...the time-varying hedge ratio, we use four methods, rolling window, EWMA, GARCH model and B-S model. Firstly, we explain the methods we used, including the assumptions, formulas and implications. Also, we implement the methods in the Excel to get the value of hedge ratios. Finally, we show the advantages and disadvantages of every method by comparing between every two methods. We evaluate the methods both in theory and practical application. Introduction: We want to hold a long position in S&P 500 index, at the same time we want to minimum-variance. As this reason, we introduce to hedge the long position in S&P 500 index with a short position in the FTSE 100 index. We suppose that the return on the hedged portfolio is: rp,t=rS&P-htrFTSE Then the variance of hedged profile will be: δF2=δS&P2+h2δFTSE2-2hδS&P,FTSE If we want to minimum the variance of the hedged portfolio, we must derivate of h in this function and let the equal to zero. Where ht is the time-varying hedge ratio, given by: ht=δS&P,FTSE,tδS&P2 Because we want to get the result only focus on the two-index, we ignore the currency flotation by assume that the currency rate is perfectly hedged. At very beginning, risk manager have assumed that the volatility is constant over time, which allow us to estimate it use sample variance of past time: δ2=1T-1t=1T(rt-r)2 By estimate the historical data, our find the variance tend to be clustered, it is obvious to see...
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...Chapter 14 Factor analysis 14.1 INTRODUCTION Factor analysis is a method for investigating whether a number of variables of interest Y1 , Y2 , : : :, Yl, are linearly related to a smaller number of unobservable factors F1, F2, : : :, Fk . The fact that the factors are not observable disquali¯es regression and other methods previously examined. We shall see, however, that under certain conditions the hypothesized factor model has certain implications, and these implications in turn can be tested against the observations. Exactly what these conditions and implications are, and how the model can be tested, must be explained with some care. 14.2 AN EXAMPLE Factor analysis is best explained in the context of a simple example. Students entering a certain MBA program must take three required courses in ¯nance, marketing and business policy. Let Y1, Y2 , and Y3 , respectively, represent a student's grades in these courses. The available data consist of the grades of ¯ve students (in a 10-point numerical scale above the passing mark), as shown in Table 14.1. Table 14.1 Student grades Student no. 1 2 3 4 5 Finance, Y1 3 7 10 3 10 Grade in: Marketing, Y2 6 3 9 9 6 Policy, Y3 5 3 8 7 5 °Peter Tryfos, 1997. This version printed: 14-3-2001. c 2 Chapter 14: Factor analysis It has been suggested that these grades are functions of two underlying factors, F1 and F2, tentatively and rather loosely described as quantitative ability and verbal ability, respectively. It is...
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...[Type the company name] | [Type the document title] | [Type the document subtitle] | | | [Pick the date] | [Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.] | Contents Executive Summary 3 Introduction 3 Analysis and methods section 3 Do charges incurred by a patient depend on the type of insurance the patient has? If so how? 5 Do charges incurred by patients depend on which doctor treats them? If so how? 5 Bibliography 7 Appendix 8 Executive Summary Hospital are required to bill for individual items or services provided to a patient. Patients admitted to hospitals are charged for their room, supplies, drugs, labs, x-rays, operating room time and other care. It is important to know that hospitals submit a bill to the insurance company for all the services provided to the patient and the payor determines the amount owed to the hospital based upon the insurance company’s contract with the hospital for specific services [ (Henry Ford Health) ]. Introduction The purpose of this case study is to understand the relationship between hospital charges for certain physicians and insurance carriers. Cost finding and cost analysis are the techniques of allocating data that we were provided as part of the case study. The information that we are going to use to analyze...
