What is Diversification?

Transcription

1 Lesson Summary What Is Diversification? teaches students the importance of diversification and helps them diversify their own SMG portfolios. Lesson Objectives Create a diversified portfolio selecting stocks. Conduct Internet research on different investment options. Interpret company and industry charts to determine which investments to make with their SMG teams. Define diversification, risk tolerance, industry, and index. NCTM Standards 1A - Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 1B - Understand meanings of operations and how they relate to one another. 5A - Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. 5B - Select and use appropriate statistical methods to analyze data. 5C - Develop and evaluate inferences and predictions that are based on data. 5D - Understand and apply basic concepts of probability. 6B - Solve problems that arise in mathematics and in other contexts. 6C - Apply and adapt a variety of appropriate strategies to solve problems. 7B - Make and investigate mathematical conjectures. 8A - Organize and consolidate mathematical thinking through communication. 8B - Communicate mathematical thinking coherently and clearly to peers, teachers, and others. 8C - Analyze and evaluate the mathematical thinking and strategies of others. 8D - Use the language of mathematics to express mathematical ideas precisely. 9C - Recognize and apply mathematics in contexts outside of mathematics. Mathematical Strands Thinking Algebraically Interpreting Statistics Communicating Quantitative Information Tackling Complex Problems Students calculate percentages to determine sectors in a diverse portfolio. Students determine which sectors an investor is most and least invested in, and identify which portfolios are diversified based on profiles of investor s portfolios with investments disaggregated by industry sector. Students create bar charts, pie charts and other graphical representations of information on diversification. Students are given a sample SMG portfolio of stocks to analyze for diversification in terms of cap size. 52

2 THINKING ALGEBRAICALLY To calculate the percentage of a given investment category in a portfolio, divide the money in that category (for example, all the money invested in small cap firms) by the total amount of money in the portfolio, and multiply by 100%. money _ invested _ in _ a _ sector % of portfolio invested in a sector = 100% total _ value _ of _ investment Company Size Sector Value A Small Telecommunications $ 1,500 B Large Industrial Goods $31,000 C Small Health $15,500 D Mid Energy $ 5,000 E Large Energy $27,000 F Mid Utilities $19, What is the total value of the investment portfolio above? 2. Using the portfolio above, calculate the percentage of the total investment in each sector. 3. Calculate the percentage of the investment in each size company. 53

3 INTERPRETING STATISTICS Below is the profile of a portfolio s holdings (displayed within industry sectors). Sector % Holdings Utilities 0.00 Business Services Financials Telecommunications 4.71 Media 0.00 Consumer goods 8.71 Energy 2.33 Hardware Health 5.18 Software 0.00 Consumer Services Industrial Materials In which three sectors does the investor have the most money invested? 2. In which three sectors does the investor have the least money invested? 3. Would you say that this portfolio is well-diversified or not well-diversified? Why? 54

4 INTERPRETING STATISTICS Below is the profile of another portfolio s holdings (displayed within industry sectors). Sector % Holdings Utilities 0.00 Business Services 0.00 Financials Telecommunications 0.00 Media 0.00 Consumer Goods 0.00 Energy 0.00 Hardware 0.00 Health 0.00 Software 0.00 Consumer Services 0.00 Industrial Materials In which sector does the investor have the most money invested? 2. In which sector does the investor have the least money invested? 3. Would you say that this portfolio is well-diversified or not well-diversified? Why? 55

5 INTERPRETING STATISTICS Below is the profile of a third portfolio s holdings (displayed within industry sectors). Sector % holdings Utilities 0.00 Business Services Financials 2.13 Telecommunications 0.00 Media 4.81 Consumer Goods 7.38 Energy 0.00 Hardware 4.98 Health 0.84 Software Consumer Services 1.72 Industrial Materials In which sector does the investor have the most money invested? 2. In which sector does the investor have the least money invested? 3. Would you say that this portfolio is well-diversified or not well-diversified? Why? 4. To what type of investor would you recommend the first portfolio? What about the second portfolio? What about the third? 56

