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Business Finance

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all requirement, question, data are under PDF and excel file.

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Project 1 Due on January 20 by 5:00 pm MGT 252 - Winter 2021 Investments and Portfolio Management c 2021 Alexander Barinov 1 Price Momentum (50 points) The file Project 1.xls in the Projects folder contains the monthly data on risk-free rate (RF), the excess return to the market (MKT-RF), and the returns to the momentum strategy (MOM) between January 1964 and June 2009. The momentum strategy buys the stocks with the most positive returns in the past year and shorts the stocks with the most negative returns in the past year. For this problem, assume that the risk-free rate RF is not constant. i. Compute the monthly average and the monthly standard deviation for MOM and RF. (5 points) ii. Based on these sample estimates, build the 95% confidence interval for the return to the MOM portfolio in the next year. Provide a concise explanation of what this interval means in economic terms. (10 points) iii. Repeat (ii) for the average annual return. Explain the difference. (10 points) iv. Assume that MOM and RF are uncorrelated. Compute the mean and standard deviation of the daily return to strategy S, which is 70% MOM and 30% RF. Assume 22 trading days in a month. (5 points) v. Can you reject the hypothesis that the true expected monthly return to MOM is zero? Use all three ways to test the hypothesis we discussed in class. (10 points) vi. Bonus question: Test the equality of the average returns to the MOM strategy and the average excess return to the market, MKT-RF. (10 points) vii. Compute VaR for strategy S if $1,000,000 is invested for one quarter. Assume 63 trading days per quarter. (10 points) 1 2 Event Study (50 points) Consider a stock that responded to a certain event by gaining 0.25% on the day before the announcement, 1.75% at the announcement date, and 0.5% on the following day. On the same dates, the market return was 0.1%, 0.3%, and -0.3%, respectively. The risk-free rate was constant at 0.05%. Assume that the event window includes all three days and the standard deviation of the stock return in the pre-event window is 4.6% per month. The market model estimated for the stock in the pre-event window yields Rett − RFt = 0.13 + 1.18 (M KTt − RFt ) + t , (0.08) (0.37) R2 = 0.31 i. Use the market model to calculate the cumulative abnormal return to the stock in the event window. (5 points) ii. Use the R-square of the market model to compute the daily standard deviation of abnormal return (aka regression residual). Assume 22 trading days per month.