| FIN
7447 - Financial Theory II (Asset Pricing Theory) |
Course Syllabus - Fall 2007
University of Florida
Course
Overview and Objectives
This
course is an introductory Ph.D. level course in mathematical techniques of modern portfolio theory and asset
pricing. These include:
Fisher separation, the theory of choice, Arrow-Debreu state pricing,
implications of no arbitrage, multi-period exchange economies with complete
and incomplete markets, continuous time mathematics, stochastic discount
factors, Hansen-Jagannathan bounds, the consumption-based asset pricing model,
the capital asset pricing model, arbitrage pricing theory, dynamic
programming, Merton’s intertemporal CAPM, the mathematics of the efficient
frontier, and option pricing (binomial, partial differential equation, and
risk-neutral valuation approaches). In this class, the primary emphasis is on mathematical tools
that are useful in finance.
However, each class includes brief student presentations and class discussions
that step aside from the math to consider interesting facts and important
intuition related to asset pricing.
Prerequisites
This
course presumes an MBA level understanding of finance and business and a math
background that includes upper-level undergraduate calculus, statistics, and
matrix algebra. I am assuming that you know how to solve constrained
maximization problems using Lagrange multipliers, how to take derivatives with
respect to vectors, and how to solve ordinary differential equations.
Textbooks
and Materials
The
required texts for this class are:
Pennacchi,
George, Theory
of Asset Pricing, Pearson
Education, 2008.
Cochrane,
John H., Asset Pricing (Revised
edition), Princeton
University Press, 2005.
Ingersoll,
Jr., Jonathan E., Theory of Financial
Decision Making, Rowman & Littlefield, 1987.
Shimko,
David C., Finance in Continuous Time: A
Primer, Kolb Publishing Co., 1992.
We
will also use material from the following sources:
Campbell,
John Y., Andrew W. Lo, and A. Craig MacKinlay, The Econometrics of
Financial Markets, Princeton University Press, 1997.
Copeland,
Thomas E., and J. Fred Weston, Financial
Theory and Corporate Policy, Third Edition, Addison-Wesley Publishing Co.,
1988.
Cox,
John C., and Mark Rubinstein, Options
Markets, Prentice Hall, 1985.
Duffie,
Darrell, Dynamic Asset Pricing Theory,
Princeton University Press, 1992.
Huang, Chi-fu, and
Robert H. Litzenberger, Foundations for Financial Economics,
North-Holland, 1988.
Hull,
John C., Options, Futures, and Other
Derivatives, Third Edition, Prentice Hall, 1997.
Kreps,
David M., A Course in Microeconomic Theory, Princeton University Press,
1990.
Megginson,
William L., Corporate Finance Theory,
Addison-Wesley Publishing Co., 1997.
Pennacchi, George, Theory of Asset Pricing, Addison-Wesley Publishing
Co., forthcoming.
Grading
The grading components will be as follows:
|
Research
paper video summaries
|
10%
|
|
Problem
sets
|
5%
|
|
Quizzes
|
20%
|
|
Midterm
|
30%
|
|
Final
|
35%
|
Research
Paper Video Summaries:
Each student will create four 5- to 8-minute paper summaries using
Camtasia. In each video, students will explain the main motivation and
findings of the paper(s) in a way that is very easy for someone without any
explicit finance background to understand. It is important to highlight
real world examples or scenarios during these videos. Although students
are welcome to use the video component during the talk, the emphasis should be
mostly on the audio. The idea is that you are describing to one of your
smart friends who is not in your field what the paper says (i.e. what is the
main issue the paper addresses, why is that issue important, how do the
authors answer the question, and what is the answer). You may choose articles from the Journal
of Finance, the Journal of Financial Economics, the Review of Financial
Studies, the Journal of Financial and Quantitative Analysis, and the Journal of Business.
Before you start on a video, student must first get instructor approval on the
particular paper(s).
Problem
sets: We will have six problem sets during the semester.