6 There are many ways to represent a diversified portfolio. There are also different ways to determine if an investment portfolio is diversified or not. Company Cap Sector Investment Value A Small Media $ 6,000 B Mid Software $11,000 C Mid Consumer Goods $10,000 D Small Consumer Goods $ 7,500 E Large Utilities $36,000 F Small Business Services $12,000 G Large Utilities $10,000 H Small Consumer Goods $ 4,500 I Mid Energy $25,000 J Large Health $27,000 K Small Media $13,000 The following graphs present the information above in different ways. Next to each graph, write a brief description of what information each graph presents. 57

7 Size of Companies small, $43,000, 27% large, $73,000, 45% mid, $46,000, 28% Description 58

8 Investment by Sector health, $27,000, 17% media, $19,000, 12% software, $11,000, 7% energy, $25,000, 15% consumer goods, $22,000, 14% business services, $12,000, 7% utilities, $46,000, 28% Description 59

9 Investment by Sector $50,000 $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 media software consumer goods utilities business services energy health Description 60

10 Types of Companies $80,000 $70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 small mid large Description 61

11 Portfolio by Sector and Cap small mid large $50,000 $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 media software consumer goods utilities business services energy health Description 62

12 Below is a practice portfolio. The stocks listed include information on the size of the company, the industry it operates within, and the value of the investment. Company Cap Sector Investment Value size A Mid Consumer Services $9,500 B Mid Software $30,000 C Small Software $13,500 D Large Media $20,000 E Mid Telecommunications $15,000 F Large Software $12, On a separate sheet of paper, use the information above to create two graphical representations that show the diversification (in terms of both cap size and sector) of the portfolio. 2. On a separate sheet of paper, represent graphically the diversification of your own group s portfolio. 63

13 TACKLING COMPLEX PROBLEMS Below is a list of a team s portfolio holdings. They claim that their portfolio is diversified because they have an equal number of stocks from each company. Do you agree? Stock Price per Share Number of Shares Cap Size British Airways PLC (BAB) $ Large Eddie Bauer Holdings Inc. $ Small (EBHI) Handleman Company (HDL) $ Small Krispy Kreme Doughnuts Inc. $ Small (KKD) Scholastic Corporation $ Mid (SCHL) SunPower Corporation $ Mid (SPWR) Symantec Corporation $ Large (SYMC) The Stanley Works (SWK) $ Mid United Health Group Inc. (UNH) $ Large 1. What is the total value of their portfolio? 2. How much money is invested in: Small cap stocks? Mid cap stocks? Large cap stocks? 3. What percentage of their investment is in: Small cap stocks? Mid cap stocks? Large cap stocks? 4. Would you advise them to increase their diversity? Why or why not? Can you make recommendations about what stocks they might buy more of and which they might sell? 64

14 INTERPRETING STATISTICS ANSWER KEY Please Note: 1. Prices included in lesson are not representative of actual market data and are for instructional purposes only. 2. Discrepancies may occur between student responses and the answer keys as a result of how far calculations were taken past the decimal point. In most instances, numbers were rounded from the thousandth or ten thousandth place To calculate the percentage of a given investment category in a portfolio, divide the money in that category (for example, all the money invested in small cap firms) by the total amount of money in the portfolio, and multiply by 100%. money _ invested _ in _ a _ sector % of portfolio invested in a sector = 100% total _ value _ of _ investment Company Size Sector Value A Small Telecommunications $ 1,500 B Large Industrial Goods $31,000 C Small Health $15,500 D Mid Energy $ 5,000 E Large Energy $27,000 F Mid Utilities $19, What is the total value of the investment portfolio above? Answer: The total value of this portfolio is $99, Using the portfolio above, calculate the percentage of the total investment in each sector. Answer: Telecommunications: ($1,500 $99,000) x 100% = 1.52% Industrial Goods: ($31,000 $99,000) x 100% = 31.31% Health: ($15,500 $99,000) x 100% = 15.66% Energy: ($32,000 $99,000) x 100% = 32.32% Utilities: ($19,000 $99,000) x 100% = 19.19% 3. Calculate the percentage of the investment in each size company. Answer: Small Cap: [($1,500 + $15,500) $99,000] x 100% = ($17,000 $99,000) x 100% = 17.17% Miid Cap: [($5,000 + $19,000) $99,000] x 100% = ($24,000 $99,000) x 100% = 24.24% Large Cap: [($31,000 + $27,000) $99,000] x 100% = ($58,000 $99,000) x 100% = 58.59% Answer Key 49

