1. Verizon

ATT:

2.

Verizon:

ATT:

Problem 1 On Monday January 17, 2017 an investor wanted to invest $1,000,000 in two stocks Verizon (VZ) and ATT (T). Using historical adjusted weekly closes from January 2, 2016 to January 15, 2017 1. Find the proportions of the portfolio with minimal risk. 2. As of June 23, 2017, find the market value of this portfolio and deduce the rate of return of this investment. Date Open High Low Close Adj Close Volume 2016-01-01 45.669998 46.549999 45.000000 45.270000 37.050316 71814700 2016-01-08 45.660000 45.740002 44.049999 44.869999 37.174633 83670000 2016-01-15 44.040001 46.330002 43.790001 45.869999 38.003132 108002500 2016-01-22 46.410000 49.490002 46.000000 49.009998 40.604607 123876300 2016-01-29 49.389999 51.020000 49.220001 50.430000 41.781082 119130300 2016-02-05 50.320000 51.200001 49.270000 49.389999 40.919437 124636400 2016-02-12 49.540001 51.099998 49.349998 50.939999 42.203606 72258300 2016-02-19 50.740002 51.299999 50.169998 51.110001 42.344452 63261200 2016-02-26 51.150002 52.220001 50.689999 51.889999 42.990681 71196700 2016-03-04 51.750000 52.959999 51.400002 52.320000 43.346935 73740300 2016-03-11 52.650002 53.810001 52.230000 53.630001 44.432270 66516900 2016-03-18 53.810001 53.849998 52.660000 53.560001 44.374279 69552900 2016-03-25 53.560001 54.369999 53.200001 54.080002 44.805096 46254500 2016-04-01 53.320000 54.490002 51.770000 52.000000 43.081814 74258800 2016-04-08 52.200001 52.580002 50.840000 51.360001 43.000736 69345000 2016-04-15 51.279999 52.220001 49.470001 50.029999 41.887215 85163000 2016-04-22 50.150002 51.810001 50.049999 51.020000 42.716084 70395100 2016-04-29 50.950001 51.450001 50.200001 50.840000 42.565380 57511900 2016-05-06 50.910000 51.700001 50.610001 51.470001 43.092846 44831600 2016-05-13 51.410000 51.490002 49.119999 49.630001 41.552322 54397000 2016-05-20 49.799999 50.279999 49.049999 50.160000 41.996059 60970600 2016-05-27 50.389999 51.160000 50.119999 50.770000 42.506767 45875900 2016-06-03 50.770000 52.000000 50.599998 51.950001 43.494717 55124100 2016-06-10 51.860001 53.480000 51.720001 53.459999 44.758949 60962600 2016-06-17 53.430000 54.680000 53.009998 54.669998 45.772015 70362700 2016-06-24 54.470001 55.919998 53.880001 55.840000 46.751587 124520900 2016-07-01 | 55.849998 56.950001 55.099998 55.380001 46.366463 66131100 2016-07-08 | 55.389999 56.099998 55.009998 55.840000 47.223568 65782600 2016-07-15 | 56.049999 56.080002 55.240002 55.369999 46.826099 55653900 2016-07-22 | 55.439999 56.250000 54.439999 54.860001 46.394791 68322700 2016-07-29 | 54.990002 55.820000 53.630001 53.930000 45.608295 73110900 2016-08-05 | 53.939999 53.990002 53.330002 53.860001 45.549099 47897200 2016-08-12 53.959999 53.980000 52.380001 52.869999 44.711861 53974000 2016-08-19 | 52.889999 52.910000 52.160000 52.750000 44.610371 45530800 2016-08-26 | 52.639999 53.009998 51.900002 52.560001 44.449703 56606900 2016-09-02| 52.799999 53.880001 52.520000 53.599998 45.329224 50128500 2016-09-09 | 53.130001 53.240002 51.119999 51.980000 43.959190 76488700 2016-09-16| 51.889999 52.490002 51.020000 52.349998 44.272091 75703700 2016-09-23 52.299999 52.820000 51.770000 52.119999 44.077587 55916600 2016-09-30 | 52.430000 52.570000 49.970001 50.259998 42.504597 64866100 2016-10-07 | 50.459999 50.540001 49.630001 50.290001 43.014580 56279400 2016-10-14| 50.340000 50.630001 48.900002 49.139999 42.030945 67914800 2016-10-21 | 48.790001 48.930000 47.580002 48.540001 41.517750 98020800 