You have been directed to study U.S stock markets, and have been provided the monthlyadjusted close price of Apple Inc. (APPL), S&P500 index and NASDAQ index for the period of January 2001 ? December 2016.

Please complete the following questions:

1. Calculate monthly discrete returns (hint: holding period returns) for the S&P 500 index, NASDAQ index, and Apple Inc. (APPL) stock prices, respectively.

2. Compute descriptive statistics for monthly Apple Inc. (APPL) stock prices, S&P500 index and NASDAQ index, respectively.

3. Construct the frequency distributions (including relative frequency and cumulative frequency) for APPL returns, S&P 500 index returns and NASDAQ index returns, respectively. Use 10 intervals.

4. What is the probability of the S&P 500 index returns above 10%? What is the probability of the NASDAQ index returns being between 2% and 8%?

5. Is the distribution of monthly APPL returns Normal distribution? Are the distributions of S&P 500 index returns and NASDAQ index returns different? Provide evidences.

6. In order to predict the monthly APPL returns, your supervisor advised two simple linear regression models: Model A: Assuming a linear relationship between monthly APPL returns and S&P 500 index returns. Model B: Assuming a linear relationship between monthly APPL returns and NASDAQ index returns

6.1: For model A, test if the intercept coefficient is significant at the 5% level; Calculate 95% confidence interval for the slope coefficient.

6.2: For model B, Predict the APPL return when NASDAQ index return being 2%, and calculate its 90 percent prediction interval.

