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Question:
This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest rate. We will use this variable to compute excess returns on our preferred stock (either Boeing or IBM) and Market excess returns.

1.Comparison of Stock Returns
1.1 Graphical Display
1.2 Computation of Returns
1.3 Summary of Returns
1.4 Hypothesis Testing on Stock Returns
1.5 Comparison of Risks
1.6 Comparison of mean Return
1.7 Calculation of Excess Returns
1.8 Estimation of CAPM for IBM
1.9 Determination of Neutral Stock
1.Comparison of Stock Returns
1.1 Graphical Display

Comparison of the stock prices has been done in the following figures 2.1, 2.2 and 2.3. The stock prices of S&P, Boeing and IBM have been plotted in the graph over the selected time frame. It has been observed that the stock prices for both the companies Boeing and IBM follow an increasing trend. The S&P stock prices also follow an increasing trend.

1.2 Computation of Returns

The returns on the closing stock prices for S&P, BE and IBM are given in the following table:

 Date Price Series Returns S&P Boeing IBM US TN (10 Year) Return S&P Return Boeing Return IBM 2/1/2010 1104.49 63.16 127.16 3.595 – – – 3/1/2010 1169.43 72.61 128.25 3.833 5.71 13.94 0.85 4/1/2010 1186.69 72.43 129 3.663 1.47 -0.25 0.58 5/1/2010 1089.41 64.18 125.26 3.301 -8.55 -12.09 -2.94 6/1/2010 1030.71 62.75 123.48 2.951 -5.54 -2.25 -1.43 7/1/2010 1101.6 68.14 128.4 2.907 6.65 8.24 3.91 8/1/2010 1049.33 61.13 123.13 2.477 -4.86 -10.86 -4.19 9/1/2010 1141.2 66.54 134.14 2.517 8.39 8.48 8.56 10/1/2010 1183.26 70.64 143.6 2.612 3.62 5.98 6.81 11/1/2010 1180.55 63.77 141.46 2.797 -0.23 -10.23 -1.50 12/1/2010 1257.64 65.26 146.76 3.305 6.33 2.31 3.68 1/1/2011 1286.12 69.48 162 3.378 2.24 6.27 9.88 2/1/2011 1327.22 72.01 161.88 3.414 3.15 3.58 -0.07 3/1/2011 1325.83 73.93 163.07 3.454 -0.10 2.63 0.73 4/1/2011 1363.61 79.78 170.58 3.296 2.81 7.62 4.50 5/1/2011 1345.2 78.03 168.93 3.05 -1.36 -2.22 -0.97 6/1/2011 1320.64 73.93 171.55 3.158 -1.84 -5.40 1.54 7/1/2011 1292.28 70.47 181.85 2.805 -2.17 -4.79 5.83 8/1/2011 1218.89 66.86 171.91 2.218 -5.85 -5.26 -5.62 9/1/2011 1131.42 60.51 174.87 1.924 -7.45 -9.98 1.71 10/1/2011 1253.3 65.79 184.63 2.175 10.23 8.37 5.43 11/1/2011 1246.96 68.69 188 2.068 -0.51 4.31 1.81 12/1/2011 1257.6 73.35 183.88 1.871 0.85 6.56 -2.22 1/1/2012 1312.41 74.18 192.6 1.799 4.27 1.13 4.63 2/1/2012 1365.68 74.95 196.73 1.977 3.98 1.03 2.12 3/1/2012 1408.47 74.37 208.65 2.216 3.09 -0.78 5.88 4/1/2012 1397.91 76.8 207.08 1.915 -0.75 3.22 -0.76 5/1/2012 1310.33 69.61 192.9 1.581 -6.47 -9.83 -7.09 6/1/2012 1362.16 74.3 195.58 1.659 3.88 6.52 1.38 7/1/2012 1379.32 73.91 195.98 1.492 1.25 -0.53 0.20 8/1/2012 1406.58 71.4 194.85 1.562 1.96 -3.46 -0.58 9/1/2012 1440.67 69.6 207.45 1.637 2.39 -2.55 6.27 10/1/2012 1412.16 70.44 194.53 1.686 -2.00 1.20 -6.43 11/1/2012 1416.18 74.28 190.07 1.606 0.28 5.31 -2.32 12/1/2012 1426.19 75.36 191.55 1.756 0.70 1.44 0.78 1/1/2013 1498.11 73.87 203.07 1.985 4.92 -2.00 5.84 2/1/2013 1514.68 76.9 200.83 1.888 1.10 4.02 -1.11 3/1/2013 1569.19 85.85 213.3 1.852 3.54 11.01 6.02 4/1/2013 1597.57 91.41 202.54 1.675 1.79 6.28 -5.18 5/1/2013 1630.74 99.02 208.02 2.164 2.06 8.00 2.67 6/1/2013 1606.28 102.44 191.11 2.478 -1.51 3.40 -8.48 7/1/2013 1685.73 105.1 195.04 2.593 4.83 2.56 2.04 8/1/2013 1632.97 103.92 182.27 2.749 -3.18 -1.13 -6.77 9/1/2013 1681.55 117.5 185.18 2.615 2.93 12.28 1.58 10/1/2013 1756.54 130.5 179.21 2.542 4.36 10.49 -3.28 11/1/2013 1805.81 134.25 179.68 2.741 2.77 2.83 0.26 12/1/2013 1848.36 136.49 187.57 3.026 2.33 1.65 4.30 1/1/2014 1782.59 125.26 176.68 2.668 -3.62 -8.59 -5.98 2/1/2014 1859.45 128.92 185.17 2.658 4.22 2.88 4.69 3/1/2014 1872.34 125.49 192.49 2.723 0.69 -2.70 3.88 4/1/2014 1883.95 129.02 196.47 2.648 0.62 2.77 2.05 5/1/2014 1923.57 135.25 184.36 2.457 2.08 4.72 -6.36 6/1/2014 1960.23 127.23 181.27 2.516 1.89 -6.11 -1.69 7/1/2014 1930.67 120.48 191.67 2.556 -1.52 -5.45 5.58 8/1/2014 2003.37 126.8 192.3 2.343 3.70 5.11 0.33 9/1/2014 1972.29 127.38 189.83 2.508 -1.56 0.46 -1.29 10/1/2014 2018.05 124.91 164.4 2.335 2.29 -1.96 -14.38 11/1/2014 2067.56 134.36 162.17 2.194 2.42 7.29 -1.37 12/1/2014 2058.9 129.98 160.44 2.17 -0.42 -3.31 -1.07 1/1/2015 1994.99 145.37 153.31 1.675 -3.15 11.19 -4.55 2/1/2015 2104.5 150.85 161.94 2.002 5.34 3.70 5.48 3/1/2015 2067.89 150.08 160.5 1.934 -1.75 -0.51 -0.89 4/1/2015 2085.51 143.34 171.29 2.046 0.85 -4.59 6.51 5/1/2015 2107.39 140.52 169.65 2.095 1.04 -1.99 -0.96 6/1/2015 2063.11 138.72 162.66 2.335 -2.12 -1.29 -4.21 7/1/2015 2103.84 144.17 161.99 2.205 1.95 3.85 -0.41

