Essays on Analytical Methods in Economics and Finance Assignment

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The paper "Analytical Methods in Economics and Finance" is a worthy example of an assignment on macro and microeconomics. 1.a The fluctuation of the two variables XOM and MKT shows that XOM when registering positive returns has on several occasions outperformed the market return. Also, XOM has been registering less negative returns than the market portfolio expected returns when they are negative. Thus, XOM has generally been able to beat the market consistently over the ten years period. (b) The MSFT and MKT premium risk from 1998 to 2008 is as follows; OBS MST premium risk MKT premium risk Jan-98 0.122152 -0.027574 Feb-98 0.104051 0.041127 Mar-98 0.023944 0.019219 Apr-98 -0.02512 -0.021241 May-98 -0.091049 -0.057858 Jun-98 0.245716 -0.000149 Jul-98 -0.017685 -0.055367 Aug-98 -0.159448 -0.18977 Sep-98 0.115128 0.031733 Oct-98 -0.07015 0.042254 Nov-98 0.120199 0.029883 Dec-98 0.10468 0.03095 Jan-99 0.229727 0.006243 Feb-99 -0.174246 -0.070208 Mar-99 0.161902 0.005759 Apr-99 -0.124851 0.016897 May-99 -0.039789 -0.052823 Jun-99 0.085635 0.018917 Jul-99 -0.080613 -0.062738 Aug-99 0.046557 -0.042086 Sep-99 -0.05371 -0.05497 Oct-99 -0.010019 0.029945 Nov-99 -0.048477 0.004753 Dec-99 0.250203 0.051822 Jan-00 -0.193773 -0.071856 Feb-00 -0.118948 -0.000333 Mar-00 0.156708 0.021449 Apr-00 -0.375632 -0.09157 May-00 -0.13515 -0.07115 Jun-00 0.246618 0.019546 Jul-00 -0.159447 -0.049208 Aug-00 -0.032103 0.043708 Sep-00 -0.168182 -0.083242 Oct-00 0.109866 -0.056667 Nov-00 -0.199072 -0.134649 Dec-00 -0.276112 -0.011757 Jan-01 0.375678 0.00743 Feb-01 -0.06588 -0.13137 Mar-01 -0.105196 -0.102393 Apr-01 0.206754 0.051801 May-01 -0.010996 -0.021542 Jun-01 0.023115 -0.049584 Jul-01 -0.125391 -0.050424 Aug-01 -0.17019 -0.091183 Sep-01 -0.135171 -0.123643 Oct-01 0.104305 -0.004136 Nov-01 0.07211 0.046631 Dec-01 -0.000332 -0.014262 Jan-02 -0.070443 -0.048163 Feb-02 -0.116391 -0.053808 Mar-02 0.001665 0.01259 Apr-02 -0.16558 -0.081752 May-02 -0.057935 -0.042561 Jun-02 0.042342 -0.102346 Jul-02 -0.154955 -0.11324 Aug-02 -0.009177 -0.024119 Sep-02 -0.140905 -0.132078 Oct-02 0.190348 0.042855 Nov-02 0.046633 0.029173 Dec-02 -0.135778 -0.085412 Jan-03 -0.114115 -0.055533 Feb-03 -0.029996 -0.047511 Mar-03 -0.010584 -0.02177 Apr-03 0.023659 0.050694 May-03 -0.06927 0.031404 Jun-03 0.00975 -0.015771 Jul-03 -0.002072 -0.008973 Aug-03 -0.027938 -0.007195 Sep-03 0.016162 -0.041205 Oct-03 -0.08606 0.028228 Nov-03 -0.048553 -0.015496 Dec-03 0.032463 0.013429 Jan-04 -0.021873 -0.009039 Feb-04 -0.072609 -0.016636 Mar-04 -0.092412 -0.042788 Apr-04 0.016032 -0.056333 May-04 -0.028276 -0.017976 Jun-04 0.056727 -0.01054 Jul-04 -0.034554 -0.069784 Aug-04 -0.071064 -0.029389 Sep-04 -0.019282 -0.011548 Oct-04 -0.02053 -0.014293 Nov-04 0.036542 0.01614 Dec-04 -0.03546 0.003077 Jan-05 -0.04857 -0.05866 Feb-05 -0.071677 -0.009408 Mar-05 -0.071451 -0.04904 Apr-05 0.014649 -0.057285 May-05 -0.009178 0.005813 Jun-05 -0.069312 -0.020572 Jul-05 -0.001105 0.011228 Aug-05 0.040134 -0.038046 Sep-05 -0.092366 -0.021494 Oct-05 -0.033269 -0.052887 Nov-05 0.048053 0.008303 Dec-05 -0.087378 -0.028627 Jan-06 0.044379 0.008009 Feb-06 -0.074376 -0.033747 Mar-06 -0.01945 -0.013043 Apr-06 -0.144562 -0.019135 May-06 -0.090488 -0.063145 Jun-06 -0.003405 -0.032499 Jul-06 0.000515 -0.034005 Aug-06 0.039801 -0.007018 Sep-06 0.032099 -0.012651 Oct-06 0.017623 0.004983 Nov-06 -0.00598 -0.008387 Dec-06 -0.015073 -0.02128 Jan-07 0.001387 -0.012665 Feb-07 -0.11603 -0.046101 Mar-07 -0.042753 -0.019154 Apr-07 0.04217 0.00779 May-07 -0.00371 0.006791 Jun-07 -0.071859 -0.046861 Jul-07 -0.048391 -0.063856 Aug-07 -0.037622 -0.02048 Sep-07 -0.006694 0.0088 Oct-07 0.217388 -0.006261 Nov-07 -0.116319 -0.081382 Dec-07 0.027421 -0.036445 Jan-08 -0.116373 -0.094408 Feb-08 -0.194376 -0.054143 Mar-08 0.011283 -0.042573 Apr-08 -0.02717 0.019041 May-08 -0.035259 -0.008278 Jun-08 -0.060705 -0.110728 Jul-08 -0.09717 -0.045253 Aug-08 0.033216 -0.021061 Sep-08 -0.054089 -0.130163 Oct-08 -0.19546 -0.216829 Nov-08 -0.120773 -0.117309 Dec-08 -0.070679 -0.010621 (c) Measures of central tendency and deviation of DIS, GE, GM and IBM respectively. MEAN -0.26779 -0.2349 -0.38931 -0.22645           MEDIAN 0.005859 -0.00472 -0.01302 0.006482 STD 0.080866 0.069934 0.127328 0.090485                     The mean of the four variables shows that the companies on average, in the period of ten years they registered negative returns.

