HW5 (due on Feb 28,2015)
February 23, 2015
1. The Security Market line (SML) of an asset relates the excess return of an asset to the excess
return of the market portfolio. It says that the risk premium of a security j is proportional to the risk
premium

HW 1
Do problems 1, 5, 6, 7 on pages 14 and 15 of the book and the following problems.
1. Let X have a normal distribution with mean and variance 2 and let Y = eX . Y is
said to have a lognormal distribution with parameters and 2 (since X = log(Y ) has
a

Solution to HW6
1. As the question isnt make very clear, anyone who calculated
P (L ),
or
P (L + ),
are counted as correct. Here, and are the mean and standard deviation of the
random variable L (loss). In particular, = 0.001 and = 0.015. The solution is:

1.
Please note that there is a typo in the original solution in the part (b). The correct
numbers were added after the original solution.
Please note that the number 265 in the above solution should

Solution to HW6
1.
(eu1 1)(eu2 1)
1
.
C (u1 , u2 ) = log 1 +
e 1
Fr
2. First, using the 2-increasing property, we have
C(u, v) C(u, 1) = u,
and similarly,
C(u, v) v.
They imply that C(u, v) mincfw_u, v. Second, use the property
C(u2 , v2 ) C(u1 , v2 ) C(u

HW 3
1. Do Problems 1 and 3 on page 307.
2. Let f (x, y) be a continuous and differentiable function of x and y. the function f is
said to be homogeneous of degree one if
f (cx, cy) = cf (x, y)
Eulers theorem states that if f is homogeneous of degree one,

W4290 Statistical Finance
HW6 (due on Monday, March 9, 2015)
Instruction on homework submission: You can either submit a hard copy by putting it into
Yunxiaos mail box on 10th oor, school of social work, or submit a electronic copy by uploading
it on cour

Solution to HW5
1. As the question isnt make very clear, anyone who calculated
P (L ),
or
P (L + ),
are counted as correct. Here, and are the mean and standard deviation of the
random variable L (loss). In particular, = 0.001 and = 0.015. The solution is:

W4290 Statistical Finance
Assignment 1 (due on September 17, 2015)
September 10, 2015
1. Suppose that there are two risky assets, A and B, with expected returns equal to 2.3% and 4.5%,
p
p
respectively. Suppose that the standard deviations of the returns

W4290 Statistical Finance
Assignment 6 (due on October 22, 2015)
October 15, 2015
1. Write down an explicit formula for the bivariate Frank copula.
2. Show that the following inequalities are always true for any copula function C:
C (u, v) C(u, v) C + (u,

HW4 (due on Feb 21,2015)
February 16, 2015
1. Do R lab of Chapter 11. To get credit, you NEED to provide the program you used in addition to
the answers.
2. Suppose that the risk-free rate of interest is 0.03 and the expected rate of return on the market

A Solution Manual and Notes for:
Statistics and Data Analysis for
Financial Engineering
by David Ruppert
John L. Weatherwax
November 4, 2014
[email protected]
1
Text copyright c 2014 John L. Weatherwax
All Rights Reserved
Please Do Not Redistribute Without

W4290 Statistical Finance
Assignment 6 (due on October 17, 2014)
October 10, 2014
1. Write down an explicit formula for the bivariate Frank copula.
2. Show that the following inequalities are always true for any copula function C:
C (u, v) C(u, v) C + (u,

HW 5
1. Do problem 2 on page 440
2. Do in R lab on page 335 (regression), do problems 1, 2, 3, 4,
3. Recalll that the Security Market line (SML) of an asset relates its excess return of to
the excess return of the market portfolio. It says that the risk p

Lecture 19: Principal Component
Analysis
A Dimension Reduc>on Technique
W4290
Eigenvalues and Eigenvectors
Let a be the eigenvector corresponding to l , then the eigenvectors
are orthogonal CA
Review: Pto each other.
j
j
Since V is symmetr

Lecture 17:Time Series Analysis with R
Demostration
W4290 Statistical Methods in Finance | Columbia University
W4290
Outline
The basics
ARIMA(p,d,q)
Heteroskedasticity
W4290
ARIMA(p,d,q)
For further reference, pleaser refer to Shumway & Stoffer (2005):

HW 2
1. In the R lab section on page 35, do problems 3 and 4
2. Problems 4, 7(change 828 to 818), 8, 9
3. Problem 13 on page 38
4. Problem19 on page 39
5. Recall from class that if r(t) is the forward rate function, then the price of a zero
coupon bond wi

W4290 Homework 2 Solutions
October 1, 2015
R Lab
Problem 3 The code can be
f <- function(r)cfw_
return(40 / r + (1000 - 40 / r) * (1 + r)(-2 * 30) - 1200)
uniroot(f, c(0.01, 0.05)
The yield to maturity is calculated to be 0.0324.
Problem 4 Similar to pro

W4290 Homework 5 Solutions
October 25, 2015
1.
Exe 16.11.2
(a) Use formula on page 426, we have
=
R f
0.11 0.03
=
= 0.727
M f
0.14 0.03
Therefore, we should invest 0.727 proportion of the capital to the market portfolio and 1 =
0.273 proportion of the cap

W4290 Homework 2 Solutions
October 9, 2015
Chapter 11
1.
11. 11.1
(a) Suppose we mix the two risky assets A and B in proportions ! and 1 !, then to achieve a 3%
rate of expected return, the proportions should satisfy the following equation
!)E(RB ) = ! 2.

HW 4
1. Do R lab of Chapter 11. To get credit, you NEED to provide the program you used
to do it in addition to the answers to the questions
2. Suppose a firm in planning to invest $ 1,000,000 to invest in a risk free asset and a
risky asset A. Assume tha

W4290 Homework 4 Solutions
October 12, 2015
11.10 R Lab
Problem 1?1
we modify the code on page 297 of the book by using new Amat and bvec to constrain
!i 0.5(i = 1, ., 6). Notice that we have to split the constraints into !i
0.1 and !i
0.1
0.5.
#-# 11.10

Lecture 18: Principal Component
Analysis
A Dimension Reduc?on Technique
W4290
Review on Time Series
ARMA(p,q) = AR(p)+MA(q)
The basics
!
Autoregressive Moving Average Models(p,q) is defined as
follows:
ARIMA(p,d,q)
where
For a causal AR

W4290 Statistical Finance
Assignment 3 (due on September 26, 2014)
September 17, 2014
From the textbook (Ruppert, 2011; pages 440-441): 2, 6, 8, 10.
Additional problems from Luenberger (1998):
A1. (Capital market line) Assume that the expected rate of ret

W4290 Statistical Finance
Assignment 5 (due on Mar 5, 2016)
February 27, 2016
Note 1: Q6(a) is optional.
Note 2: The normal and t distribution tables are attached. Please use them to answer the
questions.
Q1. Suppose that the daily return on a stock is no

Lecture 3
W4290: Statistical Methods in Finance
W4290: Statistical Methods in Finance
Lecture 3
Portfolio construction
Properties:
1. For a portfolio specified by weights cfw_wi , i = 1, , n, the mean and
variance of the portfolio return can be expressed