Trading and Markets Exam 1
What risk do liquidity providers assume?
1) trade is generated not from simple information acquisition due to Grossman Stiglitz and No Trade Theorem. But there are other ways to generate trade through investers adjusting their savings or portfolio allocations as well as noise traders. 2) Because trade is generated through these other scenarios it will allow the mispricings that will incentivize hedge funds to acquire costly information to make an advantageous bet to make trading profits so the market is not perfectly revealing. 3) A hedge fund will trade to make an advantageous bet so the LP might not know the true price of a security if someone is working harder than they are to acquire information to trade on 4) The LP may then end up trading with an informed trader at losing prices and will suffer financial loses.
Explain how a broker helps a client achieve access to the markets?
Brokers help clients achieve access to: 1) Exchanges - Exchanges only allow members to trade so non-members, must have a member trade on their behalf 2) Dealers - Retail traders don't have direct access to dealers who stand willing to trade because credit clearance and settlement relationships are expensive to establish. - Brokers have better information to which dealers have the best prices - Brokers have access to off-exchange dealers who aren't in the public view
How do brokers typically get paid?
Brokers primarily get paid through commissions, but this has been challenged recently.
How are dealers paid?
By collecting the spread. The price and quantity the dealer is willing to buy at is the bid and the price and are willing to sell at the ask. This is what is means to "make a market"
How do we decompose the effective spread?
Can be decomposed into the adverse selection part and realized spread part. Separates out how much the liquidity provider loses when the price goes against her (adverse selection) and how much she gains when the price stays the same (realized spread: How much the LP takes home). effective spread = Direction * [(Midpoint_t+5 - Midpoint)/ Midpoint]+ Direction * [(TradePrice_t - Midpoint_t+5)/Midpoint_t]
What is the problem with dealer markets?
Christie and Shultz (1994) argue that the avoidance of odd-eight quotes kept the bid-ask spread artificially wide as a result of conclusion by Nasdaq dealers. The bid-ask spread goes to the dealer so they made more by keeping the spread wide. SEC investigated > created reforms: 1995 Manning rule - dealers can't trade through their customers limit orders 1996 Order display rule - must display customers limit orders
Based on Glosten Milgrom, what is the formula for the expected value of the security today?
E[V] = (P(V_High) * V_High) + (P(V_Low) * V_Low) Simply the weighted average of all possibilities of the value tomorrow based on the states of the world (high/low)
What work did Gene Fama contribute to informationally efficient markets?
He defined informationally efficient markets as prices always fully reflect all information but he did so with a caveat: There are three varieties: 1) Weak 2)Semi Strong 3) Strong
How can we test if the market is efficient?
Highlights the debate between Grossman Stiglitz (never efficient) and Gene Fama (efficient up to a point). Gene Fama explains in order to test you must first have a model to test what is means for prices to fully reflect information. One model is CAPM so now we can test.
What question do Grossman and Stiglitz attempt to answer with their paper?
How do markets become informationally efficient? Informational efficiency means how do prices best reflect all available information.
What is the formula for Bid-Ask Spread
NBO - NBB = bid-ask spread
What is NBBO?
National Best Bid and Best Offer
What is NBB?
National Best Bid: The best bid among all the best bid on stock exchanges
What is NBO?
National Best Offer: The best offer among all the best offers on stock exchanges?
When might Holden and Subramanyam be more relevant than the Kyle model?
News Trading: Multiple hedge funds will see the news and there is less ambiguity about the price adjustment after the news. There is lots of competition for the obvious aspects so price impact is high and liquidity is low because people are trading aggressively. Lambda is would be high. However, for some parts of the news that are more difficult to understand or more ambiguous there is less competition because it takes more time to digest and understand so the price impact is less and liquidity is higher, but LPs still know there is news (asymmetric information) so liquidity is still worse than normal times.
What are the 2 classical theories about information and financial markets and why study them?
No Trade Theorem (1982) Grossman and Stiglitz (1980) Settings are simplistic and the models will teach us about how markets would work when information is the only variable that is changing. Will help think through problems and scenarios by having a relevant counterfactual.
Based on Grossman Stiglitz what fraction of traders will pay to acquire information? Why?
