Chapter 9, SolutionsCornett, Adair, and Nofsinger CHAPTER 9 – CHARACTERIZING RISK AND RETURN Questions LG1 1. Why is the percentage return a more useful measure than the dollar return? The dollar return is most important relative to the amount invested. Thus, a $100 return is more impressive from a $1,000 investment than a $5,000 investment. The percentage return incorporates both the dollar return and the amount invested. Therefore, it is easier to compare percentage return across different investments. LG2 2. Characterize the historical return, risk, and risk-return relationship of the stock, bond and cash markets. Examining Table 9.2, it is clear that the stock market has earned about double the return since 1950 than bonds. Bonds have earned about 50% higher return than the cash markets. The risk in the stock market is also higher than the bond and cash markets according to the standard deviation measurement (Table 9.4). Another illustration of the high risk is that the stock market frequently losses money and sometimes does not earn more than the bond and cash markets over short periods of time (Table 9.2). The riskreturn relationship tells us that we should expect higher returns for the riskier market. We do see higher realized returns over the long term to the higher risk asset classes. LG3 3. How do we define risk in this chapter and how do we measure it? Risk is defined as the volatility of an asset’s returns over time. Specifically, the standard deviation of returns is used to measure risk. This computation measures the deviation from the average return. The idea is to use standard deviation, a measure of volatility of past returns to proxy for how variable returns are expected to be in the future. LG3 4. What are the two components of total risk? Which component is part of the risk-return relationship? Why? Total risk includes firm specific risk and market risk. The firm specific risk portion can be eliminated through diversification by owning many different investments. The portion of total risk that is left after diversifying, market risk, is the risk that is expected to be rewarded. Thus, market risk in the risk of the risk-return relationship. LG3 5. What’s the source of firm-specific risk? What’s the source of market risk? Firm-specific risk stems from the uncertainty arising from micro-events that primarily impact the firm or industry. Market risk comes from the macro events that impact all firms to some extent. 9-1 Can a company change its total risk level over time? How? A company can change is risk level over time. Investors would prefer to achieve a high return with little risk. A stock that can earn a large return quickly versus the market is a very volatile stock. Companies can also change their risk by changing the amount of money they have borrowed (more borrowing is riskier). diversifying reduces the firm specific portion of each asset’s total risk. LG3 7. Thus. and own the TV network NBC. The letter claims that you should invest in a stock that has doubled the return of the S&P 500 Index over the last three months. Which company is likely to have lower total risk.Chapter 9. Explain how these two claims are inconsistent with finance theory. high risk means that it could also decrease much in price in the future. 9-2 . LG4 9. much of GE’s firm specific risk is reduced. This is realized in the coefficient of variation measure by a lower number. What does diversification do to the risk and return characteristics of a portfolio? Diversifying does little for the return of the portfolio. the overall level of the risk in the portfolio is reduced. the airline industry has much risk while the utility industry has much less risk. and Nofsinger 6. Adair. It is not a surefire safe bet. Some industries are riskier than others. By combining assets that perform differently in different economic environments. The stock may indeed increase in the future. It is computed by dividing the standard deviation of return by the total return. LG5 10. In addition. LG4 8. In other words. Coca-Cola does not have such business line diversification. It also claims that this stock is a surefire safe bet for the future. it is a high risk stock. Solutions LG3 Cornett. medical devices. It makes kitchen