2016-10-28 48.560001 48.770000 46.790001 46.869999 40,089344 65442200 2016-11-04 46.970001 48.080002 46.360001 46.689999 39.935387 83781400 2016-11-11 46.700001 48.169998 46.009998 47.840000 40.919022 86682600 2016-11-18 47.849998 50.650002 47.570000 50.230000 42.963261 667080600 2016-11-25|50.220001 51.200001 49.310001 49.869999 42.655334 69284000 2016-12-02 | 50.000000 51,430000 49.599998 51.130001 43.733059 65090400 2016-12-09 | 51.090000 52.660000 50.919998 51.810001 44.314682 72383400 2016-12-16 | 52.060001 53.740002 51.860001 53.650002 45.888496 65794600 2016-12-23 53.650002 53.900002 53.369999 53.740002 45.965473 27456900 2016-12-30 | 53.549999 54.830002 53.169998 54.639999 46.735260 67489200 2017-01-06 | 53.669998 53.779999 52.020000 52.680000 45.058811 68694500 2017-01-13| 52.720001 52.900002 52.410000 52.549999 45.427750 9458700 Date Open High Low Close Adj Close Volume 2016-01-01 34.080002 34.689999 33.509998 33.509998 26.160191 124510000 2016-01-08 33.770000 34.549999 33.410000 34.299999 27.153730 155222400 2016-01-15 33.660000 34.880001 33.430000 34.540001 27.343727 173180200 2016-01-22 34.880001 35.799999 34.700001 35.529999 28.127464 181528700 2016-01-29 35.709999 36.820000 35.680000 36.529999 28.919119 174813700 2016-02-05 36.590000 37.119999 35.910000 36.209999 28.665787 180077600 2016-02-12 36.349998 37.000000 36.049999 36.990002 29.283279 102049100 2016-02-19 36.900002 37.500000 36.509998 37.369999 29.584105 112231400 2016-02-26 37.490002 38.110001 36.950001 37.990002 30.074936 120088800 2016-03-04 37.910000 38.419998 37.610001 38.310001 30.328259 114743600 2016-03-11 38.450001 39.189999 38.099998 39.119999 30.969505 101998900 2016-03-18 39.230000 39.259998 38.369999 38.880001 30.779503 122415500 2016-03-25 39.000000 39.720001 38.810001 39.169998 31.009079 100285400 2016-04-01 38.669998 39.360001 38.220001 38.590000 30.549921 115204300 2016-04-08 38.730000 38.900002 38.189999 38.419998 30.792492 89299600 2016-04-15 38.459999 39.009998 37.849998 37.860001 30.343668 98070900 2016-04-22 37.849998 38.910000 37.730000 38.639999 30.968819 124406100 2016-04-29 38.639999 39.150002 38.480000 38.740002 31.048965 100955500 2016-05-06 38.779999 39.669998 38.470001 39.549999 31.698154 79684400 2016-05-13 39.490002 39.520000 37.770000 38.439999 30.808521 106391500 2016-05-20 38.639999 38.990002 38.259998 38.840000 31.129110 80483600 2016-05-27 38.830002 39.200001 38.580002 38.840000 31.129110 72969100 2016-06-03 38.970001 40.169998 38.930000 40.090000 32.130947 96015300 2016-06-10 39.950001 40.570000 39.880001 40.490002 32.451542 105156000 2016-06-17 40.540001 41.889999 40.330002 41.880001 33.565575 106713100 2016-06-24 41.450001 43.419998 41.290001 43.209999 34.631527 184606500 2016-07-01 43.209999 43.889999 42.130001 42.299999 33.902199 108984700 2016-07-08 | 42.130001 42.959999 41.700001 42.770000 34.662693 100221700 2016-07-15| 42.910000 43.080002 42.340000 42.520000 34.460087 78381800 2016-07-22 42.529999 43.439999 42.279999 42.580002 34.508713 98716000 2016-07-29 | 42.619999 43.500000 42.459999 43.080002 34.913933 91017400 2016-08-05| 43.160000 43.480000 42.770000 43.389999 35.165169 72128200 2016-08-12 43.410000 43.459999 41.110001 41.400002 33.552391 120327000 2016-08-19] 41.230000 41.250000 40.549999 41.070000 33.284946 95260700 2016-08-26 41.130001 41.290001 40.599998 40.959999 33.195789 76469400 2016-09-02 41.090000 41.389999 40.740002 41.189999 33.382191 661655500 2016-09-09 | 40.980000 41,080002 39.549999 