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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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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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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RISK THEORY - LECTURE NOTES 1. INTRODUCTION The primary subject of Risk Theory is the development and study of mathematical and statistical models to describe and predict the behaviour of insurance portfolios‚ which are simply financial instruments composed of a (possibly quite large) number of individual policies. For the purposes of this course‚ we will define a policy as a random (or stochastic) process generating a deterministic income in the form of periodic premiums‚ and incurring financial
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information in your discussion. What recommendations do you have if the 40-week completion time is required? 2. Suppose that management requests that activity times be shortened to provide an 80% chance of meeting the 40-week completion time. If the variance in the project completion time is the same as you found in part (1)‚ how much should the expected project completion time be shortened to achieve the goal of an 80% chance of completion within 40 weeks? 3. Using the expected activity times as the
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(RA ‚ RB ) −0.0322 = = −1. σ (RA )σ (RB ) 0.14 × 0.23 The assets are perfectly negatively correlated. Consider portfolio P formed from assets A and B such that you invest α fraction of your wealth into A and (1 − α) fraction into B. The variance of such portfolio is σ (RP )2 = = = = α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)Cov (RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)σ (RA )σ (RB )ρ(RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 − 2α(1 − α)σ (RA )σ (RB ) [ασ (RA ) − (1
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if a specific sample of portfolios have a higher risk level or lower expected return‚ compared to what may be obtained through optimisation. It also compares the return of optimised portfolios with the return of the original portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for the optimisations. With the expected return and risk level used in this thesis‚ all portfolios can obtain a higher expected return and a lower risk. Over a six-month period‚ the optimised
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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 mean of the population. Furthermore‚ all of the samples will follow an approximate normal distribution pattern‚ with all variances being approximately equal to the variance of the population divided by each sample’s size. Using the central limit theorem allows you to find probabilities for
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