Financial Markets And Empirical Regularities An Introduction to Financial Econometrics

Transcription

1 Financial Markes And Empirical Regulariies An Inroducion o Financial Economerics SAMSI Workshop 11/18/05 Mike Aguilar UNC a Chapel Hill 1

2 Ouline I. Hisorical Perspecive on Asse Prices II. III. IV. Predicabiliy of Asse Reurns Asse Pricing Models Volailiy Models 2

3 Essenial Sources Campbell, Lo, & MacKinlay, The Economerics of Financial Markes Cochrane, Asse Pricing Huang & Lizenberger, Foundaions for Financial Economics Hamilon, Time Series Analysis Greene, Economeric Analysis 3

4 I. Hisorical Perspecive on Asse Prices Types of Financial Asses: Common: Socks, Bonds, Commodiies, Foreign Exchange, Exoic: Derivaives; Opions, Fuures, 4

5 I. Hisorical Perspecive on Asse Prices A Hisory of Asse Prices Source: Campbell Harvey 5

6 I. Hisorical Perspecive on Asse Prices Definiions: Simple Gross Reurn: P R + 1 =, P 1 P = price of asse a ime. Compound Gross Reurn: R ( k) + 1= (1 + R )*(1 + R 1 )*...*(1 + R k+ 1) Annualized Reurn: k 1 j = 0 (1 + R j ) 1 / k 1 1 k k 1 j = 0 R j Coninuously Compounded Reurn: r = log( 1 + R ) = log P log P 1 6

7 I. Hisorical Perspecive on Asse Prices Why Reurns?..Because reurns end o be saionary. Saionary: The join disribuion beween wo reurns, depends only on h and NOT on. x x h 7

8 I. Hisorical Perspecive on Asse Prices A Hisory of Asse Reurns Source: Campbell Harvey 8

9 I. Hisorical Perspecive on Asse Prices Source: Campbell Harvey 9

10 I. Hisorical Perspecive on Asse Prices Source: Campbell Harvey 10

11 I. Hisorical Perspecive on Asse Prices Observaion: There exiss a Risk / Reurn Tradeoff 11

12 I. Hisorical Perspecive on Asse Prices Sas Reminder: Consider a random variable Mean: Variance: x μˆ T 1 T x = 1 T 1 T ( x = 1 2 σˆ ˆ μ ) 2 Skew: Sˆ T 1 ( ˆ ) 3 x μ T σˆ = 1 3 Kurosis: Kˆ T 1 ˆ ) 4 ( ˆ x μ T σ =

13 I. Hisorical Perspecive on Asse Prices Wha is he Disribuion of Reurns? Normal? 13

14 I. Hisorical Perspecive on Asse Prices 14

15 I. Hisorical Perspecive on Asse Prices Sylized Facs on he Disribuion of Reurns: 1. Index Volailiy < Sock Volailiy 2. Negaive Skewness 3. Excess Kurosis 15

16 II. Predicabiliy of Reurns Can We Predic Reurns? Day Traders Say Yes Efficien Marke Hypohesis Says No 16

17 II. Predicabiliy of Reurns Efficien Marke Hypohesis (EMH): Fama (1970): A marke in which prices always fully reflec available informaion is called efficien. 17

18 II. Predicabiliy of Reurns Efficien Marke Hypohesis (EMH): Fama (1970): A marke in which prices always fully reflec available informaion is called efficien. Malkiel (1992): he marke is said o be efficien wih respec o an informaion se 18

19 II. Predicabiliy of Reurns Probabiliy Theory Reminder: The Informaion Se F is a sigma field said o conain all of he relevan informaion up o ime. 19

20 II. Predicabiliy of Reurns Probabiliy Theory Reminder: The Informaion Se F is a sigma field said o conain all of he relevan informaion up o ime. Maringale: E = x [ x + 1 F ] 20

21 II. Predicabiliy of Reurns EMH: Weak Form Efficiency: Informaion Se: Asse s own hisory Tes via Random Walk 21

22 II. Predicabiliy of Reurns EMH: Weak Form Efficiency: Informaion Se: Asse s own hisory Tes via Random Walk Semisrong Efficiency: Informaion Se: Weak Form + Publicly available daa Tes via Even Sudies 22

23 II. Predicabiliy of Reurns EMH: Weak Form Efficiency: Informaion Se: Asse s own hisory Tes via Random Walk Semisrong Efficiency: Informaion Se: Weak Form + Publicly available daa Tes via Even Sudies Srong Form Efficiency: Informaion Se: Weak + Semi + Privae Info Tes via Performance Evaluaion 23

24 II. Predicabiliy of Reurns Join hypohesis problem: The EMH can be esed direcly. Even if we rejec he hypohesis of efficiency, his could eiher be because he marke is ruly inefficien, or because we have assumed an incorrec equilibrium model. 24