appliances. diversification can do much for reducing the total risk of the portfolio as measured by the standard deviation. General Electric or Coca-Cola? Why? General Electric is a firm that has diversified business lines. they would like a high return with little standard deviation. However. The portfolio return is the weighted average of the investment returns in the portfolio. You receive an investment newsletter advertisement in the mail. The company can change the mix of business lines it pursues. For example. So GE’s total risk is likely to be lower because its firm specific risk is lower. However. What does the coefficient of variation measure? Why is a lower value better for the investor? The coefficient of variation measures the amount of risk taken for each one percent of return achieved. Thus. Explain what we mean when we say that one portfolio dominates another portfolio? A dominate portfolio has a better risk return relationship. But a large decline in the employer’s stock does not mean a large decline occurs in the overall market (firm specific risk). This means that it has more volatility in its returns than the overall stock market. high volatility means large price changes. A single firm has a lot of firm specific risk. In some economic environments. and Nofsinger 11. During other times. likely reduced the total risk more? Why? A portfolio of two stocks likely still has much firm specific risk left. LG5 13. the third or the tenth. the total risk declines. How is it possible that adding some stocks (which are riskier than bonds) to the portfolio can lower the total risk of the portfolio? Bonds and stocks have a low correlation (see Table 9. You own only two stocks in your portfolio but want to add more. this means large declines for the overall stock market and all firms. Describe the diversification potential of two assets with a −0.8 correlation. Solutions LG5 Cornett.Chapter 9. a nine stock portfolio should already have much of its firm specific risk diversified away.8 correlation. This means that it either has high return for the level of risk taken or lower risk for the level of return achieved. Since these two assets tend to move in opposite directions. Assuming that the stocks are not highly correlated. Adair. LG6 16. the combination will greatly reduce the risk or volatility an investor would experience with only one of the assets. the third stock added has much more potential for reducing the risk of the portfolio than the tenth stock added. the total risk of your portfolio declines. What’s the potential if the correlation is +0. including the employer’s stock (known as market risk). You are a risk adverse investor with a low-risk portfolio of bonds. When you add a third stock. LG6 15. Adding a small portion of stocks to a bond portfolio can actually decrease the volatility of the portfolio. like +0. Also consider that if a well diversified stock portfolio falls by half. Explain what the efficient frontier is and why it is important to investors. bonds do better. LG5 12. Remember. Adding which stock.6). When you add a tenth stock to the portfolio. Many employees believe that their employer’s stock is less likely to lose half of its value than a well diversified portfolio of stocks. stocks do well and bonds do not. LG5 14. No investor should want a dominated portfolio. Explain why this belief is erroneous.8? The diversification potential is very good with two assets that have a −0. 9-3 . Therefore. There is not much diversification potential for two assets with a correlation close to one.8. Chapter 9. investors should modify their portfolios to be consistent with their level of risk.$103. should the investor change the composition of his or her portfolio? How? Yes. It ended last year at $18. It paid a $0.