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Summary Course Notes Trading and Exchanges
This document provides all the notes and the material that was handled in 'all' the lectures in the year 2023/2024. This document should be enough to understand the exam material.
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Trading and ExchangesNotes
,Part 1: Financial Market Infrastructure
CHAPTER 1: COURSE MOTIVATION AND OVERVIEW
1. Why a Course on Trading and Exchanges?
Other courses: determining optimal portfolios, hedging risks or speculate using
derivative contracts, valuation of securities (e.g. bonds, stocks, derivatives), buy/sell
recommendations etc. Why do you want to trade?
Thus: these do not consider (nor allow for) any role of the financial market infrastructure.
1. no role for the trading system You just buy or sell the asset. How the assets are traded, which participants are
present in the market, does not matter.
2. (trade) price formation is a black box
3. why can they be different from fundamental values? and what role does the trading mechanism plays?
Value based on asset pricing model (e.g. Black-Scholes).
Trading and Exchanges considers the decision to buy or sell to be given.
How they trade? How are prices formed? Efficient markets: how are prices adjusted? How can you trade?
2. A Trading Story
Problem 1: Where does an individual want to trade? Stocks can be bought at a lot of different venues.
Problem 2: Trading mechanisms seem to differ greatly. There are, for instance, lit and dark venues, auction and other venues, ...
Different trading venues, which can be divided into different trade categories (e.g. lit, auction, off-book, SI, dark).
Problem 3: Why are there two prices? How do liquidity providers set their quotes? Which trade-offs determine the choice between
different order types (limit order, market order)?
Ask price: price at which you buy.
Bid price: price at which you can sell.
Number of counterparties.
If you want to buy more than 35 shares.
Even more problems:
1. Some traders may have more information than she has
2. Some traders may be faster than she is (computer trading: flash trading, high frequency trading)
2. Once the trade has been concluded, there is still risk that the counterparty (seller) will not deliver,
i.e. that the trade will not settle
, 3. Market Microstructure
We look explicitly how trading and the trading infrastructure affects prices, and makes prices deviate from fundamental values
We draw on a large body of theoretical and empirical research on price formation, forming a subfield of financial economics called market
microstructure
Definition 1
Market microstructure is the study of the financial market infrastructure that is used for
transacting assets.
Asset can refer to various underlyings:
* financial assets: stocks, bonds, currencies, cryptocurrencies ...
* commodities such as oil, gold, corn, ...
* derivative contracts on these assets such as futures, options, swaps, CDSs, ...
* it even extends to emission permits used to control pollution
Financial market infrastructure encompasses a number of components: the first is the trading infrastructure
Definition 2
The trading infrastructure (also called trading mechanism) is the set of rules that apply during trading.
For example:
* Which order types can a trader submit?
* Which traders have access to the trading venue? E.g. do not give access to computer-trading.
* Which information is shown before and after trading? Was the order executed or not? Do you see other trades? Whom did you trade with (anonymous or not)?
* How are buyers and sellers matched? Which seller are you matched with?
The second component is the post-trading infrastructure
Definition 3
The post-trading infrastructure refers to the rules governing clearing and settlement.
1. Clearing refers to all activities made from the time that buyer and seller have agreed to trade until settlement
of the trade. It is the process of transmitting, reconciling and confirming the terms of trade, and the
establishment of final positions for settlement. Determining the positions of the parties, e.g. how many shares, the price. If there is no agreement: reconciling.
2. Settlement is the completion of all obligations. The settlement of a securities trade typically involves two
delivery processes: the transfer of the securities from the seller to the buyer, and the transfer of funds from
the buyer to the seller.
Recurring themes: how does trading and the trading mechanism affect
1. price formation
2. market liquidity = degree to which an order can be executed within a short amount of time at a price close to
the consensus value How easy and how cheap can you trade?
3. price discovery = the speed and accuracy with which information is incorporated into transaction prices
How fast and how good is information reflected in transaction prices?