(10 points) iii. Did the event have a statistically significant impact on the stock price? (10 points) iv. Use the market model to compute the daily standard deviation of the market portfolio. (10 points) v. Was the event-window run-up for the market portfolio statistically significant? (10 points) vi. Assume that returns above are the average for a portfolio of 100 stocks that had similar events and the 100 event windows do not overlap. Assume also that the standard deviation of returns and the parameters of the market model are the same for all 100 stocks. How does it change your answer to (iii)? (5 points) vii. Bonus question: Suppose someone tells you that volatility should be measured in calendar time, not in trading time, because Saturdays and Sundays have the same amount of news as business days, even though trading on the weekend news is delayed until Monday.. If you know that the event happened on Monday, how does it change your answer to (iii)? Assume 30 calendar days in a month. (10 points) 2 Date 31-Jan-64 28-Feb-64 31-Mar-64 30-Apr-64 28-May-64 30-Jun-64 31-Jul-64 31-Aug-64 30-Sep-64 30-Oct-64 30-Nov-64 31-Dec-64 29-Jan-65 26-Feb-65 31-Mar-65 30-Apr-65 28-May-65 30-Jun-65 30-Jul-65 31-Aug-65 30-Sep-65 29-Oct-65 30-Nov-65 31-Dec-65 31-Jan-66 28-Feb-66 31-Mar-66 29-Apr-66 31-May-66 30-Jun-66 29-Jul-66 31-Aug-66 30-Sep-66 31-Oct-66 30-Nov-66 30-Dec-66 31-Jan-67 28-Feb-67 31-Mar-67 28-Apr-67 31-May-67 30-Jun-67 31-Jul-67 31-Aug-67 29-Sep-67 31-Oct-67 MOM 1.06 0.27 0.70 -0.59 2.56 0.49 -0.32 -0.21 -0.39 0.18 1.09 -0.72 -1.40 0.31 0.08 2.57 0.53 -3.13 4.08 2.57 3.28 3.44 4.41 0.14 5.37 4.54 1.36 6.16 -4.70 3.33 -1.44 -2.09 -1.77 -5.11 5.68 1.05 -6.66 3.55 1.43 0.65 0.61 6.00 -1.12 -1.42 2.53 3.67 RF 0.3 0.26 0.31 0.29 0.26 0.3 0.3 0.28 0.28 0.29 0.29 0.31 0.28 0.3 0.36 0.31 0.31 0.35 0.31 0.33 0.31 0.31 0.35 0.33 0.38 0.35 0.38 0.34 0.41 0.38 0.35 0.41 0.4 0.45 0.4 0.4 0.43 0.36 0.39 0.32 0.33 0.27 0.32 0.31 0.32 0.39 MKT-RF 2.28 1.46 1.45 0.17 1.48 1.21 1.71 -1.41 2.77 0.6 0.02 0.06 3.58 0.39 -1.33 3.06 -0.75 -5.54 1.37 2.76 2.89 2.62 -0.04 1.02 0.83 -1.21 -2.47 2.14 -5.66 -1.41 -1.64 -7.95 -1.1 3.78 1.35 0.22 8.12 0.73 3.95 3.84 -4.26 2.42 4.6 -0.94 3.11 -3.13 30-Nov-67 29-Dec-67 31-Jan-68 29-Feb-68 29-Mar-68 30-Apr-68 31-May-68 28-Jun-68 30-Jul-68 30-Aug-68 