15 INTERPRETING STATISTICS Below is the profile of a portfolio s holdings (displayed within industry sectors). Sector % Holdings Utilities 0.00 Business Services Financials Telecommunications 4.71 Media 0.00 Consumer goods 8.71 Energy 2.33 Hardware Health 5.18 Software 0.00 Consumer Services Industrial Materials In which three sectors does the investor have the most money invested? Answer: Industrial Materials 20.48%, Financials 19.74%, Business Services 15.64% 2. In which three sectors does the investor have the least money invested? Answer: Health 5.18%, Telecommunications 4.71%, Energy 2.33% 3. Would you say that this portfolio is well-diversified or not welldiversified? Why? Possible Answer: From the perspective of looking only at sectors, this portfolio would be diversified. Consideration of cap size would be beneficial as well. If all of these were small cap, young companies, there would be a lot of risk involved with this portfolio and might not be considered diversified. Answer Key 50

16 INTERPRETING STATISTICS Below is the profile of another portfolio s holdings (displayed within industry sectors). Sector % Holdings Utilities 0.00 Business Services 0.00 Financials Telecommunications 0.00 Media 0.00 Consumer Goods 0.00 Energy 0.00 Hardware 0.00 Health 0.00 Software 0.00 Consumer Services 0.00 Industrial Materials In which sector does the investor have the most money invested? Answer: Financials 95.57% 2. In which sector does the investor have the least money invested? Answer: Industrial Materials 4.43% 3. Would you say that this portfolio is well-diversified or not welldiversified? Why? Possible Answer: No, 95.57% of all holdings are in the Financials sector. Answer Key 51

17 INTERPRETING STATISTICS Below is the profile of a third portfolio s holdings (displayed within industry sectors). Sector % holdings Utilities 0.00 Business Services Financials 2.13 Telecommunications 0.00 Media 4.81 Consumer Goods 7.38 Energy 0.00 Hardware 4.98 Health 0.84 Software Consumer Services 1.72 Industrial Materials In which sector does the investor have the most money invested? Answer: Software 58.39% 2. In which sector does the investor have the least money invested? Answer: Health 0.84% 3. Would you say that this portfolio is well-diversified or not welldiversified? Why? Possible Answer: I would not consider this a well diversified portfolio. Yes, it is invested in 8 different sectors; however, over half of the portfolio is in software. 4. To what type of investor would you recommend the first portfolio? What about the second portfolio? What about the third? Possible Answer: The first portfolio would be recommended for a conservative investor. The second portfolio would be more appropriate for a risk taking investor. The third portfolio would appeal to a moderate investor. Answer Key 52

18 There are many ways to represent a diversified portfolio. There are also different ways to determine if an investment portfolio is diversified or not. Company Cap Sector Investment Value A Small Media $ 6,000 B Mid Software $11,000 C Mid Consumer Goods $10,000 D Small Consumer Goods $ 7,500 E Large Utilities $36,000 F Small Business Services $12,000 G Large Utilities $10,000 H Small Consumer Goods $ 4,500 I Mid Energy $25,000 J Large Health $27,000 K Small Media $13,000 The following graphs present the information above in different ways. Next to each graph, write a brief description of what information each graph presents. Answer Key 53

19 Size of Companies small, $43,000, 27% large, $73,000, 45% mid, $46,000, 28% Description Possible Answer: This pie chart is distinguishing between small, mid & large cap companies. It displays the percentage of money allocated in the portfolio for each cap size. Answer Key 54

