Project 9 Copy 3
Problem 1:
Exponential Moving Averages smooth price data over time. Consider the
prices as per
P1
P2
P3
P4
P5
.
Pn
The definition is:
EMA1 =
EMAn =
=
P1
EMA n-1 + K (Pn EMAn-1)
KPn + (1-K) EMAn-1
Where K is the smoothing constant; 0 < K <
71. TIME SERIES
The trend is your friend.
market maxim
A time series is a function such that the independent variable is time and the
dependent variable is the data i.e.
X = f (t)
The graph of f is usually called a scatter diagram.
Time series abound in f
76. Continuous Random Variable
For a Binomial Experiment as the number of trials , n, get large clearly the probability
histogram is a s per:
0.6
1.2
0.5
1
0.4
0.8
0.3
0.6
0.2
0.4
0.1
0.2
0
0
1
1
Small n
large n
It becomes convenient to think of X as a co
Rule: E(B(1,p) = p. ( B (1, p )
p(1 p) .
Proof:
E ( B(1, p) 0 (1 p) 1 p p
2 ( B (1, p ) E ( B (1, p ) 2 ) [ E ( B(1, p )]2 0 2 (1 p ) 12 p [ p 2 ] p p 2 p (1 p )
( B(1, p) p(1 p)
Definition: A Binomial Experiment consists of n independent, identical Be
73. Appendix
Discrete Random Variables
A discrete random variable is a symbol that assumes a finite number of values, each
with an associated probability. The random variable is displayed as per table and
histogram.
X X1 X2 X3 X4 . Xn
P P1 P2 P3 P4 . Pn
n
Rule:
For a Binomial experiment
1. E(k) = n p
2. k = npq
Example:
Solution:
For the tossing of a coin 3 times find out the expected value and standard
deviation.
E(X)
x
= 3 ( ) = 1.5 and
= 3 (1/ 2) (1/ 2)
= 0.866
The coin tossing experiment can be reviewe
Comments For MSF 501 Lesson 9
1. Lesson 9 consists of the material in Ten Little Quants, labeled Moving Averages
and Random Variables. The course continues to explore Probability and Statistics
as per moving averages and random variables, the latter being
72. Probability
Chance favors the informed mind.
Louis Pasteur (1822-1895)
Consider the probability experiment of tossing a fair coin. As the number of tosses
increases, the ratio of the number of times heads has occurred to the total number of
tosses ten
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter1Learning
Objectives(LOs)
LO1.1: Describetheimportanceofstatistics.
LO 1.2: Differentiatebetweendescriptive
LO1.2:
Differentiate between descriptive
statisticsandinferentialstatistics.
LO 1 3: Explain
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter2Learning
Objectives(LOs)
LO 2 1 Summarizequalitativedatabyforming
LO2.1:
S
i
lit ti d t b f
i
frequencydistributions.
LO 2 2: Constructandinterpretpiechartsandbar
LO2.2:
Constr ct and interpret pie c
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter3Learning
Objectives(LOs)
LO 3 1 Calculateandinterpretthearithmetic
LO3.1:
C l l t
di t
t th
ith
ti
mean,themedian,andthemode.
LO3.2: Calculateandinterpretpercentilesanda
l l
di
il
d
boxplot.
LO3.3: C
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter 15 Learning
Objectives (LOs)
LO 15.1: Conduct tests of individual significance.
LO 15.2: Conduct a test of joint significance.
LO 15.3: Conduct a general test of linear restrictions.
LO 15.4: Calcula
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter 4 Learning Objectives (LOs)
Chapter4LearningObjectives(LOs)
LO4.1: Describefundamentalprobability
concepts.
p
j
LO4.2: Formulateandexplainsubjective,
empirical,andaprioriprobabilities.
LO 4.3: Calcul
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter 5 Learning Objectives (LOs)
Chapter5LearningObjectives(LOs)
LO 5 1: Distinguishbetweendiscreteand
LO5.1:
Distinguish between discrete and
continuousrandomvariables.