30-Sep-68 31-Oct-68 29-Nov-68 31-Dec-68 31-Jan-69 28-Feb-69 28-Mar-69 30-Apr-69 29-May-69 30-Jun-69 31-Jul-69 29-Aug-69 30-Sep-69 31-Oct-69 28-Nov-69 31-Dec-69 30-Jan-70 27-Feb-70 31-Mar-70 30-Apr-70 29-May-70 30-Jun-70 31-Jul-70 31-Aug-70 30-Sep-70 30-Oct-70 30-Nov-70 31-Dec-70 29-Jan-71 26-Feb-71 31-Mar-71 30-Apr-71 28-May-71 30-Jun-71 30-Jul-71 31-Aug-71 30-Sep-71 1.25 3.25 -4.70 -3.38 3.21 5.09 3.71 -1.91 -0.90 1.92 -0.60 -1.42 1.77 0.29 -0.17 -2.42 3.99 1.11 1.63 -2.27 1.71 2.18 2.50 -4.28 3.64 4.97 0.60 0.20 -0.27 -0.70 -2.63 5.78 -3.08 -6.45 -8.88 9.54 2.87 -2.21 -6.60 0.77 -1.36 1.45 0.87 2.75 -2.38 3.51 2.11 0.36 0.33 0.4 0.39 0.38 0.43 0.45 0.43 0.48 0.42 0.43 0.44 0.42 0.43 0.53 0.46 0.46 0.53 0.48 0.51 0.53 0.5 0.62 0.6 0.52 0.64 0.6 0.62 0.57 0.5 0.53 0.58 0.52 0.53 0.54 0.46 0.46 0.42 0.38 0.33 0.3 0.28 0.29 0.37 0.4 0.47 0.37 0.43 3.04 -4.03 -3.75 0.13 8.98 2.25 0.72 -2.68 1.38 4.02 0.46 5.43 -3.82 -1.2 -5.82 2.59 1.52 0.02 -7.25 -7.05 4.65 -2.88 4.96 -3.74 -2.61 -7.93 5.05 -1.04 -11.03 -6.96 -5.69 6.9 4.47 4.21 -2.28 4.58 5.65 4.82 1.36 4.18 3.05 -3.93 -0.06 -4.43 3.78 -0.87 29-Oct-71 30-Nov-71 31-Dec-71 31-Jan-72 29-Feb-72 30-Mar-72 28-Apr-72 31-May-72 30-Jun-72 31-Jul-72 31-Aug-72 29-Sep-72 31-Oct-72 30-Nov-72 29-Dec-72 31-Jan-73 28-Feb-73 30-Mar-73 30-Apr-73 31-May-73 29-Jun-73 31-Jul-73 31-Aug-73 28-Sep-73 31-Oct-73 30-Nov-73 31-Dec-73 31-Jan-74 28-Feb-74 29-Mar-74 30-Apr-74 31-May-74 28-Jun-74 31-Jul-74 30-Aug-74 30-Sep-74 31-Oct-74 29-Nov-74 31-Dec-74 31-Jan-75 28-Feb-75 31-Mar-75 30-Apr-75 30-May-75 30-Jun-75 31-Jul-75 29-Aug-75 0.50 1.49 -0.61 0.27 2.54 2.90 2.70 3.28 1.94 2.76 -5.37 1.76 0.77 -5.23 4.99 3.71 2.08 3.62 6.35 7.07 4.35 -11.56 3.44 -7.07 6.86 8.65 10.33 -8.91 0.14 -0.93 2.14 -0.36 2.33 3.10 2.99 4.14 -0.76 2.18 2.93 -13.82 -0.57 -1.99 1.35 -0.51 0.05 0.43 -0.15 0.37 0.37 0.37 0.29 0.25 0.27 0.29 0.3 0.29 0.31 0.29 0.34 0.4 0.37 0.37 0.44 0.41 0.46 0.52 0.51 0.51 0.64 0.7 0.68 0.65 0.56 0.64 0.63 0.58 0.56 0.75 0.75 0.6 0.7 0.6 0.81 0.51 0.54 0.7 0.58 0.43 0.41 0.44 0.44 0.41 0.48 0.48 -4.44 -0.5 8.76 2.55 2.88 0.6 0.26 1.34 -2.38 -0.74 3.31 -1.11 0.47 4.61 0.75 -3.2 -4.86 -1.25 -5.7 -2.96 -1.38 5.07 -3.67 4.72 -0.68 -12.64 0.5 -0.19 -0.35 -2.9 -5.35 -4.95 -2.89 -7.79 -9.38 -11.78 16.05 -4.64 -3.4 13.58 5.41 2.61 4.21 5.07 4.74 -6.52 -2.84 30-Sep-75 31-Oct-75 28-Nov-75 31-Dec-75 30-Jan-76 27-Feb-76 31-Mar-76 30-Apr-76 28-May-76 30-Jun-76 30-Jul-76 31-Aug-76 30-Sep-76 29-Oct-76 30-Nov-76 31-Dec-76 31-Jan-77 28-Feb-77 31-Mar-77 29-Apr-77 