$23. The weights are determined by the proportion of money invested in each firm. portfolios.35 300 $ Percentage Return = $1. An increase in bonds would cause a decrease in the risk of the portfolio.095 ÷ ($103. These portfolios have the highest return for each level of risk desired. Problems Basic Problems LG1 9-1 Investment Return FedEx Corp stock ended the previous year at $103. The portfolio’s return in these two cases would be different because the proportions of money invested in each stock are different.39 300 $0.050 ÷ ($23. LG6 17. It ended last year at $106.69. If an investor’s desired risk level changes over time.69 300 .36×500) = -0. Rail Haul has an average return of 12 percent and standard deviation of 25 9-4 .36 per share. One way to change the level of risk in a portfolio is to change the allocation of stocks and bonds. what was your dollar return and percent return? Dollar Return Ending Value Beginning Value Income $18.53% LG1 9-2 Investment Return Sprint Nextel Corp stock ended the previous year at $23. LG7 18. many people want to reduce their level of risk as they approach their retirement years. highest to lowest.37 per share dividend last year.37 500 $ Percentage Return = -$1.39 per share. what was your dollar return and percent return? Dollar Return Ending Value Beginning Value Income $106. Would your portfolio return be different if you instead owned 100 shares of Mattel and 200 shares of RadioShack? Why? The portfolio return would be the weighted average of the Mattel and RadioShack stock returns. For example.39×300) = 0. and Nofsinger The efficient frontier is the set of efficient. Say you own 200 shares of Mattel and 100 shares of RadioShack. Since all other portfolios are dominated by the efficient frontier portfolios.89 500 . Adair.35 per share dividend last year. If you owned 300 shares of FedEx. all investors should and these efficient portfolios.89. It paid a $2.99% LG3 9-3 Total Risk Rank the following three stocks by their level of total risk. If you owned 500 shares of Sprint. Solutions Cornett.0899 = -8. or dominating.36 500 $2.0353 = 3. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. Portfolio Blue has an expected return of 12 percent and risk of 18 percent.5. and of Fruit Fly are 16 percent and 40 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent. Name the dominated portfolio and the portfolio that dominates it. Night Ryder. Rank by coefficient of variation: Night Ryder CoV=29/13=2. The average return and standard deviation of WholeMart are 11 percent and 25 percent. and of Poker-R-Us are 9 percent and 20 percent. best to worst. Rank by standard deviation: Fruit Fly. Portfolio Yellow dominates Portfolios Blue and Purple because it has both a higher expected return and a lower risk level. LG6 9-8 Dominant Portfolios Determine which one of the three portfolios dominates another. 9-5 . Rail Haul. WholeMart CoV=25/11=2.08. The expected return and risk of portfolio Red are 13 percent and 17 percent. and then WholeMart LG4 9-5 Risk versus Return Rank the following three stocks by their risk-return relationship.Chapter 9. and for the Orange portfolio are 13 percent and 16 percent. Night Ryder has an average return of 13 percent and standard deviation of 29 percent.23.22. and of Fruit Fly are 16 percent and 40 percent. and then Poker-R-Us LG3 9-4 Total Risk Rank the following three stocks by their total risk level. and Nofsinger percent. Night Ryder has an average return of 13 percent and standard deviation of 29 percent. and of Poker-R-Us are 9 percent and 20 percent. and for the Purple portfolio are 14 percent and 20 percent. Portfolio Green has an expected return of 15 percent and risk of 21 percent. LG4 CoV=25/12=2. Poker-R-Us 9-6 Risk versus Return Rank the following three stocks by their risk-return relationship. The average return and standard deviation of WholeMart are 11 percent and 25 percent. and Idol Staff CoV=35/15=2.33. The expected return and risk of portfolio Yellow are 13 percent and 17 percent.27. Rank by coefficient of variation: Rail Haul CoV=20/9=2. Name the dominated portfolio and the portfolio that dominates it. Solutions Cornett. Adair. Rank by standard deviation: Idol Staff. LG6 9-7 Dominant Portfolios Determine which one of these three portfolios dominates another. best to worst. and Fruit Fly CoV=40/16=2. highest to lowest. The average return and standard deviation of Idol Staff are 15 percent and 35 percent. $5.000 Adobe System weight = $3. and $6. $6. Raytheon earned 4.34% + 0. 