strategy is determined by assuming that all opponents bid their own signals. If a bidder wants to win, they bid higher than the highest signal they know of, but only if their own signal is greater than it.

Moving on, the professor explains the equilibrium strategy for common value first-price auctions. He states that agents should bid below the amount they value the asset based on their private signals alone for two reasons. Firstly, they want to secure a positive profit, and secondly, there is the winner's curse, meaning that winning the auction is unfavorable regarding the asset value. The lecturer then transitions to discussing double options and their functioning in financial markets. The scenario assumes only two agents, one seller and one buyer, competing with each other but not with other sellers or buyers.

The setting of a sealed-bid auction for a buyer and seller with private valuations of an asset is explored. If the buyer's bid exceeds the seller's bid, trade occurs at the price TV. The expected profits are the same for the buyer and the seller as in the first-price auction example, with the only difference being the sign. The seller's auction is identical to a private values second-price option, while the buyer's setting resembles the private value first-price auction. The buyer's optimal strategy can be derived in the same way as in the first-price auction.

The lecture then delves into double auctions and represents them in terms of one-sided options. However, it is noted that the outcome of a double auction can be inefficient, unlike one-sided options where the outcome is efficient. The Meyerson Satterthwaite theorem is discussed, which states that there is no trading protocol that achieves an efficient outcome in a situation with one buyer and many sellers with independent private valuations. Finally, the lecturer provides some key takeaways from the lecture on auction models. They emphasize that adverse selection and the winner's curse are essentially the same thing, with the latter being a narrower concept. Second-price auctions are highlighted as a simple, robust, and efficient format, widely used in search engine ad auctions. However, achieving efficiency in bilateral trade settings with asymmetric information presents challenges. The lecture concludes by mentioning that the final lecture next week will provide a review of the course topics and a discussion on the upcoming exam, which may feature additional questions.

Continuing with the lecture, the professor concludes the discussion on auction models by highlighting the relationship between adverse selection and the winner's curse. They explain that the winner's curse is a specific manifestation of adverse selection in auctions. Adverse selection refers to the situation where one party has more information than the other, leading to potential inefficiencies in the transaction. In the case of the winner's curse, the bidder with the highest private signal tends to overestimate the value of the item, resulting in a suboptimal outcome.

The lecture emphasizes that second-price auctions are considered a favorable format due to their simplicity, robustness, and efficiency. The speaker mentions that these types of auctions are commonly used in various contexts, particularly in search engine advertising auctions. In a second-price auction, bidders are incentivized to bid their true valuations, as it is a weakly dominant strategy. This encourages truthful bidding and leads to an efficient allocation of resources.

However, the lecturer acknowledges that achieving efficiency in bilateral trade settings, where there is asymmetric information, poses challenges. While second-price auctions offer desirable properties, extending these principles to more complex scenarios with multiple buyers and sellers can be difficult. The lecture highlights the Meyerson Satterthwaite theorem, which establishes the impossibility of finding a trading protocol that guarantees an efficient outcome in a market with one buyer and multiple sellers, each having independent private valuations. This theorem underscores the inherent limitations in achieving efficiency in certain auction settings.

The professor summarizes the key points from the lecture on auction models. They reiterate the relevance of common value first-price auctions in financial markets, as well as the significance of beat shading market power resulting from a limited number of buyers and the winner's curse phenomenon. The lecture concludes by mentioning that the upcoming final lecture will provide a comprehensive review of the course topics and offer guidance for the exam, potentially including additional questions to reinforce understanding.

  • 00:00:00 The lecture discusses common value first-price auctions. This type of auction involves one item for sale with a fundamental value that is common for all bidders. Each bidder receives an informative private signal, which is a noisy estimate of the true value. The bidders make bids based on their signals and the highest bidder wins the item. However, the "winner's curse" comes into play when the highest bidder realizes that they likely overestimated the worth of the item since their bid is based on the highest private signal. The lecture explains how to solve this problem using a similar approach to the private value first-price auction.

  • 00:05:00 The video discusses how private information can inform the distribution of other signals in auction models. The distributions of y1 are still denoted as G's, but now they are conditional on the private signal received by the bidder. The video also presents a convoluted way of mimicking the private value case, where player I chooses whom to mimic instead of choosing B_di. By posing the problem in terms of the choice of Z, the expected profits from bidding like type Z become the expectation over all possible values of y that are lower than Z. The video also demonstrates taking the first-order condition to maximize profits with respect to Z.