LO 5 2 Describetheprobabilitydistr
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter 14 Learning Objectives (LOs)
LO 14.1: Conduct a hypothesis test for the population correlation coefficient.
LO 14.2: Discuss the limitations of correlation analysis.
LO 14.3: Estimate the simple line
Statistical Analysis in Fin Mkts
MSF 502
Li Cai
Chapter 13 Learning Objectives (LOs)
LO 13.1: Provide a conceptual overview of ANOVA.
LO 13.2: Conduct and evaluate hypothesis tests based on
one-way ANOVA.
LO 13.3: Use confidence intervals and Tukeys HSD
m
Discounted Cash Flow Applications
Test ID: 7658688
Question #1 of 72
Question ID: 412839
In order to calculate the net present value (NPV) of a project, an analyst would least likely need to know the:
A) internal rate of return (IRR) of the project.
B)
Cost of Capital
Test ID: 7696349
Question #1 of 86
Question ID: 467819
The 6% semiannual coupon, 7-year notes of Woodbine Transportation, Inc. trade for a price of 94.54. What is the company's
after-tax cost of debt capital if its marginal tax rate is 30%
Hypothesis Testing
Test ID: 7658784
Question #1 of 88
Question ID: 413409
Which of the following statements about parametric and nonparametric tests is least accurate?
A) The test of the difference in means is used when you are comparing means from two
i
Capital Budgeting
Test ID: 7694293
Question #1 of 57
Question ID: 414743
Polington Aircraft Co. just announced a sale of 30 aircraft to Cuba, a project with a net present value of $10 million. Investors did
not anticipate the sale because government appro
Statistical Concepts and Market Returns
Test ID: 7658721
Question #1 of 122
Question ID: 412942
For the last four years, the returns for XYZ Corporation's stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent
compound annual rate is:
A) 9.2%.
B)
The Time Value of Money
Test ID: 7658669
Question #1 of 87
Question ID: 412807
You borrow $15,000 to buy a car. The loan is to be paid off in monthly payments over 5 years at 12% annual interest. What is
the amount of each payment?
A) $456.
B) $546.
C)
Sampling and Estimation
Test ID: 7658769
Question #1 of 87
Question ID: 413309
Which of the following is the best method to avoid data mining bias when testing a profitable trading strategy?
A) Increase the sample size to at least 30 observations per yea
Probability Concepts
Test ID: 7658734
Question #1 of 117
Question ID: 413030
An empirical probability is one that is:
A) derived from analyzing past data.
B) supported by formal reasoning.
C) determined by mathematical principles.
Explanation
An empiri
Working Capital Management and Corporate Governance
Test ID: 7696566
Question #1 of 78
Question ID: 434352
Liquidating short-term assets and renegotiating debt agreements are best described as a firm's:
A) pulls and drags on liquidity.
B) primary source
Measures of Leverage & Dividends and Share Repurchase
Test ID: 7696476
Question #1 of 67
Question ID: 414840
Which of the following is a key determinant of operating leverage?
A) The competitive nature of the business.
B) Level and cost of debt.
C)
Common Probability Distributions
Test ID: 7658750
Question #1 of 104
Question ID: 413226
Assume an investor purchases a stock for $50. One year later, the stock is worth $60. After one more year, the stock price has
fallen to the original price of $50. Ca
function y=product_copula_VaR(mu1,mu2,sigma1,sigma2,cl)
% Derives VaR using bivariate product copula with specified inputs, for normal
% marginals.
%
% Inputs:
% mu1: Mean of P/L on first position.
% mu2: Mean of P/L on second position.
% sigma1: Std of
function y=normalvarplot3D(varargin)
% NORMALVARPLOT3D Plots normal VaR in 3D against confidence level and holding period
%
% Function plots the VaR of a portfolio assuming P/L is normally distributed,
% for specified ranges of confidence level and holdi