40.450001 32.782467 140369200 2016-09-16| 40.340000 41.189999 39.860001 41.110001 33.317352 113145400 2016-09-23| 41.150002 41.700001 40.439999 40.730000 33.009384 97342000 2016-09-30 | 40.910000 41.040001 38.830002 39.110001 31.696466 107494700 2016-10-07 | 39.220001 39.490002 38.209999 39.369999 32.295708 95234100 2016-10-14| 39.410000 39.580002 38.500000 38.650002 31.705078 86283500 2016-10-21| 38.400002 38.669998 36.270000 36.520000 29.957819 299898300 2016-10-28 | 36.650002 37.189999 36.299999 36.630001 30.048052 133817700 2016-11-04 | 36.779999 37.529999 36.400002 36.570000 29.998831 135223300 2016-11-11| 36.509998 37.689999 36.099998 37.410000 30.687893 114355000 2016-11-18| 37.450001 38.970001 37.299999 38.730000 31.770702 81725000 2016-11-25| 38.770000 39.669998 38.160000 38.880001 31.893757 117435800 2016-12-02 | 38.840000 40.750000 38.470001 40.410000 33.148830 115407900 2016-12-09 | 40.279999 41.680000 40.169998 41.500000 34.042969 120995200 2016-12-16| 41.650002 42.779999 41.419998 42.720001 35.043755 100996400 2016-12-23| 42.790001 42.840000 42.470001 42,660000 34.994534 44494200 2016-12-30 | 42.759998 43.029999 42.450001 42.650002 34.986332 91594800 2017-01-06|41.980000 42,000000 40.240002 41.009998 33.641014 124131200 2017-01-13| 40.919998 41.180000 40.790001 40.959999 33.990513 13932200 Currency in USD Download Date Open High Low Close* Adj Close** Volume Jun 23, 2017 45.43 45.46 45.30 45.39 39.71 10,069,700 *Close price adjusted for splits. **Adjusted close price adjusted for both dividends and splits. Currency in USD Download Date Open High Low Close* Adj Close** Volume Jun 23, 2017 38.16 38.16 37.82 37.95 31.87 22,906,600 *Close price adjusted for splits. **Adjusted close price adjusted for both dividends and splits. Problem 1 On Monday January 17, 2017 an investor wanted to invest $1,000,000 in two stocks Verizon (VZ) and ATT (T). Using historical adjusted weekly closes from January 2, 2016 to January 15, 2017 1. Find the proportions of the portfolio with minimal risk. 2. As of June 23, 2017, find the market value of this portfolio and deduce the rate of return of this investment. Date Open High Low Close Adj Close Volume 2016-01-01 45.669998 46.549999 45.000000 45.270000 37.050316 71814700 2016-01-08 45.660000 45.740002 44.049999 44.869999 37.174633 83670000 2016-01-15 44.040001 46.330002 43.790001 45.869999 38.003132 108002500 2016-01-22 46.410000 49.490002 46.000000 49.009998 40.604607 123876300 2016-01-29 49.389999 51.020000 49.220001 50.430000 41.781082 119130300 2016-02-05 50.320000 51.200001 49.270000 49.389999 40.919437 124636400 2016-02-12 49.540001 51.099998 49.349998 50.939999 42.203606 72258300 2016-02-19 50.740002 51.299999 50.169998 51.110001 42.344452 63261200 2016-02-26 51.150002 52.220001 50.689999 51.889999 42.990681 71196700 2016-03-04 51.750000 52.959999 51.400002 52.320000 43.346935 73740300 2016-03-11 52.650002 53.810001 52.230000 53.630001 44.432270 66516900 2016-03-18 53.810001 53.849998 52.660000 53.560001 44.374279 69552900 2016-03-25 53.560001 54.369999 53.200001 54.080002 44.805096 46254500 2016-04-01 53.320000 54.490002 51.770000 52.000000 43.081814 74258800 2016-04-08 52.200001 52.580002 50.840000 51.360001 43.000736 69345000 2016-04-15 51.279999 52.220001 49.470001 50.029999 41.887215 85163000 2016-04-22 50.150002 51.810001 50.049999 51.020000 42.716084 70395100 2016-04-29 50.950001 51.450001 50.200001 50.840000 42.565380 57511900 2016-05-06 50.910000 51.700001 50.610001 51.470001 