University of Bristol - School of Economics, Finance and Management QUANTITATIVE METHODS FOR FINANCE AND INVESTMENT (EFIMM005) Review Questions Question 1: Concepts a. Deﬁne a stochastic process. Give an example in Finance of a quantity that can be modelled as a stochastic process. b. Deﬁne a stationary stochastic process. c. Consider a stochastic process {Yt , t = 1, .., T }. Deﬁne the partial autocorrelation function (pacf) associated to this process. d. Explain the diﬀerence between estimator and estimate. e. Let {Ut , t = 1, .., T } be a mean zero white noise process. What is the value of pacf at lag 2 for the process Yt = .5Yt−1 + Ut ? f. Explain the diﬀerence between the autocovariance function and the sample autocovariance function.

Question 2: Application The capital asset pricing model (CAPM) can be written as E(Rjt |Rmt , Rf t ) = Rf t + βj (Rmt − Rf t ), where Rjt is the net return of security j at period t, Rmt is the return on a market portfolio proxy, and Rf t is the return on a risk-free proxy. The coeﬃcient βj is the CAPM beta for security j. Suppose that you have estimated βj by ordinary least squares and found that the estimated value was 1.37 with standard deviation 2.6. based on 3665 observations. a. A city analyst has told you that security j closely follows the market, in the sense that security j is equally risky, on average, to the market portfolio. Perform a 5% signiﬁcance level test of hypothesis to determine whether data support the analysts claim. b. Are hypotheses tested concerning the value of βj or its estimated values?

Question 3: Techniques Consider the moving average process: Yt = εt + θ1 εt−1 + θ12 εt−12 with {εt }T a mean zero white noise process with variance σ 2 > 0. t=0 a. Calculate the mean of Yt . b. Calculate the variance of Yt . c. Calculate the autocovariance function of {Yt }T . t=a T =120 d. Assume that {yt }t=1 represents the monthly tons of ice cream sold in the UK between Oct. 2001 and Oct. 2012. What type of...

...Quantitative Research MethodsQuantitative means quantity which implies that there is something that can be counted. Quantitative research has been defined in many ways. It is the kind of research that involves the tallying, manipulation or systematic aggregation of quantities of data (Henning, 1986)
John W. Creswell defined quantitative research as an inquiry into a social or human problem based on testing a theory composed a theory composed of variables, measured with numbers, and analysed with statistical procedures in order to determine whether the predictive generalisations of the theory holds true. (Creswell, 2003)
On the other hand, another author defined quantitative research as the collection of numerical data in order to explain, predict and/or control phenomena of interest. Quantitative research is explaining phenomena by collecting numerical data that are analysed using mathematically based methods (Aliaga & Gunderson, 2000)
Quantitative research can also be said to be a research based on traditional scientific methods, which generates numerical data and usually seeks to establish causal relationships (or association) between two or more variables, using statistical methods to test the strength and significance of the relationships (A dictionary of Nursing, 2008)
Simply put, quantitative...

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Quantitative Research
Research Methods in Criminal Justice and Security
Professor Beshears
27 February 2014
Quantitative research collects numerical data through surveys, questionnaires, and polls. Quantitative research main purpose is to find the relationship between two variables. According to Babbie (2010) a descriptive study establishes only associations between variables while experimental defines the casualties (pg. 1). The data that is collected from the research is usually used for bigger representation of a population. The data can also be repeated if it was considered to be very accurate and reliable. Every part of quantitative research is scrutinized very carefully before the data is actually collected. The data that is collected is always in a statistics form or number form. Quantitative research can be used to investigate causal relationships, tell the future, or generalize concepts more widely. According to Babbie (2010) to the main purpose of quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed (pg. 1). There are four approaches under the Quantitative research and they are descriptive research, correlation research, causal-comparative research, and experimental research.
The research that gathers the information to test the...

...Review Test Submission: Midterm Exam
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User
Course
QuantitativeMethods
Test
Midterm Exam
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Submitted
2/6/14 2:13 AM
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Instructions
Question 1
5 out of 5 points
Deterministic techniques assume that no uncertainty exists in model parameters.
Answer
Selected Answer:
True
Correct Answer:
True
Question 2
5 out of 5 points
An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.
Answer
Selected Answer:
True
Correct Answer:
True
Question 3
5 out of 5 points
A continuous random variable may assume only integer values within a given interval.
Answer
Selected Answer:
False
Correct Answer:
False
Question 4
0 out of 5 points
A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
Answer
Selected Answer:
True
Correct Answer:
False
Question 5
5 out of 5 points
Starting conditions have no impact on the validity of a simulation model.
Answer
Selected Answer:
False
Correct Answer:
False
Question 6
5 out of 5 points
A table of random...

