What We Will Cover in Ch. 1

Transcription

1 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 Making Sense of Data 3

2 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

3 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

4 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 The Role of Probability Probability is the language of statistics! 12

5 Section 1.6 The Role of The Computer 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

6 for Equity Returns {Example from finance} Objective: Compare the performance of a particular security (IBM) relative to the market from October 2000 through September 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 Dec Jan Feb May Jun Aug Sep Exhibit 1 17 A time series plot of adjusted closing values for ^DJI is in Figure Time Series Plot of ^DJI ^DJI Month Oct Year Oct 2002 Oct 2003 Figure 1 Is there a trend? Are the closing prices constant or do they vary? 18

7 Procedure to obtain Exhibit 1 and Figure 1: To get the data, visit 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 Aug Sep Exhibit 2 20 A time series plot of adjusted closing values for IBM is in Figure Time Series Plot of IBM 1 0 IBM Month Year 50 Oct Figure 2 Is there a trend? Are the closing prices constant or do they vary? Oct 2002 Oct

8 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 = ( ) / = -5.07% Return on IBM nov2000 = ( ) / = -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 Month Year Figure 3 24

9 40 Time Series Plot of Returns for IBM RIBM Month Year 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 Variable R^DJI RIBM 20 Data 0 Figure Month Year Which returns have more variation? Do the returns tend to move together? 26 Another way of comparing the returns. Construct a scatterplot. See Figure Scatterplot of RIBM vs. R^DJI RIBM 0 Figure R^DJI As R^DJI increase, do the RIBM increase, decrease, or remain constant?

10 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