The essay should be 5 pages in length (1250-1500 words).The sources from the same books not somewhere else please.PLEASE READ CAREFULYchoose one OR two books for the essay that mentioned in this textThe essay should be 5 pages in length (1250-1500 words).The sources from the same books not somewhere else please.Please choose a text that we have read this semester and engage in an analysis. (You may use two of the texts in your final paper, if you wish.) Expand on the terms and themes we have discussed throughout the semester and explain how these terms and themes relate to and support your argument. Your final paper should be 5 pages in length (1250-1500 words).Please use specific examples from the text to support your points. DO NOT JUST SUMMARIZE THE PLOT. I expect you to engage in an analysis of the text, and respond critically to it. All papers MUST be typed, double-spaced, size 12 Times New Roman font and adhere to MLA guidelines.Your papers will be submitted to a dropbox on Blackboard that will close at 11:59 PM on the 14th. LATE RESPONSES WILL NOT BE ACCEPTED. Your paper must be uploaded/time stamped by 11:59 at the latest. Any responses received after 11:59 will be considered late.Below are the texts that we have looked at this semester:(You may use two of the texts in your final paper, if you wish.)M34EFA May 2018 Coventry University Faculty of Business and Law M34EFA Quantitative Methods Instructions to candidates Time allowed: 2 hours Answer THREE QUESTIONS All questions are equally weighted. For this examination, you will be supplied with the following: Relevant Formula Statistical Tables Use 5% significance level unless otherwise indicated in the question. You may use a non-programmable scientific calculator for the calculation of answers. You may take this question paper away at the end of the examination: please keep it in a safe place for future reference. M34EFA Question 1 An investor is deciding as to which shares to buy in order to maximise his returns. From his initial selection he has chosen the following 4 shares with the return and standard deviations given in the table. Share Return % Standard Deviation % 1 36 3.808 2 9 3.808 3 17 7.483 4 30 7.483 a) Calculate and compare the expected return of the portfolio consisting of i. equal proportions in all stocks ii. 40% in share 1, 10% share 2, 20% share 3 and 30% share 4 (20 marks) b) Calculate the correlation coefficient between the following combinations of shares and comment on which combination of shares would minimise the portfolio risk? The table provides the covariance between the shares. (30 marks) Combinations Shares Covariance 1 1, 2 -14.5 2 1, 3 -2.75 3 1, 4 -2.75 4 2, 3 2.75 5 2, 4 2.75 6 3, 4 56 c) Calculate the standard deviations of the following portfolios and identify the least risky portfolio, using standard deviation as a measure of risk. (30 marks) Combinations Shares 1 1, 2 2 1, 3 6 3, 4 d) Explain the key statistics that can be used to measure the spread of data and explain why such measures are useful to statistical analysis. (20 marks) (100 marks total) M34EFA Question 2 Suppose a debt agency has calculated that graduates in the UK have an average debt of £56,000 with a standard deviation of £15,000. Assuming debt is a normally distributed variable. e) Calculate the probability that the debt for a graduate is more