3. Capital asset pricing model and factor models
(3.1) Capital asset pricing model and beta values
(3.2) Interpretation and uses of the capital asset pricing model
(3.3) Factor models
(3.4) Performance indexes
1
3.1
Capital asset pricing model and beta va

2. Mean-variance portfolio theory
(2.1) Markowitzs mean-variance formulation
(2.2) Two-fund theorem
(2.3) Inclusion of the riskfree asset
1
2.1
Markowitz mean-variance formulation
Suppose there are N risky assets, whose rates of returns are given by the r

1. Utility theory
(1.1) Log utility criterion investment growth model
(1.2) Construction of an utility function
(1.3) Expected utility criterion choices among investment alternatives
(1.4) Characterization of risk preference
1
1.1
Log utility criterion in

MATH 362
Fundamental of Mathematical Finance
Test Two Fall 2006
Time allowed: 60 minutes
Course Instructor: Prof. Y. K. Kwok
[points]
1. Assuming that the universe of assets consists of the riskfree asset and several risky assets
and that unlimited lendin

MATH 362 Fundamentals of Mathematical Finance
Test One
Fall, 2006 Time allowed: 60 minutes [points] 1. Suppose the financial market provides one riskfree asset and one risky asset. The risky asset either doubles with probability or halves with probability

MATH 362
Fundamentals of Mathematical Finance
Test One
Course Instructor: Prof. Y. K. Kwok
Fall, 2007
Time allowed: 60 minutes
[points]
1. Consider the portfolio with 2 risky assets whose rates of return are 3% and 5% and covariance
2 1
matrix is =
.
1 3

MATH362 Fundamentals of Mathematical Finance
Solution to Homework One
Fall, 2007
Course Instructor: Prof. Y.K. Kwok
2
1. (a) The portfolio variance P is given by
2
2
2
P = 2 A + (1 )2 B + 2(1 )A B .
2
Dierentiate P with respect to ,
2
dP
2
2
= 2A 2(1 )B +

MATH362 Fundamentals of Mathematical Finance
Solution to Homework Two
Fall, 2007
Course Instructor: Prof. Y.K. Kwok
1. Recall
i =
iM
2 =
M
2
xi i
n
2 2
j=1 xj j
since the assets are uncorrelated.
2. The market consists of $150 in shares of A and $300 in s