In: Finance
Please answer the following questions using the data in the attached Excel file.
You are thinking of investing in Abercrombie and Fitch Co. (ANF). The returns for ANF are embedded in an Excel document below (Source: yahoo.com).
1. For the investment in ANF that you are considering, for all of 2012 determine the following items:
a) the mean return
b) the median return
c) the standard deviation
d) the variance
e) the coefficient of variation
The weekly rates of return for ANF stock and the overall market are embedded. Weekly returns of the markets are based on the S&P Index. Using linear regression analysis, please answer the following questions.
a) Write the equation for the relationship between ANF’s stock price and the overall market. In other words, what is the estimated relationship between ANF’s stock price and the overall market?
b) What percentage of the variability in ANF’s stock price can be explained by the relationship to the returns of the overall market? (Note: this is a measure of the stock’s market-related risk.)
c) Would you recommend using the estimated linear relationship as an estimate of the likely change in ANF’s stock price given an estimate of the likely change in the S&P index? Why or why not? Be specific in your answer.
Weekly Investment Data | |||||||||||||||
S&P Index | ANF - Abercrombie & Fitch Co. | ||||||||||||||
Date | Open | High | Low | Close | Volume | Adj Close | Return | Open | High | Low | Close | Volume | Adj Close | Return | |
12/24/2012 | 1430.15 | 1430.15 | 1401.8 | 1418.1 | 2121390000 | 1418.1 | -0.84% | 47.33 | 48.04 | 44.87 | 46.16 | 1608500 | 46.16 | -2.55% | |
12/17/2012 | 1413.54 | 1448 | 1413.54 | 1430.15 | 4108678000 | 1430.15 | 1.17% | 47 | 49.1 | 46.2 | 47.37 | 2724100 | 47.37 | 1.26% | |
12/10/2012 | 1418.07 | 1438.59 | 1411.88 | 1413.58 | 3383768000 | 1413.58 | -0.32% | 47.48 | 47.97 | 46.17 | 46.78 | 2844000 | 46.78 | 0.84% | |
12/3/2012 | 1416.34 | 1423.73 | 1398.23 | 1418.07 | 3386154000 | 1418.07 | 0.13% | 46.03 | 46.63 | 44.79 | 46.39 | 2408200 | 46.39 | 1.09% | |
11/26/2012 | 1409.15 | 1419.7 | 1385.43 | 1416.18 | 3390836000 | 1416.18 | 0.50% | 45.1 | 46.33 | 44.02 | 45.89 | 3931800 | 45.89 | 3.36% | |
11/19/2012 | 1359.88 | 1409.16 | 1359.88 | 1409.15 | 2688502500 | 1409.15 | 3.62% | 41.26 | 44.52 | 41.09 | 44.4 | 3451900 | 44.4 | 9.06% | |
11/12/2012 | 1379.86 | 1388.81 | 1343.35 | 1359.88 | 3621476000 | 1359.88 | -1.45% | 31.41 | 42.9 | 30.74 | 40.87 | 11496600 | 40.71 | 29.69% | |
11/5/2012 | 1414.02 | 1433.38 | 1373.03 | 1379.85 | 3602274000 | 1379.85 | -2.43% | 32.69 | 34.43 | 31.16 | 31.52 | 2099400 | 31.39 | -3.86% | |
10/31/2012 | 1410.99 | 1434.27 | 1405.95 | 1414.2 | 3746493300 | 1414.2 | 0.16% | 30.79 | 33.42 | 30.18 | 32.78 | 2638400 | 32.65 | 7.19% | |
10/22/2012 | 1433.21 | 1435.46 | 1403.28 | 1411.94 | 3397482000 | 1411.94 | -1.48% | 31.92 | 32.18 | 30.06 | 30.58 | 1904400 | 30.46 | -4.45% | |
