1 Factor Models The Markowitz mean-variance framework requires having access to many parameters: If there are n risky assets‚ with rates of return ri ‚ i = 1‚ 2‚ . . . ‚ n‚ then we must know 2 all the n means (ri )‚ n variances (σi ) and n(n − 1)/2 covariances (σij ) for a total of 2n + n(n − 1)/2 parameters. If for example n = 100 we would need 4750 parameters‚ and if n = 1000 we would need 501‚ 500 parameters! At best we could try to estimate these‚ but how? In fact‚ it is easy to see
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TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #2 SOLUTIONS 1. (a) Expected returns are: E[RA ] = 0.3 × 0.07 + 0.4 × 0.06 + 0.3 × (−0.08) = 0.021 = 2.1%‚ E[RB ] = 0.3 × 0.14 + 0.4 × (−0.04) + 0.3 × 0.08 = 0.05 = 5%. Variances are: 2 σA = 0.3 × (0.07)2 + 0.4 × (0.06)2 + 0.3 × (0.08)2 − (0.021)2 = 0.004389‚ 2 σB = 0.3 × (0.14)2 + 0.4 × (0.04)2 + 0.3 × (0.08)2 − (0.05)2 = 0.00594. Standard deviations are: √ 0.004389 = 6.625%‚ σA = √ 0.00594 = 7.707%. σB = Covariance
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ECON10005 QUANTITATIVE METHODS 1 Assignment 2 Semester 1‚ 2013 This assignment has four questions‚ and is due by 5.00pm on Thursday 2 May. It is to be submitted electronically as a .pdf file using the assignment tool on the subject’s LMS page. Marks depend on your tutor being able to understand your statements and arguments‚ so marks may be deducted for poor presentation or unclear language. Use nothing smaller than 12 point font. If you wish to write your assignment by hand and scan the file into
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remove anything +/- 20% 3. Calculate historical average and historical risk X-BAR = Σx/n Calculate the sum of the total return and divide by the number of observations • Variance = σ2 = Σ(x – x bar) 2 / (n-1) Fix X-BAR‚ double click to apply to all dates‚ get the sum‚ divide by (n-1) Risk = σ = √σ = SQRT(Variance) = standard deviation 4. Average Matrix Excel Options → Add-ins → Go → Select 1st two and last one → Go Data Analysis → Descriptive Analysis → Select all data without
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random variable X has the probability density function given by 3 2 ; 0 x2 (2 x) f ( x) 8 0 ; otherwise (i) Calculate the mean of X and variance of X. (ii) Calculate . (iii) Find . b) Given X ~ Exp ( 2) and the moment generating function (MGF) of X is given M X (t ) 2 2t . Find the mean and variance of X. c) Given for x = 1‚ 2‚ 3‚ 4. Find the moment generating function of X. Question 2 a) According to a survey‚ 45% of all students at a large university
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Chapter 8 Risk and Return: Capital Market Theory 8-1. To find the expected return from James Fromholtz’s investment opportunity‚ we will use equation 7-3: where i indexes the various states of nature that are possible. We can picture the states of nature for James’s opportunity as: Despite the symmetrical appearance of the graph‚ the outcomes are not symmetrical: There are many more outcomes that are positive than negative. Only the 100% return (probability 5%) is negative; 95% of the weight
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ANACOR The ANACOR algorithm consists of three major parts: 1. 2. 3. A singular value decomposition (SVD) Centering and rescaling of the data and various rescalings of the results Variance estimation by the delta method. Other names for SVD are “Eckart-Young decomposition” after Eckart and Young (1936)‚ who introduced the technique in psychometrics‚ and “basic structure” (Horst‚ 1963). The rescalings and centering‚ including their rationale‚ are well explained in Benzécri (1969)‚ Nishisato (1980)
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NAME: SHU ZHAOHUI ID: 17329164 Q5. Descriptive Statistics | | N | Minimum | Maximum | Mean | Std. Deviation | Skewness | | Statistic | Statistic | Statistic | Statistic | Statistic | Statistic | Std. Error | Gasolinescore | 1000 | 3.00 | 21.00 | 14.9090 | 4.83654 | -.493 | .077 | Globalscore | 1000 | 3.00 | 21.00 | 17.0490 | 3.78774 | -1.073 | .077 | Valid N (listwise) | 1000 | | | | | | | The mean in the gaslinescore and globalscore stand for the average the respondents choose is
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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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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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