None. Because 1) if we start at a perfectly informationally efficient market, 2) then traders are able to deduce the info from the price schedules of other traders who did acquire the info because prices are fully revealing 3) It wouldn't make sense to pay to get info because the price is fully revealing 4) However, if no one pays to acquire the information then the prices cannot be fully revealing and cannot be informationally efficient. 5) Thus if the information is not reflected in the price then markets are not efficient 6) so then It does make sense to go out and acquire the information 7) Once I acquire information and submit my price schedule then markets now become efficient.
Based on Glosten - Milgrom, Does it ever make sense for the LP to quote more than 1 unit in a competitive market?
Not with this setup, because one assumption we make is that uninformed traders only want 1 unit so I get no additional benefit but now informed traders can buy 2 units which will increase my costs but not increase my benefits and I want to make zero economic profits, not negative profits. - There is no excess liquidity because its subject to more costs and no benefits
How might trading off-exchange raise concerns for investors?
Notably, Gamestop off-exchange trading has reached near or above 50% of total trading during the recent boom. Dark exchanges are not public and do not make available the limit order book and other relevant information regarding the trading activity of a certain security. When reaching levels around 50% this might hurt price discovery and market quality.
Based on Glosten Milgrom, what is the notation that represents the likelihood of the value of the security tomorrow being a given value.
P(V_High) or P(V_Low)
What participants make up the sell side of the market?
Participants that facilitate trade for the buy side: 1) Brokers - Help clients trade and sometimes trade on behalf of clients - Robinhood, Stratton Oakmont, Fidelity 2) Dealers - Trade with customers and provide liquidity - Market Makers, specialists, liquidity providers, HFTs and and algo traders 3) Broker-Dealers - Act as both a broker and a dealer and may sell their own financial products - Goldman Sachs, Morgan Stanley, RBC Capital Markets
Why does basic economic theory explain that stocks are traded on US Stock exchanges.
Principal-Agent Problem. Broker wishes to maximize his money so market orders will go to dark pools since they pay for those order flows. Limit orders (which aren't immediately executable) go to public exchanges and thus should never trade. All orders that will trade should never hit the stock market because the broker should simply route those to the dark pool. Non-marketable limit orders are disproportionately sent to exchanges which means they sit around for longer than necessary since all marketable orders are on dark exchanges. Current regulatory structure causes people to resist working against their temptation which will always be shaky.
What is the logic behind how the market processed Covid information?
Puzzle: Covid is bad as ever but stock market is at all time high. 1) Market went down a lot in march because it forecasted how bad Covid would be and how bad the policy response will also be. (Fastest bear market in history) 2) Information got priced in very quickly 3) as we learned more about covid we learned about how we can safely reopen the economy which then pushed the market back up again. It adjusted for new info. Example: Vaccine 4) We didn't know the trial results of the vaccine and when news came out about the vaccine the market went up because we learned more info about the extent to how bad covid is and will be.
Based on Glosten Milgrom and assuming that there are only uninformed investors in the market, what are the bid and ask prices?
Remember that the LP is quoting so that they are getting the expected value on average. uninformed traders will trade at random so the P(V_high | Buy) = 0.50. S_a = expected value - ask S_b = bid - expected value With no informed traders, then S_a and S_b must be zero since the LP is risk neutral and we are operating under zero profit condition. The price or the spread is zero. There is no one trading against the LP. However, if there was no zero profit condition, the spread would greater than zero.
Explain why Weller believes stocks with more HFT activity are less informationally efficient.
Since HFT are intermediaries they are not trying to profit they are simply trying to limit their inventory and not take anything home. 1) HFTs are good at inferring information from trading and at HFT firms there are few economists mostly mathematicians and engineers 2) HFTs try to extract this information quickly based on market participants acquiring info and trading to make a profit 3) HFTs then can trade as if they have the info themselves and they can eliminate some of the profits of market participants so hedge funds might think twice about spending money on getting that information 4) Hedge funds dedicate less money on stocks HFTs have algos for which is similar logic to grossman stiglitz.
How do informed traders impose adverse selection costs on liquidity providers?
Since liquidity providers are only concerned with getting the expected value on average since they are risk neutral they are willing to trade with informed traders and sometimes take loses because they pass these costs to the uninformed investor through the bid ask spread
Why would someone use a broker?