than £40,250? (20 marks) b) Calculate the probability that the debt for a graduate is between £30,050 and £75,050. (20 Marks) c) If there were 537,000 students who graduated from UK universities in 2016/17, how many are expected to have a debt of more than £75,050? (10 marks) Suppose that the average debt of 150 graduates who studied business subjects, over the same period was £60,500 with a standard deviation of £10,000. d) Formulate the null and the alternative hypotheses to test if the average debt of business graduate is more than the average debt of all graduates. (15 marks) e) Calculate the appropriate test statistics for the above null hypotheses. (15 marks) f) Using the critical value approach, test the above hypothesis at 5% significance level. (20 marks) (100 marks total) M34EFA Question 3 Using data on early retirement and its determinants (defined below), we estimate the following model. rtrd = f(hlth,mssec,unemp) where rtrd = % of retired men who are between the ages of 16 and 65 (Range 5.4 – 18.7) hlth = % of people between 16 and 64 years who are prevented from working due to a disability (Range 1.6 – 7.6) mssec = Mean social security income in $ (Range 3449 – 4399) unemp = Unemployment rate in percent (Range 3.6 – 9.5) Table 1: OLS, using observations 1-44 Dependent variable: retrd coefficient std. error p-value ——————————————————– const 12.3935 6.38801 0.0594 * hlth 1.56300 0.261581 5.12e-07 *** mssec −0.00275181 0.00147997 0.0703 * unemp 0.516028 0.257794 0.0521 * Mean dependent var 11.22955 S.D. dependent var 3.697742 Sum squared resid 213.1407 S.E. of regression 2.308358 R-squared 0.637486 Adjusted R-squared 0.610297 Log-likelihood −97.14408 Akaike criterion 202.2882 Schwarz criterion 209.4249 Hannan-Quinn 204.9348 a) Interpret the impact of health and mean social security income on the decision to retire and state whether the estimates are as expected. (25 marks) b) Test which coefficients are statistically significant using t-test at 5% significance level clearly explaining your procedure. (25 marks) c) Conduct the F-test to examine the model significance using 5% significance level and state your procedure clearly. (25 marks) d) Explain the classic linear regression assumptions. (25 marks) (100 marks total) M34EFA Question 4 Table 2 below presents the output for heteroskedasticity test for the model estimated in question 3 above. Table 2: White’s test for heteroskedasticity OLS, using observations 1-44 Dependent variable: uhat^2 coefficient std. error t-ratio p-value ———————————————————— const 401.960 382.445 1.051 0.3007 hlth −27.2835 14.3900 −1.896 0.0665 * mssec −0.190053 0.171722 −1.107 0.2762 unemp 12.0064 17.3325 0.6927 0.4932 sq_hlth −0.168965 0.602566 −0.2804 0.7809 X2_X3 0.00833145 0.00333653 2.497 0.0175 ** X2_X4 −0.580488 0.636074 −0.9126 0.3679 sq_mssec 2.17432e-05 1.97429e-05 1.101 0.2785 X3_X4 −0.00278861 0.00368124 −0.7575 0.4540 sq_unemp 0.0735288 0.569847 0.1290 0.8981 Unadjusted R-squared = 0.373116 a) Test if heteroskedasticity is a problem at 5% significance level using appropriate test of heteroskedasticity. (30 marks) b) The skewness and kurtosis of the residuals of the regression in Table 1 are 0.65 and 0.981 respectively. Using the test of the normality of the residuals test at 5% significance level, whether the residuals are normally distributed or not. Explain your procedure clearly. (30 marks) c) Illustrate how we can estimate the following non-linear model using OLS and what interpretation does the parameters have? (SKIP THIS QUESTION; IT IS NOT RELEVANT FOR THE DECEMBER 2020 EXAM) ! = #$!