10/15/2012 | 1428.75 | 1464.02 | 1427.24 | 1433.19 | 3692620000 | 1433.19 | 0.32% | 33.02 | 33.56 | 31.75 | 32.01 | 2308400 | 31.88 | -2.89% | |
10/8/2012 | 1460.93 | 1460.93 | 1425.53 | 1428.59 | 3115478000 | 1428.59 | -2.21% | 32.16 | 34.4 | 32.07 | 32.96 | 2085600 | 32.83 | 0.92% | |
10/1/2012 | 1440.9 | 1470.96 | 1439.01 | 1460.93 | 3429462000 | 1460.93 | 1.41% | 33.28 | 34.05 | 32.14 | 32.66 | 1857200 | 32.53 | -3.70% | |
9/24/2012 | 1459.76 | 1463.24 | 1430.53 | 1440.67 | 3394752000 | 1440.67 | -1.33% | 36.65 | 36.65 | 33.84 | 33.92 | 2321400 | 33.78 | -8.03% | |
9/17/2012 | 1465.42 | 1467.07 | 1449.98 | 1460.15 | 3705514000 | 1460.15 | -0.38% | 39.09 | 39.25 | 36.65 | 36.88 | 2212700 | 36.73 | -6.30% | |
9/10/2012 | 1437.92 | 1474.51 | 1428.98 | 1465.77 | 4004608000 | 1465.77 | 1.94% | 36.4 | 39.65 | 35.1 | 39.36 | 4790200 | 39.2 | 7.90% | |
9/4/2012 | 1406.54 | 1437.92 | 1396.56 | 1437.92 | 3564977500 | 1437.92 | 2.23% | 35.86 | 36.77 | 34.43 | 36.48 | 1656300 | 36.33 | 1.34% | |
8/27/2012 | 1411.13 | 1416.17 | 1397.01 | 1406.58 | 2628268000 | 1406.58 | -0.32% | 36.29 | 37 | 35.37 | 35.99 | 1585600 | 35.85 | -0.55% | |
8/20/2012 | 1417.85 | 1426.68 | 1398.04 | 1411.13 | 2943798000 | 1411.13 | -0.50% | 35.71 | 37.44 | 34.95 | 36.19 | 2348100 | 36.05 | 1.21% | |
8/13/2012 | 1405.87 | 1418.71 | 1397.32 | 1418.16 | 2824746000 | 1418.16 | 0.87% | 32.11 | 36.25 | 31.69 | 35.93 | 4546500 | 35.62 | 12.26% | |
8/6/2012 | 1391.04 | 1407.14 | 1391.04 | 1405.87 | 3182784000 | 1405.87 | 1.07% | 29.38 | 32.29 | 28.91 | 32.01 | 3519500 | 31.73 | 9.00% | |
7/30/2012 | 1385.94 | 1394.16 | 1354.65 | 1390.99 | 3883892000 | 1390.99 | 0.36% | 36.39 | 36.75 | 28.64 | 29.37 | 7705300 | 29.11 | -20.09% | |
7/23/2012 | 1362.34 | 1389.19 | 1329.24 | 1385.97 | 4031190000 | 1385.97 | 1.71% | 35.85 | 37 | 34.66 | 36.75 | 2309600 | 36.43 | 0.11% | |
7/16/2012 | 1356.5 | 1380.39 | 1345.07 | 1362.66 | 3608082000 | 1362.66 | 0.43% | 35.42 | 36.97 | 33.77 | 36.71 | 2861100 | 36.39 | 3.47% | |
7/9/2012 | 1354.66 | 1361.54 | 1325.41 | 1356.78 | 3333824000 | 1356.78 | 0.16% | 33.38 | 35.71 | 32.45 | 35.48 | 3820600 | 35.17 | 5.87% | |
7/2/2012 | 1362.33 | 1374.81 | 1348.03 | 1354.68 | 2801175000 | 1354.68 | -0.55% | 34.81 | 35.14 | 33.1 | 33.51 | 2195800 | 33.22 | -1.83% | |
6/25/2012 | 1334.9 | 1362.17 | 1309.27 | 1362.16 | 3752304000 | 1362.16 | 2.03% | 30.25 | 34.7 | 29.51 | 34.14 | 3268800 | 33.84 | 11.17% | |
6/18/2012 | 1342.42 | 1363.46 | 1324.41 | 1335.02 | 4027288000 | 1335.02 | -0.58% | 31.41 | 32.46 | 30.29 | 30.71 | 2327600 | 30.44 | -2.62% | |
6/11/2012 | 1325.72 | 1343.32 | 1306.62 | 1342.84 | 3715250000 | 1342.84 | 1.30% | 32.45 | 32.74 | 30.26 | 31.54 | 3239800 | 31.26 | -1.94% | |
6/4/2012 | 1278.29 | 1329.05 | 1266.74 | 1325.66 | 3887776000 | 1325.66 | 3.73% | 32.17 | 33.41 | 31.27 | 32.16 | 2580800 | 31.88 | 0.06% | |
