ECE 695 Financial Engineering
Spring 2012
Introduc:on
Ilya Pollak
School of ECE
Purdue University
Plan for the rst two lectures
We will use some example investment
scenarios to
illustrate the roles of scien:s
ECE 695 Financial Engineering Spring 2012
Problem Set 1, due Thursday March 22 at 3pm
You are not allowed to collaborate on this problem set with any other students in the
class, or ask anyone else for help. If you have questions please let me know. You m
Market Microstructure and Trade
Execu2on
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Market Microstructure: Price
Forma2on Process
2
Ilya Pollak
Limit order book
The order book for a stock at a xed 2me in
St Petersburg Paradox, Expected
U4lity, Prospect Theory, and Risk
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
St Petersburg Paradox
A coin is ipped repeatedly un4l the rst H.
If the rst H appears on th
ECE 695 Financial Engineering
Fixed Income: Default Correla:ons
Ilya Pollak
School of ECE
Purdue University
How to perform Markowitz-
type
porIolio op:miza:on for bonds?
Need a characteriza:on of the joint behavior
Fixed Income
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Fixed Income Securi>es
Owning a share = par>al ownership of the
company.
Owning a bond = loaning money to the company.
Company obligated to pay
Arbitrage Pricing Theory (APT)
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Arbitrage
Arbitrage = Nonzero probability of posiFve prot
with zero investment and zero risk.
2
Ilya Pollak
Recall: Factor Models
Capital Asset Pricing Model
(CAPM)
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Ecient FronBer and Capital
Market Line
R
CML
T
rf F
R
2
Ilya Pollak
Basic premises of CAPM
If you want to be M
Es#ma#on of Linear Factor
Models: Interpre#ng Standard
Errors
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Part I: Some background on
parameter es#ma#on, hypothesis
tes#ng, condence intervals, and
non-
normali
Es#ma#on of Linear Factor
Models: Compu#ng Standard
Errors
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Example
Suppose we are modeling Y1: with two factors, X1:, and 11:
Suppose the es#mated parameters
Es#ma#on of Linear Factor
Models: Using R2 to Measure the
Quality of Approxima#on
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Brief review
We model a time series Y1: = (Y (1), Y ( ) of scalar observations with a vec
Es#ma#on of Linear Factor
Models: Linear Regression
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
A single-
factor model
Y = + X +U
Y = random variable being modeled
X = factor, also a random variable
U = zero-mean random v
Por$olio Theory: Covariance
Es4ma4on.
Factor Models.
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Shortcomings of Markowitz por$olio
alloca4on: How to es4mate the means and
covariance matrix?
Expected r
Por$olio Theory for Dollar-
Neutral
Por$olios
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
Dollar-
Neutral Por$olios
Dollar-
neutral por$olio: total investment amount is zero,
i.e., the total of the long p
Por$olio Theory
ECE 695 Financial Engineering
Ilya Pollak
Spring 2012
(Net) return of an asset
Times t1<t2.
p1 = price at Hme t1
p2 = price at Hme t2
Return from Hme t1 to Hme t2 is (p2p1)/p1
2
Ilya Po
ECE 695 Financial Engineering Spring 2012.
Problem Set 2, due Monday April 23 at 12noon.
Please submit by email as two les:
(1) a PDF le named Lastname Firstname PS2.pdf containing your solutions (scanned
handwritten solutions are ne), and
(2) a Matlab sc