To arrange trades and to do so at a lower cost than arranging it themselves. 1) Clearing and Settlement 2) Access 3) Expertise 4) Presence
How have recent developments changed the view on how assets are priced?
Traditionally price = discounted future dividends, but Koijen and Yogo (2019), Gabaix and Koijen (2021) explain that noise traders can have an effect on markets and thus asset price = supply and demand equilibrium price. It is a function of how willing people are to buy and sell.
Why is it difficult to regulate brokers?
The principal - agent problem. The performance of a broker is based on "best execution". However, this is a vague term which is difficult to pin down the meaning to because there is an element of subjectivity to "best execution". Example: broker gets a big order for AAPL. They can 1) spread it out and try to not move prices (best price) or 2) execute the whole order immediately (quick)and move prices a lot.
How is trading important for financial markets in general?
There are people who are looking for profit opportunities by finding information not reflected in the price. Now that information is revealed by people trading on it to make a profit this endeavor is exactly what makes markets efficient. However, trading does not work when the market mechanism works too well and reveals all information perfectly then the cost of acquiring information is not worth the potential profit.
Where is equilibrium in the Grossman Stiglitz model?
There is no equilibrium in this model because of cyclical nature of information acquisition and prices being revealing.
What are the Key takeaways from Grossman Stiglitz?
Thesis: Informational efficiency in markets is impossible 1) There is no incentive to acquire costly info if the market mechanism perfectly aggregates the information into the price 2) It is rational to infer why prices are changes because prices are a good signal of available Information 3) Contradiction: The market mechanism is designed to aggregate all available price schedules which in turn reveals information about the price. But by adjusting the price to reveal available information, then there is no point in acquiring costly information because you cannot recoup that cost by trading. 4) Subtle distinction between information that is free and costly information.
How are new orders processed in a continuous limit order book?
They are processed based on the time of receipt. However, if two orders have arrived at the same time, then the tie is broken based on price-time priority.
How did brokers respond to heavy regulation of how much can be charged in comissions?
They decided to give kick-backs to clients that would allow them to charge higher commissions now and rebate back goods and services in return to make their commissions effectively equal to the competitive market price. Goods and service soft dollars could be used to purchase research, Bloomberg terminals, or even sports tickets.
What work did Holden and Subramanyam contribute to the Kyle model?
They incorporated multiple informed traders and show that even going from just one to two informed traders in the market makes a big impact on how aggressively informed traders actually trade. The reason: If I'm a hedge fund I have to take into account the other hedge fund that might take a large position and will push the price higher before I can take a position. This leads to very aggressive trading so they informed trader doesn't miss out on profits that would be consumed by the other hedge fund. Causes lambda to be very high and informed traders make less profits. This means that information gets into prices very quickly.
Is the Kyle model realistic?
This model is good at displaying how an informed trader might choose to trade (how fast/how much) - Maximize with respect to the market condition, driven by noise traders. However, this model assumes only one informed trader and many noise traders, but things change when there are multiple informed traders.
After the catalyst is received in the No trade theorem, why will there be no trade?
Typically new information results in a lot of trade because we should reallocate the resources to those who value them the most. In fact, I could maybe profit with my new information by buying low and selling high. However, the only outcome of this catalyst (new private imperfect information) is no trade because there are no incentives to trade. The only motive for someone to trade is to take an advantageous bet but every other trader knows the only reason why you would trade is to make money so they don't want to trade thus lose money.
What is the setup for the Kyle model?
Uses a series of uniform price auctions instead of a limit order book with: 1) Uncertain security value 2) Single strategic informed trader and lots of noise traders 3) Informed trader has long-lived information 4) Everyone sends market orders 5) A competitive risk-neutral liquidity provider clears the market at a price by trading with the imbalance of orders, but only sees the total order flow from noise traders and the informed trader
When might Kyle model be more relevant than Holden and Subramanyam?
Value trading: There might be disagreement regarding information and a hedge fund can't just discover this information because the direction of movement is disagreed upon. Fundamental value is hard to discover and disagreement might cause informed traders to trade less intensely and not at the same time which leads to a muted effect on the bid ask spread.
Based on Glosten Milgrom and assuming that there are only informed investors in the market, what are the bid and ask prices?