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...
Class Notes – Ch 7 Risk, Reward and the CAPM
Rational investors expect returns as a reward for taking risk. Returns are usually expressed as a performance number- either as a $ return or as a percentage.
Therefore we need to be able to measure the level of risk inherent in a potential investment, and we also need to be able to calculate the expected return for that risk.
Risk is not achieving the return that is expected
We measure risk by calculating variance and standard deviation – these show the volatility of the returns – the higher the volatility the higher the uncertainty, the higher the risk.
Look at the chart on p231 – showing the probability distribution of two companies’ expected rates of return. Probability shows the chance that the event will occur, so the chart shows the possible returns that could occur from holding the two stocks. One has a very wide distribution of probabilities – therefore more volatile results so higher risk. The other stock has a much narrower range of possible returns therefore is lower risk.
Standard deviation
Historical variance is the sum of the squared deviations from a mean divided by the number of observations minus one. SD is the positive square root of that variance. This is the level of risk. The higher the number, the higher the level of risk.State of economy Probability of state Return on A Return on B
Boom .40 30% -5%
Bust .60 -10% 25%
100% Expected return
E(RA) = .4(.30) + .6(-.10) = .06 = 6%...

...1. How you would use the concept of probabilities to apply to profiles for hiring more satisfied individuals and
2. Other ways that probability is used in business (Use the Business Source Elite Database in the Cybrary, research how probability is used in business).
Begin your email to AIU by first providing an overview of the database, i.e., a story.
Include the following pieces of information.
Part I
a) What is the gender distribution (%females and %males)?
Solution. From the database, we know that there are 168 female people, 120 male people
among 288 people. So,
168/288=58.33% is female,
120/288=41.67% is male.
b) What is the “tenure with company” distribution by gender?
We look at all males. You can do that for females similarly. We get the following table.
From this table, we know that there are 120 males:
26 with code 2 meaning they stay in the company for 2 to 5 years.”
14 with code 3 meaning they stay in the company over 5 years”
80 with code 1 meaning they stay in the company for less than 2 years
So, the “tenure with company” distribution by male is
26/120=21.67% among 120 males stays in the company for 2 to 5 years.
14/120=11.67% among 120 males stays in the company over 5 years;
80/120=66.66% among...

...Principles of QuantitativeMethods
2011
Table of Contents
Question 1 – Difference between Simple Interest and Compound Interest 3
1.0 Simple Interest 3
1.1Compound Interest 4
Question 2 – Difference between Depreciation by Straight Line Method and Depreciation by Reducing Balance Method 6
2.0 The Difference 6
Question 3 - Standard Deviation and Quartile Deviation 7
Standard Deviation 7
Quartile Deviation 8
3.0 Purpose of Calculating Standard Deviation and Quartile Deviation 8
3.1 Calculation of Standard Deviation and Quartile Deviation 8
Reference 9
Question 1 – Difference between Simple Interest and Compound Interest
To know the difference between simple and compound interest, one must have an overview of the interest concept and the rationale behind interest being paid to the lender of the funds. The concept of interest is that it is the cost of borrowing money (Salkind, 1998). The lender of the funds is foregoing the utility of using the funds at the present amount of time, and is also foregoing the opportunity to use these funds at the present moment. For this purpose, a cost is associated with the lending of the funds which is termed as interest (Henry, 1990). This concept is important for it helps to understand the difference between the concept of simple interest and compound interest, as well as their calculations.
1.0 Simple Interest
Simple interest is the cost which is levied on the...

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Investment Trusts Trading At Discount
TOPIC # 3
Introduction
According to Cheng et al. (1994, p.813), ‘an investment trust company (ITC) is a UK public limited company, the business of which consists of investing its funds mainly in securities, with the aim of spreading investment risk and giving members of the company the benefit of the results of the management of its funds.’ In the UK, investment trusts started to form as early as the mid 1800s and helped small investors to diversify their risk through pooled investment (Bengassa, 1999). Not long thereafter, institutional investors also began to participate in investment trusts. The main benefit provided by investment trusts is diversification and the access to managerial skills (Bengassa, 1999). Investment trusts are closed-ended funds that issue a finite number of shares and investors cannot come and go as in open-ended funds (Clarke, 2012). These investment trusts are usually issued at a premium above their Net Asset Value (NAV) but they eventually decline and trade at a discount to the NAV. This trend continues right up until termination when the price converges again towards the NAV (Berk & Stanton, 2004). Investment funds in the UK are invested solely in stocks (Dimson & Minio-Kozerski, 1999) and unlike the situation that obtains in the US, the majority of...