43.092846 44831600 2016-05-13 51.410000 51.490002 49.119999 49.630001 41.552322 54397000 2016-05-20 49.799999 50.279999 49.049999 50.160000 41.996059 60970600 2016-05-27 50.389999 51.160000 50.119999 50.770000 42.506767 45875900 2016-06-03 50.770000 52.000000 50.599998 51.950001 43.494717 55124100 2016-06-10 51.860001 53.480000 51.720001 53.459999 44.758949 60962600 2016-06-17 53.430000 54.680000 53.009998 54.669998 45.772015 70362700 2016-06-24 54.470001 55.919998 53.880001 55.840000 46.751587 124520900 2016-07-01 | 55.849998 56.950001 55.099998 55.380001 46.366463 66131100 2016-07-08 | 55.389999 56.099998 55.009998 55.840000 47.223568 65782600 2016-07-15 | 56.049999 56.080002 55.240002 55.369999 46.826099 55653900 2016-07-22 | 55.439999 56.250000 54.439999 54.860001 46.394791 68322700 2016-07-29 | 54.990002 55.820000 53.630001 53.930000 45.608295 73110900 2016-08-05 | 53.939999 53.990002 53.330002 53.860001 45.549099 47897200 2016-08-12 53.959999 53.980000 52.380001 52.869999 44.711861 53974000 2016-08-19 | 52.889999 52.910000 52.160000 52.750000 44.610371 45530800 2016-08-26 | 52.639999 53.009998 51.900002 52.560001 44.449703 56606900 2016-09-02| 52.799999 53.880001 52.520000 53.599998 45.329224 50128500 2016-09-09 | 53.130001 53.240002 51.119999 51.980000 43.959190 76488700 2016-09-16| 51.889999 52.490002 51.020000 52.349998 44.272091 75703700 2016-09-23 52.299999 52.820000 51.770000 52.119999 44.077587 55916600 2016-09-30 | 52.430000 52.570000 49.970001 50.259998 42.504597 64866100 2016-10-07 | 50.459999 50.540001 49.630001 50.290001 43.014580 56279400 2016-10-14| 50.340000 50.630001 48.900002 49.139999 42.030945 67914800 2016-10-21 | 48.790001 48.930000 47.580002 48.540001 41.517750 98020800 2016-10-28 48.560001 48.770000 46.790001 46.869999 40,089344 65442200 2016-11-04 46.970001 48.080002 46.360001 46.689999 39.935387 83781400 2016-11-11 46.700001 48.169998 46.009998 47.840000 40.919022 86682600 2016-11-18 47.849998 50.650002 47.570000 50.230000 42.963261 667080600 2016-11-25|50.220001 51.200001 49.310001 49.869999 42.655334 69284000 2016-12-02 | 50.000000 51,430000 49.599998 51.130001 43.733059 65090400 2016-12-09 | 51.090000 52.660000 50.919998 51.810001 44.314682 72383400 2016-12-16 | 52.060001 53.740002 51.860001 53.650002 45.888496 65794600 2016-12-23 53.650002 53.900002 53.369999 53.740002 45.965473 27456900 2016-12-30 | 53.549999 54.830002 53.169998 54.639999 46.735260 67489200 2017-01-06 | 53.669998 53.779999 52.020000 52.680000 45.058811 68694500 2017-01-13| 52.720001 52.900002 52.410000 52.549999 45.427750 9458700 Date Open High Low Close Adj Close Volume 2016-01-01 34.080002 34.689999 33.509998 33.509998 26.160191 124510000 2016-01-08 33.770000 34.549999 33.410000 34.299999 27.153730 155222400 2016-01-15 33.660000 34.880001 33.430000 34.540001 27.343727 173180200 2016-01-22 34.880001 35.799999 34.700001 35.529999 28.127464 181528700 2016-01-29 35.709999 36.820000 35.680000 36.529999 28.919119 174813700 2016-02-05 36.590000 37.119999 35.910000 36.209999 28.665787 180077600 2016-02-12 36.349998 37.000000 36.049999 36.990002 29.283279 102049100 2016-02-19 36.900002 37.500000 36.509998 37.369999 29.584105 112231400 2016-02-26 37.490002 38.110001 36.950001 37.990002 30.074936 120088800 2016-03-04 37.910000 38.419998 37.610001 38.310001 30.328259 114743600 2016-03-11 38.450001 39.189999 38.099998 39.119999 30.969505 101998900 2016-03-18 39.230000 39.259998 38.369999 38.880001 30.779503 122415500 2016-03-25 