30 percent Raytheon.96% + 0.000 / $16.46 percent. LG7 9-9 Portfolio Weights An investor owns $4. and Nofsinger Portfolio Orange dominates Portfolios Red and Green because it has the same or lower expected return with a lower risk level.54 percent.2667 Dow Chemical weight = $5.88 percent. −1.000 of Adobe Systems stock. −1. Valero Energy earned 7.4×−0. If you have a portfolio made up of 30 percent Yum Brands.26 percent and Coca-Cola earned −0.000 = 0. −1.Chapter 9.4 LG7 9-10 Portfolio Weights An investor owns $3.5×0.14 percent.000 of Dow Chemical.3×4.000 = 0. and 40 percent Coca-Cola.375 Office Depot weight = $7. What is the average monthly return? Average Return = (2.000 + $6.14%−1.000 / $16.23% Intermediate Problems 9-13 Average Return The past five monthly returns for Kohl’s are 3.47%+3. 3. During the same time period.42%+8.26% + 0.80 percent return. What is the average monthly LG1 return? Average Return = (3.000 + $6.000 Adobe System weight = $4.562% LG1 9-14 Average Return The past five monthly returns for PG&E are 2. and 50 percent McDonalds.34 percent return.58%) / 5 = 2.62 percent. 20 percent Valero Energy. and 8.000 = 0. What are the portfolio weights of each stock? Total portfolio is $3. 3. what is your portfolio return? Portfolio Return is 0. Adair.000 of Office Depot. During the same time period.000 of Adobe Systems stock.68%−1.80% + 0. Solutions Cornett.75 percent.77 percent.000 / $15.54%+3.46% = 2.42 percent.68 percent.000 = 0.000 / 16.2×7.88% = 1.1875 Dow Chemical weight = $6.000 of Office Depot.3333 Office Depot weight = $6.62%−1.4375 LG7 9-11 Portfolio Return Year-to-date.000 = $15.000 + $5.000 = 0.000 = 0.000 / 15.37 percent.37%+3. Yum Brands had earned a 3. Oracle had earned a −1. If you have a portfolio made up of 30 percent Oracle.63% LG7 9-12 Portfolio Return Year to date.000 = $16.918% 9-6 .000 of Dow Chemical. 6.3×−1.000 / $15.47 percent. What are the portfolio weights of each stock? Total portfolio is $4.77%+6. what is your portfolio return? Portfolio Return is 0.75%) / 5 = 2.000 + $7.96 percent and McDonalds earned 0.58 percent.3×3. and 3. and $7. 35 2000s 0.62% 2.75% 2.4) during each decade since 1950.77 The lower the coefficient of variation. have a poor risk return relationship for bonds. the better the risk-return relationship. Adair.562% 2 5 1 LG3 4. The 1950s coefficient of variation is not defined because the average is zero.29 9-7 2.918% 2 3. Solutions LG3 Cornett. 1950s and 1960s.562% 2 3.40 0.2 and 9.Chapter 9. and Nofsinger 9-15 Standard Deviation Compute the standard deviation of Kohls’ monthly returns shown in Problem 9-13.47% 2.86% . Compute the coefficient of variation for each decade using the standard deviation and average return: Decade 1950s 1960s 1970s 1980s CoV 0.33 0. Compute the coefficient of variation for each decade using the standard deviation and average return: Decade CoV 1950s NA 1960s 3.562% 2 1.37% 2.85 1970s 1.562% 2 8.77% 2.31% 9-16 Standard Deviation Compute the standard deviation of PG&E’s monthly returns shown in Problem 9-14.42% 2.918% 2 6.918% 2 1.918% 2 3. The poor relationship in the 1950s is caused by the very low return in that decade.29 0.918% 2 5 1 LG2&4 9-17 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.54% 2. The three full decades since 1970 have had good risk-return relationship.19 1980s 1.562% 2 1.14% 2.68% 2.2 and 9. 2. 3.58% 2.4) during each decade since 1950.12 1990s 1. The early two decades. LG2&4 9-18 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9. 88.Chapter 9.21. Since their correlation is very high. which would you pick? Why? Air Comfort and Sport Garb have similar expected returns and standard deviations. 9-8 . The correlation between Pic Image and Warm Wear is −0. The correlation between Tax Help and Warm Wear is −0.24 2000s 0. Since Sport Garb has both lower risk (standard deviation) and lower correlation with Thumb Devices than does Air Comfort. Adair.55 The lower the coefficient of variation. Combining either stock with Thumb Devices has good potential because it has higher return and they have low (negative) correlation it. Solutions Cornett. combine Sport Garb and Thumb Devices. However. The correlation between Air Comfort and Sport Garb is 0. If you can pick only two stocks for your portfolio. While they appear to have great risk-return relationships. not much risk will be reduced when combined. Combining either stock with Warm Wear has good potential because it has higher return and they have low (negative) correlation