  • 00:10:00 The lecturer discusses the optimal type to mimic in an auction and mentions the first-order condition that gives the optimal type after plugging in the equilibrium condition. He explains that it is still essential to make a bid high enough for the asset to win but low enough to limit the amount paid. The lecturer also presents a differential equation and its resultant expression that is the expectation of a devaluation of the person's signal, integrating it over the newly constructed measure L but doesn't elaborate on it.

  • 00:15:00 The concept of the winner's curse in auctions is discussed. The winner's curse arises due to the fact that the valuation of the asset, conditioned on the bids of traders who did not win the auction and had signals below the winner, is even lower than the valuation based solely on the winner's private signal. This is because the winner takes the expected value of other traders' valuations, which are far below the winner's valuation. Secondly, the lecture delves into second-price auctions, where the expression for expected profit remains virtually the same as in private and common value auctions, except for the fact that the winner pays the second-highest bid. It is shown that it is a weakly dominant strategy to bid your own valuation in second-price auctions, making them an optimal choice.

  • 00:20:00 The speaker discusses how bidding above one's true valuation can affect one's profit in a second price auction with private values. By considering different scenarios based on the location of the highest losing bid relative to the bidder's valuation, they show that bidding strictly above one's valuation is strictly worse if there is a positive probability that someone bids within that interval. Similarly, bidding below one's valuation is also suboptimal, as it can lead to losing the auction and missing out on positive expected profit. Ultimately, the strategy of beating one's own valuation is weakly dominant in a private value second price auction, and this result can be extended to other assumptions as long as the second price auction framework is applicable.

  • 00:25:00 The speaker explores the concept of a symmetric equilibrium in auction models, specifically common value second price auctions. They compare it to private value second price auctions and explain why it is optimal to bid at exactly your valuation in the latter. In common value second price auctions, the optimal strategy is to win against a bid if the valuation of the asset is higher than the bid, and lose if it's lower. The equilibrium bidding strategy is then determined by assuming all opponents bid their own signal. If a bidder wants to win, they bid higher than the highest signal they know of, but only if their own signal is greater than it.

  • 00:30:00 The professor explains the equilibrium strategy for common value first price auctions. He says that agents should bid below the amount they value the asset at based on their private signals alone for two reasons. Firstly, they want to get a positive profit, and secondly, there is a winner's curse, meaning that winning the auction is bad news regarding the asset value. The professor then moves on to discuss double options and how they work in financial markets. He assumes that there are only two agents, one seller and one buyer, who are competing with each other, but not with other sellers or buyers.

  • 00:35:00 The setting of a sealed-bid auction for a buyer and seller with private valuations of an asset is discussed. If the buyer's bid is higher than the seller's bid, trade occurs at price TV. The expected profits are the same for the buyer and the seller as in the first-price auction example, with the only difference being the sign. The seller's auction is exactly the same as a private values second-price option, while the buyer's setting is similar to the private value first-price auction. The buyer's optimal strategy can be derived in the same way as the first-price auction.

  • 00:40:00 The lecturer discusses double auctions and how they can be represented in terms of one-sided options. However, he notes that the outcome of a double auction can be inefficient, unlike one-sided options where the outcome is efficient. The Meyerson Satterthwaite theorem is discussed, which states that there is no training protocol using an efficient outcome in a situation with one buyer and many sellers with independent private valuations. Lastly, the lecturer provides some takeaways from the lecture on auction models, stating that the common value first price auction is the most relevant for financial markets and that beat shading market power arises from a limited number of buyers and the winner's curse.

  • 00:45:00 The lecturer concludes the discussion on auction models by highlighting that adverse selection and winner's curse are essentially the same thing, with the latter being narrower. He also mentions that second-price auctions are a simple, robust, and efficient format, which is used in search engine ad options. However, attaining efficiency in bilateral trade settings where there is asymmetric information is challenging. The final lecture next week will provide a review of the course topics and a discussion on the exam, which might feature more questions.
Lecture 15, part 2: Auction Models (Financial Markets Microstructure)
Lecture 15, part 2: Auction Models (Financial Markets Microstructure)
  • 2020.05.13
  • www.youtube.com
Lecture 15, part 2: Auction ModelsFinancial Markets Microstructure course (Masters in Economics, UCPH, Spring 2020)***Full course playlist: https://www.youtu...