qattachments_7385adcfbe1800a6042cbf2ba7876566b7e16a51 Date S&P500 NASDAQ APPLE 2/01/2001 1366.01001 2772.72998 1.4 1/02/2001 1239.939941 2151.830078 1.18 1/03/2001 1160.329956 1840.26001 1.43 2/04/2001 1249.459961 2116.23999 1.65 1/05/2001 1255.819946 2110.48999 1.29 1/06/2001 1224.380005 2160.540039 1.51 2/07/2001 1211.22998 2027.130005 1.22 1/08/2001 1133.579956 1805.430054 1.2 4/09/2001 1040.939941 1498.800049 1 1/10/2001 1059.780029 1690.199951 1.14 1/11/2001 1139.449951 1930.579956 1.38 3/12/2001 1148.079956 1950.400024 1.42 2/01/2002 1130.199951 1934.030029 1.6 1/02/2002 1106.72998 1731.48999 1.41 1/03/2002 1147.390015 1845.349976 1.53 1/04/2002 1076.920044 1688.22998 1.57 1/05/2002 1067.140015 1615.72998 1.51 3/06/2002 989.820007 1463.209961 1.15 1/07/2002 911.619995 1328.26001 0.99 1/08/2002 916.070007 1314.849976 0.96 3/09/2002 815.280029 1172.060059 0.94 1/10/2002 885.76001 1329.75 1.04 1/11/2002 936.309998 1478.780029 1 2/12/2002 879.820007 1335.51001 0.93 2/01/2003 855.700012 1320.910034 0.93 3/02/2003 841.150024 1337.52002 0.97 3/03/2003 848.179993 1341.170044 0.92 1/04/2003 916.919983 1464.310059 0.92 1/05/2003 963.590027 1595.910034 1.16 2/06/2003 974.5 1622.800049 1.23 1/07/2003 990.309998 1735.02002 1.37 1/08/2003 1008.01001 1810.449951 1.46 2/09/2003 995.969971 1786.939941 1.34 1/10/2003 1050.709961 1932.209961 1.48 3/11/2003 1058.199951 1960.26001 1.35 1/12/2003 1111.920044 2003.369995 1.38 2/01/2004 1131.130005 2066.149902 1.46 2/02/2004 1144.939941 2029.819946 1.55 1/03/2004 1126.209961 1994.219971 1.75 1/04/2004 1107.300049 1920.150024 1.67 3/05/2004 1120.680054 1986.73999 1.82 1/06/2004 1140.839966 2047.790039 2.11 1/07/2004 1101.719971 1887.359985 2.09 2/08/2004 1104.23999 1838.099976 2.23 1/09/2004 1114.579956 1896.839966 2.51 1/10/2004 1130.199951 1974.98999 3.39 1/11/2004 1173.819946 2096.810059 4.34 1/12/2004 1211.920044 2175.439941 4.17 3/01/2005 1181.27002 2062.409912 4.98 1/02/2005 1203.599976 2051.719971 5.81 1/03/2005 1180.589966 1999.22998 5.4 1/04/2005 1156.849976 1921.650024 4.67 Page 1 qattachments_7385adcfbe1800a6042cbf2ba7876566b7e16a51 2/05/2005 1/06/2005 1/07/2005 1/08/2005 1/09/2005 3/10/2005 1/11/2005 1/12/2005 3/01/2006 1/02/2006 1/03/2006 3/04/2006 1/05/2006 1/06/2006 3/07/2006 1/08/2006 1/09/2006 2/10/2006 1/11/2006 1/12/2006 3/01/2007 1/02/2007 1/03/2007 2/04/2007 1/05/2007 1/06/2007 2/07/2007 1/08/2007 4/09/2007 1/10/2007 1/11/2007 3/12/2007 2/01/2008 1/02/2008 3/03/2008 1/04/2008 1/05/2008 2/06/2008 1/07/2008 1/08/2008 2/09/2008 1/10/2008 3/11/2008 1/12/2008 2/01/2009 2/02/2009 2/03/2009 1/04/2009 1/05/2009 1/06/2009 1/07/2009 3/08/2009 1/09/2009 1191.5 1191.329956 1234.180054 1220.329956 1228.810059 1207.01001 1249.47998 1248.290039 1280.079956 1280.660034 1294.869995 1310.609985 1270.089966 1270.199951 1276.660034 1303.819946 1335.849976 1377.939941 1400.630005 1418.300049 1438.23999 1406.819946 1420.859985 1482.369995 1530.619995 1503.349976 1455.27002 1473.98999 1526.75 1549.380005 1481.140015 1468.359985 1378.550049 1330.630005 1322.699951 1385.589966 1400.380005 1280 1267.380005 1282.829956 1166.359985 968.75 896.23999 903.25 825.880005 735.090027 797.869995 872.809998 919.140015 919.320007 987.47998 1020.619995 1057.079956 2068.219971 2056.959961 2184.830078 2152.090088 2151.689941 2120.300049 2232.820068 2205.320068 2305.820068 2281.389893 2339.790039 2322.570068 2178.879883 2172.090088 2091.469971 2183.75 2258.429932 2366.709961 2431.77002 2415.290039 2463.929932 2416.149902 2421.639893 2525.090088 2604.52002 2603.22998 2546.27002 2596.360107 2701.5 2859.120117 2660.959961 2652.280029 2389.860107 2271.47998 2279.100098 2412.800049 2522.659912 2292.97998 2325.550049 2367.52002 2091.879883 1720.949951 1535.569946 1577.030029 1476.420044 1377.839966 1528.589966 1717.300049 1774.329956 1835.040039 1978.5 2009.060059 2122.419922 5.15 