# Essays on I will provide the details shortly Coursework

Finance and Accounting work Question A) Individual hypothesis testing is the ability to test the given statistical hypothesis with the objective of accepting or rejecting a null hypothesis. On the other hand, joint hypothesis testing involves testing of the statistical method without giving a level of overall certainty of the fulfillment of the given objective. A given statistical phenomena can be fulfilled with respect to the method used. B) The F test is based on the ratio of variances and is used to make comparison of two means or treatments.

Therefore, the F test is used for experiments involving more than two treatments. Therefore, it determines whether one can assume that two independent estimates of variance can be assumed to estimate the same variance. The ability of the treatments to differ implies that the variation in treatment means will be greater than variation arising from random differences among individuals. C) A single index model is a pricing model that measures that risk and the return on the stock of an organization with its common applications being in the financial industry.

The multi-factor model also has its applications in the financial sector. However, the model involves utility of multiple factors in its computations that are used to explain the market phenomena such as equilibrium of prices. Its applications include explanation of individual or portfolio security. An example of a multifactor model is displayed below and is used to stock market factors. Ri = ai + βi(m) Rm + βi(1)F1 + βi(2)F2 +…+βi(N)FN + ei Where: Ri represents the returns of security i Rm represents the market return F(1,2,3…N) represents each of the factors used β represents the beta with respect to each factor including the market (m) e represents the error term a represents the intercept Question 2 a) t-values ri = 0.080 + 0.801Si + 0.321MBi + 0.164PEi - 0.084BETAi (0.064) (0.147) (0.136) (0.420) (0.120) 1.25 5.45 2.36 0.390 -0.700 The t ratios are calculated by division of estimates by the standard error.

Based on the provided estimates, and standard errors, the calculated t values are as indicated below each value in the above equation.

The null hypothesis is rejected at the 5% level if the absolute value of the test statistic is greater than the critical value. The above values indicate that the absolute values are greater than the critical t values except for beta. This means that we reject the null hypothesis and confirm that the firm size and the market to book value have a significant impact in the returns of the stock of the firm. b) The initial regression carried out is the unrestricted regression while the second is the restricted one.

The F test is used to test the hypothesis with the sample values being: F = [(RSSr – RSSu)/m]/(RSSu/(n-k) F = [(222.7 – 203.8)/2]/(203.8/216-3-1) = 9.83 This is followed by calculation of the critical value of F from the tables at 5% level. The outcome is 3.00. The absolute value of F is higher than the critical value, thereby implying that we reject the null hypothesis and accept the alternative hypothesis that β2 and β3 are not jointly equal to zero. In addition, HML and SMB have a significant impact on the excess return of the portfolio of the company.

Question 3: The reported results indicate that there is evidence for the day-of-the-week effect. The outcome indicates that the day of the week effect has a positive impact on an individual due to the positive intercept. Similarly, Tuesday has a positive effect. However, the rest of the days of the week have a negative effect on an individual. Only the Monday dummy is significant at the 5% level of significance. This suggests that the Mondays returns are significantly smaller than Wednesdays returns on average (note that the coefficient is interpreted as the difference in average returns between Wednesday and Monday. Exercise 5A: Lab Questions 1) a).

The intercept is negative indicating that autonomous returns of all share FTSE is negative. b). The slope coefficient beta is 1.408, which implies that the price of the stock is more volatile than the market. The stock price is 40.8% more volatile than the market. c). The coefficient of determination R is 0.4874. This implies that the changes in the market explain 48.74% of the changes in the price of the stock.

