financial market microstructure - hec paris...the market microstructure approach it recognizes the...

Financial Market Microstructure

Stefano Lovo

HEC, Paris

Illiquidity and Price Impact

Standard approach in Financial Economics (e.g. CAPM,Asset pricing, Derivatives pricing etc . . . ): investors can tradeany quantities at equilibrium prices.

Law of one price: Two identical assets must trade for thesame price. The same asset must trade for the same pricein all locations.

Informational efficiency of the stock market: the price of anasset reflects all information about the asset’sfundamentals.

Stefano Lovo, HEC Paris Key concepts 2 / 1

Market Informational Efficiency

DefinitionWeak form efficiency: Trading prices incorporate all pastpublic information.Semi-Strong form efficiency: Trading prices incorporateall present and past public information.Strong form efficiency: Trading prices incorporate allpublic and private information available in the economy.


Actual markets: low of one price?

US treasury bills: bonds with maturity of less than 2 years.US treasury notes: bonds with maturity of more than 2 years.

At any time there are coexist bill and notes with only oneresidual payment at the same future date.

Amihud and Mendelson (1991): On average notes trade at adiscount

notes’ average annual yield ' bills’ average annual yield +0.43%


Actual markets: price reflects fundamentals?


Market liquidity

DefinitionAn asset’s liquidity is a measure of

The speed at which an asset can be bought and sold. (thefaster, the more liquid)

The price impact of the traded quantity. (the smallerimpact, the more liquid)

The cost of a "round-trip". (the cheapest, the more liquid)


Why do we care?

Illiquidity means lower returns on portfolios: (i)portfolio managers care about market liquidity and (ii) thebrokerage industry devises trading strategies to minimizecosts due to illiquidity.

Illiquidity affects asset prices/cost of capital: (i)illiquidity = "tax" on asset payoffs + (ii) source of risk.

Price discovery affects the allocation of capital in theeconomy.


An example on liquidity and cost of capital

Mid quote =(18.25 + 18.375)/2 = 18.3125Transaction price ' 18.3125± 0.0625transaction cost ' 0.34% of 18.3125

Example

Stock A is an immediate perpetuity paying $1 per year. The requiredreturn of capital is r = 5% per year. What is the current price for stockA? Answer $21

Suppose that at resale transaction costs are s = 0.34% of the price.What is the current price for stock A? Answer $19.66 ' $21(1−6.4%)


Main Questions

1 Liquidity: What are the determinants of market liquidity?Liquidity risk? Measures (bid-ask spreads and depth)?

2 Price Discovery: How and to what extent do pricesimpound new information? At which speed?

3 Volatility: What are the determinants of price changes atthe high frequency? How do volatility and liquidity interact?

Answers have implications for (i) asset pricing (illiquiditypremium), (ii) the design of trading systems, (iii) regulation offinancial markets (best execution, insider trading, highfrequency trading ...), (iv) portfolio management (v) marketreactions to news, interventions etc...


The Market Microstructure Approach

Some definitions (the term is originally due to Garman (1976))

O’Hara (1995) : "The study of the process and outcomesof exchanging assets under explicit trading rules..."

Madhavan (2000) : "The process by which investors?latent demands are ultimately translated into transactions".

Biais, Glosten and Spatt (2005) : "The investigation ofthe economic forces affecting trades, quotes and prices"


Roadmap

Key conceptsAuctionsQuote driven markets: static models

Inventory modelsInformation models

Quote driven markets: dynamic modelsMarket efficiency and herd behaviorRobust price formation

Limit Order MarketsOTC markets


The Market Microstructure Approach

It recognizes the role of:Heterogeneity among Market Participants. Participantsto security markets have various objectives (e.g. dealersare different from final investors; hedgers different fromspeculators etc...).

Institutional framework. Market design and marketregulation matter.

Private Information. Informational asymmetries amongmarket participants are prevalent in securities markets.


Market Participants

Costumers

Dealers

Intermediaries


Market Participants

Costumers: Agents that are willing to trade the security:Institutional investors (pension funds, mutual funds,foundations): Hold and manage the majority of assets;account for the bulk of trading volume; trade largequantities.Individual Investors (retail traders, household, banks):Account for the bulk of trades; trade smaller quantities.

Dealers

Intermediaries


Market Participants

Costumers

Dealers: Large professional traders who do trade for theirown account and provide liquidity to the market.

Intermediaries


Market Participants

Costumers

Dealers

Intermediaries:Brokers: Match costumer orders but do not trade for theirown account.Specialists (NYSE): Are responsible for providing liquidityand smoothing trade on given securities.Market Makers: Agents that stand ready to buy and sell thesecurity at their bid and ask prices respectively. Liquiditysuppliers.