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...mean: x= Sample variance: s2 x 1 = n−1 n This has mean nθ and variance nθ(1 − θ). The Poisson distribution: p(x) = λx exp(−λ) for x = 0, 1, 2, . . . . x! 1 n n This has mean λ and variance λ. xi . i=1 Continuous distributions n Distribution function: x2 i − nx 2 i=1 1 (xi − x) = n−1 2 . F (y) = P (X ≤ y) = y i=1 f (x) dx. −∞ Sample covariance: g= 1 n−1 n Density function: 1 n−1 n (xi −x)(yi −y) = i=1 xi yi − nx y i=1 . f (x) = Evaluating probabilities: d F (x). dx Sample correlation: r= g . sx sy b P (a < X ≤ b) = a f (x) dx = F (b) − F (a). Probability Addition law: P (A ∪ B) = P (A) + P (B) − P (A ∩ B). Multiplication law: P (A ∩ B) = P (A)P (B|A) = P (B)P (A|B). Partition law: For a partition B1 , B2 , . . . , Bk k k Expected value: ∞ E(X) = µ = −∞ xf (x) dx. Variance: ∞ ∞ Var(X) = −∞ (x − µ)2 f (x) dx = −∞ x2 f (x) dx − µ2 . Hazard function: h(t) = P (A|Bi )P (Bi ). i=1 f (t) . 1 − F (t) P (A) = i=1 P (A ∩ Bi ) = Normal density with mean µ and variance σ 2 : 1 f (x) = √ exp 2πσ 2 . Weibull density: f (t) = λκtκ−1 exp(−λtκ ) for t ≥ 0. Exponential density: − 1 2 x−µ σ 2 Bayes’ formula: P (A|Bi )P (Bi ) P (Bi |A) = = P (A) P (A|Bi )P (Bi ) k i=1 for x ∈ [−∞, ∞]. P (A|Bi )P (Bi ) Discrete distributions Mean value: E(X) = µ = xi ∈S f (t) = λ exp(−λt) for t ≥ 0. xi p(xi ). This has mean λ−1 and variance λ−2 . Variance: Var(X) = xi...
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...“expected returns” and “risks” of the individual securities in a particular way. • There are two ways to calculate the portfolio’s expected return and standard deviation from information about the individual securities. Method 1 STEP 1: Compute the return distribution of the portfolio. STEP 2: Then compute the expected value and the standard deviation of that distribution. Method 1 Example • Consider a “50-50” portfolio of two securities. • You are provided with the individual return distributions of the two securities: State Probability Return Security A Return Security B Portfolio Return 1 20% 50% 30% .5*50%+.5*30% 2 60% 0% 0% 0% 3 20% -50% -30% -.5*50%-.5*30% • STEP 1: Compute the portfolio return distribution. Method 1 Example State Probability Portfolio Return 1 20% 40% 2 60% 0% 3 20% -40% • STEP 2: Compute the expected value and standard deviation of the portfolio return distribution. – Expected portfolio return: 0% – Portfolio return variance: (.4-0)^2*20%+(0-0)^2*60%+(-.40)^2*20%=6.4% – Portfolio standard deviation: (.064)^(1/2)=29.3% (When squaring or taking the root of percentages, first convert to decimal numbers.) Method 1 Example • What if I change the original distribution a...
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...Sharrain Walls Variance Analysis Grand Canyon University: HCA-530 July 5, 2016 Introduction Various reports help with viewing and keeping track of the productivity of a department. Managers find these reports very helpful with assisting to find an issue, trend, overspending, and underspending. A report commonly used is a variance report, which compares the planned amount to the actual amount. This report is critical in determining major decisions and viewing fluctuations. The report can be in the form of a table or graph and can be considered favorable or unfavorable based on the results. Vice Presidents look for the report to be clear and direct. Managers should include all factors associated with the variance report as well as the relationships between variance reporting, interpreting variance report results, and actual reports. Variance Analysis When viewing the results of the report consider the hospital size and utilization of the services offered by the hospital. When performing a variance analysis, relationships can be identified. Favorable (positive) and unfavorable (negative) correlations are critical in business planning. An example would be, variance analysis may show that when sales for product a rise in sales for product B. This type of relationship may be used for success of other products (Cross, N.d.). When using a variance report for forecasting variance data allows managers to identify factors such as seasonal changes for the favorable and unfavorable...