4. volatility
5. market stability
6. welfare of different participants
,4. Trading Infrastructure
Real-world financial markets feature great diversity and evolve over time (stock markets,
FOREX markets, bond markets) no complete classification will be given
We focus mainly on a general classification along 3 lines (many others are possible):
1. order execution system: order driven (LOM) vs quote driven (DM)
2. type of trading session: call market vs continuous trading
3. transparency
note: most real world trading systems are hybrid form
Quote driven vs order driven
First distinction: quote driven (dealer market) vs order driven (limit order market)
Quote Driven (Dealer Market) Order Driven (Limit Order Market)
* dealers are present E.g. JP Morgan, investment banks. * no dealers, traders interact directly
* take the opposite side of each trade * traders supply liquidity via limit orders
* quote bid and ask prices (or schedules) Specify a limit price at which you want to buy or sell. See slide 13.
* supply liquidity to the market * they demand liquidity with market orders
I.e. allows traders to trade easy & cheap. Specify how much you want to buy, sell etc.
E.g. FOREX, derivative contracts, London Stock Exchange * order precedence rule: usually price - time priority
(until a couple of years ago). Trade-off between limit and market orders: you can choose
wether you want to put in a limit order or a market order.
E.g. Euronext (mostly works like this, but firms can pay a designated liquidity
Markets are very often hybrid! E.g. New York Stock Exchange. provider, like KBC, to make sure their stock is sufficiently liquid, easy to trade).
Continuous vs periodic market
Continuous Market = trading is possible at any point (during opening hours)
Example: most stock markets (Euronext etc), FOREX, option markets, ...
Periodic Market (Call Market) = trading occurs only at specific points in time
Example: call (batch) auctions = traders submit orders simultaneously Trading takes place
Orders are matched
Example: crossing networks (traders submit buy and sell order during a predetermined .........
Orders are submitted Orders are submitted
period, but these are not executed. At given points in the day, using matching rule, buyers
and sellers are matched.
Markets can be a hybrid form! E.g. Euronext: from 9.00-17.30 it is a continuous market.
Before 9.00, there is a pre-open session. After 17.30, the is a closing session.
E.g. if there is high volatility, trading is sometimes suspended. At some exchanges, there is a volatility
auction to resume trading.
Transparency
Pre-trade
* quotes (ask and bid)
* depth Number of shares you can trade at ask/bid.
* best prices only or more?
* identity of traders E.g. until 2001, you could see on Euronext whom you were trading with.
Post-trade
size of orders executed
direction of orders executed
identity of the traders
,Stock markets are transparent!
Also past trades are observable on Euronext (+ whether it is continuous vs auction)
The other extreme: dark pools (although some transmit some information)
Other distinctions
Other characteristics:
* Tick size (minimum price movement or increment by which the price of a financial asset can change in a given market)
* Trading floor vs electronic
* Regulated vs OTC
* Precedence rules
* Pricing: uniform, discriminatory (as in limit order book), derivative (see crossing networks later)
* Fragmentation
Hybrid markets
In practice, trading systems are often hybrid:
1. NYSE has both market makers and a limit order book
2. Euronext is in general an order driven market, but some stocks can have “Liquidity Provider (Rule 4107)”
3. During the trading day, stock exchanges are in general continuous, but they also have an opening and closing auction
Evolution over time
Market infrastructure is not static & can change over time (and this has an impact), for example
1. NYSE introduced Openbook (bid and ask quotes) in January 2002
2. Euronext Paris introduced anonymous trading by removing trader ids in April 2001
3. tick size has been reduced in US markets from $1/8 to 1 cent, now a pilot will start to
increase it again for smaller capitalization companies
,CHAPTER 2: KEY CONCEPTS
1. Efficient Markets
Efficient Market Hypothesis (EMH)
Assume that you can trade a (financial) asset in the market
Definition 1
The fundamental value (also called true or fair value) V of an asset is the value at which the asset can be liquidated in a frictionless and efficient
market after trading has ended.
