Problems on Risk and Return 1) Using the following returns‚ calculate the arithmetic average returns‚ the variances and the standard deviations for X and Y. Year X Y 1 8% 16% 2 21 38 3 17 14 4 -16 -21 5 9 26 2) You bought one of the Great White Shark Repellant Co’s 8 per cent coupon bonds one year ago for $1030. These bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today ‚when the required return on the bonds is 7 per cent
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A population of measurements is approximately normally distributed with mean of 25 and a variance of 9. Find the probability that a measurement selected at random will be between 19 and 31. Solution: The values 19 and 31 must be transformed into the corresponding z values and then the area between the two z values found. Using the transformation formula from X to z (where µ = 25 and σ √9 = 3)‚ we have z19 = (19 – 25) / 3 = -2 and z31 = (31 - 25) / 3 = +2 From the area between z =±2 is 2(0
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Investment Science Chapter 3 Dr. James A. Tzitzouris 3.1 Use A= 1− rP 1 (1+r)n with r = 7/12 = 0.58%‚ P = $25‚ 000‚ and n = 7 × 12 = 84‚ to obtain A = $377.32. 3.2 Observe that since the net present value of X is P ‚ the cash flow stream arrived at by cycling X is equivalent to one obtained by receiving payment of P every n + 1 periods (since k = 0‚ . . . ‚ n). Let d = 1/(1 + r). Then ∞ P∞ = P k=0 (dn+1 )k . Solving explicitly for the geometric series‚ we have that P∞ = Denoting
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The Potential of Bamboo(Bambusa vulgaris) Shoot as Pancit Bautista National High School Bautista‚ Pangasinan Werner J G Junio Proponent Mrs. Febren Velasquez Research Adviser i TABLE OF CONTENTS Page Project Title. . . . . . . . . . . . . . . . . . . i Table of Contents. . . . . . . . . . . . . . . . . ii CHAPTER 1. THE PROBLEM: RATIONALE AND BACKGROUND Background of the Study. . . . . . . . . . . . . . 1 Conceptual Framework. . . . . . . . . . . . . . .
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exponential probability density function. If then the cumulative distribution function of the exponential distribution is The following is the plot of the exponential cumulative distribution function. Mean and variance of an exponential function The mean and variance of an exponential function are respectively Example 28 If jobs arrive every 15 seconds on average‚ λ= 4 per minute‚ what is the probability of waiting less than or equal to 30 seconds‚ i.e .5 min
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Covariance = 1/5 (-0.1-0.035)(0.21-0.04) + (0.2-0.035)(0.3-0.12) + (0.05-0.035)(0.07-0.12) + (-0.05-0.035)(-0.03-0.12) + (0.02-0.035)(-0.08-.012) + (0.09-0.035)(0.25-.012) = 0.00794 Variance of A = 1/5 (-0.1-0.035)2 + (0.2-0.08)2 + (0105 – 0.035)2 + (-0.05-0.035)2 + (0.02-0.035)2 + (0.09-0.035)2 = 0.01123 Variance of B = 1/5 (0.21-0.12)2 + (0.3-0.12)2 + (0.07-0.12)2 + (-0.03-0.12)2 (-0.08-0.12)2 + (0.25-0.12)2 = 0.02448 C. Correlation = 0.00794/(0.01123) (0.02448) = 0.479 12-4. Suppose all
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and an expected return of 3.5%‚ what kind of asset is it? Is it really risk-free? 5.Take the HMC management’s views of expected returns‚ standard deviation‚ and covariance of real returns as correct. Also‚ assume that cash is riskless (i.e. zero variance and covariance). If the board allows HMC to invest in only one asset class‚ which asset classes would you advise HMC to discard right away? Why? 6.If the board allows HMC to invest in assumed riskless cash and one other asset class‚ which asset
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Executive Summary: Par‚ Inc has developed a new coating designed to resist cuts and provide a more durable ball. One concern for Par‚ Inc was the effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls‚ 40 balls of both new and current models were subjected to distance test. The testing was performed with a mechanical hitting machine
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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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regression parameters obtained by the method of least squares. (c) An estimator being a random variable‚ its variance‚ like the variance of any random variable‚ measures the spread of the estimated values around the mean value of the estimator. (d) The (positive) square root value of the variance of an estimator. (e) Equal variance. (f) Unequal variance. (g) Correlation between successive values of a random variable. (h) In the regression context‚ TSS
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