5/29/2012 | 1318.9 | 1334.93 | 1277.25 | 1278.04 | 4050725000 | 1278.04 | -3.02% | 36.49 | 36.6 | 31.82 | 32.14 | 3554400 | 31.86 | -11.28% | |
5/21/2012 | 1295.73 | 1328.49 | 1295.73 | 1317.82 | 3765818000 | 1317.82 | 1.74% | 36.37 | 37.01 | 34.45 | 36.23 | 3505500 | 35.91 | 1.44% | |
5/14/2012 | 1351.93 | 1351.93 | 1291.98 | 1295.22 | 4251866000 | 1295.22 | -4.30% | 46.22 | 46.77 | 35.67 | 35.89 | 6231600 | 35.4 | -23.01% | |
5/7/2012 | 1368.79 | 1373.91 | 1343.13 | 1353.39 | 3941332000 | 1353.39 | -1.15% | 50.41 | 50.41 | 45.19 | 46.62 | 2962000 | 45.98 | -7.73% | |
4/30/2012 | 1403.26 | 1415.32 | 1367.96 | 1369.1 | 3833174000 | 1369.1 | -2.44% | 50.84 | 54.05 | 49.78 | 50.52 | 3129300 | 49.83 | -0.70% | |
4/23/2012 | 1378.53 | 1406.64 | 1358.79 | 1403.36 | 3790184000 | 1403.36 | 1.80% | 48.36 | 51.3 | 46.98 | 50.88 | 2106000 | 50.18 | 3.72% | |
4/16/2012 | 1370.27 | 1392.76 | 1365.38 | 1378.53 | 3701492000 | 1378.53 | 0.60% | 47.59 | 49.68 | 46.01 | 49.05 | 2171500 | 48.38 | 4.00% | |
4/9/2012 | 1397.45 | 1397.45 | 1357.38 | 1370.26 | 3818638000 | 1370.26 | -1.99% | 49.1 | 49.11 | 46.75 | 47.16 | 1787300 | 46.52 | -5.52% | |
4/2/2012 | 1408.47 | 1422.38 | 1392.92 | 1398.08 | 3659032500 | 1398.08 | -0.74% | 50.84 | 52.87 | 49.74 | 49.92 | 1855800 | 49.24 | 0.63% | |
3/26/2012 | 1397.11 | 1419.15 | 1391.56 | 1408.47 | 3698456000 | 1408.47 | 0.81% | 51.72 | 52.03 | 48.92 | 49.61 | 2095900 | 48.93 | -3.17% | |
3/19/2012 | 1404.17 | 1414 | 1386.87 | 1397.11 | 3682996000 | 1397.11 | -0.50% | 52.39 | 53.25 | 50.46 | 51.23 | 2056600 | 50.53 | -2.36% | |
3/12/2012 | 1370.78 | 1405.88 | 1366.69 | 1404.17 | 4281244000 | 1404.17 | 2.43% | 50.67 | 54.1 | 50.35 | 52.47 | 3129300 | 51.75 | 3.29% | |
3/5/2012 | 1369.59 | 1374.76 | 1340.03 | 1370.87 | 3676690000 | 1370.87 | 0.09% | 48.18 | 51.14 | 47.45 | 50.79 | 2656800 | 50.1 | 5.21% | |
2/27/2012 | 1365.2 | 1378.04 | 1354.92 | 1369.63 | 3782622000 | 1369.63 | 0.28% | 47.82 | 48.69 | 45.67 | 48.28 | 3208200 | 47.62 | 0.29% | |
2/21/2012 | 1361.22 | 1368.92 | 1352.28 | 1365.74 | 3680180000 | 1365.74 | 0.33% | 48.8 | 48.92 | 47.03 | 48.14 | 2276800 | 47.48 | -0.34% | |
2/13/2012 | 1343.06 | 1363.4 | 1340.8 | 1361.23 | 3882884000 | 1361.23 | 1.38% | 45.35 | 50.44 | 43.41 | 48.48 | 4778300 | 47.64 | 7.56% | |
2/6/2012 | 1344.32 | 1354.32 | 1335.92 | 1342.64 | 3861272000 | 1342.64 | -0.17% | 40.38 | 45.79 | 40.26 | 45.07 | 4189500 | 44.29 | 11.25% | |
1/30/2012 | 1316.16 | 1345.34 | 1300.49 | 1344.9 | 4225678000 | 1344.9 | 2.17% | 46.68 | 47.45 | 40.25 | 40.51 | 6803000 | 39.81 | -14.22% | |
1/23/2012 | 1315.29 | 1333.47 | 1306.06 | 1316.33 | 4080966000 | 1316.33 | 0.07% | 44.89 | 47.56 | 43.77 | 47.23 | 3111900 | 46.41 | 6.10% | |
1/17/2012 | 1290.22 | 1315.49 | 1290.22 | 1315.38 | 4121290000 | 1315.38 | 2.04% | 45.46 | 48.02 | 44.4 | 44.51 | 3630100 | 43.74 | -1.06% | |
1/9/2012 | 1277.83 | 1296.82 | 1274.55 | 1289.09 | 3854788000 | 1289.09 | 0.88% | 44.3 | 45.82 | 43.56 | 44.99 | 4016700 | 44.21 | 0.18% | |