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...This is page 57 Printer: Opaque this 3 Time Series Concepts 3.1 Introduction This chapter provides background material on time series concepts that are used throughout the book. These concepts are presented in an informal way, and extensive examples using S-PLUS are used to build intuition. Section 3.2 discusses time series concepts for stationary and ergodic univariate time series. Topics include testing for white noise, linear and autoregressive moving average (ARMA) process, estimation and forecasting from ARMA models, and long-run variance estimation. Section 3.3 introduces univariate nonstationary time series and defines the important concepts of I(0) and I(1) time series. Section 3.4 explains univariate long memory time series. Section 3.5 covers concepts for stationary and ergodic multivariate time series, introduces the class of vector autoregression models, and discusses long-run variance estimation. Rigorous treatments of the time series concepts presented in this chapter can be found in Fuller (1996) and Hamilton (1994). Applications of these concepts to financial time series are provided by Campbell, Lo and MacKinlay (1997), Mills (1999), Gourieroux and Jasiak (2001), Tsay (2001), Alexander (2001) and Chan (2002). 58 3. Time Series Concepts 3.2 Univariate Time Series 3.2.1 Stationary and Ergodic Time Series Let {yt } = {. . . yt−1 , yt , yt+1 , . . .} denote a sequence of random variables indexed by some time subscript t. Call such...
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...159(Cluster#4) is 177.043. When looking at the chart, there is a biggest jump between clusters 3 and 4, indicating that there is a biggest difference between those two clusters. This is backed up by the Dendrogram as shown to the left, when putting a straight line through the longest horizontal lines; the line is cut by three clusters. Also, when looking at the Ward Scree Plot, the biggest kink is at 3 as shown by the arrow above which shows an abrupt change in angle (elbow.) Which indicates the 3rd cluster being more unique than the forth. The single linkage message also shows we should use 3 clusters, because looking at the Dendrogram, if we put a line through the longest horizontal distances it would be cut at 3 points. I would choose Wards method over Single Linkage because it is much clearer, the dendogram has much clearer clusters and there are fewer clusters. The agglomeration schedule is easier to figure out 2) 1 means not at all considered 2 unlikely to consider 3 would possibly consider 4 would actively consider 5 already do As shown in the Initial Cluster Centers to the left, cluster 1 shows that every variable except cooking on gas, most the respondents would not at all consider the other 5 variables however, most respondents already do cook on gas. In cluster 2, it could be seen that the respondents already do all the variables except installing energy in efficient heating systems, which they would not at all consider. In cluster 3, the...
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...DATA ANALYSIS for MANAGERS MScBA Instituto Universitário de Lisboa (ISCTE-IUL) JOSÉ DIAS CURTO dias.curto@iscte.pt 2015/2016 i Contents Contents 1 Math introductory concepts 1 1.1 The real numbers system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The concept of sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Relations and functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Linear function 3 1.3.2 Exponential function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.3 Logarithmic function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.4 Functions of two or more independent variables 5 1.3.5 The concepts of derivative and elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Matrices and vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6 How to prepare a le for statistical analysis . . . . . . . . . . . . . . . . . . . . . . 7 1.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.7.1 Investment Bank 1 . . . . . . . . . . . . . . . . . . . . . . . . ....
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...return and variance of each security under consideration for inclusion in the portfolio along with all the covariances between securities. With these measures the investors proceed to calculate the expected return and risk of alternative portfolios to evaluate their desirability and derive a set of efficient portfolios. Notations wi = percentage of investor’s funds invested in security i wj = percentage of investor’s funds invested in security j [pic] = expected return on security i [pic] = expected return on security j (2i = variance of return on security i (2j = variance of return on security j (ij = covariance of return on security i and j (ij = correlation of return on security i and j [pic] = expected return on the portfolio (2p = variance of return on the portfolio 2-Security Case The expected return of a portfolio is an weighted average of the expected return of the securities, where the weights are percentage of investor’s funds invested in the securities: [pic] = wi [pic] + wj [pic] The variance of a portfolio is a weighted average of the variance of the individual securities plus the covariance between the two securities in the portfolio: (2p = w2i (2i + w2j (2j + 2wi wj (ij Minimum Variance Portfolio The formulation of variance can be used to identify the minimum variance portfolio. This portfolio has the lowest variance of all possible combination of two securities. We can minimize portfolio variance by setting...