Institutional Framework: Market types

Call Auction Markets: Occur at specific time (ex. at theopening and or at the fixing); investors place orders thatare executed at a single clearing price that maximizes thevolume of trade.

Continuous Auction Markets (or limit order markets):Investors trade against resting orders placed earlier byother investors (Euronext, Toronto SE, ECNs).

Dealer Markets (or quote driven markets) :Market-makers post bid and ask quotes at which investorscan trade. (Bond Markets MTS, FX markets).

Alternative Trading Systems (ATS)Electronic Communication Networks (ECN): Continuousorder driven anonymous markets (Island, Instinet,Archipelago, Redibook)Crossing Networks (CN): Cross multiple orders at a singleprice determined in a base market. (POSIT, Xtra XXL)


Most common orders

Buy limit order: Order to buy up to a quantity q for a pricenot larger than p.Sell limit order: Order to sell up to a quantity q for a pricenot smaller than p.

Buy market order: Order to buy a quantity q at the bestcurrent market conditions.Sell market orders: Order to buy a quantity q at the bestcurrent market conditions.


A game theoretical approach

The market for one financial asset can be represented asfollows:

Market Participants: set of players NInstitutional framework:

Set of actions Xi available to market participant iAsset allocation rule Q : ×i∈NXi → RN

Cash allocation rule P : ×i∈NXi → RN∑i

Qi =∑

i

Pi = 0

Asset fundamental value vParticipant i ’s monetary payoff from transaction:

vQi + Pi

Participant i ’s utility after transaction, given initial wealthWi :

Ui(Wi + vQi + Pi)


Modelling uncertainty

Ω: set of all possible states of Nature (finite).A: Set of all subsets of Ω.π : A → [0,1]: probability measure of A.

v : Ω→ R: Value of the asset (v ).Wi : Ω→ R: Value of agent i initial portfolio (Wi ).


Partitions

DefinitionA partition P of Ω is a collection of nonempty, pairwisedisjoint subsets of Ω whose union is Ω.P(ω) denotes the element of P that contains the state ω.

Let P and P ′ be two partitions of Ω.

DefinitionPartition P is said to refine partition P ′ if every element θ of P iscontained in some element θ′ of P ′.

DefinitionThe meet of the partitions Pi and Pj , that we will denoteMij , isthe finest partition that is refined by both Pi and Pj .


Modelling incomplete information using partitions

All agents start with common prior π over Ω.Agent i receive private information that we described as apartition Pi over Ω:if the true state is ω, then agent i is informed that the truestate belongs to the set Pi(ω).If the true state is ω, the type of agent i is θi = Pi(ω).


An example

Ω = ω1, ω2, ω3, ω4, π(ω) = 0.25v(ω1) = 2; v(ω2) = 3, v(ω3) = 3, v(ω4) = 4P1 = ω1, ω2, , ω3 ω4P2 = ω1, ω3, , ω2 ω4P3 = ω1, ω2, , ω3, ω4P3 = ω1, ω2, ω3, ω4

Agent 1 and 2 receive different partial information; Agent 3is perfectly informed; Agent 4 is perfectly uninformed.

If for example ω = ω3, thenfor agent 1 E [v |P1(ω3)] = 3.5for agent 2 E [v |P2(ω3)] = 2.5for agent 3 E [v |P3(ω3)] = 3for agent 4 E [v |P4(ω3)] = 3


Bayesian Equilibrium

Let Pi = θ1i , . . . θ

ki be the set of possible types for agent i .

A strategy for player i is a mapping

σi : Pi → ∆Xi

A Bayesian Nash equilibrium is a strategy profileσi , . . . , σN such that

σi(θi) ∈ arg maxxi∈Xi

E [Ui(Wi + vQi(xi , σ−i) + Pi(xi , σ−i))|θi ,h]

where h represents what is common knowledge at the timeof trading.


Common knowledge

Something is common knowledge if we both know that it’strue;

1 and I know that you know it’s true;2 and you know that I know it’s true;3 and I know that you know that I know that you know that I

know that you know it’s true;. . .

4 and so on, for any string of beliefs we put together.

More formally,

LemmaIf the true state is ω, then what is common knowledge for playeri and j isMij(ω).


Agreen to Disagree

Theorem( Aumann 1976) If two agents have the same priors, and afterreceiving private information their posterior on an event a ∈ Aare common knowledge, then these posteriors are equal.