1.3 Summary of Returns

From the results of the summary statistics, it can be seen that BE provides higher returns than IBM. It can also be seen that the returns provided by BE is less than S&P 500. On the other hand, it can be said that BE experiences higher risks than IBM. The risks suffered by IBM has a similarity with that of the S&P 500.

 Summary Statistics Return S&P Return Boeing Return IBM Mean 0.99 1.27 0.37 Standard Error 0.45 0.74 0.57 Median 1.47 1.65 0.33 Mode #N/A #N/A #N/A Standard Deviation 3.65 5.97 4.57 Sample Variance 13.34 35.58 20.85 Kurtosis 0.46 -0.32 0.56 Skewness -0.34 -0.22 -0.47 Range 18.78 26.04 24.26 Minimum -8.55 -12.09 -14.38 Maximum 10.23 13.94 9.88 Sum 64.44 82.53 24.21 Count 65 65 65

From the Jarque-Berra test, it can be seen that the returns provided by BE and IBM are normally distributed. Normality test is performed on the data because any test performed on a data which is not normal might not give a proper result on performing any tests.

 Jarque Berra Test Return S&P Return Boeing Return IBM Test Statistic 1.850 0.793 3.254 P-Value 0.396 0.673 0.197

1.4 Hypothesis Testing on Stock Returns

To test whether the returns on Boeing stocks exceeds 3 percent, z-test has to be conducted. From the comparison of the returns on Boeing stock, it has been observed that the returns on the Boeing stocks do not exceed 3 percent.