31-May-77 30-Jun-77 29-Jul-77 31-Aug-77 30-Sep-77 31-Oct-77 30-Nov-77 30-Dec-77 31-Jan-78 28-Feb-78 31-Mar-78 28-Apr-78 31-May-78 30-Jun-78 31-Jul-78 31-Aug-78 29-Sep-78 31-Oct-78 30-Nov-78 29-Dec-78 31-Jan-79 28-Feb-79 30-Mar-79 30-Apr-79 31-May-79 29-Jun-79 31-Jul-79 0.39 -0.12 -0.45 -0.12 4.46 0.38 0.18 0.49 -1.11 -0.45 -0.11 -0.86 0.21 -0.45 2.95 0.75 3.97 0.35 0.53 4.22 2.13 1.77 0.36 -1.69 2.07 -0.06 2.20 1.61 -0.70 1.97 1.31 0.82 2.87 2.77 4.18 2.87 -3.13 -8.38 5.43 3.04 -1.40 -1.09 2.90 0.73 -0.44 0.85 -1.08 0.53 0.56 0.41 0.48 0.47 0.34 0.4 0.42 0.37 0.43 0.47 0.42 0.44 0.41 0.4 0.4 0.36 0.35 0.38 0.38 0.37 0.4 0.42 0.44 0.43 0.49 0.5 0.49 0.49 0.46 0.53 0.54 0.51 0.54 0.56 0.55 0.62 0.68 0.7 0.78 0.77 0.73 0.81 0.8 0.82 0.81 0.77 -4.33 5.03 2.71 -1.58 12.13 0.39 2.28 -1.46 -1.31 4.02 -1.09 -0.56 2.01 -2.45 0.14 5.76 -3.99 -1.93 -1.3 0.12 -1.45 4.74 -1.7 -1.78 -0.27 -4.42 4.04 0.33 -6.01 -1.39 2.87 7.74 1.81 -1.62 5.11 3.69 -1.31 -11.78 2.68 0.99 4.18 -3.41 5.75 0.05 -2.18 3.88 0.73 31-Aug-79 28-Sep-79 31-Oct-79 30-Nov-79 31-Dec-79 31-Jan-80 29-Feb-80 31-Mar-80 30-Apr-80 30-May-80 30-Jun-80 31-Jul-80 29-Aug-80 30-Sep-80 31-Oct-80 28-Nov-80 31-Dec-80 30-Jan-81 27-Feb-81 31-Mar-81 30-Apr-81 29-May-81 30-Jun-81 31-Jul-81 31-Aug-81 30-Sep-81 30-Oct-81 30-Nov-81 31-Dec-81 29-Jan-82 26-Feb-82 31-Mar-82 30-Apr-82 28-May-82 30-Jun-82 30-Jul-82 31-Aug-82 30-Sep-82 29-Oct-82 30-Nov-82 31-Dec-82 31-Jan-83 28-Feb-83 31-Mar-83 29-Apr-83 31-May-83 30-Jun-83 -0.26 5.32 2.14 7.93 4.77 7.47 7.89 -9.58 -0.43 -1.13 1.57 0.39 3.26 5.44 7.31 15.21 -6.63 -7.93 -1.39 0.76 -0.92 3.75 -5.90 -2.47 -1.10 2.04 4.10 -0.28 1.33 1.70 4.88 2.93 -0.43 2.52 5.01 4.42 -3.51 4.21 0.01 5.92 0.05 -1.72 3.80 0.92 1.79 -1.58 1.78 0.77 0.83 0.87 0.99 0.95 0.8 0.89 1.21 1.26 0.81 0.61 0.53 0.64 0.75 0.95 0.96 1.31 1.04 1.07 1.21 1.08 1.15 1.35 1.24 1.28 1.24 1.21 1.07 0.87 0.8 0.92 0.98 1.13 1.06 0.96 1.05 0.76 0.51 0.59 0.63 0.67 0.69 0.62 0.63 0.71 0.69 0.67 5.7 -0.69 -8.14 5.37 1.87 5.76 -0.79 -13.23 3.97 5.2 3.16 6.41 1.72 2.2 1.06 9.53 -4.75 -5.05 0.48 3.41 -2.21 0.21 -2.37 -1.55 -6.91 -7.62 4.81 3.52 -3.68 -3.42 -6.03 -1.99 3.2 -3.88 -3.35 -3.1 11.14 1.17 11.27 4.56 0.78 3.5 2.4 2.84 6.71 0.63 3.11 29-Jul-83 31-Aug-83 30-Sep-83 31-Oct-83 30-Nov-83 30-Dec-83 31-Jan-84 29-Feb-84 30-Mar-84 30-Apr-84 31-May-84 29-Jun-84 31-Jul-84 31-Aug-84 28-Sep-84 31-Oct-84 30-Nov-84 31-Dec-84 31-Jan-85 28-Feb-85 29-Mar-85 30-Apr-85 31-May-85 28-Jun-85 31-Jul-85 30-Aug-85 30-Sep-85 31-Oct-85 29-Nov-85 31-Dec-85 31-Jan-86 