Formulas you learn in asset pricing etc.
In general, this value will realize at some point in the future, and you do not know it for sure today
We stress this in notation by the tilde above the variable, where the tilde indicates a random variable
Friction refers to difficulties with which market participants are faced when trading the asset
Let time be divided in discrete periods, indexed by subscript t, so t = 0, 1, 2, 3, ...
At which price can you trade the asset at time t? Can be a fraction of a second etc.
If markets are efficient and there are no frictions, then prices reflect all available information
Hence, the price is simply the expectation of the fundamental value of the asset, based on the information that is available
This is the efficient market hypothesis (EMH).
Definition 2
The efficient market hypothesis (EMH) states that the price at which an asset trades, should be equal to the
best possible assessment about asset’s fundamental value, given all information available at t. Technically,
where conditional expectation is denoted in 2 equivalent ways
* is the expectations operator conditional on all information at time t
* when we need to make explicit the information set, we use , with the information set.
Depending on the information set, the EMH has three forms:
1. weak-form efficiency = information set contains the history of prices
2. semi-strong-form efficiency = the information set contains all publicly available information
E.g. financial statements, media announcements.
3. strong-form efficiency = information set contains all information available to any single market
participants, this includes all private information
Interpretation: the EMH says that at each point in time, the price at which you can trade the asset is equal to the expected value of
the asset, incorporating all available information at that time
The definition does not discount to account for the time value of money
we will often look at very short time periods: intraday, hours, minutes, seconds or even as short as a fraction of a second
Long term Medium term Short term
including a discount rate would change very little for such short time intervals and just increase the complexity of the model
it is therefore customary to leave it out.
Implications of the EMH
The EMH implies that prices change only due to the arrival of new information (news).
When news arrived, investors revise their expectation about the fundamental value and prices will adjust immediately
Formally: denote news, also called the innovation in the value of the asset, by the random variable defined as
Interpretation: is the update of the expectation of investors due to news arriving between time t and t + 1
,It must hold that
Ext + 1) = 0
and E(t) =
0 .
If this is not the case, you expect part of the innovation and news is not really news
Moreover,
E(r) = 0 for t N .
No relationship or correlation between news at time t and news at time s.
Past information should not allow you to forecast (part of the) news
Next, assume we now are in period t, and you are asked to give your expectation about the price at which you can trade
the asset in the next period t + 1
Under the EMH, the answer is easy: prices between t and t + 1 only change to news, which you cannot predict anyway
So, your best answer is that your expectation about the price next period is simply Pe
Hence, under the EMH, the best predictor of future prices, given current information, is the current price. Technically,
we say that prices are a martingale
Theorem 1
Under the EMH transaction prices follow a martingale
Pt =
Et)Pt+ 1)
Proof:
We know that
Ef(t + 1) = 0
Substituting t , it follows that +e
Et Fety(V) -
Et Ez(V) = o
Et Ette(v) =
Ef(v)
Since Pt =
Et(v), we have
Et(Pt 1) +
=
PE -
An immediate consequence of Theorem 1 is the following result
Corollary 1
Price changes over a given interval are serially uncorrelated. Inventory models: price changes are serially correlated.
Proof:
This can be seen by computing the change of PE :
> Pt+
-
1
=
Pe+ -Pe
=
Etty() -
Et() =
Ette :
for each t, so
Cov Capt , apri =
Cov (t , r)
From the definition of covariance:
Cov (Et ,
Er) = E [t-ELEt)3EEr-E(Er)3
Expected value of news is zero.
= E(tr)
= O
since E(tEr) = 0
for s t.
Intuition:
Under the EMH, prices only change (instantaneously) due to new information, and we argued that this news must be unexpected and unpredictable
So current information cannot be used to predict news, and since news causes prices changes, it means it can also not be used to predict price changes
In particular, current information about price changes cannot help to predict future price changes, so the latter must be uncorrelated over time
Stated differently, since innovations are uncorrelated over time, also price changes resulting from them are uncorrelated.