 Hypothesis Test for µ Hypotheses Null Hypothesis H0: µ ≤ 3 Alternative Hypothesis HA: µ > 3 Test Type Upper Level of significance alpha α set to: 0.05 Critical Region Degrees of Freedom 64 Critical Value 1.6690 Sample Data Sample Standard Deviation s 5.97 Sample Mean x bar 1.27 Sample Size n 65 Is Pop StDev known? Y/N N Standard Error of the Mean 0.7399 t Sample Statistic -2.3385 p-value from the t distribution 0.0112 Hypothesis test decision: Reject the Null Hypothesis

1.5 Comparison of Risks

Decision has to be made on which stock would be better to invest. In order to do that, the risks of the stocks have to be compared. From the results of the comparison of stock returns of BE and IBM, it can be seen that the variation in the returns are not same. Moreover, the variation is higher in case of BE. Thus, IBM would be a preferred choice for investment.

 F-Test Two-Sample for Variances Boeing IBM Mean 94.97 174.97 Variance 905.08 582.33 Observations 66 66 df 65 65 F 1.554 P(F<=f) one-tail 0.039 F Critical one-tail 1.508

1.6 Comparison of mean Return

Further, it has to be compared whether both the stocks have the same average returns. From the results of the analysis, it has been observed that the average stock returns for both the companies BE and IBM are same. There is no significant difference between the average returns on the stocks of BE as well as IBM.

 t-Test: Two-Sample Assuming Equal Variances Return Boeing Return IBM Mean 1.27 0.37 Variance 35.58 20.85 Observations 65 65 Pooled Variance 28.22 Hypothesized Mean Difference 0 df 128 t Stat 0.963 P(T<=t) one-tail 0.169 t Critical one-tail 1.657 P(T<=t) two-tail 0.337 t Critical two-tail 1.979

Thus, from the analysis above it has been observed that the stocks of BE and IBM provide same returns with lesser risk in case of IBM and higher risk in case of BE. Thus, the preferred choice of investment will be in the stocks of BE.