%(#$!) &'(& (15 marks) d) Briefly outline the following terms with an example: i. Type 1 error ii. Discrete variable iii. Cross-sectional dataset iv. Autocorrelation v. R2 of a regression (25 marks) M34EFA (100 marks total) Question 5 Suppose you estimate the following extended CAPM using 100 monthly observations for company xyz. !” = $!%&'(( + $”*’+ + $#,%-.100 + $$’1, + $%*., + $&231 + 5 Where ER monthly returns on xyz tbill monthly yield on the 3 month t-bill div monthly dividend yield on E-phones ftse100 monthly returns of the ftse100 equity index inf monthly data on the annualised rate of inflation def difference between indices of baa-rated and caa-rated bonds Jan January dummy a) How do we interpret the coefficient on the FTSE100 variable (α3)? (10 marks) b) Suppose α3 = 0.978 with a standard error of 1.027. Test if this is significantly different from 1 at 5% significance level? Why might we be interested in this specifically? (30 marks) c) Suppose α6 = -1.098 and had standard error of 0.045. How would you interpret the Jan coefficient? Test whether α6 is statistically significant at 5% significant level. (30 marks) d) Test whether the following model suffers from autocorrelation problem using appropriate test. Outline your procedure and use 5% significant level. (30 marks) Table 3: OLS, using observations 1950:2-1983:4 (T = 135) Dependent variable: P Coefficient Std. Error t-ratio p-value Const −0.872965 0.156018 −5.595 <0.0001 *** M1 −0.0313870 0.0176514 −1.778 0.0777 * M1_1 0.0494991 0.0182446 2.713 0.0076 *** P_1 0.981389 0.0136899 71.69 <0.0001 *** Mean dependent var 99.77148 S.D. dependent var 46.23796 Sum squared resid 54.98892 S.E. of regression 0.647891 R-squared 0.999808 Adjusted R-squared 0.999804 F(3, 131) 227454.0 P-value(F) 3.2e-243 M34EFA Rho 0.673881 Breusch-Godfrey test for autocorrelation up to order 2 OLS, using observations 1950:2-1983:4 (T = 135) Dependent variable: uhat coefficient std. error t-ratio p-value ——————————————————– const 0.264153 0.112323 2.352 0.0202 ** M1 0.0213913 0.0131608 1.625 0.1065 M1_1 −0.0124773 0.0136699 −0.9128 0.3631 P_1 −0.0235278 0.00994490 −2.366 0.0195 ** uhat_1 0.516165 0.0860992 5.995 1.91e-08 *** uhat_2 0.351564 0.0915188 3.841 0.0002 *** Unadjusted R-squared = 0.511641 (100 marks total) M34EFA Formulas Sample variance: -” = ∑(8′ − 8)” 1 − 1 Properties of variance: ;3< =>3′?’ ( ‘)! @ = >3′ “;3<(?’) ( ‘)! + 2 > 3’3*BC+(?’, ?*) !+’+*+( z-score: E’ = 8′ − 8 – Sample covariance: -,- = ∑(8′ − 8)(F’ − F) 1 − 1 Correlation coefficient: <,- = -,- -,– Test statistic for hypothesis tests about population mean (σ unknown): % = 8̅− H. -/√1 Coefficient of determination: “” = KK” KKL Adjusted coefficient of determination: “/ ” = 1 − (1 − “”) 1 − 1 1 − M − 1 Test statistic for significance in linear regression: % = 0! 