We assume that informed investors will always trade to make an advantageous bet so P(Buy | V_high) = 1 and P(Sell | V_Low) = 1 The LP is willing to gamble as long as she can trade at the expected value. Given the LP is trading with an informed investor the LP is willing to sell at V_high and buy at V_low. Therefore, if I trade with an informed investor I can deduce something about the real value of the security today because they only take advantageous bets.
Why do we see different bid-ask spreads for different securities?
We can use the Glosten Milgrom model to explain why spreads differ across securities. - There could be different fractions of informed traders to investors - Could also be related to amount of public information available
Based on Glosten Milgrom, what is the notation that represents the value of a security tomorrow? what is the notation for the value of the security today
We will know for certain the value of the security tomorrow but we just wont know the value of the security tomorrow as of today. value of security tomorrow = V_high or V_low value of security today = V
When is a trade executed in the market?
When an incoming order crosses a resting limit order
What is adverse selection?
When there is asymmetric information, it is possible for those who are using that information to select against those who are less informed. Examples: buying used lemon cars (owner knows but buyer doesn't) or affordable care act (young people probably don't need insurance and people that do need insurance are likely to buy insurance so individual mandate tries to fix adverse-selection problem)
Can uninformed investors use limit orders to avoid adverse selection costs?
You can't avoid/earn the spread because you either won't be able to trade it or the market will run away from you and you wont trade at all 1) Submit at the Bid (first in line): - Will pay zero if investor is first in line at the bid - He won't collect the spread -50% of the time investor will not trade - However, if a buy trade comes in the, the price, bid, and ask are all higher in the next period 2) Join the bid (second in line) - Get adversely selected and don't trade with noise traders because the liquidity provider has no incentive to trade more than one unit because there are only costs with no additional benefit 3) Ahead of the bid (improve the price): - price time priority makes the price trade first. If you improve the price by a dollar you will decrease your expected profit by a dollar on average and the market can still run away from you as well
Can we reduce the transaction cost (how much investors have to pay) to trade?
You could through price discrimination, but lack of identities makes it difficult for LPs to price discriminate. -Off-exchange or dark pools try to keep out informed traders to mitigate adverse selection costs In reality, spread will still be narrower, but LPs still have other costs such as inventory costs, operating costs, etc so wouldn't be zero
What are the key takeaways of the Glosten-Milgrom model
1) prices are based on the expected value of the security conditional on the likelihood of informative flow. More uninformed traders means lower spreads and more informed traders means higher spreads 2)Information is revealed in the price - if the value is high more likely to see people showing up to buy rather than to sell. If there are a lot of people showing up to buy you can infer that people know something about the price that you don't know. Order flow on average is informative. 3) The bid-ask spread is a function of how informed the other traders. How much I'm charging people is based on how likely I am to make a losing trade. 4) It is a model of adverse selection
What is a dealer?
- Profit motivated traders that trade based on when other market participants wish to trade. - They are liquidity providers and market makers. - Provide the service of being willing to buy or sell at any given time and will make profits off of the bid-ask spread. - Some dealers may only offer one side of the trade: only a bid or only an ask. - Will quote on exchanges or make their own private markets
Explain how a broker's presence helps a client trade more favorably
1) Brokers are active across time and markets 2) Allow the end users (buy side) focus on other things while the broker acts as an agent on the clients behalf
Explain how a broker's expertise helps a client trade more favorably
1) Brokers know more about who wants to trade 2) Can hide identities, manage orders, adjust to market conditions 3) Understand market structure
What is the set up/context for the No Trade Theorem?
- There is a single asset (stock, futures contract) - Lots of traders that are identical in that they are risk averse (prefer 100 for sure as opposed to 100 on a gamble) - Interpret information the same way (signal means the same to everyone: good/bad) - traders are happy with how much of the asset they have now and if they value the asset more than someone else then they will probably own more of it - All traders know about the preceding assumptions and everyone knows what others know (common knowledge) - No risk sharing element only reason why someone would trade is to make them better off -Implication: Beginning of the trading game more of the assets is held by people that value it the most and if someone doesn't value it as highly and holds a lot then they should trade so that everyone starts off happy with how much asset they have.
Based on Glosten Milgrom what are the key assumptions about each type of trader that shows up to the LP?