d) In Q2, the p value is 0.0108. This means that there is relative evidence against the null hypothesis in favor of the alternative hypothesis. This is the reason for the rejection of the null hypothesis. e) beta values are significant to the study and indicate that the stock price is highly volatile than the market. f) the significance F is 1.3, which implies the variation among groups. This means that the null hypothesis is rejected. 5b Q1, Q2, Q3 Prices Log Returns Date PFT100 PBARC RFT100 RBARC Jan-2003 3567.4 240.63     Feb-2003 3655.6 260.69 0.02442 0.08007 Mar-2003 3613.3 259.27 -0.01164 -0.00546 Apr-2003 3926 307.04 0.08300 0.16911 May-2003 4048.1 305.44 0.03063 -0.00522 Jun-2003 4031.2 319.65 -0.00418 0.04547 Jul-2003 4157 332.61 0.03073 0.03974 Aug-2003 4161.1 331.51 0.00099 -0.00331 Sep-2003 4091.3 332.77 -0.01692 0.00379 Oct-2003 4287.6 358.17 0.04686 0.07356 Nov-2003 4342.6 369.34 0.01275 0.03071 Dec-2003 4476.9 359.07 0.03046 -0.02820 Jan-2004 4390.7 356.73 -0.01944 -0.00654 Feb-2004 4492.2 358.14 0.02285 0.00394 Mar-2004 4385.7 354.8 -0.02399 -0.00937 Apr-2004 4489.7 376.46 0.02344 0.05926 May-2004 4430.7 352.03 -0.01323 -0.06710 Jun-2004 4464.1 347.77 0.00751 -0.01218 Jul-2004 4413.1 340.55 -0.01149 -0.02098 Aug-2004 4459.3 386.99 0.01041 0.12784 Sep-2004 4570.8 398.65 0.02470 0.02968 Oct-2004 4624.2 400.16 0.01162 0.00378 Nov-2004 4703.2 406.17 0.01694 0.01491 Dec-2004 4814.3 440.77 0.02335 0.08175 Jan-2005 4852.3 437.77 0.00786 -0.00683 Feb-2005 4968.5 436.34 0.02367 -0.00327 Mar-2005 4894.4 417.8 -0.01503 -0.04342 Apr-2005 4801.7 414.71 -0.01912 -0.00742 May-2005 4964 402.74 0.03324 -0.02929 Jun-2005 5113.2 429 0.02961 0.06317 Jul-2005 5282.3 430.16 0.03254 0.00270 Aug-2005 5296.9 434.01 0.00276 0.00891 Sep-2005 5477.7 449.71 0.03356 0.03554 Oct-2005 5317.3 439.51 -0.02972 -0.02294 Nov-2005 5423.2 463.45 0.01972 0.05304 Dec-2005 5618.8 479.53 0.03543 0.03411 Jan-2006 5760.3 471.69 0.02487 -0.01648 Feb-2006 5791.5 524.66 0.00540 0.10643 Mar-2006 5964.6 542.71 0.02945 0.03382 Apr-2006 6023.1 551.98 0.00976 0.01694 May-2006 5723.8 497.99 -0.05097 -0.10293 Jun-2006 5833.4 495.17 0.01897 -0.00568 Jul-2006 5928.3 506.05 0.01614 0.02173 Aug-2006 5906.1 538.44 -0.00375 0.06204 Sep-2006 5960.8 551.95 0.00922 0.02478 Oct-2006 6129.2 579.38 0.02786 0.04850 Nov-2006 6048.8 557.27 -0.01320 -0.03891 Dec-2006 6220.8 597.81 0.02804 0.07022 Jan-2007 6203.1 606 -0.00285 0.01361 Feb-2007 6171.5 606 -0.00511 0.00000 Mar-2007 6308 607.49 0.02188 0.00246 Apr-2007 6449.2 612.96 0.02214 0.00896 May-2007 6621.4 608.33 0.02635 -0.00758 Jun-2007 6607.9 586.42 -0.00204 -0.03668 Jul-2007 6360.1 588.95 -0.03822 0.00431 Aug-2007 6303.3 526.42 -0.00897 -0.11224 Sep-2007 6466.8 510.97 0.02561 -0.02979 Oct-2007 6721.6 518.26 0.03864 0.01417 Nov-2007 6432.5 483.08 -0.04396 -0.07029 Dec-2007 6456.9 432.46 0.00379 -0.11069 Jan-2008 5879.8 403.29 -0.09363 -0.06983 Feb-2008 5884.3 409.51 0.00077 0.01531 Mar-2008 5702.1 408.84 -0.03145 -0.00164 Apr-2008 6087.3 412 0.06537 0.00770 May-2008 6053.5 338.44 -0.00557 -0.19668 Jun-2008 5625.9 263.08 -0.07326 -0.25189 Jul-2008 5411.9 305.05 -0.03878 0.14802 Aug-2008 5636.6 330.3 0.04068 0.07953 Sep-2008 4902.5 305.51 -0.13954 -0.07802 Oct-2008 4377.3 167.4 -0.11331 -0.60160 Nov-2008 4288 158.51 -0.02061 -0.05457 Dec-2008 4434.2 143.54 0.03353 -0.09920 Jan-2009 4149.6 99.28 -0.06634 -0.36867 Feb-2009 3830.1 87.39 -0.08012 -0.12756 Mar-2009 3926.1 138.48 0.02476 0.46035 Apr-2009 4243.7 263.4 0.07779 0.64295 May-2009 4417.9 278.37 0.04023 0.05528 Jun-2009 4249.2 264.8 -0.03893 -0.04998 Jul-2009 4608.4 282.86 0.08115 0.06598 Aug-2009 4908.9 355.8 0.06317 0.22942 Sep-2009 5133.9 346.21 0.04482 -0.02732 Oct-2009 5044.5 301.29 -0.01757 -0.13897 Nov-2009 5190.7 274.42 0.02857 -0.09341 Dec-2009 5412.9 259.08 0.04192 -0.05752 Jan-2010 5188.5 253.96 -0.04234 -0.01996 Feb-2010 5354.5 294.76 0.03149 0.14898 Mar-2010 5679.6 339.84 0.05894 0.14231 Apr-2010 5553.3 319.04 -0.02249 -0.06316 May-2010 5188.4 288.66 -0.06797 -0.10007 Jun-2010 4916.9 255.97 -0.05375 -0.12019 Jul-2010 5258 314.87 0.06707 0.20710 Aug-2010 5225.2 286.97 -0.00626 -0.09278 Sep-2010 5548.6 284.31 0.06005 -0.00931 Oct-2010 5675.2 260.59 0.02256 -0.08712 Nov-2010 5528.3 243.97 -0.02623 -0.06590 Dec-2010 5899.9 249.21 0.06506 0.02125 Jan-2011 5862.9 279.78 -0.00629 0.11571 Feb-2011 5994 307.02 0.02211 0.09291 Mar-2011 5908.8 266.42 -0.01432 -0.14184 Apr-2011 6069.9 270.98 0.02690 0.01697 May-2011 5990 266.49 -0.01325 -0.01671 Jun-2011 5945.7 247.03 -0.00742 -0.07583 Jul-2011 5815.2 214.81 -0.02219 -0.13976 Aug-2011 5394.5 165.4 -0.07510 -0.26139 Sep-2011 5128.5 156.3 -0.05057 -0.05659 Oct-2011 5544.2 189.18 0.07794 0.19092 Nov-2011 5505.4 175.57 -0.00702 -0.07466 Dec-2011 5572.3 171.48 0.01208 -0.02357 Jan-2012 5681.6 207.03 0.01942 0.18840 Feb-2012 5871.5 241.56 0.03288 0.15425 Mar-2012 5768.5 231.95 -0.01770 -0.04060 Apr-2012 5737.8 215.19 -0.00534 -0.07500 May-2012 5320.9 174.6 -0.07543 -0.20902 Jun-2012 5571.1 161.28 0.04595 -0.07936 Jul-2012 5635.3 166.38 0.01146 0.03113 Aug-2012 5711.5 182.49 0.01343 0.09242 Sep-2012 5742.1 213.96 0.00534 0.15909 Oct-2012 5782.7 226.56 0.00705 0.05722 Nov-2012 5866.8 246 0.01444 0.08232 Dec-2012 5897.8 262.4 0.00527 0.06454 4) Descriptive statistics Descriptive statistics   RFT100 RBARC Mean 0.0042 0.0007 Standard Error 0.0036 0.0120 Median 0.0098 -0.0016 Mode - - Standard Deviation 0.0395 0.1313 Sample Variance 0.0016 0.0172 Kurtosis 1.3820 8.6869 Skewness -0.8062 0.3187 Range 0.2225 1.2445 Minimum -0.1395 -0.6016 Maximum 0.0830 0.6429 Sum 0.5027 0.0866 Count 119 119 5) Histograms for the two return series 6) Comments on descriptive statistics The means of RFT100 is higher than that of RBARC (0.0007).

the standard error in RFT100 is 0.0036, which is lower than 0.012 of RBARC. The former has a higher median of 0.0098 compared to -0.0016. On the contrary, RBARC has a higher standard deviation of 0.1313 while its variance is 0.0172. RFT100 is skewed to the left at -0.8062 while RBARC is skewed to the right at 0.3187. Both have negative and positive minimums and maximums respectively while the sum varies. 7) Time series plot of prices