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fficiency –current price incorporates allpublicly available information.
3.Strong form efficiency–current price incorporates allinformation including insider information.
Tests of EMH are usually of the weak or semi-strong form variety.Warwick Business School 9
Tests of weak/semi-strong form EMH (Brooks 5.2)Analysis of the ACF of returnsIn any given sample even ifThe null hypothesis……can be tested with the Ljung-Box Q statistic (‘portmanteau’statistic): ()()()0 ,0 0 ,1var,cov0 ,0,cov>====⇒>=−−ssrrrsrrtsttssttρImplied by linear independence0ˆ≠sρThe population ACF of a linearly independent process is flat at zero for all positive lags.Risk adjusted returns have exactly the same ACF as here (assuming constant equilibrium returns).A mean zero, linearly independent process (such asrisk adjusted returns) is a WHITE NOISE process.White noise has an ACF with the shape given here. 0=sρ0...:210====kHρρρ()()()2121~ˆ2kakiiiTTTkQχρΣ=−−+=Large sample/asymptotic distributionWarwick Business School 10
ACFsof return series
Date: 01/11/07 Time: 13:50Sample: 1974M01 2006M02Included observations: 386AutocorrelaPartial CorLagAC PAC Q-Stat Prob .|. .|. 10.0620.0621.49910.221 .|. .|. 20.0080.0051.5270.466 .|. .|. 3-0.002-0.0031.52840.676 .|. .|. 40.0180.0181.65320.799 .|. .|. 50.0260.0241.91260.861 *|. *|. 6-0.063-0.0673.48750.746 .|. .|. 700.0083.48750.837 .|. .|. 80.0160.0173.59220.892 .|* .|* 90.0710.0685.58480.781 .|. .|. 10-0.041-0.0496.26270.793 .|* .|* 110.1180.12811.7910.38 .|. .|. 12-0.004-0.02611.7980.462 .|. .|. 130.0270.02612.0850.521 *|. *|. 14-0.137-0.14719.6590.141 *|. .|. 15-0.075-0.04721.9080.11Date: 01/11/07 Time: 13:58Sample: 12/31/1985 1/05/2006Included observations: 5051AutocorrelaPartial CorLagAC PAC Q-Stat Prob |** |** 10.2160.216236.190 |* |* 20.110.067297.750 |* | 30.0780.044328.660 |* |* 40.1240.098407.010 | | 50.051-0.002420.020 | | 60.016-0.013421.360 | | 70.060.049439.510 |* | 80.0760.045468.850 |* | 90.0770.045498.530 | | 100.0450.011508.620 |* | 110.0690.038532.450 | | 120.026-0.016535.960 | | 130.001-0.024535.960 | | 140.020.0145380 | | 150.0290.011542.220
FTSE 250 returns
UK-US exchange rate returns
Linear independence/EMH rejected
Linear independence/EMH cannotbe rejectedWarwick Business School 11
Tests of semi-strong EMH (Cuthbertson& Nitzsche4.2-4.3)
Regression tests of return predictability:If excess returns are a fair game, , then the elements of the k×1 vector of coefficients βare jointlyzero.A test of EMH is therefore: This can be tested using an F-test (see Gujarati Chp8/ Brooks Chp3):11+++Ω′+=ttturβμ()01=−+μttrE.0' theof oneleast At : versus0...:1210≠====sHHkββββ()[]().under ~1//01,HFkTRSSkESSFkTk+−+−=Warwick Business School 12
Regression tests of return predictability
What variables are included in ?1.Data on past returns (another test of ‘weak form’efficiency).2.Data on past news : Autoregressive moving average models.3.Data on other financial variables such as dividend yields, E/P and interest rates (see Fama, 1991, for a discussion).4.Data related to various ‘anomalies’(e.g., small firm and calendar effects: see Cuthbertson& Nitzsche18.4). Ω0 ,≥−jjtεWarwick Business School 13
A fifth order autoregressionwith calendar effects for FTSE250 returnsDependent Variable: FTSE_250_RETURNSMethod: Least SquaresSample (adjusted): 1/09/1986 1/05/2006Included observations: 5046 after adjustmentsConvergence ach