1″! M34EFA Tables of statistical distributions M34EFA M34EFA M34EFA t-distribution The table gives the values of where Pr(Tn > t a; n ) = a , with n degrees of freedom a n 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 1 3.078 6.314 12.076 31.821 63.657 318.310 636.620 2 1.886 2.920 4.303 6.965 9.925 22.326 31.598 3 1.638 2.353 3.182 4.541 5.841 10.213 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 1.397 1.860 2.306 2.896 3.355 4.501 5.041 9 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.500 2.807 3.485 3.767 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 1.314 1.703 2.052 2.473 2.771 3.421 3.690 28 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 1.311 1.699 2.045 2.462 2.756 3.396 3.659 30 1.310 1.697 2.042 2.457 2.750 3.385 3.646 40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 1.296 1.671 2.000 2.390 2.660 3.232 3.460 120 1.289 1.658 1.980 2.358 2.617 3.160 3.373 ¥ 1.282 1.645 1.960 2.326 2.576 3.090 3.291 ; ta n M34EFA Chi-squared distribution DF 0.20 0.10 0.05 0.025 0.01 0.005 0.002 0.001 1 1.642 2.706 3.841 5.024 6.635 7.879 9.550 10.828 2 3.219 4.605 5.991 7.378 9.210 10.597 12.429 13.816 3 4.642 6.251 7.815 9.348 11.345 12.838 14.796 16.266 4 5.989 7.779 9.488 11.143 13.277 14.860 16.924 18.467 5 7.289 9.236 11.070 12.833 15.086 16.750 18.907 20.515 6 8.558 10.645 12.592 14.449 16.812 18.548 20.791 22.458 7 9.803 12.017 14.067 16.013 18.475 20.278 22.601 24.322 8 11.030 13.362 15.507 17.535 20.090 21.955 24.352 26.124 9 12.242 14.684 16.919 19.023 21.666 23.589 26.056 27.877 10 13.442 15.987 18.307 20.483 23.209 25.188 27.722 29.588 11 14.631 17.275 19.675 21.920 24.725 26.757 29.354 31.264 12 15.812 18.549 21.026 23.337 26.217 28.300 30.957 32.909 13 16.985 19.812 22.362 24.736 27.688 29.819 32.535 34.528 14 18.151 21.064 23.685 26.119 29.141 31.319 34.091 36.123 15 19.311 22.307 24.996 27.488 30.578 32.801 35.628 37.697 16 20.465 23.542 26.296 28.845 32.000 34.267 37.146 39.252 17 21.615 24.769 27.587 30.191 33.409 35.718 38.648 40.790 18 22.760 25.989 28.869 31.526 34.805 37.156 40.136 42.312 19 23.900 27.204 30.144 32.852 36.191 38.582 41.610 43.820 20 25.038 28.412 31.410 34.170 37.566 39.997 43.072 45.315 21 26.171 29.615 32.671 35.479 38.932 41.401 44.522 46.797 22 27.301 30.813 33.924 36.781 40.289 42.796 45.962 48.268 23 28.429 32.007 35.172 38.076 41.638 44.181 47.391 49.728 24 29.553 33.196 36.415 39.364 42.980 45.559 48.812 51.179 25 30.675 34.382 37.652 40.646 44.314 46.928 50.223 52.620 26 31.795 35.563 38.885 41.923 45.642 48.290 51.627 54.052 27 32.912 36.741 40.113 43.195 46.963 49.645 53.023 55.476 28 34.027 37.916 41.337 44.461 48.278 50.993 54.411 56.892 29 35.139 39.087 42.557 45.722 49.588 52.336 55.792 58.301 30 36.250 40.256 43.773 46.979 50.892 53.672 57.167 59.703 31 37.359 41.422 44.985 48.232 52.191 55.003 58.536 61.098 32 38.466 42.585 46.194 49.480 53.486 56.328 59.899 62.487 33 39.572 43.745 47.400 50.725 54.776 57.648 61.256 63.870 34 40.676 44.903 48.602 51.966 56.061 58.964 62.608 65.247 35 41.778 46.059 49.802 53.203 57.342 60.275 63.955 66.619 36 42.879 47.212 50.998 54.437 58.619 61.581 65.296 67.985 37 43.978 48.363 52.192 55.668 59.893 62.883 66.633 69.346 38 45.076 49.513 53.384 56.896 61.162 64.181 67.966 70.703 39 46.173 50.660 54.572 58.120 62.428 65.476 69.294 72.055 40 47.269 51.805 55.758 59.342 63.691 66.766 70.618 73.402 M34EFA M34EFA F Distribution critical values for P=0.05 Denominator Numerator DF DF 1 2 3 4 5 7 10 15 20 30 60 120 500 1000 1 161.45 199.50 215.71 224.58 230.16 236.77 241.88 245.95 248.01 250.10 252.20 253.25 254.06 254.19 2 18.513 19.000 19.164 19.247 19.296 19.353 19.396 19.429 19.446 19.462 19.479 