Quantitative Methods for Finance and Investment

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 Central Limit Theorem

A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve, Liapounov and Markov and they came up with the central limit theorem. The central limit theorem allows you to measure the variability in your sample results by taking only one sample and it gives a pretty nice way to calculate the probabilities for the total , the average and the proportion based on your sample of information. A statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the…

Econometrics Chapter Summaries

2) Basic Ideas of Linear Regression: The Two-Variable Model In this chapter we introduced some fundamental ideas of regression analysis. Starting with the key concept of the population regression function (PRF), we developed the concept of linear PRF. This book is primarily concerned with linear PRFs, that is, regressions that are linear in the parameters regardless of whether or not they are linear in the variables. We then introduced the idea of the stochastic PRF and discussed in detail the nature and role of the stochastic error term u. PRF is, of course, a theoretical or idealized construct because, in practice, all we have is a sample(s) from some population. This necessitated the discussion of the sample regression function (SRF)….

Probability Solution Formula

14. If x has the probability distribution f(x) = 12x for x = 1,2,3,…, show that E(2X) does not exist. This is famous Petersburg paradox, according to which a player’s expectation is infinite (does not exist) if he is to receive 2x dollars when, in a series of flips of a balanced coin, the first head appears on the xth flip. 17. The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable having the probability distribution f(x) = 16 for x = 0,1,2,3,4, and 5. He also knows that there is a profit of $ 1.00 for each cake which he sells and a loss (due to…

Essay Questions

Essay 1 In an experimental research, the use of a research question answers the thesis statement that enables one to research about a problem (Yin, 2013). From the experiment, the research question can be clearly stated as “which vaccine is more effective for preventing getting the flu”. In this case, the problem being researched about is the flu the possible solutions to this problem which the use of vaccines is being analyzed. The null hypothesis of this experiment states that there is no effective vaccine for preventing getting the flu while the alternative hypothesis states that there is an effective vaccine for preventing getting the flu. The results obtained from such an experiment should be significant in that they should…

Problem Set

What is sampling error? It is the difference between the sample mean and the population mean Could the value of the sampling error be zero? Yes it is possible to have a zero sampling error. However, it is very low probability that this could happen. If it were zero, what would this mean? This means that the population is uniform and the sample mean and the population mean are equal. Exercise 22 List the reasons for sampling. Give an example of each reason for sampling. 1. Contacting whole population is time consuming. If the population is California residents, it will take a long time to send everyone a survey and then process the results. 2. Contacting whole population is costly….

Variance analysis

When dealing with profitability, every company has to make a good decision. It is quite critical for manager to use the variance analysis tools properly. By using variance, managers can make adjustment on their company performance in order to achieve the highest profit. Variance is actually a difference between actual and what planned. What we plan is also called budgeted. Variances analysis is so important when there are a planning and controlling management. They help managers in sketching their strategies properly. To be more precise, mangers can focus on some specific areas that are not operating as expected and they can make an adjustment to fix the problems. Consider ingredients costs at a restaurant, if actual costs are higher than…

Budgeting and Performance Evaluation at the Berkshire Toy Company

Executive Summary In 1974, Berkshire Toy Company (BTC) was founded by Franklin Berkshire, Janet McKinley’s farther. Janet was soon became the CEO of the company when her father retires on 1993. After two years, BTC was acquired by Quality Products Corporation, a manufacturer of different products, for a common stock of $23.2 million. The preliminary statement of divisional operating income for the year ended June 30, 1998 presented the actual values generated together with the master (static) budget and master budget variances for the period. The company obtained higher Total Revenue than their budget but it turned out to an Operating Loss near a million dollars. This paper aims to study the budgets from actual results, and to compute the…

Inferential Statistics and Findings

Inferential Statistic is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. Our team uses inferential statistic to compare two groups, which are Melks and DHL. This paper outlines the sampling and data collection procedure used to test the null hypothesis. The null and alternate hypotheses are: (There is no significant difference in brand awareness based on the marketing channel used). (There is a significant difference in brand awareness on the basis of the marketing channel used). Here is an example of the statistics of our results describing the total number of people from minimum age to maximum from ages 35 to 55. Mock data for the independent variables…

Analysis of Variance

How would you explain the analysis of variance, assuming that your audience has not had a statistics class before? When one does a study of data, generally this implies an evaluation of the “mean” or average of that data. .i.e. What is the average time it takes a 5th grader to complete his final math exam? A t test is used to test differences between two means. i.e. the mean of the experiment group vs a control group. An ANOVA test, on the other hand, is indicated when there are three or more means or populations to be examined. When only two samples are looked at, the t test and ANOVA test will yield the same results. Beyond two examples,…

Solution of investment

1. The Fisher equation tells us that the real interest rate approximately equals the nominal rate minus the inflation rate. Suppose the (expected or realized) inflation rate increases from 3% to 5%. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest? Explain. The Fisher equation relates nominal rates required by investors to real rates required by investors and inflation. You can think about this from two perspectives: i. Ex-ante (before) required Nominal Return as a function of required Real Return and Expected Inflation: (1 + rNominal) = (1 + rReal)(1 + E(i)) ii. Ex-post (afterward) realized Real Return as a function of Nominal Return and Realized Inflation: (1 + rReal)…

Basic Statistics for Business and Economics

Over the last four weeks of being in the QNT/351 course our team has learned a lot about researching a hypothesis and understanding the mean. The hypothesis testing begins with the statement and the assumption that determines the population of the mean, (Lind, 2011, p.288.). There are five steps taken which include; state the hypothesis, select level of significance for it, identify the test statistics, formulate decision rule, and take a sample to arrive at a decision. On the contrary, however, McClave, 2011 states that there are seven steps including; null hypothesis, alternate hypothesis, test statistic, rejection region, assumptions, experiment and calculation of test statistic, and the conclusion. With setting a hypothesis and testing it is important to understand the…

New Look Jackets Inc. : Variance Analysis

Introduction New Look Jackets Inc. (NLJ) is a well-established manufacturing company that makes leather and nylon jackets. The company has many long standing customers due to their excellent service and quality of products. In 2012, they had some difficulty with quality and filling orders on time due to the increase of demand to the leather jackets. A variance analysis has been completed and this report will break down the results. Sales Volume Variance Analysis The sales volume for NLJ is favourable as a whole because 10,000 more jackets were sold then budgeted. The sales volume for the nylon jacket is unfavourable because 1,500 fewer jackets were sold then budgeted. However the leather jackets sales volume is favourable because 11,500 more…