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Chaoyang University of Technology Department of Finance

Ming-Chin Lin

Information and Market Microstructure

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Outline

Part I The Literature

Part II Empirical Observations

Part III From Idea to Writing

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Part I The Literature

Grossman and Stiglitz (AER, 1980)

Kyle (Econometrica, 1985)

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Grossman and Stiglitz (AER, 1980)

• Joint normality of signals and payoffs – Exponential Utility – Linear demand functions – Normally distributed price• Rational Expectations – Traders use correct models

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Grossman and Stiglitz Model: Only Informed Traders

• Informed Traders – Continuum of identical traders – Risk Averse with exponential utility – Private signal = value + noise – Rational – Perfect Competitors – Condition on Price

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Assumptions

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Grossman and Stiglitz Model: AddUninformed Traders

• Uninformed Traders (= Market Makers) – Continuum of identical traders – Risk Averse with Exponential Utility – Continuum of Perfect Competitors – Condition on Price• Could stop here (no other traders) – Price = weighted average of “signal” and

“prior” mean – Private information can be inferred from

price

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Information Acquisition Puzzle

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Grossman and Stiglitz Model: AddNoise Traders

• “Noise traders” : Who are they? – Random endowment, hedging – Liquidity needs• Optimization by noise traders not

modeled

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Problem with Competitive Models

• Large traders affect prices and know they affect prices.

• G&S impossibility results if perfect competition assumed.

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Kyle (Econometrica, 1985): Single-Period Model

• Informed Trader – Monopolist, exercises monopoly power – Risk Neutral • Market order model: This model

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• Uninformed Traders = Market Makers – Perfect Competitors – Risk Neutral• Take other side of market orders• Noise Traders trade randomly as in

G&S.• Microstructure: Informed and noise

trades batched, anonymously.

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Kyle (1985): Equilibrium

• Informed trader maximizes profits (quadratic problem): x = β*(V-P)• Pricing Rule: P = E{V | order flow = x + noise} = u + λ * [order flow]

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• Equilibrium: 1/λ = [market depth] =

stdev(noise) / stdev(V) β = [market depth]/2

Price Informativeness

Var(V|P) = ½ Var(V)

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Bid – Ask Spread:

Order flow = -1, market maker sets bid price = u + λ(-1) = u – λ

Order flow = 1, market maker sets ask price = u + λ

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1/λ = [market depth] = stdev(noise) / stdev(V)

stdev(noise)

stdev(V)

φ=1/2

1-φ=1/2q

1-q

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Maug (JF, 1998)

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Maug’s Definition of Market Depth

the degree in which a trade moves the price

λ = E(P|B) – E(P|S) / H - L

λ= 0, infinitely deep market;

λ= 1, fully revealing

Market Depth : the probability that market prices are not fully revealing

= 1- λ= 1/2

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Why does “liquidity” matter ?

market liquidity is essential in finance literature

The idealized assumptions : - frictionless - perfectly liquid markets (traded at no cost ) - agents take prices as given.

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If markets are not frictionless and are disturbed by some form of illiquidity?

Moreover, if the assumptions that price-taking

investors have the same information and are present in the market at all times are relaxed?

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create an adverse selection problem that implies differing bid and ask

prices set by market maker. In this case, market liquidity is priced by the

bid/ask spread and the competitive equilibrium can

not be applied.

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Remark: Market Microstructure

Loose Definition: examining the process by which

securities are traded affects prices, volume and trading behavior

Key concepts: market efficiency market liquidity

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Order Driven Market

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Quote Driven Market

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Empirical Studies:Decompose bid-ask spread

- Order Processing Costs

- Inventory Costs

- Adverse Selection Costs

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Part II Empirical Observations

Monetary Liquidity - in the sense of monetary factors,

monetary policy Market Liquidity - measured by transaction costs, trading volume, turnover rate, bid-ask spread, market depth

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Monetary policy Asset Prices

Monetary policy Market Liquidity

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Fig.1 Fed target federal funds rate

Source : Monetary Policy Report to the Congress July 15, 2004

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Fed target federal funds rate (cont.)

Source : Monetary Policy Report to the Congress Feb. 24, 2009

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Fig. 2 Interest rate

Source : Monetary Policy Report to the Congress Feb. 24, 2009

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Fig.3 NYSE Turnover rate

Turnover

0%

50%

100%

150%

200%

1數列

Source : NYSE

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NYSE Turnover rate (cont.)

