251y063t 4/20/06 ECO251 QBA1 THIRD EXAMApr 25, 2005TAKE HOME SECTION- Name: ____Computer Solution____ Student Number: _________________________Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you are using.Part III. Do all the Following (19+ Points) Show your work! Neatness counts!1. Ben Horim and Levy present the following actual returns for stock in Republic Steel and General Foodsover a ten year period.Year R1 R2 1 22.5 -23.7 2 9.3 8.6 3 -18.6 4.3 4 48.1 -52.2 5 44.4 62.4 6 56.0 61.4 7 -20.1 9.8 8 -11.0 52.6 9 17.1 17.1 10 22.3 11.7Before you start, personalize the data below as follows. Take the third to last digit of your student number and subtract it from -52.2 in the R2 column. This will make the results for year 4 even more disappointingthan they actually were. (Example: Seymour Butz’s student number is 123450. He subtracts the 4 from -52.2 getting -56.2) . a) Find the sample mean, variance and coefficient of variation for R2. Use computational formulas. The results must look as if you calculated them by hand, although it is perfectly reasonable to check the results using a computer or a calculator. (2.5)b) Find the sample covariance and correlation between R1 and R2. (3)c) Using a conventional measure of risk, explain which stock is riskier. (1). [6.5] d) Make a table showing 11 portfolios. Start with a portfolio with all your money invested in stock 1(P1 = 1, P2 = 0), then move to a portfolio with 90% in stock 1 and 10% in stock 2 (P1 = .90, P2 = .10), and move by tenths until you get a portfolio that is all stock 2. (5). The table should look as follows with much wider columns. CsRP01.2.3.4.5.6.7.8.9.11Here R is the weighted average return, s is the standard deviation of the portfolio return, and C is the coefficient of variation. [11.5]1251y063t 4/20/06e) Make a graph . Put the mean return on the y axis and the standard deviation on the x axis. (3) Connect your points in a curve. The C-like curve you will probably get illustrates the tradeoffs between return and risk and is called an investment opportunities frontier. f) Looking at the graph and the coefficients, are there stock portfolios that you would never recommend? Why? What portfolio would you recommend to an 80-year old widow? Why? What portfolio would you pick for yourself? Why? (1.5) [16]2. It’s time for a jorcillator problem! As everyone knows a jorcillator has two components, a Phillinx and aFlubberall.The life of a Phillinx, x, is described by a continuous uniform distribution between 50 hc and630 hd , where 5h and 6h are the last two digits of your student number .The life of a Flubberall, y, is described by a Normal distribution with a mean of 520 h and a standard deviation of 10.5. (Example: Seymour Butz’s student number is 123450. 550 c, 30030 d and25520 ). a) Find the following probabilities for the Phillinx: (i) 1001 xPPHP, the probability that it dies before the end of the tenth year, (ii) 2PHP 2010 xP, the probability that it dies between the end of the tenth and the end of the twentieth year and (iii) 3PHP)20( xP, the probability that it lasts beyond the twentieth year. (1.5)b) Find the following probabilities for the Flubberall: (i) 1001 yPFP, the probability that it dies before the end of the tenth year, (ii) 2FP 2010 yP, the probability thatit dies between the end of the tenth and the end of the twentieth year and (iii) 3FP)20( yP, the probability that it lasts beyond the twentieth year. (3)c) Make a joint probability table using the 6 events described above. Assume independence. (1)d) Assume that the Jorcillator will fail only if both components fail. Find the following probabilities for the Jorcillator: (i) 1JP, the probability that it dies before the end of the tenth year, (ii) 2JP, the probability that it dies between the end of the tenth and the end of the twentieth yearand (iii) 3JP, the probability that it lasts beyond the twentieth year. (3) [23.5]e) (Extra credit) Find the following conditional probabilities: : (i) 13FJP, (ii) 23FJP (iii) 31FJP, 21JFP (2).Computations for the portfolio problem and probabilities for the uniform and Normal distribution follow.2251y063t 4/20/06Computations for the Portfolio ProblemVersion 0Descriptive Statistics: R1 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3R1 10 0 17.00 8.68 27.46 -20.10 -12.90 19.70 45.33Variable MaximumR1 56.00 Descriptive Statistics: R2 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 MaximumR2 10 0 15.2 11.6 36.6 -52.2 -2.7 10.8 54.8 62.4 Data Display Row x xsq y ysq xy 1 22.5 506.25 -23.7 561.69 -533.25 2 9.3 86.49 8.6 73.96 79.98 3 -18.6 345.96 4.3 18.49 -79.98 4 48.1 2313.61 -52.2 2724.84 -2510.82 5 44.4 1971.36 62.4 3893.76 2770.56 6 56.0 3136.00 61.4 3769.96 3438.40 7 -20.1 404.01 9.8 96.04 -196.98 8 -11.0 121.00 52.6 2766.76 -578.60 9 17.1 292.41 17.1 292.41 292.41 10 22.3 497.29 11.7 136.89 260.91 Data Display sumx 170.000sumx2 9674.38sumy 152.000sumy2 14334.8sumxy 2942.63n 10.0000xbar 17.0000ybar 15.2000svarx 753.820svary 1336.04scovxy 39.8478sx 27.4558sy 36.5519rxy 0.0397063rxy2 0.00157659Data Display R1mean 17.0000R1stdv 27.4558R2mean 15.2000R2stdv 36.5519corr 0.0397063Data Display Row Pin1 Pmean Pstdv CofV 1 0.0 15.20 36.5519 2.40473 2 0.1 15.38 33.1196 2.15342 3 0.2 15.56 29.9662 1.92585 4 0.3 15.74 27.1890 1.72738 5 0.4 15.92 24.9141 1.56496 6 0.5 16.10 23.2893 1.44654 7 0.6 16.28 22.4559 1.37936 8 0.7 16.46 22.5023 1.36709 9 0.8 16.64 23.4230 1.407633251y063t 4/20/06 10 0.9 16.82 25.1222 1.49359 11 1.0 17.00 27.4558 1.61505 Version 1.00000Descriptive Statistics: R1 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3R1 10 0 17.00 8.68 27.46 -20.10 -12.90 19.70 45.33Variable MaximumR1 56.00 Descriptive Statistics: R2 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 MaximumR2 10 0 15.1 11.6 36.8
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