19.487 19.494 19.495 3 10.128 9.5522 9.2766 9.1172 9.0135 8.8867 8.7855 8.7028 8.6602 8.6165 8.5720 8.5493 8.5320 8.5292 4 7.7086 6.9443 6.5915 6.3882 6.2560 6.0942 5.9644 5.8579 5.8026 5.7458 5.6877 5.6580 5.6352 5.6317 5 6.6078 5.7862 5.4095 5.1922 5.0504 4.8759 4.7351 4.6187 4.5582 4.4958 4.4314 4.3985 4.3731 4.3691 7 5.5914 4.7375 4.3469 4.1202 3.9715 3.7871 3.6366 3.5108 3.4445 3.3758 3.3043 3.2675 3.2388 3.2344 10 4.9645 4.1028 3.7082 3.4780 3.3259 3.1354 2.9782 2.8450 2.7741 2.6996 2.6210 2.5801 2.5482 2.5430 15 4.5431 3.6823 3.2874 3.0556 2.9013 2.7066 2.5437 2.4035 2.3275 2.2467 2.1601 2.1141 2.0776 2.0718 20 4.3512 3.4928 3.0983 2.8660 2.7109 2.5140 2.3479 2.2032 2.1241 2.0391 1.9463 1.8962 1.8563 1.8498 30 4.1709 3.3159 2.9223 2.6896 2.5336 2.3343 2.1646 2.0149 1.9317 1.8408 1.7396 1.6835 1.6376 1.6300 60 4.0012 3.1505 2.7581 2.5252 2.3683 2.1666 1.9927 1.8365 1.7480 1.6492 1.5343 1.4672 1.4093 1.3994 120 3.9201 3.0718 2.6802 2.4473 2.2898 2.0868 1.9104 1.7505 1.6587 1.5544 1.4289 1.3519 1.2804 1.2674 500 3.8601 3.0137 2.6227 2.3898 2.2320 2.0278 1.8496 1.6864 1.5917 1.4820 1.3455 1.2552 1.1586 1.1378 1000 3.8508 3.0047 2.6137 2.3808 2.2230 2.0187 1.8402 1.6765 1.5811 1.4705 1.3318 1.2385 1.1342 1.1096 M34EFA Durrbin Watson values a = 0.05 k’ 1 2 3 4 5 6 7 8 9 10 n dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU 6 0.390 1.142 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– 7 0.435 1.036 0.294 1.676 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– 8 0.497 1.003 0.345 1.489 0.229 2.102 —– —– —– —– —– —– —– —– —– —– —– —– —– —– 9 0.554 0.998 0.408 1.389 0.279 1.875 0.183 2.433 —– —– —– —– —– —– —– —– —– —– —– —– 10 0.604 1.001 0.466 1.333 0.340 1.733 0.230 2.193 0.150 2.690 —– —– —– —– —– —– —– —– —– —– 11 0.653 1.010 0.519 1.297 0.396 1.640 0.286 2.030 0.193 2.453 0.124 2.892 —– —– —– —– —– —– —– —– 12 0.697 1.023 0.569 1.274 0.449 1.575 0.339 1.913 0.244 2.280 0.164 2.665 0.105 3.053 —– —– —– —– —– —– 13 0.738 1.038 0.616 1.261 0.499 1.526 0.391 1.826 0.294 2.150 0.211 2.490 0.140 2.838 0.090 3.182 —– —– —– —– 14 0.776 1.054 0.660 1.254 0.547 1.490 0.441 1.757 0.343 2.049 0.257 2.354 0.183 2.667 0.122 2.981 0.078 3.287 —– —– 70 1.429 1.485 1.400 1.514 1.372 1.546 1.343 1.577 1.313 1.611 1.283 1.645 1.253 1.680 1.223 1.716 1.192 1.754 1.162 1.792 75 1.448 1.501 1.422 1.529 1.395 1.557 1.368 1.586 1.340 1.617 1.313 1.649 1.284 1.682 1.256 1.714 1.227 1.748 1.199 1.783 80 1.465 1.514 1.440 1.541 1.416 1.568 1.390 1.595 1.364 1.624 1.338 1.653 1.312 1.683 1.285 1.714 1.259 1.745 1.232 1.777 85 1.481 1.529 1.458 1.553 1.434 1.577 1.411 1.603 1.386 1.630 1.362 1.657 1.337 1.685 1.312 1.714 1.287 1.743 1.262 1.773 90 1.496 1.541 1.474 1.563 1.452 1.587 1.429 1.611 1.406 1.636 1.383 1.661 1.360 1.687 1.336 1.714 1.312 1.741 1.288 1.769 95 1.510 1.552 1.489 1.573 1.468 1.596 1.446 1.618 1.425 1.641 1.403 1.666 1.381 1.690 1.358 1.715 1.336 1.741 1.313 1.767 100 1.522 1.562 1.502 1.582 1.482 1.604 1.461 1.625 1.441 1.647 1.421 1.670 1.400 1.693 1.378 1.717 1.357 1.741 1.335 1.765 150 1.611 1.637 1.598 1.651 1.584 1.665 1.571 1.679 1.557 1.693 1.543 1.708 1.530 1.722 1.515 1.737 1.501 1.752 1.486 1.767 200 1.664 1.684 1.653 1.693 1.643 1.704 1.633 1.715 1.623 1.725 1.613 1.735 1.603 1.746 1.592 1.757 1.582 1.768 1.571 1.779 M34EFA
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