Definition of Value at Risk (VaR) Value at risk is a statistical technique which measures the level of financial risk in a portfolio over a specific time frame. For example‚ if a firm states that it has a 1% one week value at risk of $5 million; this would mean that for any given week‚ the firm would have a 1% chance of losing $5 million. In order words‚ 1 out of every 100 weeks‚ the firm would expect to have a loss of $5 million. This can be viewed as the standard deviation of portfolio value
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CASE STUDY : Beta Management Company The Context Beta Management Group is a small investment management company based in Boston. It was founded in 1988 by Ms. Sarah Wolfe (The founder and CEO of the Beta Management Group). Ms. Wolfe follows a market timing investment strategy based on two portfolios; the Vanguard index and money market instruments. The goals of Beta Management were to enhance returns-but-reduce risks for clients via market timing. Majority of Beta’s
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to polar coordinate Thus Mean By symmetry if g(x) is odd function g-x=-g(x) then -abgxdx=0 Variance Notation CDF is standard Normal CDF by symmetric ‚CDF ‚ ‚ All the odd moment of standard normal are zero. However‚ even moment is not easy to calculate by integral (Symmetry) Then we say Most of Statistics books will write the pdf then explain the mean and variance but it is not intuitive. Standardization Find PDF of CDF: The PDF is derivative of the CDF
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the resulting variances will be assigned to the cost of goods sold. If the variances are significant‚ they should be prorated to the cost of goods sold and to the inventories. Standard costing and the related variances is a valuable management tool. If a variance arises‚ management becomes aware that manufacturing costs have differed from the standard (planned‚ expected) costs. * If actual costs are greater than standard costs the variance is unfavorable. An unfavorable variance tells management
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MULTIPLE CHOICE QUESTIONS In the following multiple choice questions‚ circle the correct answer. 1. Which of the following provides a measure of central location for the data? a. standard deviation b. mean c. variance d. range Answer: b 2. A numerical value used as a summary measure for a sample‚ such as sample mean‚ is known as a a. population parameter b. sample parameter c. sample statistic d. population mean Answer: c 3. Since
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first. The seminal paper of Markowitz [8] opened a new era in portfolio optimization. The paper formulated the investment decision problem as a risk-return tradeoff. In its original formulation it was‚ in fact‚ a mean-variance optimization with the mean as a measure of return and the variance as a measure of risk. To solve this problem the distribution of random returns of risky assets must be known. In the standard Markowitz formulation returns of these risky assets are assumed to be distributed according
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on sample information such as tables‚ graph‚ the mean‚ median‚ mode and etc. c) A researcher will use the F distribution to make an inference on the ratio between two population variances. d) To construct a 90% confidence interval for u‚ if a small sample was selected randomly from normal population with unknown variance‚ the t distribution is used. e) The significance level a is the probability of rejecting the null hypothesis when it is false. f) Non-parametric test is used when the data are not
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assignment you turn in needs to be your own work. 1. Suppose . That is‚ X has a normal distribution with μ=30 and σ2=144. 1a. Find a transformation of that will give it a mean of zero and a variance of one (ie.‚ standardize ). 1b. Find the probability that . 1c. Supposing 5X‚ find the mean of . 1d. Find the variance of . 2. A bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. The bank prides itself on its mortgage application
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INVESTMENT & PORTFOLIO MANAGEMENT FIN3IPM TUTORIAL ANSWERS TUTORIAL 1: INTRODUCTION CHAPTER 1: QUESTION 1 a The process of investment concerns the purchase of assets which will provide a future return to allow for future consumption or further investment. Individuals have to make choices between current and future consumption and because their pattern of income does not always match their pattern of consumption‚ they are required to make investments. Throughout an individual’s life
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a lot higher than promised in the budget. The following cost formulas were used to construct the planning budget: Required: 1. Prepare a new performance report for September using the fl exible budget approach. 2. Do you think any of the variances in the report you prepared should be investigated? Why? 1. Performance should be evaluated using a flexible budget performance report. In this case‚ the report will not include revenues (shown in East Caribbean dollars). St. Lucia Blood Bank
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