Corollary

Take anyMij(ω). If the agents i and j have the same priorsthen for all ω′ ∈Mij(ω), we have

πi(ω′|Mij(ω)) = πj(ω

′|Mij(ω)),

i.e. posterior beliefs conditional on a common knowledge eventdo not differ.


Trade Motivation

There are two possible reasons for trading:

Speculate on private information about v .Hedging, when Ui is concave.


No trade theorem (simplified version)

TheoremConsider two agents with common prior, with the same weaklyconcave utility function U and with the same initial wealth W .Suppose each trader receives some private information. Then

In equilibrium there cannot occur any trade that allows atleast one trader to be strictly better off.If the utility function is strictly concave, then in equilibriumthere is no trade.


No trade theorem (Migrom and Stokey 1982)

TheoremIf traders start from common priors and it is commonknowledge that all traders are rational and the current allocationis ex-ante Pareto efficient, then new asymmetric information willnot lead to trade, provided that traders are strictly risk averse.

CorollaryIf traders start from common priors and have no reason to tradea priori, then they will not trade based on the arrival of newprivate information.


Proof (simplified version)

Suppose that there is a trade leading agent 1 to trade Q1asset for P1 dollars.The resulting change in i ’s wealth from the trade in state ωis

T (ω) := v(ω)Q1 + P1

Agent 1’s post trade utility is

U(W + T )

The resulting change in 2’s wealth from the trade in state ωis −T (ω).Agent 1’s post trade utility is

U(W − T )



Suppose agent 1 is of type θ1 and he is willing to agree on thetrade.

Conditional on agent 2 agreeing, agent 1’s posterior belief onagent 2’s type being θ2 is

π(θ2|θ1, trade)

Thus, agent 1 evaluates the trade at∑θ2∈P2

π(θ2|θ1, trade)E[U(W + T )|θ1, θ2

]

If agent 1 strictly prefers trading, this is strictly larger than∑θ2∈P2

π(θ2|θ1, trade)E[U(W )|θ1, θ2

]



Multiplying by π(θi , trade) :∑θ2∈P2

π(θ1, trade)π(θ2|θ1, trade)E[U(W + T )|θ1, θ2

]=

∑θ2∈P2

π(θ1, θ2, trade)E[U(W + T )|θ1, θ2

]>

∑θ2∈P2

π(θ1, θ2, trade)E[U(W )|θ1, θ2

]Suming across θ1:∑

θ1∈P1

∑θ2∈P2

π(θ1, θ2, trade)E[U(W + T )|θ1, θ2

]=

E[U(W + T )|trade

]> E

[U(W )|trade

]Because agent 1 strictly prefers trading for some θ1 one has



Let Ω+ (resp. Ω−)be the set of states ω where agent 1 gains (resp. does not gain) from trading:

Ω+ := ω ∈ Ω|T (ω) > 0

Ω− := ω ∈ Ω|T (ω) ≤ 0

Then E[U(W + T )|trade

]> E

[U(W )|trade

]implies

∑ω∈Ω+

π(ω|trade)(U(W (ω) + T (ω))− U(ω)) >∑

ω∈Ω−π(ω|trade)(U(ω)− U(W (ω) + T (ω)))

Because U is weakly concave:

∑ω∈Ω+

π(ω|trade)(U(ω)− U(W (ω)− T (ω))) ≥∑

ω∈Ω+

π(ω|trade)(U(W (ω) + T (ω))− U(ω))

∑ω∈Ω−

π(ω|trade)(U(ω)− U(W (ω) + T (ω))) ≥∑

ω∈Ω−π(ω|trade)(U(W (ω)− T (ω))− U(ω))

These three inequalities together imply

E[U(W − T )|trade

]< E

[U(W )|trade

]that is player 2 will not agree to trade.


Summary

1 Financial markets display frictions and illiquidity.2 Market microstructure: The investigation of the economic

forces affecting trades, quotes and prices.3 Market Participants.4 Market Mechanism.5 Asymmetric information.6 No trade theorem: trade cannot purely for speculation on

private information.


References

Yakov Amihud and Haim Mendelson (1991); “Liquidity,maturity, and teh yields on U.S. treasury securities”,Journal of Finance.Robert Aumann (1976), “Agreeing to Disagree” Annals ofStatistics.John J. Geanakoplos and Herakles Polemarchakis (1982),“We Can’t Disagree Forever,” Journal of Economic Theory.Paul Milgrom and Nancy Stokey (1982), “Information,Trade and Common Knowledge,” Journal of EconomicTheory.


financial market microstructure - hec paris...the market microstructure approach it recognizes the...

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