Markets are definitely not strong-form efficient! Markets do seem to be weak-form
efficient. Semi-strong-form efficiently: some evidence, some evidence not.
But how do markets become efficient? Often pictured as a black box. See later.
,2. Friction
The discussion so far assumed that markets were without frictions
Friction is a measure of how difficult/costly it is to trade an asset
An overview of frictions and how to measure them can be found in Stoll (2000)
This leads to the question what are the sources of frictions in real-life markets?
A distinction can be made between real and informational frictions
Real sources of friction
1. Order processing costs
To process and execute orders from clients (traders), a dealer has to hire and train qualified
personnel, build a supporting infrastructure, commit capital, pay exchange and clearing and settlements fees, ... He
requires compensation for these costs E.g. fee per order. Completely ignored in EMH.
2. Competition between dealers may be imperfect
Dealer then enjoys market power allowing him to adjust his quoted prices to extract monopoly rents
3. Inventory risk Can also be seen as a friction!
General idea: a dealer obtains an unwanted position in the asset if he executes an order from a trader Pushed away from the optimal portfolio.
If the dealer is risk-averse, he wants compensation for this risk
Informational sources of friction
Next to the real sources of friction (costs, market power, inventory risk), also information is a source of friction
* more specifically, some market participants can have more information than others (for example, think of a hedge fund that
employs a number of analysts to follow certain stocks in detail)
* as such, a dealer may have less information than a trader (hedge fund) Extreme case: insider trading, i.e. people trade
* this means that he may quote a price that is wrong, more specifically, the dealer may sell at on information they should not have.
a price that too low, or buy at a price that is too high
* traders with superior information will then obtain a profit, while the dealer faces a loss
* dealer will also require compensation for expected losses, due to information asymmetries
How does friction affects market participants and prices at which you trade, market liquidity,
and how markets ultimately become efficient?
3. Market Liquidity
Definitions
We now define market liquidity, a crucial concept for all participants in financial markets
Definition 3
Market liquidity (for short, liquidity) is the degree to which an order can be executed within a short time frame at a price close to the security’s
consensus value.
I.e. how easy, cheap and quick you can trade.
How can we make this definition operational, e.g., to measure liquidity?
In illiquid markets, due to frictions, transaction prices (these are prices at which you can actually buy or sell) can deviate substantially from
the asset’s fundamental value. Illiquidity is a consequence of the frictions, described in Section 2
Illiquidity will push prices away from the fundamental value.
So prices at which you can buy or sell are different.
,Definition 4
Bid = price at which the trader can sell immediately
Ask = price at which the trader can buy immediately
Midquote = average of ask and bid
Bid-ask spread (in short Spread) = Ask - Bid
Depth = number of shares that are available at ask or bid quote
Tick size = minimum price variation, i.e., the minimum amount by which prices need to change prices are typically discrete E.g. one cent.
Spread: * Always positive. Sometimes though: crossed or locked markets, but then trading is suspended.
* When markets are perfectly liquid, this is equal to 0.
* Minimum bid-ask spread is the tick size (if spread is not 0).
Question: if you can buy or sell immediately, who is then quoting this price?
* intermediary: dealer (market maker, specialist) Part 2 course
* limit order trader Part 3 course
* HFTs High frequency traders, flash traders.
In the remainder of this chapter, the liquidity supplier is referred to as “dealer” Sets bid and ask prices. Allows other people to trade.
The trader wants to trade immediately and is then a liquidity demander
Hence:
* bid = price at which trader sells and dealer buys
* ask = price at which trader buys and dealer sells
You can sell # shares at that price!
A trader wants to buy 1,200 shares. She observes the quotes from a dealer from JPMorgan
You can buy # shares at that price!
(assume tick size = $0.01 or 1 cent).