These will help you to practice using the tools that we cover in class. Solution sets for homework
problems are available for download from the web, but I strongly advise you to
solve the problems on your own before you look at the solutions (since you
will not have solutions available for the exam problems). Because the
solutions are available, I will not grade your problem sets, but I will check
to make sure you have turned them in on time.
Quizzes:
We will have seven quizzes during the semester that will cover the following items:
articles from the WSJ and business magazines (see the WSJ link on the class
website's table of contents), cocktail hour papers (previous semesters' as
well as this semester's), student research paper videos from current and prior
semesters, and videos. Most of the videos will
be provided to you on a CD on the first day of class, and the remaining videos
are viewable online.
Exams:
We will have a midterm and a final.
I will give you some guidance as to what material will be covered as
those exam dates get closer.
Course
Schedule
To
see the course schedule, click here.
Topics
We
will cover the following topics [source material in brackets]:
Lecture
1--Fisher Separation
MBA
background material
Sub-fields
of finance
What
should theory do?
Positive
vs. normative theory
Fisher
separation of production and investment
(1)
No market / no production
(2) No market / production
(3) Market / no production
(4) Market / production
[Megginson,
chapter 1]
[Copeland
and Weston, chapters 1, 2]
Lecture
2--Utility Theory
St.
Petersberg paradox
Axioms
for utility functions
Violations (Allais paradox)
Ordinal vs. cardinal
Proof of vNM utility
U(wealth, state of world)
How
vNM fixes paradox
Define
risk aversion
Risk
aversion Û
concave utility
Derive
Arrow-Pratt measure: R(W) = -U''/U'
Recover
U from R(W)
Equivalency
statement for R(W)
Common
forms of utility functions
Model
with risk and end-of-period U(W)
DARA =>
dA/dW0 > 0
CARA =>
dA/dW0 = 0
DRRA =>
h
> 1
CRRA
=>
h
= 1
[Ingersoll,
chapter 1]
[Huang
and Litzenberger, chapter 1]
[Pennacchi,
Choice Under Uncertainty and Risk Aversion and Risk Premia]
Lecture
3--State Preference Theory
Payoff
tableau--assets and states
Arrow-Debreu
security/insurable state
Type
I and II arbitrage
State
prices
No
arbitrage and existence of p > 0
Complete
markets
State
prices and Rf
3
types of probabilities
Standard
risk-adjusted rate
Risk-neutral
valuation method
Asset
pricing kernel
v = E(my); p = E(mx)
Model
with risk and end-of-period U(C)
Max U(C0,Cs) s.t. W0
U'(C0)ps = dpsU'(Cs)
Euler equations
Risk premium
Proof of CAPM using quadratic utility and arbitrary returns
[Ingersoll,
chapter 2]
[Huang
and Litzenberger, chapter 3]
[Pennacchi,
State Preference Theory]
Lecture
4--Asset Pricing Kernels
m
-- measure of aggregate discomfort
E(m)
= 1/Rf (first restriction on m)
Each
m defines an asset pricing model
What
affects Rf?
Patience
Consumption growth
Volatility of consumption growth
m
inversely related to consumption
Risk
correction to expected returns
Only
systematic risk priced
Efficient
frontier
HJ
bounds (second restriction on m)
Capital
market line
Security
market line
Any
efficient portfolio carries all pricing info
Time-varying
expected returns
[Cochrane,
chapter 2]
Lecture
5--More on Stochastic Discount Factors
State
pricing examples
Equity
premium puzzle
Failure
of consumption-based models
State
prices and the sdf : m = p/true
prob.
Risk
neutral probabilities
Geometry
of state pricing vector
No
arbitrage <=>
m > 0
[Cochrane,
chapters 3 and 4]
Lecture
6--Efficient Frontier Mathematics
When
do you only care about E(r) and s2?
Show
EU increases
as E(r)
increases
Show EU increases as variance falls
Indifference
curves
Benefit
of diversification
Derive
efficient frontier
Find
all efficient portfolios from just 2
Other properties of efficient portfolios
Efficient
frontier with riskless asset
CARA
with normal returns
Find wM, derive SML and CML
Market price of systematic risk
[Huang
and Litzenberger, chapter 3]
[Pennacchi,
Mean Variance Analysis and CAPM]
[Ingersoll,
chapter 4]
Lecture
7--SDFs vs. Factor Models
What
is a factor?
