Key Definitions
Descriptive Statistics
Population - collection of things under study
Sample - a portion of the population
Parameter - a number computed to describe
a feature of the population
Statistic - a number computed to describe a
feature of the samp
Important Terms
Basic Probability
Experiment any process that generates
outcomes
Sample space the collection of all possible
outcomes of an experiment
Experiment Sample Space
Ex.1
Throw a die once
Ex.2
Draw one card from a bridge deck
Experiment Sample Sp
Bernoulli Experiment
The Binomial Distribution
An experiment for which there are only 2 possible
outcomes : success (S) or failure (F), e.g.
Toss a coin once : head / tail
Quality inspection : acceptable / unacceptable
Market research survey : buy / n
Why Study Sampling Distributions
Sampling Distribution of the Mean
Otis Lift Company is responsible for repair and maintenance
of its lifts. A typical lift has a capacity for roughly 20
persons and carries a maximum weight of 3000 lb.
What is the chance t
Random Variable
Random Variables
and Their Properties
Outcomes of an experiment expressed
numerically
e.g. Throw a die twice; X = number of 4
(0, 1, 2)
e.g. Toss a coin once; Y = the number of heads
(0, 1)
T
Probability Distribution
Experiment : Toss a fa
Scatter Plot
Linear relationships
Linear Correlation Analysis
Nonlinear relationships
Y
Y
X
X
Y
Y
X
X
Linear Correlation Coefficient
i 1
n
X
i 1
i X
2
n
Y Y
i 1
i
2
X
i
X Yi Y
n 1
i 1
n
i 1
X
i
X
n 1
2
n
i 1
Y
Y Y
i
n 1
2
0<r<1
X
Sign reflects the
Exploring Data Patterns
Components of a Time Series
A time series consists of data that are recorded
over regular or irregular intervals of time.
e.g. Daily closing price of a stock
Strength of earthquakes
Seasonal pattern - change that repeats itself yea
The Normal Distribution as an Approximation to
a Binomial Distribution
Normal Distribution
Equation of a Normal Curve
The Normal Distribution
Bell-shaped
Symmetrical
Area under curve = 1
X ~ N()
y
y
Mean
x
1
2
e
1 x
2
2
e 2.7183 (base of natural logar
Point Estimates
Interval Estimation of the Mean
Estimate Population
Parameters
Mean
Variance
Proportion
Point Estimation
Population
Population
mean, , is
unknown
Random
Sample
Mean
X = 50
I estimate
to be 50, but
how about its
accuracy ?
2
with Sample
S
What is a Hypothesis ?
A hypothesis is an assumption
about a population parameter
e.g. population mean, sd or
proportion
Hypothesis Testing for the Mean
The Null Hypothesis, H0
In many problems, this is the assumption held to be true
unless proved to the
Assignment 2 (for Ch 5-10, 12)
Question 1
The current price of a stock is $94, and 3-month European call
options with an exercise price of $95 currently sell at $4.70. An
investor who feels that the price of the stock will increase is trying
to decide bet
8, 9)
10)
Interest rate mismatch = 30 5 = $25billion
If interest rate increases x%, interest income decreases by x%*$25billion
(Net interest income*0.7)/2 = -0.12
Net interest income = -$0.343 billion
0.343 = x * 25
x = 0.0137
Increase in interest rate of
Ch 8 How Traders Manage Their Risks
The trading function within a financial institution is the front
office;
the part of the financial institution concerned with the total risk,
capital adequacy and regulatory compliance is the middle office;
the record k
Ch 9 Interest Rate Risk
Interest rate risk is more difficult to manage than the risk arising
from market variables such as equity prices, exchange rates and
commodity prices.
One complication is that there are many different interest rates in
any given cu
Ch 10 Volatility
It is important for a financial institution to monitor the volatilities
of market variables (such as interest rates, exchange rates,
equity prices and commodity prices) on which the value of its
portfolio depends.
The chapter starts by e
Ch 12 Value at Risk and Expected Shortfall
Chapters 8 and 9 describe how a trader, responsible for a financial
institutions exposure to a particular market variable (e.g. an
equity index, an interest rate or a commodity price), quantifies
and manages risk
Topic 4 Assignment
Question
An organization is considering launching an entirely new service. If the market reaction to this
service is good with probability 0.2, the organization will make $3000 a week. If market reaction
is medium with probability 0.5,
Topic 1 Questions and Suggested Solutions
Question 1
Assume that you are to analyze the results of a conjoint analysis on a single subject, say the CEO
(the chief executive officer) for type of desk preferred. Two features are employed: size (regular,
mas
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
B
C
D
E
F
G
H
I
J
K
Job Selection Using Analytical Hierarchy Process
Pairwise comparisons among objectives
Salary Life quality Work interest
Salary
1
5
2
Life quality
MS 5211 Quantitative Methods
Lecturer: Dr Francis LEUNG
Office: P7507
Tel. No.: 3442-8589
E-mail: msknleun@cityu.edu.hk
Assessment
Exam: 60%
one 2-hour written exam
Continuous assessment: 25%
four assignments, each is done by a team having 3 or 4
studen
Topic 1 Assignment
Question (Household Cleaner)
A problem involves preference for spot removers for upholstery and carpets. The following features were analyzed:
Package design (A, B, C)
Brand names (K2R, Glory, Bissell)
Price ($1.19, $1.39, $1.59)
Good H
Topic 2 Assignment
AHP Application: Site-location Selection
Assume that you want to determine the best retail site within a geographic area for a small ice-cream
store catering to young children and families. You have narrowed down the site alternatives t
Topic 1 Questions and Suggested Solutions
Question 1
Assume that you are to analyze the results of a conjoint analysis on a single subject, say the CEO
(the chief executive officer) for type of desk preferred. Two features are employed: size (regular,
mas
Topic 3 DM under Risk: Questions and Suggested Solutions
Question 1
Dorothy Stanyard has three major routes to take to work. She can take Tennessee Street the entire
way, she can take several back streets to work, or she can use the expressway. The traffi
Topic 2 Questions and Suggested Solutions
Question 1 (20 marks)
Linda is thinking about buying a new car. There are three different car models she is considering:
car 1, car 2 and car 3. Three important factors for Linda are price, warranty and style.
Lin
Topic 2 Analytic Hierarchy Process (AHP)
When multiple objectives (or criteria) are important to a decision maker, it is often difficult to
choose between alternatives (or options).
For example, if you are choosing a job, one job might offer the highest s
Topic 3 Decision Making (DM) under Risk i.e. DM with Probabilities
Step 1: Formulate a DM problem
A typical DM problem has four elements:
(1) enumerate all possible alternatives (or called options) to tackle the problem,
(2) predict all possible outcomes
Topic 1 Conjoint Analysis (CA)
One of the basic tenets of marketing is that firms should be customer oriented, offering goods or
services (hereafter we simply call products) that provide values to customers. This raises an
obvious question: how do we asse