- Uninformed traders: Randomly want to buy or sell 1 unit of security and are equally likely to buy or sell. Will not know the value of the security today until the information is priced in. Can be noise trader or investor rebalancing a portfolio. - Informed traders know the value of the security with certainty today before the public realized the value tomorrow. Informed traders only trade to make profits based on their information and the limit order book then leaves.
What is the catalyst for the no trade theorem trading game?
At some point in the future, new information about an asset arrives. Each trader will receive a private signal and will have a piece of information about the assets future value. This information does not give the whole value with certainty there will still be uncertainty regarding the future value of the asset. Everyone sees a slightly different piece of information
Based on Glosten Milgrom , what is the bid and the ask?
1) Conditional expected prices 2) No-regrets liquidity provision - upon recieving a buy order (trading at the LP's ask), the LP has no regrets trading there because: - her expected profit is equal to her expected loss - The LP trades at a price that reflects all the information after having received the trade (the "true" price considering the information that the trade contains)
What is a market order?
A type of order that does not state a price, but implicitly states it. Market Buy orders implicitly have a price of infinity Market Sell orders implicitly have a price of zero
How does dishonesty and fraud aggravate the principal- agent problem?
1) Front running: If a broker receives a huge buy order that will push prices up, the broker might decided to buy before their clients trade is executed in order to make money 2) Inappropriate order exposure: Telling the world a mutual fund placed a huge order in order to benefit someone other than the mutual fund would be a breach of fiduciary duty 3) Fraudulent Trade Assignment: Maybe I get two identical orders from one client I have a relationship with and one that I do not then I might swap the execution price to benefit the client I am friends with and give the other client a worse execution price even if they are entitled to the better price 4) Prearranged trading and kickbacks: arranging a trade without exposing the order in return for compensation 5) Churning: Making unauthorized trades on behalf of clients in order to generate excess commissions
What type of information that gets into prices is relevant?
1) Fundamental information such as earnings (regulation that makes companies only release info after hours) - we can all agree on like 80% of the info but the other 20% might disagree which breaks Grossman stiglitz assumption. 2) Macroeconomic Data - hiring data or interest rates might give information about the overall economy. 3) Technical analysis - everyone has past price info so it should be incorporated into the market quickly 4) Inside information - inside info does not reflect current price so it should give you profit motive to trade. 5) Satellite Data - Quarterly earnings of best buy already priced in partially by hedge funds using satellite data to determine how many people are buying.
What are the key takeaways from Kyle Model?
1) If you get rid of the noise traders, then the informed traders won't be able to make any money and there would be no incentive to get info it its costly 2) Order flow is informative. the fact that an informed trader is trading reveals information and the LP updates prices as its trades.
What is the set up/context of Grossman Stiglitz model?
1) Information must be acquired and it costs money to acquire said information (report of apples future earnings that anyone can pay for) Starting point: 1) Risky asset with some uncertain payoff (FV is unknown) 2) Lots of identical, profit seeking traders and each trader knows the entire distribution of an assets payoff (as if they have the bell curve graph in front of them based on all possible states of the world in the future) 3) All traders have the ability to pay some price (the same for everyone) to get the same piece of imperfect information which will help (imperfectly )reveal the assets payoff in the future. 4) Each trader will submit the entire schedule of limit orders based on how much they wish to buy or sell at a given price (if price = $80 then sell 10 units; if price is $100, then sell 20 units etc) 5) Run something that looks like an auction based on aggregate schedules of everyone and let everyone trade. Figure out where you can do the most trading, set that price, and execute the respective trades (supply - demand). Clarifications: 1) All traders trade to make profit and no motive for hedging 2) Informed traders pay to get the signal which they hope to recover the cost of by trading for a profit 3) Uninformed traders attempt to deduce the signal the informed traders paid for based on the current price of the asset since every trader submits their schedule (i.e. the price is fully revealing). Uninformed traders can submit orders conditional on the price in order to extract information about the price.
Based on Glosten Milgrom, how does the LP quote?
1) Must quote a standing bid and ask, quantity and price. 2) We assume that the LP quotes in a way that balances out costs and revenue. 3) LP will make money from investors and will lose to informed traders. Will make the spread from both investors and informed traders, but trading with the informed traders will result in a bigger loss than the spread that the LP makes. 4) LP will balance out the costs and benefits knowing she might lose or might win to quote the bid and the ask quantities and prices.