28-Feb-86 31-Mar-86 30-Apr-86 30-May-86 30-Jun-86 31-Jul-86 29-Aug-86 30-Sep-86 31-Oct-86 28-Nov-86 31-Dec-86 30-Jan-87 27-Feb-87 31-Mar-87 30-Apr-87 29-May-87 -3.13 -5.44 -0.09 -4.54 -0.17 0.81 -2.47 0.20 1.04 2.11 1.65 -0.68 2.87 -5.64 3.69 3.21 1.67 1.51 -6.93 1.82 1.70 3.03 3.98 3.62 -3.93 1.77 1.48 4.87 -0.46 -0.09 2.96 2.70 2.46 -0.50 2.03 5.14 1.80 -5.02 -5.86 2.69 -0.31 0.37 2.12 -2.17 1.61 0.23 -0.73 0.74 0.76 0.76 0.76 0.7 0.73 0.76 0.71 0.73 0.81 0.78 0.75 0.82 0.83 0.86 1 0.73 0.64 0.65 0.58 0.62 0.72 0.66 0.55 0.62 0.55 0.6 0.65 0.61 0.65 0.56 0.53 0.6 0.52 0.49 0.52 0.52 0.46 0.45 0.46 0.39 0.49 0.42 0.43 0.47 0.44 0.38 -3.9 -0.41 0.85 -3.56 2.26 -1.78 -2.06 -4.62 0.61 -0.56 -6.01 1.59 -2.88 10.44 -0.82 -1.01 -1.8 1.73 7.92 1.11 -0.79 -0.94 4.92 1.16 -0.65 -1.03 -4.58 3.79 6.31 3.66 0.42 6.72 4.79 -1.31 4.59 0.9 -6.49 6.16 -8.35 4.47 1.12 -3.13 12.43 4.36 1.9 -2.14 0.13 30-Jun-87 31-Jul-87 31-Aug-87 30-Sep-87 30-Oct-87 30-Nov-87 31-Dec-87 29-Jan-88 29-Feb-88 31-Mar-88 29-Apr-88 31-May-88 30-Jun-88 29-Jul-88 31-Aug-88 30-Sep-88 31-Oct-88 30-Nov-88 30-Dec-88 31-Jan-89 28-Feb-89 31-Mar-89 28-Apr-89 31-May-89 30-Jun-89 31-Jul-89 31-Aug-89 29-Sep-89 31-Oct-89 30-Nov-89 29-Dec-89 31-Jan-90 28-Feb-90 30-Mar-90 30-Apr-90 31-May-90 29-Jun-90 31-Jul-90 31-Aug-90 28-Sep-90 31-Oct-90 30-Nov-90 31-Dec-90 31-Jan-91 28-Feb-91 28-Mar-91 30-Apr-91 -0.20 2.66 -0.87 0.71 -7.89 -1.17 5.78 -7.63 -1.55 0.64 2.28 0.68 -2.93 0.61 0.31 0.27 1.31 0.42 0.42 -0.17 0.88 3.57 1.71 1.55 0.66 5.38 -0.16 3.37 1.39 2.57 2.78 -3.27 -0.54 1.66 2.42 3.04 2.42 5.87 1.79 5.52 6.74 -5.68 0.15 -6.52 -4.81 2.80 -2.37 0.48 0.46 0.47 0.45 0.6 0.35 0.39 0.29 0.46 0.44 0.46 0.51 0.49 0.51 0.59 0.62 0.61 0.57 0.63 0.55 0.61 0.67 0.67 0.79 0.71 0.7 0.74 0.65 0.68 0.69 0.61 0.57 0.57 0.64 0.69 0.68 0.63 0.68 0.66 0.6 0.68 0.57 0.6 0.52 0.48 0.44 0.53 3.89 3.96 3.24 -2.53 -23.14 -7.58 6.64 4.2 4.71 -2.1 0.64 -0.47 4.66 -1.24 -3.39 3.1 1.15 -2.21 1.48 6.06 -2.25 1.48 4.15 3.14 -1.2 7.01 1.47 -0.8 -3.61 1.09 1.22 -7.58 0.92 1.77 -3.52 8.21 -1.05 -1.62 -9.85 -5.98 -1.93 6 2.35 4.39 7.1 2.45 -0.2 31-May-91 28-Jun-91 31-Jul-91 30-Aug-91 30-Sep-91 31-Oct-91 29-Nov-91 31-Dec-91 31-Jan-92 28-Feb-92 31-Mar-92 30-Apr-92 29-May-92 30-Jun-92 31-Jul-92 31-Aug-92 30-Sep-92 30-Oct-92 30-Nov-92 31-Dec-92 29-Jan-93 26-Feb-93 31-Mar-93 30-Apr-93 28-May-93 30-Jun-93 30-Jul-93 31-Aug-93 30-Sep-93 29-Oct-93 30-Nov-93 31-Dec-93 31-Jan-94 28-Feb-94 31-Mar-94 29-Apr-94 31-May-94 30-Jun-94 29-Jul-94 31-Aug-94 30-Sep-94 31-Oct-94 30-Nov-94 