1.7 Calculation of Excess Returns

 Date US TN (10 Year) Return S&P Return IBM Excess Return (Yt) Excess Market Return (Xt) 2/1/2010 3.595 3/1/2010 3.833 5.7133 0.8535 -2.9795 1.8803 4/1/2010 3.663 1.4651 0.5831 -3.0799 -2.1979 5/1/2010 3.301 -8.5532 -2.9421 -6.2431 -11.8542 6/1/2010 2.951 -5.5388 -1.4312 -4.3822 -8.4898 7/1/2010 2.907 6.6516 3.9071 1.0001 3.7446 8/1/2010 2.477 -4.8612 -4.1910 -6.6680 -7.3382 9/1/2010 2.517 8.3928 8.5643 6.0473 5.8758 10/1/2010 2.612 3.6193 6.8148 4.2028 1.0073 11/1/2010 2.797 -0.2293 -1.5015 -4.2985 -3.0263 12/1/2010 3.305 6.3256 3.6782 0.3732 3.0206 1/1/2011 3.378 2.2393 9.8798 6.5018 -1.1387 2/1/2011 3.414 3.1457 -0.0741 -3.4881 -0.2683 3/1/2011 3.454 -0.1048 0.7324 -2.7216 -3.5588 4/1/2011 3.296 2.8097 4.5025 1.2065 -0.4863 5/1/2011 3.05 -1.3593 -0.9720 -4.0220 -4.4093 6/1/2011 3.158 -1.8426 1.5390 -1.6190 -5.0006 7/1/2011 2.805 -2.1708 5.8307 3.0257 -4.9758 8/1/2011 2.218 -5.8468 -5.6211 -7.8391 -8.0648 9/1/2011 1.924 -7.4467 1.7072 -0.2168 -9.3707 10/1/2011 2.175 10.2307 5.4311 3.2561 8.0557 11/1/2011 2.068 -0.5072 1.8088 -0.2592 -2.5752 12/1/2011 1.871 0.8497 -2.2159 -4.0869 -1.0213 1/1/2012 1.799 4.2660 4.6332 2.8342 2.4670 2/1/2012 1.977 3.9787 2.1217 0.1447 2.0017 3/1/2012 2.216 3.0851 5.8826 3.6666 0.8691 4/1/2012 1.915 -0.7526 -0.7553 -2.6703 -2.6676 5/1/2012 1.581 -6.4699 -7.0933 -8.6743 -8.0509 6/1/2012 1.659 3.8793 1.3798 -0.2792 2.2203 7/1/2012 1.492 1.2519 0.2043 -1.2877 -0.2401 8/1/2012 1.562 1.9571 -0.5783 -2.1403 0.3951 9/1/2012 1.637 2.3947 6.2660 4.6290 0.7577 10/1/2012 1.686 -1.9988 -6.4304 -8.1164 -3.6848 11/1/2012 1.606 0.2843 -2.3194 -3.9254 -1.3217 12/1/2012 1.756 0.7043 0.7756 -0.9804 -1.0517 1/1/2013 1.985 4.9198 5.8402 3.8552 2.9348 2/1/2013 1.888 1.1000 -1.1092 -2.9972 -0.7880 3/1/2013 1.852 3.5355 6.0241 4.1721 1.6835 4/1/2013 1.675 1.7924 -5.1762 -6.8512 0.1174 5/1/2013 2.164 2.0550 2.6697 0.5057 -0.1090 6/1/2013 2.478 -1.5113 -8.4785 -10.9565 -3.9893 7/1/2013 2.593 4.8278 2.0355 -0.5575 2.2348 8/1/2013 2.749 -3.1798 -6.7716 -9.5206 -5.9288 9/1/2013 2.615 2.9316 1.5839 -1.0311 0.3166 10/1/2013 2.542 4.3630 -3.2770 -5.8190 1.8210 11/1/2013 2.741 2.7663 0.2619 -2.4791 0.0253 12/1/2013 3.026 2.3289 4.2975 1.2715 -0.6971 1/1/2014 2.668 -3.6231 -5.9812 -8.6492 -6.2911 2/1/2014 2.658 4.2213 4.6934 2.0354 1.5633 3/1/2014 2.723 0.6908 3.8770 1.1540 -2.0322 4/1/2014 2.648 0.6182 2.0466 -0.6014 -2.0298 5/1/2014 2.457 2.0812 -6.3619 -8.8189 -0.3758 6/1/2014 2.516 1.8879 -1.6903 -4.2063 -0.6281 7/1/2014 2.556 -1.5195 5.5787 3.0227 -4.0755 8/1/2014 2.343 3.6964 0.3282 -2.0148 1.3534 9/1/2014 2.508 -1.5635 -1.2928 -3.8008 -4.0715 10/1/2014 2.335 2.2936 -14.3826 -16.7176 -0.0414 11/1/2014 2.194 2.4237 -1.3657 -3.5597 0.2297 12/1/2014 2.17 -0.4197 -1.0725 -3.2425 -2.5897 1/1/2015 1.675 -3.1533 -4.5458 -6.2208 -4.8283 2/1/2015 2.002 5.3439 5.4764 3.4744 3.3419 3/1/2015 1.934 -1.7549 -0.8932 -2.8272 -3.6889 4/1/2015 2.046 0.8485 6.5064 4.4604 -1.1975 5/1/2015 2.095 1.0437 -0.9621 -3.0571 -1.0513 6/1/2015 2.335 -2.1236 -4.2075 -6.5425 -4.4586 7/1/2015 2.205 1.9550 -0.4128 -2.6178 -0.2500