Based on two classical theories we see no trading, but we obviously see lots of trading in markets. So what assumptions do the theories make that are not good reflection of reality? In other words what additional assumptions can we add to these theories in order to make them reflect reality?
1) Non-Informational reasons to trade - Noise traders (people randomly wanting to buy and sell), liquidity traders, and investors - this helps contribute to our model mathematically but still isn't a great approximation of reality. 2) Disagreement - central assumption of both models is everyone interprets signals the same way, but this isn't true in reality. Breaks the "Common Knowledge" assumption from Milgrom-Stokey No trade theorem 3) Irrationality - Overconfidence (maybe I'm a better analyst than someone else Dunning - Kruger) or they make human mistakes in their algorithms.
How does the principal-agent problem manifest itself in broker-dealers?
1) Prices paid - A broker who is trying to execute on behalf of a client has a duty to get the best price. However, the dealer is trying to get the highest price possible which means the client could be paying a higher spread. (conflict of interest). Broker-dealers are incentivized to send orders to their own institution maybe because they understand their own echange better which could lead to better execution but this is always fishy. 2) Product Choice - BDs also sell their own financial products and might push clients to those
How might the principal-agent problem of brokers be aggravated?
1) Small Traders - Don't have access to the execution prices of all exchanges (including dark pools) at that particular millisecond and compare it to the price that the small trader received and no one has time to do this either 2) Order routing - Brokers might have connections with certain dealers that give the best kick-backs based on volume of trades. Difficult for Investment managers to track which retail investors contributed to end of month rebate so the investment manager just keeps it.
Orders always specify the following:
1) The Instrument (AAPL) 2) The Direction (Buy or Sell) 3) The Quantity (1000) 4) Implicitly have a price (sometimes not specified) 5) Duration (Good Till Canceled)
What are some key takeaways from the No Trade Theorem?
1) Trade can't arise from purely informational reasons when everyone has the same prior knowledge even if we all get different private signals because there are two sides to every trade and I should infer something about the other trader 2) It is correct and rational to draw inferences for other traders motives to trade (to make an advantageous bet) and I should consider the other traders motive. "I don't want to belong to any club that would accept me as one of its members"
What is a limit order?
A type of order that explicitly states the price If it trades, it will trade at that price or better.
What is the limit order book in a continuous market?
A continuous double auction that uses discriminatory pricing. Continuous: processes orders continuously. Different from a call auction which aggregates all orders and processes them all at the same time. Double Auction: buyers and sellers can both submit orders. Different from an auction where there is a fixed supply of units for sale and only buyers submit orders. Discriminatory Pricing: Buy and Sell based on current outstanding orders as opposed to a fixed price.
How did Goldman Sachs (Dealer) act fraudulently and breach their fiduciary duty?
Abacus 2007 - AC1 Paulson asked GS to create an instrument to give him short exposure. GS found buyers but did so by misleading investors. Goldman Sachs had a fiduciary duty as a dealer according to congressional hearing. Failed to disclose material information.
What is a bid?
An order to buy
What is an ask?
An order to sell
Explain the logic behind Glosten Milgrom model as related to NYT Editorial board endorsement prediction
Because buy orders keep coming suggests that because its possible that informed traders are in the market the probability that the value is high increases as perceived by the market maker with each trade to buy, the ask was updated which pushed the price higher by updating the expected value with the previous ask and updating the new ask to E[V | buy] likely to have high spread because there probably was not many noise traders (weird market)
To the average retail investor why is the market basically efficient but not to an institutional investor?
Because there is an entire industry dedicated to beating the market by exploiting mispricing so to someone who doesnt have the time and resources its efficient but for institutions that do have the resources then they can actually exploit mispricing.
Explain how a broker helps a client achieve clearing and settlement.
Between the time that a trader finds a party to trade with and the trade is actually settled there is a risk that the other party may: 1) not acknowledge the trade 2) refuse to settle the trade or 3) be financially unable to settle the trade Brokers explicitly or implicitly (with their reputation) guarantee their clients will settle their trades. This means that traders don't have to run credit checks on each party they trade with because the broker handles this.