* depth at $25.00 is only 1,000, so she can buy only this number of shares at $25
* she needs to buy the remaining 200 shares of her order at $25.02
* if a trader wants to trade a larger quantity, she has to accept a worse price
note: from trader perspective, a worse price is a lower bid or higher ask!
Minimum price variation: one cent! Differences between prices
are multiples of one cent.
Spread = 0.03 Spread: difference between best ask and best bid.
Best: always from a traders perspective! Best bid: highest price at which you can sell, best ask: lowest price at which you can buy.
You can look at the spread in 2 ways
Buy and sell immediately
1. Cost for the trader look at round-trip trade to see this
assume the trader buys one share: price = ask = $25.00 Trader: she -0.03
she sells the share immediately again: price = bid = $24.97 Dealer: he +0.03 Compensation for costs and risks.
difference is spread = cost
2. Profit/compensation for dealer compensation for costs, inventory risk, asymmetric information risk, . . . (see later)
he buys at $24.97 and sells at $25.00
Measure of illiquidity: spread/2 (since often you only buy or sell).
The higher the spread, the less liquid the market.
Spread can be interpreted as a cost of trading!
Often: midqoute is taken as the fundamental value.
, Spread is a (inverse) measure for liquidity: higher spread = lower liquidity, higher illiquidity
Depth is another measure of liquidity: higher depth = higher liquidity You can trade more before pushing prices up at the ask side or down at the bid side.
Exercise 1
Explain why it always holds that Spread 0 and thus Ask Bid, and in practice Spread > 0 or Ask > Bid.
Solution:
Suppose we would have Spread < 0. Then the dealer makes a loss on each trade: he buys at the bid and sells at the ask and since Spread < 0 we have Ask < Bid.
In addition, each trader would like to trade as much as possible: she buys at the ask and sells at the bid and since Spread < 0 we have Ask < Bid, so she makes a
profit on each share traded. Obviously, this can never be an equilibrium since the dealer would be out of business soon.
In theory, Spread = 0 is possible, but then the dealer has no compensation at all for costs.
So in practice, the spread will be strictly positive, Spread > 0.
Market Liquidity in Efficient Markets
Assumptions
* the EMH holds
* no other frictions in markets, among others
1. dealers are perfectly competitive and risk-neutral
2. no trading fees
3. zero tick size Prices can be anything!
Recall: market liquidity = degree to which an order can be executed within a short amount of time at a price close to
the consensus value
spread = a measure of cost of trading
Market liquidity and trading costs are two sides of the same medal The higher market liquidity is, the lower the cost of trading.
Using the spread as an inverse measure of market liquidity (low spread corresponds to high liquidity), we have
the following result
Proposition 1
In frictionless, efficient markets, the bid-ask spread is equal to zero, i.e., markets are perfectly liquid.
Proof:
If the dealer quotes ask price , this yields him an expected profit of
Obviously, the dealer will never quote a price that gives a (strictly) negative expected profit, so it must hold that
Assume that the dealer quotes an that gives a strictly positive expected profit (markets are perfectly competitive)
But in this case, another dealer will immediately step in and improve the ask i.e., quote a lower ask . In this way, he snoops the
order away and makes an expected profit himself (thus the market is not in equilibrium)
Such price improvement continues (since the tick size is zero) until no dealer has an incentive anymore to step in and improve the price
This is when profits are zero (the market is finally in equilibrium) and
Conversely, suppose the dealer quotes bid price , this yields him an expected profit of
Obviously, the dealer will never quote a price that gives a (strictly) negative expected profit, so it must hold that
Assume that the dealer quotes an that yields a strictly positive expected profit
In this case, another dealer will immediately step in and improve the bid i.e., quote a higher bid . In this
way, he snoops the order away and makes an expected profit himself
Such price improvement continues until no dealer has an incentive anymore to step in and improve the price
This is when profits are zero and
This implies a zero spread
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