2.9 (a), (b)
(a) Since f is a smooth function of , we can switch the order of dierentiation and expectation,
E( log f (X1 , . . . , Xn ) = E
=
=
f (X1 , . . . , Xn )
f (X1 , . . . , Xn )
f (X1 , . . .
Hints to Assignment 2
October 31, 2012
Problem 2.9
No need to decompose the joint density as log f (Xn , . . . , X1 ) = log f (Xt |Xt1 . . .),
instead use the joint density directly in your proof. Jus
#Although results are not given in the solution, you should provide necessary values,
#plots or tables in your assignment.
#Unless the formula you used can be easily read from the code, e.g. mu <- mea
Stat240: Homework 1 - due at beginning of class on Friday October 21, 2011
LX = Lai and Xing, Statistical Models and Methods for Financial Markets
1. Problem 1.7 in LX.
2. Problem 2.3 in LX.
3. Proble
#Codes and results must be provided for full credits
#Unless the formula you used can be easily read from the code, e.g. mu <- mean(x)
#otherwise you have to write out the formula you used but not jus
STATS 240 Team Project
Due Dec 5, 2014 by 5pm
Each team can consist of 1 to 4 students. All members names should be included in the
project; each member of the same team will get the same grade.
Hand
Black-Litterman Asset Allocation and
Mean-Variance Portfolio Optimization when
Means and Covariances of Asset Returns are
Unkown
Tze Leung Lai
Stanford University
2014
1 / 31
Outline
Review of Markowi
Black-Litterman Asset Allocation in a Bayesian
Framework
Black and Litterman start with a normal assumption for the asset return rt at period t with
expected return :
rt |, N (, ).
(1)
To simplify the
Tze Leung Lai Haipeng Xing
Statistical Models and
Methods for Financial
Markets
123
Haipeng Xing
Department of Statistics
Columbia University
New York, NY 10027
USA
[email protected]
Tze Leung La
Introduction to Black-Litterman Asset Allocation in a
Bayesian Framework
October 30, 2012
Although Markowitzs mean-variance portfolio optimization is sound in theory, in practice
it has many issues. T
Part II
6
Method of maximum likelihood (Sect. 2.4.1)
Suppose X1 , . . . , Xn have joint density
function f (x1 , . . . , xn ) where is an
unknown parameter vector written as a
column vector of dimens
An Introduction to R
Notes on R: A Programming Environment for Data Analysis and Graphics
Version 2.13.0 (2011-04-13)
W. N. Venables, D. M. Smith
and the R Development Core Team
Copyright
Copyright
Co
Part I
9
Linear regression models and
ordinary least squares OLS
(Sect. 1.1)
A linear regression model relates output
(or response) yt to q input (or predictor) variables xt1 , . . . , xtq , also cal