Title: Empirical Financial Economics
1Empirical Financial Economics
- 2. The Efficient Markets Hypothesis - Generalized
Method of Moments
Stephen Brown NYU Stern School of Business UNSW
PhD Seminar, June 19-21 2006
2Random Walk Hypothesis
- Random Walk hypothesis a special case of EMH
- Overidentification of model
- Provides a test of model (variance ratio
criterion) - Allows for estimation of parameters (GMM
paradigm)
3Variance ratio tests
using sample quantities
The variance ratio is
asymptotically Normal
4Overlapping observations
Non-overlapping observations
ln(pt)
t
tT
Overlapping observations
ln(pt)
unbiassed estimators
Variance ratio is asymptotically Normal
5Random walk model and GMM
aggregate into moment conditions
and express as three observations of a nonlinear
regression model
6Generalized method of moment estimators
- Choose to minimize . is
referred to as the optimal weighting matrix,
equal to the inverse covariance matrix of - Estimators are asymptotically Normal and
efficient - Minimand is distributed as Chi-square with d.f.
number of overidentifying information - Methods of obtaining
- 1. Set (Ordinary Least Squares).
Estimate model. Set (Generalized
Least Squares). Reestimate . - 2. Use analytic methods to infer
7GMM and the Efficient Market Hypothesis
1 asset and 1 instrument
1 equation and k unknowns
m assets and 1 instrument
m equations and gtk unknowns
m assets and n instrument
mxn equations and gtk unknowns
8Autocovariances and cross autocovariances
xt
yt
t
tk
t-k
9Cross autocovariances are not symmetrical!
Autocovariances are given by
Cross autocovariances are given by
10Cross autocovariances and the weighting function
11Assuming stationarity
12Apply this to cross covariances
13A simple expression for the inverse weighting
matrix
14Some applications of GMM
- Fixed income securities
- Construct moments of returns based on
distribution of it? - Estimate ? by comparing to sample moments
- Derivative securities
- Construct moments of returns by simulating PDE
given ? - Estimate ? by comparing to sample moments
- Asset pricing with time-varying risk premia