4.77 5.53 6.08 6.95 7.46 8.79 9.31 9.78 8.87 8.13 9.12 7.74 7.42 8.8 8.79 9.97 10.5 11.88 10.99 11.11 10.96 12.04 12.93 15.7 15.81 17.07 17.94 19.88 24.61 23.61 25.66 17.54 16.2 18.59 22.54 24.45 21.69 20.59 21.96 14.73 13.94 12.01 11.06 11.68 11.57 13.62 16.3 17.6 18.45 21.17 21.79 24.01 Page 2 qattachments_7385adcfbe1800a6042cbf2ba7876566b7e16a51 1/10/2009 2/11/2009 1/12/2009 4/01/2010 1/02/2010 1/03/2010 1/04/2010 3/05/2010 1/06/2010 1/07/2010 2/08/2010 1/09/2010 1/10/2010 1/11/2010 1/12/2010 3/01/2011 1/02/2011 1/03/2011 1/04/2011 2/05/2011 1/06/2011 1/07/2011 1/08/2011 1/09/2011 3/10/2011 1/11/2011 1/12/2011 3/01/2012 1/02/2012 1/03/2012 2/04/2012 1/05/2012 1/06/2012 2/07/2012 1/08/2012 4/09/2012 1/10/2012 1/11/2012 3/12/2012 2/01/2013 1/02/2013 1/03/2013 1/04/2013 1/05/2013 3/06/2013 1/07/2013 1/08/2013 3/09/2013 1/10/2013 1/11/2013 2/12/2013 2/01/2014 3/02/2014 1036.189941 1095.630005 1115.099976 1073.869995 1104.48999 1169.430054 1186.689941 1089.410034 1030.709961 1101.599976 1049.329956 1141.199951 1183.26001 1180.550049 1257.640015 1286.119995 1327.219971 1325.829956 1363.609985 1345.199951 1320.640015 1292.280029 1218.890015 1131.420044 1253.300049 1246.959961 1257.599976 1312.410034 1365.680054 1408.469971 1397.910034 1310.329956 1362.160034 1379.319946 1406.579956 1440.670044 1412.160034 1416.180054 1426.189941 1498.109985 1514.680054 1569.189941 1597.569946 1630.73999 1606.280029 1685.72998 1632.969971 1681.550049 1756.540039 1805.810059 1848.359985 1782.589966 1859.449951 2045.109985 2144.600098 2269.149902 2147.350098 2238.26001 2397.959961 2461.189941 2257.040039 2109.23999 2254.699951 2114.030029 2368.620117 2507.409912 2498.22998 2652.870117 2700.080078 2782.27002 2781.070068 2873.540039 2835.300049 2773.52002 2756.379883 2579.459961 2415.399902 2684.409912 2620.340088 2605.149902 2813.840088 2966.889893 3091.570068 3046.360107 2827.340088 2935.050049 2939.52002 3066.959961 3116.22998 2977.22998 3010.23999 3019.51001 3142.129883 3160.189941 3267.52002 3328.790039 3455.909912 3403.25 3626.370117 3589.870117 3771.47998 3919.709961 4059.889893 4176.589844 4103.879883 4308.120117 24.42 25.9 27.3 24.88 26.51 30.45 33.83 33.28 32.59 33.33 31.5 36.76 38.99 40.31 41.79 43.96 45.76 45.15 45.36 45.06 43.49 50.59 49.86 49.4 52.44 49.52 52.47 59.14 70.28 77.68 75.66 74.85 75.66 79.13 86.56 86.8 77.46 76.5 69.56 59.54 58.03 58.2 58.21 59.52 52.48 59.89 64.91 63.51 69.63 74.51 75.17 67.08 70.93 Page 3 qattachments_7385adcfbe1800a6042cbf2ba7876566b7e16a51 3/03/2014 1/04/2014 1/05/2014 2/06/2014 1/07/2014 1/08/2014 2/09/2014 1/10/2014 3/11/2014 1/12/2014 2/01/2015 2/02/2015 2/03/2015 1/04/2015 1/05/2015 1/06/2015 1/07/2015 3/08/2015 1/09/2015 1/10/2015 2/11/2015 1/12/2015 4/01/2016 1/02/2016 1/03/2016 1/04/2016 2/05/2016 1/06/2016 1/07/2016 1/08/2016 1/09/2016 3/10/2016 1/11/2016 1/12/2016 1872.339966 1883.949951 1923.569946 1960.22998 1930.670044 2003.369995 1972.290039 2018.050049 2067.560059 2058.899902 1994.98999 2104.5 2067.889893 2085.51001 2107.389893 2063.110107 2103.840088 1972.180054 1920.030029 2079.360107 2080.409912 2043.939941 1940.23999 1932.22998 2059.73999 2065.300049 2096.949951 2098.860107 2173.600098 2170.949951 2168.27002 2126.149902 2198.810059 2238.830078 4198.990234 4114.560059 4242.620117 4408.180176 4369.77002 4580.27002 4493.390137 4630.740234 4791.629883 4736.049805 4635.240234 4963.529785 4900.879883 4941.419922 5070.029785 4986.870117 5128.279785 4776.509766 4620.160156 5053.75 5108.669922 5007.410156 4613.950195 4557.950195 4869.850098 4775.359863 4948.049805 4842.669922 5162.129883 5213.220215 5312 5189.140137 5323.680176 5383.120117 72.35 79.54 85.8 88.18 90.71 97.74 96.07 102.98 113.9 105.71 112.2 123.51 119.64 120.33 125.78 121.1 117.11 109.36 106.98 115.9 115.23 102.52 94.81 94.69 106.73 91.8 98.39 94.19 102.67 105.1 111.99 112.47 110.04 115.32 Page 4