it. LG4&5 9-19 Diversifying Consider the characteristics of the following three stocks: Expected Standard Return Deviation Thumb 13% 23% Devices Air Comfort 10% 19% Sport Garb 10% 17% The correlation between Thumb Devices and Air Comfort is −0. it is because the risk is very low.19. combine Pic Image and Warm Wear. which would you pick? Why? Pic Image and Tax Help have similar expected returns and standard deviations. they offer very low returns. and Nofsinger 1990s 0. not much risk will be reduced when combined.85. Since their correlation is very high. All these CoVs are very low. LG4&5 9-20 Diversifying Consider the characteristics of the following three stocks: Expected Standard Return Deviation Pic Image 11% 19% Tax Help 10% 19% Warm Wear 14% 24% The correlation between Pic Image and Tax Help is 0. the better the risk-return relationship. Since Pic Image has both higher expected return and lower correlation with Warm Wear than does Tax Help. T-bills are very safe instruments. The correlation between Thumb Devices and Sport Garb is −0. If you can pick only two stocks for your portfolio.13.12. 000 / $19.953.000 of Nike.409×−0.34 / $26. and −0.000 + $8. and $9. what are the portfolio weights of each stock? Total portfolio is 300×$42.953.500 of Starbucks.666.29% Advanced Problems LG2&5 9-25 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks.50 Xerox weight = 400×$17.13 percent. $5. What’s your portfolio return? Total portfolio is $6.000 = 0.88 + 350×$51.36 percent.500 + $7.000 = 0.500 / $22.065 LG7 9-22 Portfolio Weights If you own 400 shares of Xerox at $17.341×−1.308 First Data weight = $5.436×10.25×6.15.59% + 0.000 + $5.000 General Motors weight = $5.24% + 0. and Nike were 6.50 = 0.15 + 350×$44.500 = 0.22% = 1.15 / $26.545 Ford Motor weight = 250×$8.390 Best Buy weight = 350×$51. and $8.666.Chapter 9.32 / $32.32 + 250×$8.500 + $9. Adair.15% LG7 9-24 Portfolio Return At the beginning of the month.436 So Portfolio Return is 0. Solutions LG7 Cornett. Use these weights and the returns in Table 9.73 / $26.260 Qwest weight = 500×$8.34 + 500×$8.500 / $22.50 Alaska Air weight = 300×$42.953.80 percent. The monthly returns for News Corp. you owned $6.256×−2.587 LG7 9-23 Portfolio Return At the beginning of the month.000 / $22.666. The monthly returns for General Motors. −2.51.80% + 0. What is your portfolio return? Total portfolio is $5.500 of General Motors. 40 percent long-term Treasury Bonds. and 250 shares of Ford Motor at $8.153 Liz Claiborne weight = 350×$44. and 350 shares of Liz Claiborne at $44.000 of News Corp.34. $7.50 = 0.341 Nike weight = $9.88 / $32.22 percent.000 = 0.51 = $32. 500 shares of Qwest at $8.50 = 0. and 10.13% = 6.24 percent.88.000 / $19. Starbucks.51 / $32.500 = 0. First Data. and Whirlpool were 8.500 / $19.666.73 = $26.2 to compute the return of the portfolio in the year 2000 and each year 9-9 .500 = $19.50 = 0.500 = 0. 350 shares of Best Buy at $51. and Nofsinger 9-21 Portfolio Weights If you own 300 shares of Alaska Air at $42.59 percent.256 Whirlpool weight = $8.32.500 of Whirlpool. you owned $5.000 = $22. and 10 percent T-bills.25 Starbucks weight = $7.953.36% + 0.409 So Portfolio Return is 0. what are the portfolio weights of each stock? Total portfolio is 400×$17. −1.000 of First Data.50 = 0.50 = 0.500 News Corp weight = $6.73.308×8. 70% 1.1% 5. Adair.11% +0.4% 8.9% 6. The portfolio return is computed as: 0.5% -5.17% 1.72% 6.20% 2006 15.02% 2003 28.5% 9.38% Ave = 2.3×20.1% 20.08% 2001 -11.85% 4.1% + 0.06% 1. LG2&5 9-26 Asset Allocation You have a portfolio with an asset allocation of 60 percent stocks. The portfolio return is computed as: 0.8% 1.4% 6.42% 2002 -22.11% 2007 3.11% 5.6×-9. Use these weights and the returns in Table 9. and 10 percent T-bills.9% 4.81% 3.11% +0.9% = 4.6% -4.2 to compute the return of the portfolio in the year 2000 and each year since. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. Combining these assets achieved some risk reduction.7% 10.11% 5.94% 2004 10.8% 1.95% 2003 28.51% 2007 3.Chapter 9.1×5.5×-9.1% 5.09% 6.9% 4.9% 1.1% + 0. 