Which side of the CLOB are bids? Which side are asks?
Bids: Left Asks: Right
Explain the logic of the No Trade Theorem
If I already have the optimal holding of an asset and I receive a partial signal, I will use that information to recalculate how much I value the asset thus how much of the asset I wish to hold. This means I probably wish to trade based on model assumptions. This means that I would need to find someone else who wishes to sell at an agreed upon price. If I actually find that person, then I need to consider what possible private information the other trader received making them willing to trade with me. Therefore, I can infer something about the other traders signal that reveals information about the price and if they are willing to sell then that means they must have received a negative signal even if I received a positive signal. Now with this new information (a trader willing to sell), I should update my own signal and the other trader should update his so this now means that neither of us should want to trade anymore.
What is the Value factor?
If you categorize stocks as value (Price to fundamentals ratio is low) vs growth (price to fundamentals is high), value stocks on average outperform growth stocks. Academics argue value is a violation of market efficiency. Some argue that value stocks are riskier and thats why they earn higher returns on average.
What is the joint hypothesis problem?
In order to test whether prices fully reflect information then you need a model that determines this. For example CAPM. However, if we do find that prices are incorrect based on our model, we are unable to tell if our model is incorrect or if our prices are incorrect. You are testing if your model is correct and if the market is efficient at the same time.
Based on Kyle model, how should the hedge fund trade?
Informed trader should trade in such a way to keep market conditions constant specifically keeping lambda constant. The informed trader would like to hide in the weeds of the noise generated by uninformed traders. They must balance. Balance of two different tradeoffs 1) If I trade a lot then I give away information and the price will move up a lot before I can get into a large position 2) I can also submit a small order, this will not move the price, but I won't be able to put on a bet that is advantageous enough to balance out costs.
Who pays for adverse selection in financial markets?
Investors because in the GM model, liquidity providers make zero profits thus all profits for informed traders come from the investors paying the spread.
What issues do soft-dollar commissions pose to the retail investor?
It highlights the principal - agent problem. Since investment managers are now receiving goods and services for free that they normally had to pay for they are able to reduce their expense ratio. However, the performance of the fund would be slightly reduced as a result of paying higher commissions. Fund performance is hard to track because fund returns are noisy while expense ratios are public and very visible. This causes 2 specific problems: 1) It allows investment managers to transfer management costs to fund performance which is less visible to a retail investor 2) some kickbacks could be things like sports tickets which don't actually help the fund perform better but instead transfer investors money to the manager rather than to research which could help the fund improve its performance
What is the principal-agent problem?
It is a problem caused by agents pursuing their own interests rather than the interests of the principals who hired them. For example, choosing a specific broker because you can get kickbacks in the form of super bowl tickets. Another example is a homeowner and realtor because the realtor is concerned about making a deal go through rather than holding out to get the best price for the house. The principal-agent problem is compounded when it is difficult to monitor the agent to ensure they are acting in the principals best interest.
How does the relaxed assumption in Holden and Subramanyam affect market liquidity?
It makes the market very illiquid because informed traders trade more aggressively since hedge funds are competing to not miss out on these positions. As a result hedge funds make less profits as well. because they are maximizing profits with competition.
How does RegNMS prevent the NBB and the NBO from crossing?
It requires that brokers route their order to the exchanges with the best available price. This means that a bid can't cross the NBO and an ask can't cross the NBB.
What is Kyle's lambda?
Its a measure of liquidity - Measure of price impact - the greater the lambda the more the price moves in response to order flow. Very small lambda means a very liquid market or a narrow bid-ask spread - you can trade a lot without moving the price - Lambda is affected by how much noise trading there is relative to informed trading
Explain the set up of Glosten and Milgrom (1985)
Main point: Determine how the LP quotes 1) Single security trading in a limit order book market and has an uncertain value 2) We don't know the value of the stock, but we know with certainty the value of the stock tomorrow will be one of two possibilities. 3) There are lots of LPs in the model, but they are operating in purely competitive market so that LPs earn zero economic profit. Essentially because they are selling perfect substitutes they can be considered as one single LP within the model. 4) Liquidity providers are risk neutral as long as they can can get the average so they are fine with taking the gamble 5) Liquidity providers are only considering information costs. (trading with others that know more than they do). They are not concerned with inventory costs etc. 6) The single LP will post a standing bid and ask which are available to anyone and she must trade based on those standing quotes 7) orders arrive sequentially like a CLOB 8) Orders arrive from either uninformed or informed traders 9) Liquidity providers can't tell whether an order arrives from an investor or informed trader, but knows the probability of each event occurring.