Fama-French
three factor construction
Equivalency
theorems
p = E(mx)
E(r) = a
+ b'
lambda
Mean-variance frontier
Market
efficiency
Tests
are necessarily joint tests
Difference
between sdf and mv approaches
[Cochrane,
chapters 5 and 6]
Lecture
8--Discrete-time Dynamic Programming
When
to use
State
vs. control variables
Partial
vs. general equilibrium
Derived
utility of wealth
Bellman
equation
Euler
equations
Envelope
condition
Principle
of optimality
Optimal
consumption and investment policies
Example
using log utility
C*
depends on T-t, d,
and W(t)
wi*
depnds on Zs and R (not W(t))
[Pennacchi--Intertemporal
Consumption and Portfolio Choice]
[Ingersoll,
chapter 11]
Lecture
9--Conditioning Information and Multifactor Models
Conditional
vs. unconditional models
Conditioning
down
Law
of iterated expectations
Managed
portfolios
E(ztpt) = E(mt+1xt+1zt)
Five
classic derivations of CAPM
Does
CAPM price options?
Arbitrage
Pricing Theory
No arbitrage condition
Exact factor structure
Approximate factor structure
Asymptotic arbitrage opportunity
Proof of APT
When does APT hold?
[Cochrane,
chapters 7 and 8]
[Pennacchi,
Arbitrage Pricing Theory]
[Ingersoll,
chapter 7]
Lecture
10--Hansen and Jagannathan Bounds
Bounds
on moments of m
Purposes
of HJ bounds
HJ
bound for a single return
Sharpe
ratio interpretation
HJ
bound for a vector of returns
Hyperbola
in {E(m), sigma(m)}
space
How
to use HJ bounds to rule out asset pricing models
Adding
an asset can:
Expand the efficient frontier
Reduce the HJ bounds
[Cochrane,
chapter 24]
Midterm Here
Lecture
11--Continuous-Time Stochastic Calculus
Discrete
processes
Wiener
process
Properties
(strange)
Stochastic
integrals
Diffusion
process
Arithmetic Brownian motion
Geometric Brownian motion
Stochastic
differential equations
Ito's
Lemma
Univariate
Multivariate
Shimko
example
[Shimko,
chapter 1]
[Pennacchi,
Essentials of Diffusion Processes and Ito's Lemma]
[Ingersoll,
chapter 16]
Lecture
12--Jump Diffusion Processes; Solving ODEs and PDEs
Poisson
jump process
Ito's
Lemma for jump-diffusion processes
Solving
ODEs (time invariant cases)
Case I:
Arithmetic
Brownian motion
Case II: Geometric
Brownian motion
Solving
PDEs (time to maturity)
Laplace
transforms
Case III: Arithmetic
Brownian motion
Case IV: Geometric
Brownian motion
Shimko
example
Lecture
13--Basics of Options
Terminology
Payoff
and profit diagrams
Strategies
Put-call
parity
Option
pricing
Partial derivatives
Bounds
Early exercise
Dividends
Portfolios
of options vs. option on portfolio
[Hull,
chapter 7]
[Pennacchi,
Option Pricing]
[Ingersoll,
chapter 14]
Lecture
14--Binomial Option Pricing
Hedge
ratio
One-period
model
Risk-neutral
probabilities
Multi-period
model
Complementary
binomial distribution
Convergence
to Black-Scholes (1st way)
Calibrating
u and d to match volatility
American
puts--early exercise
American
calls--early exercise with dividends
[Cox
and Rubinstein, chapter 5]
[Pennacchi,
Cox-Ross-Rubinstein Option Pricing Model, Option Pricing Using the Binomial
Model]
Lecture
15--PDE Option Pricing and Risk-Neutral Valuation
Black-Scholes
PDE (2nd way)
Prove
delta = N(d1)
Risk-neutral
valuation
Forward contracts
Options
Derive Black-Scholes (3rd way)
Properties
of Black-Scholes formula
Implied
volatility
Discrete
dividends
[Pennacchi,
Option Pricing in Continuous Time and the Black-Scholes Equation]
Lecture