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...Budget Management Analysis Budget management is an important concern for organizations, especially today with the economic strain on businesses. The strategies to manage budgets and possible variances will be addressed within the context of this paper. A comparison of five expense results with the budgetary expectations and reasons for possible variances will be presented. Benchmarking techniques that may improve budget accuracy in future forecasts will also be concentrated on within the body of information presented Managing a Budget within the Forecasts According to Finkler, Kovner, and Jones, (2007), organizations exercise control over operations through the use of a management control system. The determination of whether a business is able to appropriately budget for future expenses, economic downturns, and risks is critical in today’s economic crisis. The methods by which a budget is created are specific and take into consideration several factors that provide target, actual, and variance results. The strategies used to create a budget vary among industry, organization, department, and/or manager just to name a few. Budget variances, strategies, and benchmarking techniques are critical to the final budget formulated for a business. A budget is a way to assist managers to follow a set strategic plan to ensure resources are used to efficiently to achieve the goals and follow the mission of the organization. A budget provides estimates of revenue, expenditures...
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...STATISTICAL METHODS STATISTICAL METHODS Arnaud Delorme, Swartz Center for Computational Neuroscience, INC, University of San Diego California, CA92093-0961, La Jolla, USA. Email: arno@salk.edu. Keywords: statistical methods, inference, models, clinical, software, bootstrap, resampling, PCA, ICA Abstract: Statistics represents that body of methods by which characteristics of a population are inferred through observations made in a representative sample from that population. Since scientists rarely observe entire populations, sampling and statistical inference are essential. This article first discusses some general principles for the planning of experiments and data visualization. Then, a strong emphasis is put on the choice of appropriate standard statistical models and methods of statistical inference. (1) Standard models (binomial, Poisson, normal) are described. Application of these models to confidence interval estimation and parametric hypothesis testing are also described, including two-sample situations when the purpose is to compare two (or more) populations with respect to their means or variances. (2) Non-parametric inference tests are also described in cases where the data sample distribution is not compatible with standard parametric distributions. (3) Resampling methods using many randomly computer-generated samples are finally introduced for estimating characteristics of a distribution and for statistical inference. The following section deals with methods for processing...
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...Chapter 8 The comparison of two populations 8-1. n = 25 [pic] = 19.08 [pic] = 30.67 H0: [pic]D = 0 H1: [pic]D [pic] 0 t (24) = [pic] = 3.11 Reject H0 at [pic] = 0.01. |Paired Difference Test | | | |Evidence | | | | | |Size |25 |n |Assumption | | |Average Difference |19.08 |μD |Populations Normal | | |Stdev. of Difference |30.67 |sD | | | | | | |Note: Difference has been defined as | | |Test Statistic |3.1105 |t | | | |df |24 | | | |Hypothesis Testing | | |At an α of | | |Null Hypothesis |p-value |5% | | |H0: μ1 − μ2 = |0 |0.0048 |Reject | 8-2. n = 40 [pic] = 5 [pic] = 2.3 H0: [pic]D = 0 H1: [pic]D [pic] 0 t(39) = [pic] = 13...
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...environment and load on the company. The returns on equity and assets are also significantly low for the firm in the current year and these projections provided will most likely cause the stock price of the company to be under downward pressure. The company has not considered any dividend payouts making the company not very attractive to dividend seeking investors while growth is not strong so growth investors will also keep away this further supports that the firm will find it difficult to maintain its stock price or raise new equity capital. The firm has a 12% accounts receivable average balance however there is no evidence noticed if the firm has had any provisions made for bad debts. 2. Evaluate the flexible budget and the variances. The Flexible budget is a valuable tool to...
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...Disadvantages of Markowitz approach: The Markowitz method is very sensitive to small changes in the initial conditions, that is in the choice of the data period. Sometimes even changing the analysed period by a few days will greatly alter the composition of the portfolio. Therefore, there is no certainty that the used parameters are stable enough over time. Markowitz’ optimizers maximize errors. It is not possible to estimate exactly the expected returns, variances and covariances. It is assumed that the returns of the optimised assets follow a normal distribution, which in practice does not hold in all cases. Therefore, estimation errors are inevitable. This is especially true when the number of stocks under consideration is large when compared to the return history in the sample - which is the typical situation in practice. As a result, the investor is suggested to invest in extremely under-diversified portfolios or in the portfolios which contain large short positions - which can be seen inVariance is a method of risk calculation through measuring variance around the expected return. However, only losses represent a real risk – therefore it is questionable, if variance is a proper risk-measuring tool. In Markowitz approach, only the expected return is taken into account when modelling the future expected uncertainties. It is a great simplification, as in fact many more factors are relevant – such as the employment rate, economic growth etc. In times of economic crisis the...
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