39.000000 39.720001 38.810001 39.169998 31.009079 100285400 2016-04-01 38.669998 39.360001 38.220001 38.590000 30.549921 115204300 2016-04-08 38.730000 38.900002 38.189999 38.419998 30.792492 89299600 2016-04-15 38.459999 39.009998 37.849998 37.860001 30.343668 98070900 2016-04-22 37.849998 38.910000 37.730000 38.639999 30.968819 124406100 2016-04-29 38.639999 39.150002 38.480000 38.740002 31.048965 100955500 2016-05-06 38.779999 39.669998 38.470001 39.549999 31.698154 79684400 2016-05-13 39.490002 39.520000 37.770000 38.439999 30.808521 106391500 2016-05-20 38.639999 38.990002 38.259998 38.840000 31.129110 80483600 2016-05-27 38.830002 39.200001 38.580002 38.840000 31.129110 72969100 2016-06-03 38.970001 40.169998 38.930000 40.090000 32.130947 96015300 2016-06-10 39.950001 40.570000 39.880001 40.490002 32.451542 105156000 2016-06-17 40.540001 41.889999 40.330002 41.880001 33.565575 106713100 2016-06-24 41.450001 43.419998 41.290001 43.209999 34.631527 184606500 2016-07-01 43.209999 43.889999 42.130001 42.299999 33.902199 108984700 2016-07-08 | 42.130001 42.959999 41.700001 42.770000 34.662693 100221700 2016-07-15| 42.910000 43.080002 42.340000 42.520000 34.460087 78381800 2016-07-22 42.529999 43.439999 42.279999 42.580002 34.508713 98716000 2016-07-29 | 42.619999 43.500000 42.459999 43.080002 34.913933 91017400 2016-08-05| 43.160000 43.480000 42.770000 43.389999 35.165169 72128200 2016-08-12 43.410000 43.459999 41.110001 41.400002 33.552391 120327000 2016-08-19] 41.230000 41.250000 40.549999 41.070000 33.284946 95260700 2016-08-26 41.130001 41.290001 40.599998 40.959999 33.195789 76469400 2016-09-02 41.090000 41.389999 40.740002 41.189999 33.382191 661655500 2016-09-09 | 40.980000 41,080002 39.549999 40.450001 32.782467 140369200 2016-09-16| 40.340000 41.189999 39.860001 41.110001 33.317352 113145400 2016-09-23| 41.150002 41.700001 40.439999 40.730000 33.009384 97342000 2016-09-30 | 40.910000 41.040001 38.830002 39.110001 31.696466 107494700 2016-10-07 | 39.220001 39.490002 38.209999 39.369999 32.295708 95234100 2016-10-14| 39.410000 39.580002 38.500000 38.650002 31.705078 86283500 2016-10-21| 38.400002 38.669998 36.270000 36.520000 29.957819 299898300 2016-10-28 | 36.650002 37.189999 36.299999 36.630001 30.048052 133817700 2016-11-04 | 36.779999 37.529999 36.400002 36.570000 29.998831 135223300 2016-11-11| 36.509998 37.689999 36.099998 37.410000 30.687893 114355000 2016-11-18| 37.450001 38.970001 37.299999 38.730000 31.770702 81725000 2016-11-25| 38.770000 39.669998 38.160000 38.880001 31.893757 117435800 2016-12-02 | 38.840000 40.750000 38.470001 40.410000 33.148830 115407900 2016-12-09 | 40.279999 41.680000 40.169998 41.500000 34.042969 120995200 2016-12-16| 41.650002 42.779999 41.419998 42.720001 35.043755 100996400 2016-12-23| 42.790001 42.840000 42.470001 42,660000 34.994534 44494200 2016-12-30 | 42.759998 43.029999 42.450001 42.650002 34.986332 91594800 2017-01-06|41.980000 42,000000 40.240002 41.009998 33.641014 124131200 2017-01-13| 40.919998 41.180000 40.790001 40.959999 33.990513 13932200 Currency in USD Download Date Open High Low Close* Adj Close** Volume Jun 23, 2017 45.43 45.46 45.30 45.39 39.71 10,069,700 *Close price adjusted for splits. **Adjusted close price adjusted for both dividends and splits. Currency in USD Download Date Open High Low Close* Adj Close** Volume Jun 23, 2017 38.16 38.16 37.82 37.95 31.87 22,906,600 *Close price adjusted for splits. **Adjusted close price adjusted for both dividends and splits