ANALYZING A PORTFOLIO a 58. You want your portfolio beta to be 1.20. Currently‚ your portfolio consists of $100 invested in stock A with a beta of 1.4 and $300 in stock B with a beta of .6. You have another $400 to invest and want to divide it between an asset with a beta of 1.6 and a risk-free asset. How much should you invest in the risk-free asset? a. $0 b. $140 c. $200 d. $320 e. $400 ANALYZING A PORTFOLIO d 59. You have a $1‚000 portfolio which is invested in stocks A
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A NOTE ON HYPOTHESIS TESTING |Significance Level |One-Sided Test |Two-Sided Test | |0.10 |1.285 |1.645 | |0.05 |1.645 |1.960 | |0.01 |2.33 |2.575 | Part A. Single-Sample
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After real estate is added to the portfolio‚ there are four asset classes in the portfolio: stocks‚ bonds‚ cash and real estate. Portfolio variance now includes a variance term for real estate returns and a covariance term for real estate returns with returns for each of the other three asset classes. Therefore‚ portfolio risk is affected by the variance (or standard deviation) of real estate returns and the correlation between real estate returns and returns for each of the other asset classes
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SAMPLE Population – the group of ALL people or objects that are under study Sample – a sub-set of the population Parameter – a numerical characteristic of a population 1. Population & Sample Means 2. Expected Values 3. Population & Sample Variances 4. Population & Sample Covariances 5. Population & Sample Correlation Coefficients 6. Estimators Statistic – a numerical characteristic of a sample Statistical inference – drawing conclusion about a population based on information contained
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are well defined but some of the possible factors can cause to the deviations and variances. Those possible factors can be eradicated through extra efforts into the process. However the small chances of variance will remain the same because the real business scenarios may vary sometimes than the forecasted one. This report is an attempt to investigate the operational standards and the possible causes of variance in standards and how does it affect customer satisfaction.
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7) Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Number of sales people working | Sales (in $1000) | 4 | 12 | 5 | 13 | 8 | 15 | 10 | 16 | 12 | 20 | 12 | 22 | 14 | 22 | 16 | 25 | 18 | 25 | 20 | 28 | x=11.9 | y=19.8 | SD(x)=5.30 | SD(y)=5.53 | a) Find the slope estimate‚ b1. Use technology or the formula below to find the slope. b1=rsysx Enter x‚y Data in TI-84 under STAT > STAT
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1.2 Below we list several variables. Which of these variables are quantitative and which are qualitative? Explain. a. The dollar amount on an accounts receivable invoice. Answer – Quantitative as the value is a number b. The net profit for a company in 2009. Answer – Quantitative as the value is a number. c. The stock exchange on which a company’s stock is traded Answer – Qualitative as it is descriptive or categorical. d. The national debt of the united states in 2009. Answer
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at the end of module 1 3 6 4 7 5 4 6 4 7 1 8 1 More 0 Q1 Descriptive Statistics Excel Worksheet b Q2 d Q3 e Q4 b 5. For the following sample of scores: 2‚ 6‚ 1‚ 4‚ 2‚ 2‚ 4‚ 3‚ 2 Mean variance standard deviation 2.889 2.099 1.537 Find the mean‚ variance and standard deviation 6. A sample of size 7 (n = 7) has a mean of M = 9. One of the sample scores is changed from x = 19 to x = 5. What is the value for the new sample mean? New Sample Mean 7 7. Using Excel
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a criterion for maximizing the between-class variance of pixel intensity to perform picture thresholding. However‚ Otsu’s method for image segmentation is very time-consuming because of the inefficient formulation of the between-class variance. In this paper‚ a faster version of Otsu’s method is proposed for improving the efficiency of computation for the optimal thresholds of an image. First‚ a criterion for maximizing a modified between-class variance that is equivalent to the criterion of maximizing
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normal random variable: Theorem 1: Suppose Y = ln X is a normal distribution with mean m and variance v‚ then X has mean exp( m + v /2 ) Proof: The density function of Y= ln X Therefore the density function of X is given by Using the change of variable x = exp(y)‚ dx = exp(y) dy‚ We have = Note that the integral inside is just the density function of a normal random variable with mean (m-v) and variance v. By definition‚ the integral evaluates to be 1. Proof of Black Scholes Formula Theorem
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