RMSC4003
Homework 2
Due: October 12, 2017
1. The correlation between assets A and B is 0.1, and other data are
given in Table 1.
Table 1: Two Correlated Assets
Assets
A
B
10.0%
18.0%
15%
30%
(a) Find the proportions of A and (1) of B that define a portfol
RMSC 4003
Statistical Modeling in Financial Markets
Additional Materials for Assignment 2
XING Yue, Kelly
October 7, 2017
This tutorial is for your reference on using R to solve Question 4 in Homework 2. The question
is a little bit different.
Example 0.1
RMSC 4003
Statistical Modeling in Financial Markets
Tutorial 3 Solution
XING Yue, Kelly
September 24, 2017
1
Portfolio Variance and Feasible Sets
1.1
Portfolio Variance
Example 1.1 (Portfolio Variance). Let rP =
Pn
i=1 wi ri .
Show that Var(rP ) =
n X
n
X
RMSC 4003
Statistical Modeling in Financial Markets
Tutorial 3
XING Yue, Kelly
September 24, 2017
1
1.1
Portfolio Variance and Feasible Sets
Portfolio Variance
Example 1.1 (Portfolio Variance). Let rP =
Pn
i=1 wi ri .
Show that Var(rP ) =
n X
n
X
i=1 j=1
RMSC 4003
Statistical Modeling in Financial Markets
Tutorial 5
XING Yue, Kelly
October 7, 2017
1
Efficient Frontier
1
2. MARKET MODEL
2
Market Model
Denote ri to be the return of asset i and rM to be the market return.
2.1
Estimation of Beta
Consider the
RMSC 4003
Statistical Modeling in Financial Markets
Solution to Homework 1
(1) Assume that the initial wealth is 1. Note that rA N (0.08, 0.12 ) and rB N (0.12, 0.22 ). Let
XA and XB be the terminal wealth of portfolio A and portfolio B respectively. Then
RMSC2001 Introduction to Risk Management
II. Theory of Interest
III. Bond Fundamentals
Term 1, 2017-8| Department of Statistics, The Chinese University of Hong Kong
References:
1. Ruppert, D. (2010) Statistics and Data Analysis for Financial Engineering:
RMSC2001 Introduction to Risk Management
Preamble
Term 1, 2017-18 | Department of Statistics, The Chinese University of Hong Kong
Logistics
Time and Venue:
Wednesdays:
Mondays:
4.30 5.15 at LT6, LSB and
9.30 11.15 at ERB LT
Instructor:
John Wright
112 Lad
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term 1, 2017-18
Course Outline
Description
This course introduces some basic concepts of risk management and its applications to finance
and insuranc
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term 1, 2017-8
Problem Sheet 1 due on 5.30 p.m. Monday, 9th October 2017
1. Prove the following inequality, which is known as Markov inequality: If X
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term , 2017-8
Sanity Check
Students are advised to attempt all of the following questions and see whether or not you feel comfortable
with handling p
RMSC2001 Introduction to Risk Management
I. Introduction
Term 1, 2017-8| Department of Statistics, The Chinese University of Hong Kong
References:
1. George E. Rejda, G. E. and McNamara, M. (2012) Principles of Risk Management and Insurance, 12th Ed:
Pear
RMSC 2001
Introduction to Risk Management
Tutorial 1
September 23, 2015
1
Review of Basic Statistics and Probability Concepts
(1) Probability is a mathematical tool to quantify the uncertainty in the future.
(2) Risks and uncertainties can be handled (man
RMSC 2001
Introduction to Risk Management
Tutorial 5
October 28, 2015
1
Convex Functions
Definition 1.1. Let I R be an interval. A function f : I R is said to be convex on I if for
any t satisfying 0 t 1 and any points x1 , x2 I, we have
f (1 t)x1 + tx2 )
RMSC 2001
Introduction to Risk Management
Tutorial 9
November 11, 2015
1
Callable Bull/Bear Contracts
Bull market and bear market describe upward and downward market trends, respectively, and can
be used to describe either the market as a whole or specifi
RMSC 2001
Introduction to Risk Management
Tutorial 7
November 2, 2015
1
Convex Functions
Definition 1.1. Let I R be an interval. A function f : I R is said to be convex on I if for
any t satisfying 0 t 1 and any points x1 , x2 I, we have
f (1 t)x1 + tx2 )
RMSC 2001
Introduction to Risk Management
Tutorial 4 Solution
October 15, 2015
1
Utility Theory
Example 1.1. For each of the following expected utility functions, determine if the individual is
risk averse, risk neutral, or risk seeking.
(a)
(i) u(w) = 5
RMSC2001Introduction
IntroductiontotoRisk
RiskManagement
Management
RMSC2001
V. Market risk management
Term 1, 2015-16 | Department of Statistics, The Chinese University of Hong Kong
References:
1. Hull, J.C. (2002) Options, Futures and other Derivatives
RMSC 2001 Introduction to Risk Management Science (Term 1, 2015/16)
Mid-term Examination Preparation
The exam covers all the materials that have been discussed so far in this course, including
i. Introduction to risk management: Meaning of risk, various t
RMSC 2001
Introduction to Risk Management
Tutorial 6 Solution
November 23, 2015
1
Financial Instruments and Related Terms
1.1
Financial Instruments
Two classes: Fundamental instruments (stocks and bonds are our focus) and Derivatives (forwards/futures, op
RMSC 2001
Introduction to Risk Management
Tutorial 7
November 11, 2015
1
Callable Bull/Bear Contracts
Bull market and bear market describe upward and downward market trends, respectively, and can
be used to describe either the market as a whole or specifi
RMSC 2001
Introduction to Risk Management
Tutorial 3
October 7, 2015
1
Financial Risks
Market Risks: the risk of a change in the value of a financial position due to changes in the
value of the underlying components on which that position depends, such a
RMSC 2001
Introduction to Risk Management
Tutorial 6
November 4, 2015
1
Financial Instruments and Related Terms
1.1
Financial Instruments
Two classes: Fundamental instruments (stocks and bonds are our focus) and Derivatives (forwards/futures, options and
RMSC 2001
Introduction to Risk Management
Tutorial 9
November 24, 2015
1
Forward and Futures
Definition 1.1. (1) A forward contract is an agreement to buy or sell an asset at a certain
future time for a certain price.
(2) If you assume a long position, yo
RMSC 2001
Introduction to Risk Management
Tutorial 8 Solution
November 23, 2015
Remark 0.1. If the interest rate r is compounded m times per year. Then, after n years, $1 will
r
r
grow to $ (1+ )mn . Continuous compounding means m goes to infinity. That i
RMSC 2001
Introduction to Risk Management
Tutorial 3
October 7, 2015
1
Financial Risks
Market Risks: the risk of a change in the value of a financial position due to changes in the
value of the underlying components on which that position depends, such a
RMSC2001 Introduction to Risk Management
RMSC2001 Introduction to Risk Management
IV. Financial instruments
Term 1, 2015-16 | Department of Statistics, The Chinese University of Hong Kong
References:
1. Hull, J.C. (2002) Options, Futures and ot
RMSC 2001
Introduction to Risk Management
Tutorial 8
November 18, 2015
Remark 0.1. If the interest rate r is compounded m times per year. Then, after n years, $1 will
r
r
grow to $ (1+ )mn . Continuous compounding means m goes to infinity. That is lim (1+
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term 1, 2015-16
Assignment 3, NO NEED TO HAND IN
1. Which of the following utility functions are valid for modelling the preference of a risk-averse