0%

50%

100%

150%

200%

01/20

04

07/20

04

01/20

05

07/20

05

01/20

06

07/20

06

01/20

07

07/20

07

01/20

08

07/20

08

01/20

09

1數列

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Fig.4 CBOE VIX Index (a measure of equity market volatility)

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VIX Index 2007-2009 (cont.)

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從實際資料觀察

圖一和圖二來看 , 當 目標利率調高的同時 , 30 天期商業本票報酬率也走高 .

但若觀察圖三和圖四－反映市場流動性的指標－則似乎和圖一並沒有明顯的關係。

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然而若我們縮小範圍，觀察某一段特定時間的變化，又會有一些

新發現。

1. 2006 年 5~6 月份

油價高漲造成通膨壓力，市場預期 FOMC 持續調升利率的機率很

高，此時的週轉率低 ( 圖三 ) 而波動程度高 ( 圖四 ) ；

2. 2007 年 8~9 月份

因為次級房貸危機造成經濟下跌的隱憂，市場預期 FOMC 持續調

降利率的機率很高，此時的週轉率高 ( 圖三 ) 而波動程度低 ( 圖

四 )

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此觀察結果似乎指出 monetary policy and market liquidity 存在某種關聯。

從實證研究的結果的確發現二者之間的聯繫。

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Empirical Findings

Chordia, Roll and Subrahmanyam (JF, 2001)

Depth rises prior to macroeconomic data release and falls back toward its normal level on the day of announcement.

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Empirical Findings

Chordia, Sarkar and Subrahmanyam (RFS, 2005)

They found monetary expansion increases (decreases) in the federal fund rate lead to decreases (increases) in liquidity and increases (decreases) in stock and bond volatility.

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上述屬於實證研究，然關於理論方面的研究則尚不多見。

因此不論是觀察實際資料或是實證研究的結果都指出建立 macro liquidity and market liquidity 之理論關係是值得探討的議題。

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An Example

We focus on the transmission mechanisms :

from “market expectation about monetary stance of the Fed”

to “market liquidity in terms of

adverse selection costs”

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Why is the linkage so important?

如果藉由理論探討所提供的各種可能結果，能夠了解貨幣

政策將如何影響市場流動性，對於中央銀行制定貨幣政策

以及進行公開市場操作時是很重要的參考。

市場流動性影響價格揭露訊息的程度，透過不同水準的市

場流動性可以映照出市場對於貨幣政策的預期看法和對基

本面的信心。

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Microstructure Model

藉由 Kyle (1985) and Maug (1998) 模型探討：

market maker 因為考慮面臨 informed traders 產生的逆選擇問題所訂定的交易價格，在加入了市場對貨幣政策的預期看法後，將會有什麼影響？

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藉此模型回答如下問題：

if market beliefs about the Fed policy change,

how will the informativeness of price be affected?

Will the market depth or the adverse selection be more serious?

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Presentation 需要注意哪些 引起聽眾的興趣和注意 以直覺的方式表達 文章打散再重組 技術性的地方可以省略 不需太花俏

Part III From Idea to Writing

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Idea 怎麼來

敏銳而細膩的觀察 – 對現象的關注

深刻而嚴密的思考 – 對事理的分析 活潑而豐富的想像 – 對本質的好奇

抽象與具體的轉換 – 對方法的熟稔

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養分的來源

小說 電影 不同形式的藝術創作 報章 雜誌 隨處可得的網路資訊 不同領域成功或失敗的故事自己生活中的體會

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從 Idea 到 Paper

做和寫的差別 good research ≠ good paper ≠ good publication

寫作的講究 小火慢燉 v.s. 大火快炒

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文章結構的佈局邏輯的嚴密 文筆的好壞 中英文間的穿梭 左腦和右腦交互

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好文章的元素

一個動人的故事 一個巧妙的開場 一個引人入勝的鋪排 一個高潮迭起的劇情 一個讓人深思的結局

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Three Levels of Writing

First Level People focus solely on the document

itself and on getting into shape Second Level People try to improve their writing style

Third Level Good writing touches the soul

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Our own misunderstandings are all that

prevent us from seeing that.

Writing is so difficult for so many people

Writing creates an opportunity for real

personal growth and a greater understanding

of why we are here.

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The End