That means the company's returns in the last ten years were making a loss on aggregate. The median of the four variables shows the middle rate of return during the ten years fluctuation. From the calculation above, two companies registered positive returns at the center of ten years fluctuation while the other two had negative returns.

The standard deviation of the four variables shows how the returns are spread on either side from the mean returns. DIS returns are relatively spread from the average return of -0.26779 by 0.080866, GE returns are spread far from the average return of -0.2349 by 0.069934, GM returns are spread by 0.127328 from the average return of -0.38931 and IBM returns are spread from the average return of -0.22645 by 0.090485. (d) CAPM = rf + Ba(rm – rf) MISFT ra = 0.032 + 0.574488* - 0.023771242 MISFT ra = 0.032 + - 0.0133656 MISFT ra = 0.0186 GM ra = 0.032 + 0.338807* -0.023771242 GM ra = 0.032 + -0.008054 GM ra = 0.0239 The beta value of the two variables is less than one which means the stocks of the two companies are less than one which means the value of the stock is defensive.

Thus, the two variables of stock values are valued at a lower price than the market value. (e) rj – rf = α j + β j (rm – rf) In the case of MSFT; 0.0186 – 0.032103 = α j + - 0.0133656 -0.0135103 + 0.0133656 = α j - 0.0001447 = α j In the case of GM; 0.0239 - 0.032103 = α j -0.008054 0 = α j In the case of MSFT, the value of alpha is not equal to zero but in the case of GM the value of alpha is equal to zero. (f) The null hypothesis in this case is that the beta value of Microsoft is 1.

The test statistics is as follows. t = (bk – β k)/ se(bk) N- 2 = 131 – 2 = 129 degree of freedom, the critical value is the 99th percentile of the t- distribution, t(0.99,129) = 1.282.

Thus, if the null hypothesis t value calculated amounts to 1.282< t < 1.282, the null hypothesis is rejected. If t =1, the null hypothesis will not be rejected. t = 0.574488/ -0.0716 t = -8.024 The null hypothesis is rejected. (g) The risk premium for Microsoft when the market premium risk is 2% and 7% respectively. 0.0186 – 0.032103 = Bm * 0.02 -0.013503 = Bm* 0.02 -0.013503/ 0.02 = Bm -0.67515 = Bm Thus, the risk of holding Microsoft is 1- 0.675 = 0.325 Under 7%; 0.0186 – 0.032103 = Bm * 0.07 -0.013503 = Bm* 0.07 -0.013503/ 0.07 = Bm -0.1929 = Bm Thus, the risk of holding on the Microsoft stock under market premium risk of 7% is 1- 0.1929 = 0.807. (h) t = (bk – β k)/ se(bk) The null hypothesis is that alpha and beta values are equal.

Thus, the difference between the two is zero. Under the first half;   beta   0.704079 alpha   -0.0151   The difference between the two = 0.71919 Degree of freedom = 50 – 2 = 48 and the significance level is 5% t (0.95.48)­ = 1.671 t = (0.71919)/ 0.024099 t = 29.84, the null hypothesis is rejected. Under the second half; beta   -0.15519 alpha   -0.02587   The difference between the two is 0.12932; t (0.95.48)­ = 1.671 t = 0.12932/ 0.010845 t = 11.92 The null hypothesis is rejected because it is not equal to the t statistic. (i) Microsoft stock has a beta value which is less than one which means the stock volatility during fluctuation of the stock market is relatively low.

With a beta value that is less than one, it means that the stock value has to be undervalued.

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