20 Investment by Sector health, $27,000, 17% media, $19,000, 12% software, $11,000, 7% energy, $25,000, 15% consumer goods, $22,000, 14% business services, $12,000, 7% utilities, $46,000, 28% Description Possible Answer: This pie chart shows the portfolio divided into sectors. It also gives the percentage of each sector in relationship to the whole portfolio. Answer Key 55

21 Investment by Sector $50,000 $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 media software consumer goods utilities business services energy health Description Possible Answer: This bar graph displays each sector and how much money is allocated for each one within the portfolio. Answer Key 56

22 Types of Companies $80,000 $70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 small mid large Description Possible Answer: This bar graph shows the cap size (small, mid & large) of the different companies in the portfolio, and the dollar value for each size. Answer Key 57

23 Portfolio by Sector and Cap small mid large $50,000 $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 media software consumer goods utilities business services energy health Description Possible Answer: In this graph, the bars indicate how much money is allocated to each sector. The color, pattern, or shade of the bar symbolizes the cap size of the particular sector. Answer Key 58

24 Below is a practice portfolio. The stocks listed include information on the size of the company, the industry it operates within, and the value of the investment. Company Cap Sector Investment Value size A Mid Consumer Services $9,500 B Mid Software $30,000 C Small Software $13,500 D Large Media $20,000 E Mid Telecommunications $15,000 F Large Software $12, On a separate sheet of paper, use the information above to create two graphical representations that show the diversification (in terms of both cap size and sector) of the portfolio. 2. On a separate sheet of paper, represent graphically the diversification of your own group s portfolio. Answers will vary: Students should use the graphs and charts from the previous pages as examples. The total value of this portfolio is $100,000. Small cap ($13,500 $100,000) x 100% = x 100 = 13.5% Mid cap ($54,500 $100,000) x 100% = x 100 = 54.5% Large cap ($32,000 $100,000) x 100% = 0.32 x 100 = 32.0% Consumer Services ($9,500 $100,000) x 100% = x 100 = 9.5% Software ($55,500 $100,000) x 100% = x 100 = 55.5% Media ($20,000 $100,000) x 100% = 0.20 x 100 = 20.0% Telecommunications ($15,000 $100,000) x 100% = 0.15 x100 = 15.0% Answer Key 59

25 TACKLING COMPLEX PROBLEMS Below is a list of a team s portfolio holdings. They claim that their portfolio is diversified because they have an equal number of stocks from each company. Do you agree? Stock Price per Share Number of Shares Cap Size British Airways PLC (BAB) $ Large Eddie Bauer Holdings Inc. $ Small (EBHI) Handleman Company (HDL) $ Small Krispy Kreme Doughnuts Inc. $ Small (KKD) Scholastic Corporation $ Mid (SCHL) SunPower Corporation $ Mid (SPWR) Symantec Corporation $ Large (SYMC) The Stanley Works (SWK) $ Mid United Health Group Inc. (UNH) $ Large 1. What is the total value of their portfolio? The total value of this portfolio is $49, You find this value by summing the product of each stock s price by the number of shares. 2. How much money is invested in: Small cap stocks? Answer: $4, Mid cap stocks? Answer: $20, Large cap stocks? Answer: $25, What percentage of their investment is in: Small cap stocks? Answer: Small cap stocks = ($4, $49,849.50) x 100% = 8.74% Mid cap stocks? Answer: Mid cap stocks = ($20, $49,849.50) x 100% = 40.26% Large cap stocks? Answer: Large cap stocks = ($25, $49,849.50) x 100% = 51.01% Answer Key 60

26 TACKLING COMPLEX PROBLEMS 4. Would you advise them to increase their diversity? Why or why not? Answers will vary. Possible answers may include: It is important to note that buying equal shares of stock for each company does not necessarily make a portfolio diversified. What makes a portfolio diversified is having a variety of stocks from different sectors. They might consider reinvesting some of their money in small cap companies. Can you make recommendations about what stocks they might buy more of and which they might sell? Answers will vary. Perhaps they should sell some of the British Airways (90 shares or so). Also, the team might sell between 30 and 40 shares each of The Stanley Works, SunPower Corp., and United Health Group. Answer Key 61