25 II. Predicabiliy of Reurns Implicaion of Weak Form EMH: Expeced Reurns follow a maringale. Random Walk Hypohesis 25

26 II. Predicabiliy of Reurns P = μ + P + 1 ε Random Walk 1: i.i.d Incremens Random Walk 2: Independen, No Indenical Random Walk 3: Uncorrelaed Incremens 26

27 II. Predicabiliy of Reurns Time Series Economerics Reminder: Auo Correlaion Correlaion beween wo observaions of he same series a differen daes AuoCovariance : γ (k) Cov( x, x k ) AuoCorrelaion : ρ(k) γ ( k) γ (0) 27

28 II. Predicabiliy of Reurns Time Series Economerics Reminder: Auo Correlaion Correlaion beween wo observaions of he same series a differen daes AuoCovariance : γ (k) Cov( x γ ( k) AuoCorrelaion : ρ(k) γ (0) Box Pierce Q Saisic : Q m, x k ) = T ( T + 2) m k = 1 2 ρ ( k ) T k 28

29 II. Predicabiliy of Reurns 29

30 III. Asse Pricing Models Capial Asse Pricing Model (CAPM) Sharpe (1964) and Linner (1965) Consumpion Based-CAPM Iner-emporal-CAPM Arbirage Pricing Theory Ross (1976) 30

31 III. Asse Pricing Models - CAPM CAPM: Differences in excess reurns across asses are due o differences in he riskiness of each asse. Bea: Measure of riskiness Marke Model : ( Ri R f ) = β ( Rm R f ) + u There exiss a linear Risk/Reward Tradeoff Cov[( Ri R f ),( Rm R f )] OLS β = Var( R R ) m f 31

32 III. Asse Pricing Models - CAPM CAPM Pricing Equaion: E[ Ri ] = R f + βim( E[ Rm ] R f ) 32

33 III. Asse Pricing Models - CAPM CAPM Pricing Equaion: E[ Ri ] = R f + βim( E[ Rm ] R f ) Tesable Implicaions: 1) Only bea is required o price asses. 2) There is a linear risk/reurn relaionship. 33

34 III. Asse Pricing Models - CAPM Tesing he CAPM: Fama & MacBeh (1973) Sep 1:For each ime period esimae he cross - secional regression : 2 ( Ri R f ) = θ0 + θ1βim + θ2βim + θ3s sandard deviaion of u. i + u i, where s is he Sep 2 : Aggregae ha θ = E[ θ ] k = k k parameer 0,1,2,3 esimaes over ime such 34

35 III. Asse Pricing Models - CAPM There is an errors -in - he β' s mus Fama & MacBeh con d firs variables (EIV) problem because be esimaed. Fama & MacBeh soluion: Sor socks ino porfolios. Shanken soluion: correc variance of esimaors pos esimaion. H 0 : θ0 = θ1 = θ2 = θ3 = 0 β is he only facor necessary o price asses & here is a posiive, linear risk - reurn radeoff. 35

36 III. Asse Pricing Models - CAPM 36

37 III. Asse Pricing Models - CAPM CAPM Anomalies: Small Firm effec (Keim `81) P/E Raio Effec (Ball `78 and Basu `83) Book-o-Marke Effec (Saman `80 and Rosenberg `85) Momenum Effec (Jegadeesh and Timan `93) Is Bea Dead? 37

38 III. Asse Pricing Models - CAPM 38

39 III. Asse Pricing Models Consumpion Based Models Consumpion Based Asse Pricing Model U ( C ) = 1 γ C 1 γ Max = 0 β U ( C ) subjec o C + N P Q N i i i= 0 i= 0 P Q i i 1 + W E [ β ( C C + 1 γ ) R ] 1 = U : Uiliy Funcion C : Consumpion γ : Coefficien of Risk Aversion β :Ineremporal Rae of Subsiuion P : Value of asse Q : Amoun of asses owned N : Number of asses in he economy W : Real Labor Income 39

40 40 III. Asse Pricing Models Consumpion Based Models e Z m z R e T C C ' ) ( : 1 ] ) ( [ ], [ 1 1 = = = θ β β γ θ γ ime insrumens a of Vecor GMM Esimaion

41 41 III. Asse Pricing Models Consumpion Based Models ) dim( & p ) dim( q ; where Min ime insrumens a of Vecor z e TJ z z e e S S W Wm m J e Z m z R e p q T T T C C = = = = = = = = = ] [ ) ( )' ( ' ) ( : ] ) ( [ ], [ 1 χ θ θ θ β β γ θ γ GMM Esimaion

42 IV. Volailiy Models 42

43 43 IV. Volailiy Models ARCH Auoregressive Condiional Heeroscedasiciy Engle (`82) & French, Schwer, Sambaugh (`87) = = = + + = + = p j j j q i i i q i i i q p GARCH q ARCH ) :, ( ) : ( σ β α ε ω σ α ε ω σ

44 IV. Volailiy Models 44

45 Financial Economerics is he Applicaion of Economeric Mehods o Financial Markes Economerics: Time Series,GMM,ARCH,.. Finance: Reurns no Predicable? Volailiy is Predicable? 45