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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TUTORIAL 1 -95253936900 Each of the following processes involves sampling from a population. Define the population‚ and state whether it is tangible or conceptual. A shipment of bolts is received from a vendor. To check whether the shipment is acceptable with regard to shear strength‚ an engineer reaches into the container and selects 10 bolts‚ one by one to test. The resistance of a certain resistor is measured 5 times with the same ohmmeter 8 welds are made with the same process‚ and the
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Group 7 MOTION PICTURES INDUSTRY- CASE STUDY The data collected for a sample of 100 motion pictures produced in 2005 is given below. A survey is carried out to analyze how different variables of the Motion Picture Industry contribute to the success of its motion pictures. The study focuses on four major variables‚ Opening Gross Sales‚ Total Gross Sales‚ Number of Theatres and weeks in top 60. Motion Picture Opening Gross Sales( $millions) Total Gross Sales ($ millions) Number of Theaters
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Extra Exercise: Estimation and Hypothesis Testing 1. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information. 8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01 Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment. From a second large consignment‚ another 16 screws are selected at random and their mean and standard deviation found to be
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FALSE For a random variable X‚ let µ = E (X). The variance of X can be expressed as: V ar(X) = E X 2 − µ2 7. TRUE For random variables Y and X‚ the variance of Y conditional on X = x is given by: V ar(Y |X = x) = E Y 2 |x − [E (Y |x)]2 8. TRUE An estimator‚ W ‚ of θ is an unbiased estimator if E (W ) = θ for all possible values of θ. 9. FALSE The central limit theorem states that the average from a random sample for any population (with finite variance) when it is standardized‚ by subtracting the mean
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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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| |COMPANY A | | | | | |BANK OF AMERICAN CO | |Date |Open |Close |Dividend |Return | |12/1/2005 |46 |46.15 |0.5 |0.014130435 | |11/1/2005 |43.75 |45.89 |0.5 |0.060342857 | |10/3/2005 |42.47 |43.74 |0.5 |0.041676478
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each question is independent of the others and assumptions from one question do not carry over to the others. 4. Use of a calculator is allowed. 5. Some useful equations are printed below. (a) Standard deviation: n (ri − r¯)2 i=1 σ(r) = n−1 (b) Variance of a portfolio: σ 2 = w12 σ12 + w22 σ22 + 2w1 w2 σ1 σ2 cov(R1 ‚ R2 ) = w12 σ12 + w22 σ22 + 2w1 w2 σ1 σ2 ρ1‚2 (c) Weighted average cost of capital: W ACC = ke × D E + kd (1 − t) × V V GOOD LUCK! Q UESTIONS 1 AND 2 (16 MARKS EACH ) 1. Inflation
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The value of an annuity of $RM1 per period for t years (t-year annuity factor) is: Measures of Risk: Variance of returns = σ2 = expected value of Standard deviation of returns‚ σ = Covariance between returns of stocks 1 & 2 = σ1‚2 = expected value of Correlation between returns of stocks 1 & 2: Beta of stock i = βi = The variance of returns on a portfolio with proportion xi invested in stock i is: A Growing Perpetuity (Gordon
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ASSIGNMENT 1- BU1007 Question 1 (i) The following data represent the cost of electricity during July 2006 for a random sample of 50 one-bedroom apartment in a large city Electricity Charge ($) | 96 | 157 | 141 | 95 | 108 | 171 | 185 | 149 | 163 | 119 | 202 | 90 | 206 | 150 | 183 | 178 | 116 | 175 | 154 | 151 | 147 | 172 | 123 | 130 | 114 | 102 | 111 | 128 | 143 | 135 | 153 | 148 | 144 | 187 | 191 | 197 | 213 | 168 | 166 | 137 | 127 | 130 | 109 | 139 | 129 | 82 | 165
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