30-Dec-94 31-Jan-95 28-Feb-95 31-Mar-95 -0.12 0.46 4.38 1.57 1.71 3.21 1.23 8.28 -2.44 -0.64 -0.32 -2.57 0.09 -0.60 1.42 -0.54 1.44 2.71 -0.32 4.42 4.83 3.10 3.70 0.33 0.27 4.51 3.21 2.52 3.41 -2.70 -4.70 2.28 0.00 -0.28 -1.32 0.38 -2.22 -0.83 0.18 1.54 1.32 1.47 -0.18 3.52 -1.83 -0.36 0.43 0.47 0.42 0.49 0.46 0.46 0.42 0.39 0.38 0.34 0.28 0.34 0.32 0.28 0.32 0.31 0.26 0.26 0.23 0.23 0.28 0.23 0.22 0.25 0.24 0.22 0.25 0.24 0.25 0.26 0.22 0.25 0.23 0.25 0.21 0.27 0.27 0.32 0.31 0.28 0.37 0.37 0.38 0.37 0.44 0.42 0.4 0.46 3.6 -4.82 4.19 2.22 -1.56 1.36 -4.12 10.3 -0.46 1.06 -2.71 1.02 0.36 -2.25 3.68 -2.34 0.98 0.87 3.79 1.5 1.03 0.32 2.26 -2.78 2.74 0.29 -0.32 3.7 -0.2 1.59 -2.01 1.72 2.9 -2.63 -4.85 0.68 0.62 -3.1 2.78 3.89 -2.21 1.07 -4.09 0.82 1.62 3.56 2.24 28-Apr-95 31-May-95 30-Jun-95 31-Jul-95 31-Aug-95 29-Sep-95 31-Oct-95 30-Nov-95 29-Dec-95 31-Jan-96 29-Feb-96 29-Mar-96 30-Apr-96 31-May-96 28-Jun-96 31-Jul-96 30-Aug-96 30-Sep-96 31-Oct-96 29-Nov-96 31-Dec-96 31-Jan-97 28-Feb-97 31-Mar-97 30-Apr-97 30-May-97 30-Jun-97 31-Jul-97 29-Aug-97 30-Sep-97 31-Oct-97 28-Nov-97 31-Dec-97 30-Jan-98 27-Feb-98 31-Mar-98 30-Apr-98 29-May-98 30-Jun-98 31-Jul-98 31-Aug-98 30-Sep-98 30-Oct-98 30-Nov-98 31-Dec-98 29-Jan-99 26-Feb-99 1.82 -0.43 2.91 2.57 0.11 2.77 4.16 -0.61 2.51 0.56 0.66 -1.88 -0.90 1.61 0.99 -0.17 -0.04 2.70 3.85 -2.39 0.57 1.95 -2.04 0.98 4.89 -5.19 2.58 3.81 -2.52 1.47 -0.43 0.29 3.95 0.19 -1.13 2.11 0.77 1.81 7.30 3.74 1.89 -0.64 -5.35 1.22 8.93 3.01 -0.13 0.44 0.54 0.47 0.45 0.47 0.43 0.47 0.42 0.49 0.43 0.39 0.39 0.46 0.42 0.4 0.45 0.41 0.44 0.42 0.41 0.46 0.45 0.39 0.43 0.43 0.49 0.37 0.43 0.41 0.44 0.42 0.39 0.48 0.43 0.39 0.39 0.43 0.4 0.41 0.4 0.43 0.46 0.32 0.31 0.38 0.35 0.35 2.06 2.86 2.65 3.63 0.46 3.21 -1.6 3.85 1.03 2.38 1.24 0.7 2.09 2.26 -1.23 -5.83 2.84 4.86 0.94 6.14 -1.6 4.89 -0.5 -4.91 3.8 6.67 4.04 7.22 -4.04 5.4 -3.87 2.66 1.3 0.02 6.93 4.74 0.66 -2.98 2.79 -2.73 -16.2 5.92 7.12 5.89 5.93 3.48 -4.16 31-Mar-99 30-Apr-99 28-May-99 30-Jun-99 30-Jul-99 31-Aug-99 30-Sep-99 29-Oct-99 30-Nov-99 31-Dec-99 31-Jan-00 29-Feb-00 31-Mar-00 28-Apr-00 31-May-00 30-Jun-00 31-Jul-00 31-Aug-00 29-Sep-00 31-Oct-00 30-Nov-00 29-Dec-00 31-Jan-01 28-Feb-01 30-Mar-01 30-Apr-01 31-May-01 29-Jun-01 31-Jul-01 31-Aug-01 28-Sep-01 31-Oct-01 30-Nov-01 31-Dec-01 31-Jan-02 28-Feb-02 28-Mar-02 30-Apr-02 31-May-02 28-Jun-02 31-Jul-02 30-Aug-02 30-Sep-02 31-Oct-02 29-Nov-02 31-Dec-02 31-Jan-03 -1.36 -9.12 -5.24 4.99 1.64 3.06 6.50 5.52 5.62 13.02 1.82 18.39 -6.78 -8.48 -9.13 