Chapter 1: Making Sense of Data Hildebrand, Ott and Gray Basic Statistical Ideas for Managers Second Edition 1 What We Will Cover in Ch. 1 Meaning of data Purpose of collecting data Use of data in Finance 2 Section 1.1 1.4 Making Sense of Data 3
What Do We Mean by Data? Data About What? Gathering Data Summarizing Data 4 State the purpose of the study before collecting data. Example: Determine the percentage of the United States electorate favoring a national policy. A population is a collection of objects upon which measurements could be taken. Example: Who is the U.S. electorate? Provide operational definitions. Example: Include U.S. citizens living abroad? Include residents of the District of Columbia? 5 How should the question be phrased? Example: Do you favor the national policy? You do favor the national policy, don t you? Suppose the question is Do you favor the national policy? Responses are: Yes, No, Uncertain. Ignoring the uncertain responses, Yes is coded as 1. No is coded as 0. 6
A sample is a subset of the population. Issues that need to be addressed: Determine how to select the sample. Use voter registration lists? Deficiencies? Determine the size of the sample. What criterion should be used? 7 Example: Randomly select 500 voters from all of the people eligible to vote; record their responses. The numerical values of the 500 responses is the data. The data values are 0 s and 1 s. Data are numerical results of measurements on specified variables. Hildebrand, Ott and Gray, Basic Statistical Ideas for Managers, 2nd edition 8 If 300 voters said Yes, the sample percentage is 300/500 = 0.6. How should this sample percentage be used to make inferences about the population percentage? 9
What is statistics? Statistics is the process whereby data is transformed into information. Use the information to reach conclusions about the population. Example: DATA PROCESS INFORMATION The sample percentage is 60%. What conclusion can be reached about the population percentage? Section 1.5 The Role of Probability 11 1.5 The Role of Probability Probability is the language of statistics! 12
Section 1.6 The Role of The Computer 13 1.6 The Role of The Computer Facilitates the statistical analysis Software falls in two categories: Dedicated statistical software, such as Minitab, SPSS, and SAS. Spreadsheet software. 14 15
for Equity Returns {Example from finance} Objective: Compare the performance of a particular security (IBM) relative to the market from October 2000 through September 2003. The performance of the market will be determined using some index, such as ^DJI. 16 Index: The Dow Jones Industrial Average (^DJI). The adjusted closing values are in Exhibit 1. Date Open High Low Adj. Close Volume Oct-00 835.4 118.8 681.1 971.1 27328000-00 966.2 11152.0 204.8 414.5 342300 Dec-00 416.8 144.7 158.2 788.0 11620655 Jan-01 790.9 11224.4 325.7 887.4 12151623 Feb-01 884.8 11140.1 225.1 495.3 12036684-01 493.3 940.5 9047.6 9878.8 13221550-01 9877.2 973.2 9303.5 735.0 13272245 May-03 8478.5 8897.0 8328.6 8850.3 15543285 Jun-03 8851.5 9406.5 8823.5 8985.4 15622190-03 8983.7 9398.0 8843.6 9233.8 15073272 Aug-03 9232.7 9536.0 8964.1 9415.8 12298366 Sep-03 9416.7 9719.5 9199.4 9275.1 15014576 Exhibit 1 17 A time series plot of adjusted closing values for ^DJI is in Figure 1. 100 Time Series Plot of ^DJI 500 000 ^DJI 9500 9000 8500 8000 7500 Month Oct Year 2000 2001 Oct 2002 Oct 2003 Figure 1 Is there a trend? Are the closing prices constant or do they vary? 18
Procedure to obtain Exhibit 1 and Figure 1: To get the data, visit http://chart.yahoo.com/d Choose the starting date, ending date and the Monthly option Input your ticker symbol ^DJI and click on Get Data When the data appears, click on Download Spreadsheet Format Open the Excel file Click on the Data >Sort menu and choose Sort By Date, Ascending Paste the Excel file to the Minitab worksheet Format the cells To get the time series plot, click on Graph > Time Series Plot >Simple Enter series name: ^DJI Click on Time Scale > Calendar > Month Year Enter for month and 2000 for year 19 The performance of IBM will be examined over the same period of time. Security: IBM The adjusted closing values are in Exhibit 2. Date Open High Low Adj. Close Volume Oct-00 93.8 99.1 93.8 96.4 21808200-00 98.4 4.4 91.6 91.7 6720342-03 81.4 87.0 80.6 80.9 7362086 Aug-03 81.2 84.7 78.7 81.9 5624661 Sep-03 82.4 93.5 82.3 88.2 8523800 Exhibit 2 20 A time series plot of adjusted closing values for IBM is in Figure 2. 120 Time Series Plot of IBM 1 0 IBM 90 80 70 60 Month Year 50 Oct 2000 2001 Figure 2 Is there a trend? Are the closing prices constant or do they vary? Oct 2002 Oct 2003 21
The return over time is the interest earned per month. Indext Index t -1 Note: Return on Index t =, Indext -1 using adjusted closing values. Securityt Security t -1 Return on Security t = Security, t -1 using adjusted closing values. Example: Return on ^DJI nov2000 = (414.5 971.1) / 971.1 = -5.07% Return on IBM nov2000 = (91.67 96.44) / 96.44 = -4.96% 22 Procedure to obtain R^DJI (returns on ^DJI) and RIBM (returns on IBM) using Minitab: Suppose the adjusted closing prices for ^DJI are in Column 1 (C1) Copy and paste C1 into C2 Delete the first row of column C2 Click on calculator For store results in variable: Enter C3 For expression: enter (C2-C1)/C1 C3 will contain the returns for the DJIA over the time period of interest 23 Time series plots of R^DJI and RIBM are in Figures 3 and 4. Time Series Plot of Returns for ^DJI 5 R^DJI 0-5 - -15 Month Year 2000 2001 2002 2003 Figure 3 24
40 Time Series Plot of Returns for IBM 30 20 RIBM 0 - -20-30 Month Year 2000 2001 2002 2003 Figure 4 Is there a trend? Which returns have more variation? Why? 25 Comparing the returns One approach superimpose the time series plots. Time Series Plot of R^DJI, RIBM 40 30 Variable R^DJI RIBM 20 Data 0 Figure 5 - -20-30 Month Year 2000 2001 2002 2003 Which returns have more variation? Do the returns tend to move together? 26 Another way of comparing the returns. Construct a scatterplot. See Figure 6. 40 Scatterplot of RIBM vs. R^DJI 30 20 RIBM 0 Figure 6 - -20-30 -15 - -5 R^DJI As R^DJI increase, do the RIBM increase, decrease, or remain constant? 0 5 27
The simple market model for equity returns, Return on Security = a + b (Return on ket). The constant b is referred to as a security s beta. Securities with large betas tend to give larger expected returns (on average, over time) than securities with smaller betas. Example: Suppose a straight line is fit through the scatterplot in Figure 6. Is the slope of this line (>, =, <) 0? The slope of the best fitting line is beta. 28 Additional questions: In Figure 4, for RIBM, are the returns for January 2001 and October 2002 unusual? [Chapter 2] How will volatility be measured? [Chapter 2] Did the volatility in either RDJIA or RIBM change over the horizon examined? How is the value of beta determined? [Chapter 11] In the scatterplot, does the point (R^DJI=0.92, RIBM=31.76) affect the determination of beta? If so, how? [Chapter 11] 29 Summary of Chapter 1 Meaning of data Need to collect data Purpose of collecting data Statistical software makes life easier uses statistical analysis 30