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:

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

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,

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:

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

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

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
wax@alum.mit.edu
1
Text copyright c 2014 John L. Weatherwax
All Rights Reserved
Please Do Not Redistribute Without

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

Lecture 10
W4290: Statistical Methods in Finance
W4290: Statistical Methods in Finance
Lecture 10
Copula Methods (See Chapter 8)
Copula
Financial data often display a great deal of dependency. A Classical
statistical method for multivariate analysis assum

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

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

Capital Asset Pricing Model (CAPM)
Professor: Hammou El Barmi
Columbia University
Professor: Hammou El Barmi Columbia University
Capital Asset Pricing Model (CAPM)
In this chapter, we assume an idealized framework for an open market place,
where all the r

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 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

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

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

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

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 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.

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 8
W4290: Statistical Methods in Finance
W4290: Statistical Methods in Finance
Lecture 8
Review: Yield to marturity, Spot rate and Forward rate
Term structure for all maturities up to n years can be described by any
one of the following sets:
Term

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

Lecture 5
W4290: Statistical Methods in Finance
W4290: Statistical Methods in Finance
Lecture 5
Review
Value at Risk (VaR)
Consider a single asset or portfolio. Let R be its rate of return and
L = R the loss. The (unit currency) value at risk (VaR) of lev

Lecture 3
W4290: Statistical Methods in Finance
W4290: Statistical Methods in Finance
Lecture 3
Multivariate Linear Regression
Multivariate Linear Regression
The Security Characteristic Line (SCL),
Ri = f + i (RM f ) + i ,
may be viewed as a multivariate

Returns
Professor: Hammou El Barmi
Columbia University
Professor: Hammou El Barmi Columbia University
Returns
Introduction
Let Pt be the price of an asset at time t. Assuming no dividends are
paid, the net return is defined as
Rt =
Pt
Pt Pt1
=
1.
Pt1
Pt1

Chapter 6
Continuous Distributions
The focus of the last chapter was on random variables whose support can be written down in
a list of values (finite or countably infinite), such as the number of successes in a sequence of
Bernoulli trials. Now we move t

FIxed Income Securities
Professor: Hammou El Barmi
Columbia University
Professor: Hammou El Barmi Columbia University
FIxed Income Securities
Introduction
When you own a share of a stock, you have partial ownership. In
which case you share in both the pro