16.41 -0.06 5.73 2.15 -4.72 -2.49 6.85 -25.06 12.59 8.39 -8.10 2.16 0.29 5.59 5.54 11.53 -8.41 -8.59 0.00 3.70 6.84 -1.70 7.92 3.05 6.17 3.41 1.68 9.09 -5.17 -16.26 9.63 1.53 0.43 0.37 0.34 0.4 0.38 0.39 0.39 0.39 0.36 0.44 0.41 0.43 0.47 0.46 0.5 0.4 0.48 0.5 0.51 0.56 0.51 0.5 0.54 0.39 0.44 0.39 0.32 0.28 0.3 0.31 0.28 0.22 0.17 0.15 0.14 0.13 0.13 0.15 0.14 0.13 0.15 0.14 0.14 0.14 0.12 0.11 0.1 3.36 4.53 -2.41 4.7 -3.44 -1.39 -2.68 5.81 3.33 7.95 -4.39 2.75 4.89 -6.41 -4.4 4.76 -2.19 7.08 -5.62 -3.02 -10.76 1.53 3.41 -10.32 -7.47 8 0.74 -2.03 -2.13 -6.22 -9.43 2.58 7.7 1.63 -1.75 -2.3 4.34 -5.11 -1.19 -7.15 -8.26 0.66 -10.14 7.36 6.01 -5.44 -2.44 28-Feb-03 31-Mar-03 30-Apr-03 30-May-03 30-Jun-03 31-Jul-03 29-Aug-03 30-Sep-03 31-Oct-03 28-Nov-03 31-Dec-03 30-Jan-04 27-Feb-04 31-Mar-04 30-Apr-04 28-May-04 30-Jun-04 30-Jul-04 31-Aug-04 30-Sep-04 29-Oct-04 30-Nov-04 31-Dec-04 31-Jan-05 28-Feb-05 31-Mar-05 29-Apr-05 31-May-05 30-Jun-05 29-Jul-05 31-Aug-05 30-Sep-05 31-Oct-05 30-Nov-05 30-Dec-05 31-Jan-06 28-Feb-06 31-Mar-06 28-Apr-06 31-May-06 30-Jun-06 31-Jul-06 31-Aug-06 29-Sep-06 31-Oct-06 30-Nov-06 29-Dec-06 1.29 1.50 -9.48 -10.79 -1.06 -0.35 -0.55 -0.07 3.70 1.63 -5.67 2.58 -1.14 0.20 -5.33 1.64 2.08 -2.32 -1.54 5.28 -1.54 3.24 -2.82 3.12 3.19 0.93 -0.84 0.46 2.10 0.05 2.24 3.50 -1.37 0.39 0.77 2.77 -1.80 1.22 0.65 -3.66 1.52 -2.24 -3.48 -0.98 -0.18 -1.00 0.81 0.09 0.1 0.1 0.09 0.1 0.07 0.07 0.08 0.07 0.07 0.08 0.07 0.06 0.09 0.08 0.06 0.08 0.1 0.11 0.11 0.11 0.15 0.16 0.16 0.16 0.21 0.21 0.24 0.23 0.24 0.3 0.29 0.27 0.31 0.32 0.35 0.34 0.37 0.36 0.43 0.4 0.4 0.42 0.41 0.41 0.42 0.4 -1.63 0.93 8.18 6.26 1.53 2.24 2.42 -0.99 5.96 1.59 4.47 2.24 1.49 -1.16 -2.5 1.35 2.08 -3.87 0.16 1.95 1.67 4.67 3.36 -2.82 2.11 -1.9 -2.73 3.55 0.92 4.09 -0.89 0.77 -2.35 3.73 0.03 3.66 -0.5 1.54 0.94 -3.53 -0.44 -0.59 2.09 1.54 3.3 1.95 0.68 31-Jan-07 28-Feb-07 30-Mar-07 30-Apr-07 31-May-07 29-Jun-07 31-Jul-07 31-Aug-07 28-Sep-07 31-Oct-07 30-Nov-07 31-Dec-07 31-Jan-08 29-Feb-08 31-Mar-08 30-Apr-08 30-May-08 30-Jun-08 31-Jul-08 29-Aug-08 30-Sep-08 31-Oct-08 28-Nov-08 31-Dec-08 30-Jan-09 27-Feb-09 31-Mar-09 30-Apr-09 29-May-09 30-Jun-09 0.22 -1.32 2.48 -0.14 -0.33 0.40 2.80 0.14 4.64 4.86 0.93 6.48 -7.89 6.23 4.12 -0.38 3.20 12.45 -5.12 -3.82 0.36 7.91 7.20 -5.03 -2.00 4.31 -11.60 -34.75 -12.45 5.36 0.44 0.38 0.43 0.44 0.41 0.4 0.4 0.42 0.32 0.32 0.34 0.27 0.21 0.13 0.17 0.17 0.17 0.17 0.15 0.12 0.15 0.08 0.02 0.09 0 0.01 0.01 0.01 0 0 1.5 -1.78 0.86 3.55 3.48 -1.88 -3.58 0.74 3.77 2.26 -5.27 -0.7 -6.44 -2.33 -1.22 4.94 2.21 -8.03 -1.46 0.98 -9.96 -18.55 -8.54 2.06 -7.74 -10.11 8.76 11.05 6.73 -0.28 Statistics Bootcamp Professor Alexander Barinov School of Business Administration University of California Riverside MGT 252 Investments and Portfolio Management Alexander Barinov (SoBA, UCR) Statistics Bootcamp MGT 252 Investments 1 / 40 Outline 1 Averages 2 Variance and Standard Deviation 3 Confidence Intervals 4 Hypothesis Testing 5 Event Studies 6 Market Model 7 Event Study Revisited 8 Idiosyncratic Risk 9 Forecasting Alexander Barinov (SoBA, UCR) Statistics Bootcamp MGT 252 Investments 2 / 40 Averages Notation E(R) is the notation for mean return (population average) R is the notation for average return (sample average) We will never know what the true mean is, but we will approximate it by the sample average On average, we will make no mistake, i.e. E(R − R) = 0 The longer is the sample, the closer we are to the population average Alexander Barinov (SoBA, UCR) Statistics Bootcamp MGT 252 Investments 3 / 40 Averages Average is Linear You can always multiply average by a number If you invest $1 into the market for one year, your expected gain is E($1 · R) = $1 · E(R) = $0.1139 If you invest $100 into the market for one year, your expected gain is E($100 · R) = $100 · E(R) = $11.39 You can always add two (or more) averages If you invest $1 into the market and $1 into Treasury bills for one year, your expected gain is E(RMKT + RF ) = E(RMKT ) + E(RF ) = $0.1139 + $0.0376 = $0.1515 If you invest $100 for one year, 70% in the market and the rest in Treasury bills, what is your expected gain? E($70RMKT + $30RF ) = $70 · E(RMKT ) + $30 · E(RF ) = $70 · 0.1139 + $30 · 0.0376 = $9.10 Alexander Barinov (SoBA, UCR) Statistics Bootcamp MGT 252 Investments 4 / 40 Variance and Standard Deviation Multiplying by a Constant If you multiply the random variable by a number, multiply the variance by this number squared Because standard deviation is the square root of the variance, if you multiply the random variable by a number, multiply the standard deviation by this number (do not square) The standard deviation of monthly market return is 5.45% What is the standard deviation of the expected gain on the $100 invested for a month? σ($100 · RMKT ) = $100 · σ(RMKT ) = $100 · 0.0545 = $5.45 Interpretation: it is not unusual to gain or lose $11 on a $100 bet within a month Alexander Barinov (SoBA, UCR) Statistics Bootcamp MGT 252 ...
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