What are Dealer Markets?
Markets where dealers dominate trading. Only dealers are quoting and investors always trade with a dealer. Example: nasdaq in the 90's - in the 90's the tick sizes were moved from 0.25 to 0.125. Typically you'd expect a random distribution of price fraction of inside quotes, but instead you see significant clustering around 0.25 tick sizes. The dealers were not quoting at 0.125 ticks despite fair value (midpoint).
What participants make up the buy side of the market?
The end users of financial markets. There is a whole industry that helps them trade: 1) Investors (Individuals, Pension Funds, Insurance Funds, Mutual Funds, Endowments) 2) Borrowers (Homeowners, Students, Companies) 3) Hedgers (Farmers, Companies(manufacturers)) 4) Proprietary Traders
What are Liquidity Providers
Sometimes called dealers, sometimes called market makers. They are the market participants standing ready to buy and sell at all times. - Provide the service of immediacy - (Almost) always willing to take the other side - connect final buyers and sellers across points in time
What is the formula (decomposition) of the Bid-Ask Spread?
Spread = Glosten-Milgrom spread (adverse selection) + Other costs of providing liquidity (Inventory, volatility, fees) + Liquidity provider profits
What was the aftermath of the Nasdaq press release
Spreads decreased from average > 0.25 to averaging around 0.125 (1/8)
What does it mean to make a market?
Standing willing to buy or sell at any given time.
We know that Macro information is relevant to prices such as Job information. So based on the huge job losses because of covid we have seen job numbers that have not returned to their original numbers, but the stock market is performing at record highs. Why is this?
Stocks recovered much quicker than jobs have so it seems that macro news is not getting incorporated into the stock price. This is because the stock market is all about the future regarding information and how its based on prices. For example, we see bad jobs report we would expect the stock market to go down. But since we have already forecasted and estimated how bad the jobs report might be, when we receive a jobs report that isn't as bad as expected the stock market will go up. Because the market has already priced in the fact that it was bad. What is the report relative to current expectations. All stocks are the present value of future dividends so for the next 3 months things would be bad, but the market also figured out that the dividends 1 year from now and 5 years from now people realized that dividends would return to normal soon.
What is the market mechanism of Grossman Stiglitz model?
The market mechanism aggregate the information content of traders and reflect the information in the price. Information gets reflected into the price by people trading on it. If the price is cheap and people think it should be higher people will trade on it to push the price higher.
What is the limit order book?
The outstanding bids and asks from most market participants at any moment in time (when the market is open).
Based on Glosten Milgrom and assuming that there are only uninformed investors in the market, what can the LP deduce about the true price?
The LP cannot deduce anything about the true value today because an uninformed investors trading behavior in uncorrelated to whether the security's value is high or low. We assume they are buying and selling at random.
Based on Glosten Milgrom and assuming there are both uninformed and informed traders in the market, how does the LP set the ask price?
The LP will set the ask price (willing to sell) based on the expected value conditional on someone wanting to buy. ask = E[V | buy] E[V | buy] = P(V_low | buy) * V_low + P(V_high | buy) * V_high
Based on Glosten Milgrom and assuming there are both uninformed and informed traders in the market, how does the LP set the bid price?
The LP will set the bid price (willing to buy) based on the expected value conditional on someone wanting to sell. bid = E[V | sell] E[V | sell] = P(V_low | sell) * V_low + P(V_high | sell) * V_high
What is the adverse selection component of the bid-ask spread in the Glosten Milgrom model?
The adverse selection component of this is the whole spread because the only cost in GM is adverse selection so not realized spread because no profits and no other costs. Can also be considered to be the GM half spread if only one trade (buy or sell).
What is for formula for effective spread?
effective spread = direction(-1:sell & +1 for buy)*((trade price-midpoint)/midpoint) think of basically half the bid-ask spread in percentage terms