1/3/2012 | 1258.86 | 1284.62 | 1258.86 | 1277.81 | 3877267500 | 1277.81 | 1.61% | 49.58 | 50.26 | 44.52 | 44.91 | 2866900 | 44.13 | -8.06% | |
12/28/2011 | 1265.38 | 1265.85 | 1248.64 | 1257.6 | 2299986600 | 1257.6 | 49.02 | 49.19 | 47.94 | 48.84 | 922000 | 48 | |||
Please refer to the table while checking the answers | SUMMARY OUTPUT | |||||||||||||
Market | ANF Stock Price | Regression Statistics | ||||||||||||
1418.1 | 46.16 | Multiple R | 0.070500058 | |||||||||||
Mean Return | 0.25% | 1430.15 | 47.37 | R Square | 0.004970258 | |||||||||
Median Return | 0.24% | 1413.58 | 46.78 | Adjusted R Square | -0.014540129 | |||||||||
Standard Dev | 8.09% | 1418.07 | 46.39 | Standard Error | 49.58342729 | |||||||||
Variance | 0.65% | 1416.18 | 45.89 | Observations | 53 | |||||||||
Coeff Of variation | 31.8 | 1409.15 | 44.4 | |||||||||||
1359.88 | 40.71 | ANOVA | ||||||||||||
1379.85 | 31.39 | df | SS | MS | F | Significance F | ||||||||
1414.2 | 32.65 | Regression | 1 | 626.3054 | 626.3054 | 0.254749 | 0.615925 | |||||||
1411.94 | 30.46 | Residual | 51 | 125384.3 | 2458.516 | |||||||||
1433.19 | 31.88 | Total | 52 | 126010.6 | ||||||||||
1428.59 | 32.83 | |||||||||||||
1460.93 | 32.53 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||
1440.67 | 33.78 | Intercept | 1397.960671 | 39.85006 | 35.08051 | 2.24E-37 | 1317.958 | 1477.963 | 1317.958 | 1477.963 | ||||
1460.15 | 36.73 | X Variable 1 | -0.490712323 | 0.972233 | -0.50473 | 0.615925 | -2.44255 | 1.461127 | -2.44255 | 1.461127 | ||||
1465.77 | 39.2 | |||||||||||||
1437.92 | 36.33 | |||||||||||||
1406.58 | 35.85 | |||||||||||||
1411.13 | 36.05 | |||||||||||||
1418.16 | 35.62 | |||||||||||||
1405.87 | 31.73 | |||||||||||||
1390.99 | 29.11 | |||||||||||||
1385.97 | 36.43 | |||||||||||||
1362.66 | 36.39 | |||||||||||||
1356.78 | 35.17 | |||||||||||||
1354.68 | 33.22 | |||||||||||||
1362.16 | 33.84 | |||||||||||||
1335.02 | 30.44 | |||||||||||||
1342.84 | 31.26 | |||||||||||||
1325.66 | 31.88 | |||||||||||||
1278.04 | 31.86 | |||||||||||||
1317.82 | 35.91 | |||||||||||||
1295.22 | 35.4 | |||||||||||||
1353.39 | 45.98 | |||||||||||||
1369.1 | 49.83 | |||||||||||||
1403.36 | 50.18 | |||||||||||||
1378.53 | 48.38 | |||||||||||||
1370.26 | 46.52 | |||||||||||||
1398.08 | 49.24 | |||||||||||||
1408.47 | 48.93 | |||||||||||||
1397.11 | 50.53 | |||||||||||||
1404.17 | 51.75 | |||||||||||||
1370.87 | 50.1 | |||||||||||||
1369.63 | 47.62 | |||||||||||||
1365.74 | 47.48 | |||||||||||||
1361.23 | 47.64 | |||||||||||||
1342.64 | 44.29 | |||||||||||||
1344.9 | 39.81 | |||||||||||||
1316.33 | 46.41 | |||||||||||||
1315.38 | 43.74 | |||||||||||||
1289.09 | 44.21 | |||||||||||||
1277.81 | 44.13 | |||||||||||||
1257.6 | 48 | |||||||||||||
Liner regression output using solver is only giving output with R^2 = 0.005 which is less and hence cannot be used , we can use multiple linear regresssion of order 3 or higher. |