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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RC Coleman Mnagerial report Managerial Report 1. Activity | Expected time | Variance | A | 6 | 0.44 | B | 9 | 2.78 | C | 4 | 0.44 | D | 12 | 7.11 | E | 10 | 1.00 | F | 6 | 0.44 | G | 8 | 7.11 | H | 6 | 0.44 | I | 7 | 2.78 | J | 4 | 0.11 | K | 4 | 0.44 | Total Expected time 76 weeks Activity | ES | EF | LS | LF | Slack | Critical | A | 0 | 6 | 3 | 9 | 3 | No | B | 0 | 9 | 0 | 9 | 0 | Yes | C | 9 | 13 | 9 | 13 | 0 | Yes | D | 13 | 25 | 17 | 29 | 4 |
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other descriptive statistics have been intended for this variable and are given as follows: Descriptive Statistics: | Size | Mean | 3.42 | Standard Error | 0.24593014 | Median | 3 | Mode | 2 | Standard Deviation | 1.73898868 | Sample Variance | 3.02408163 | Kurtosis | -0.7228086 | Skewness | 0.52789598 | Range | 6 | Minimum | 1 | Maximum | 7 | Sum | 171 | Count | 50 | Frequency Distribution: | Size | Frequency | 1 | 5 | 2 | 15 | 3 | 8 | 4 | 9 | 5 | 5 |
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first. The seminal paper of Markowitz [8] opened a new era in portfolio optimization. The paper formulated the investment decision problem as a risk-return tradeoff. In its original formulation it was‚ in fact‚ a mean-variance optimization with the mean as a measure of return and the variance as a measure of risk. To solve this problem the distribution of random returns of risky assets must be known. In the standard Markowitz formulation returns of these risky assets are assumed to be distributed according
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Assignment 1 1. Looking at SCORE variable‚ the skewness is -0.0511422 and excess kurtosis is 0.208336. For the normal distribution‚ skewness is zero. Since the skewness for SCORE variable is negative‚ this indicates that the distribution is skewed to the left (the long tail will be in the negative direction). For the normal distribution‚ kurtosis is three. So K-3 measures excess kurtosis. Since the excess kurtosis for SCORE variable is positive‚ the distribution is leptokurtic (it has thick tails
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ECON 140 Section 13‚ November 28‚ 2013 ECON 140 - Section 13 1 The IV Estimator with a Single Regressor and a Single Instrument 1.1 The IV Model and Assumptions Consider the univariate linear regression framework: Yi = β0 + β1 Xi + ui Until now‚ it was assumed that E (ui |Xi ) = 0‚ i.e. conditional mean independence. Let’s relax this assumption and allow the covariance between Xi and ui to be dierent from zero. Our problem here is that ui is not observed. Doing OLS
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FINAL EXAM PBHE525 Complete the final exam offline during the final exam week. Once you have complete the exam‚ input your exam into the final exam shell in the exam folder on the course webpage. Good luck 1. 2. 3. 4. 5. 6. 7. 8. US Census statistics show that college graduates make more than $254‚000 more in their lifetime than non-college graduates. If you were to question the validity of this observation‚ what would be your basis for doing so? A. Definition of a college graduate
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d. Calculate 20 p0 . 4. Show that if X is a random variable such that P(X ≥ 0) = 1 then ∞ a. E[X] = € ∫ s(x)dx 0 ∞ 0 € b. E[X 2 ] = 2 ∫ xs(x)dx where s(x) is the survival function for X . € 5. Find the expected value E[X] and the variance Var(X) for the following random variables ( X ): a. X for which µ (x) = 0.5 for x ≥ 0 . € € € x € b. X for which the CDF F(x) = € for 0 ≤ x ≤ 100 . 100 € € 6. Given that px = 0.99 ‚ px +1 = 0.985 ‚ 3 px +1 = 0.95 and qx +3 = 0.02
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