16--Equivalent Martingale Measures
Define
all three terms
Radon-Nikodym
derivative (Rfm)
Self-financing
strategy
No
arbitrage in continuous-time
No
arbitrage <=> there exists an equivalent martingale measure
Girsanov's
theorem
Prove Black-Scholes (4th way)
Deflated
prices follows a martingale
N(d2) -- risk-neutral
probability interpretation
m
as an Ito process
[Duffie,
chapter 2, appendices A and D]
[Pennacchi,
Arbitrage, Equivalent Martingale Measures, Risk-Neutral Valuation, and Pricing
Kernels]
Lecture
17--Bond Pricing
Short
rate
Derive
cost of carry formula
Feynman-Kac
solution
One-factor
term structure models
Cox, Ingersoll, Ross
Vasicek
Pricing
options on bonds
Binomial
term structure models
No
arbitrage restrictions
Fit
volatilities
[Duffie,
chapter 7]
[Pennacchi,
An Equilibrium Model of the Term Structure of Interest Rates]
[Pennacchi,
Arbitrage-Free Binomial Models of the Term Structure]
[Ingersoll,
chapter 18]
Lecture
18--Continuous-Time Dynamic Programming
Budget
constraint
Bellman
equation
Dynkin
operator
Euler
conditions
Solve
PDE for J
Constant
investment opportunity set
Merton's continuous-time CAPM
Two-mutual fund theorem
Stochastic
investment opportunity set
Merton's
intertermporal CAPM
Three-fund
separation
ICAPM
factors vs. APT factors
Breeden's
consumption CAPM
[Pennacchi,
Intertemporal Consumption and Portfolio Choice in Continuous-Time]
[Pennacchi,
An Intertemporal Capital Asset Pricing Model]
[Ingersoll,
chapter 13]
Lecture
19--How Is Asymmetric Information Reflected in Asset Prices?
Rational
expectations
Nash
equilibrium
Grossman (1976 JF) "On
the Efficiency of Competitive Stock Markets Where Trades Have Diverse
Information"
Noisy signals of end-of-period price
Factors that affect asset demand
Bayes rule
Which
signals receive more weight in equilibrium?
Fully-revealing RE equilibrium (not robust)
Grossman-Stiglitz paradox
Kyle (1985) "Continuous Auctions and Insider Trading"
Partially-revealing equilibrium
Market maker, noise traders, insider
Market maker's price schedule (function of aggregate demand)
Insider's optimal demand
Kyle lambda (market depth)
Profits: MM = 0, NT < 0, Insider > 0
Second source of uncertainty (amount of noise trading)
Caveats
How to estimate Kyle lambda empirically
[Pennacchi,
Notes on Grossman]
[Pennacchi,
Notes on Kyle]
Lecture
20--How Well Do CAPM and Black-Scholes Work in the Real World?
Empirical
predictions of CAPM
Problems
with testing CAPM
BJS
(1972) time series approach
Fama
and MacBeth (1973) cross-sectional approach
EIV
problem
Theoretical
and empirical SMLs
Generally
supportive of CAPM
Anomalies
Fama
and French (1992)--Beta is dead
Fama
and French (1993)--Three-factor model
Statistical
vs. economic significance
Problems
with Fama and French approach
Five
categories of candidate factors
LSV
(1994)
Risk
vs. behavioral explanation of average HML premium
Assumption
violations of Black-Scholes
Price jumps
Implied volatility smiles and term structure
[Campbell,
Lo, and MacKinlay]
Accommodations for
Students with Disabilities
Students
requesting classroom accommodation must first register with the Dean of Students
Office. The Dean of Students Office will provide documentation to the student
who must then provide this documentation to the Instructor when requesting
accommodation.
Contents written by Jason
Karceski
Last modified on
August 21, 2007 .