1..8 Estimation of CAPM for IBM

 Date CAPM Date CAPM 2/1/2010 11/1/2012 -3.56455 3/1/2010 -2.98785 12/1/2012 -1.76906 4/1/2010 -3.04909 1/1/2013 1.17901 5/1/2010 -4.97757 2/1/2013 -2.99866 6/1/2010 -3.84307 3/1/2013 1.372211 7/1/2010 -0.56164 4/1/2013 -5.34834 8/1/2010 -5.23661 5/1/2013 -0.86307 9/1/2010 2.515487 6/1/2013 -7.85119 10/1/2010 1.390917 7/1/2013 -1.51123 11/1/2010 -3.792 8/1/2013 -6.97573 12/1/2010 -0.94387 9/1/2013 -1.79999 1/1/2011 2.792546 10/1/2013 -4.71902 2/1/2011 -3.29795 11/1/2013 -2.68279 3/1/2011 -2.83062 12/1/2013 -0.3962 4/1/2011 -0.43582 1/1/2014 -6.4445 5/1/2011 -3.62345 2/1/2014 0.069555 6/1/2011 -2.1584 3/1/2014 -0.46782 7/1/2011 0.673323 4/1/2014 -1.53805 8/1/2011 -5.95061 5/1/2014 -6.54798 9/1/2011 -1.30356 6/1/2014 -3.73579 10/1/2011 0.813767 7/1/2014 0.671498 11/1/2011 -1.32939 8/1/2014 -2.39976 12/1/2011 -3.66299 9/1/2014 -3.48857 1/1/2012 0.556555 10/1/2014 -11.3636 2/1/2012 -1.08317 11/1/2014 -3.34162 3/1/2012 1.064031 12/1/2014 -3.14822 4/1/2012 -2.79936 1/1/2015 -4.96399 5/1/2012 -6.45982 2/1/2015 0.94685 6/1/2012 -1.34161 3/1/2015 -2.89502 7/1/2012 -1.95643 4/1/2015 1.547989 8/1/2012 -2.47621 5/1/2015 -3.03515 9/1/2012 1.650793 6/1/2015 -5.16013 10/1/2012 -6.11967 7/1/2015 -2.76733

The CAPM is calculated from the regression analysis. The calculation of the CAPM is given by the following equation:

CAPM = -1.17 + 0.61 * Excess Return

 Regression Statistics Multiple R 0.4951 R Square 0.2452 Adjusted R Square 0.23 Standard Error 3.96 Observations 65

 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1.17 0.53 -2.225 0.03 -2.22 -0.12 Xt 0.61 0.13 4.524 0.000 0.34 0.88

The coefficients of the regression analysis show that, if the excess return on the stocks is zero, then the market return of the stocks will be -1.17. With one-unit increase in the excess return of the stocks, the market return of the stocks will increase by 0.61.

The coefficient of determination (R Square) value indicates that the excess return on the stocks will be able to explain 24.51 percent of the variability in the market return of the stocks. The average excess stock returns of IBM are supposed to lie between 0.34 and 0.88 with 95 percent confidence.

1.9 Determination of Neutral Stock

It can be seen clearly from the computations of the confidence interval that the average return on the stocks of IBM lies between -0.76 and 1.50 with 95 percent confidence. There is always a possibility that the stocks will not have any returns. Thus, this stock can be termed as a neutral stock.

 Confidence Interval for the mean Data Sample Standard Deviation 4.5661 Sample Mean 0.37 Sample Size 65 Confidence Level 95% Is Pop StDev known? Y/N N Intermediate Calculations Standard Error of the Mean 0.5664 Degrees of Freedom 64 t Value 1.9977 Margin of Error 1.1314 Confidence Interval Interval Lower Limit -0.76 Interval Upper Limit 1.50

From the results of the Jarque-Berra test, it can be said that the errors in the developed model of prediction of CAPM is normally distributed. The following figure also shows that the errors are normally distributed as they follow a linear trend.

 Test for Normality of Residuals Skewness -0.755 Kurtosis 2.915 Count 65 Jarque-Berra test Statistic 29.181 P-Value 0.000

Introduction:

There is availability of two different stocks in the market. One is the stock prices of Boeing company and the other is the stock prices of IBM (International Business Machines). Historical data on the monthly stock prices of these two companies have been collected from finance.yahoo.com for the time frame of 2nd Feb, 2010 to 31st July, 2015. The S&P price index of this time frame and the interest rate of the 10 year US Treasury Note has been collected from the same website. The client is interested to invest in the stocks of one of two available companies Boeing or IBM. Thus, the main interest of this study is to identify which of the two stocks will be better and safer to invest. For this, the risk on the stock prices and the returns from the stocks are to be compared over the time frame to assess which stock would be better to invest. The necessary analysis will be conducted using appropriate statistical techniques and on Microsoft Excel.

Referance:

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2016. Statistics for business & economics. Nelson Education.

Ruppert, D., 2014. Statistics and finance: an introduction. Springer.

Swift, L. and Piff, S., 2014. Quantitative methods: for business, management and finance. Palgrave Macmillan.

Asongu, S.A. and Moulin, B., 2016. Research in International Business and Finance.

Sullivan III, M., 2015. Fundamentals of statistics. Pearson.

Cite This Work

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