30 percent long-term Treasury Bonds.4×20.1% 17.9% 7.81% 3.70% 1.06% 1.59% StdDev= 16.48% 8.16% Portfolio Stocks Bonds T-bills Return 2000 -9.27% 2004 10.01% Ave = 2.5% -3.42% 8.50% 3.56% 3.85% 4.67% 2005 4.9% 7.37% 2006 15.99% 2005 4.7% 9.1% 17.0% 15. and Nofsinger since.1% 20.08% 1. These answers were computed using a spreadsheet.7% 2. Solutions Cornett.08% Portfolio Stocks Bonds T-bills Return 2000 -9.16% 2001 -11.08% 1.73% 3.50% 3.1×5.42% 8. These answers were computed using a spreadsheet.9% 4.4% 5.5% 9.56% 3.6% -7. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class.4% 8.70% 5.7% 2.73% 3.59% StdDev= 16.78% 2002 -22.9% = 1.70% 4.72% 6.17% 1.9% 6.51% The portfolio has the second highest return with the second lowest risk.47% 9-10 .0% 17. 440.51 = 528 shares Because of rounding up.57% 9-11 .00) $1. So.00 $597.816.00 Duke $6.00 JDS Uniphase $9.00) $0. 40 percent Best Buy.45 $1.30×$15.55 JDS Uniphase 500 $18.000÷$44.06 $43.73.000÷$8. and the stock prices a the end of the year.00) $618.90.00 $315. Xerox: 0.000÷$42.Chapter 9. you will still have a cash balance of $24.50 $2.08 $1. 40 percent Qwest. Solutions Cornett. LG7 9-28 Portfolio Weights You have $20.73 = 156 shares Excluding commissions paid.000 to invest.88.76% 25.000÷$8.43 PepsiCo 200 $59.00 ($1. Best Buy at $51.32. You want to purchase shares of Xerox at $17.00 -11.287016 Capital Gain Income Total Return Percentage Return ($21.755.88 = 105 shares Best Buy: 0.21 Solution by spreadsheet: Company beginning value Washington Mutual $13. and 30 percent Ford Motor? Report only whole stock shares.31699 0.000÷$17. and Nofsinger The portfolio has the second highest return with the second highest risk. and Ford Motor at $8.00 $926.34.25×$20.84% 0.050. and Liz Claiborne at $44. How many shares of each company should you purchase so that your portfolio consists of 25 percent Xerox.50 portfolio weight 0.000.229302 ($1.66 Duke Energy 250 $27.35×$20. and 35 percent Liz Claiborne? Report only whole stock shares. one less share of one of these stocks should be purchased.000÷$51.00 4.00 0. Qwest at $8.00 $232. the dividends that each stock paid during the year. Alaska Air: 0.862.40×$20.88 $16.16 $62.166693 $1.40×$15.32 = 117 shares Ford Motor: 0.57% 7.00 $694. Adair.30×$15. this adds up to slightly more than $15. How many shares of each company should you purchase so that your portfolio consists of 30 percent Alaska Air.34 = 288 shares Qwest: 0.26 $33.440.15. LG7 9-27 Portfolio Weights You have $15.110. Combining these assets achieved some risk reduction.15 = 982 shares Liz Claiborne: 0. You want to purchase shares of Alaska Air at $42.110. What is your portfolio dollar return and percentage return? Beginning Dividend End of Company Shares of Year per share Year Price Price Washington Mutual 300 $43.000 to invest.51. LG7 9-29 Portfolio Return The table below shows your stock positions at the beginning of the year.00 PepsiCo $11. 00 0.94 $24.45 $37.873.470.6% 4.322.00) -2.00 Portfolio Return = 5.00) $0.00 $351.50 $2.27% 9-30 Portfolio Return The table below shows your stock positions at the beginning of the year.91 $1.039.514.50) $112. Return.50 Total Return Percentage Return $4. Which stock appears better? Why? Solution by spreadsheet: 9-12 . What is your portfolio dollar return and percentage return? Beginning Dividend End of Company Shares of Year per share Year Price Price Johnson Controls 300 $72.9% 48.23% $2.168.00 0.17 $85.39 Qualcomm 250 $43.57 $0.254.1% 2004 17. standard deviation. and Nofsinger $41.00 Direct TV $12.903. Solutions Energy total = LG7 Cornett.Chapter 9.190192 ($1. and coefficient of variation.00) -6.51 Direct TV 500 $24.00 total = $56.0% 16.0% 2005 −26.00) $82.627.0% 2002 −16.770.00 19. the dividends that each stock paid during the year.220213 ($275. and the stock prices a the end of the year.41 $53. and Their Relationship Consider the following annual returns of Estee Lauder and Lowe’s Companies: Estee Lauder Lowe’s Companies 2006 23.60% LG3&4 9-31 Risk.00 Portfolio Return = 3.92 Medtronic 200 $57.2% 2003 49.08 $0.00 0.4% −6.386265 $3.210.8% −19.0% Compute each stock’s average return. Adair.203331 ($812.00) -11.00 Qualcomm $10.00 Medtronic $11.168.79 Solution by spreadsheet: Company beginning value Johnson Controls $21.45% ($730.34% ($275.00 portfolio weight Capital Gain Income 0.21% ($1. 5% 2004 36. and Nofsinger Estee Lowe’s Lauder Companies Ave = 30. Nikkei 225 of Japan. Adair.6% 2002 16.5% −0.77% StDev= 17.2% −11. LG3&4 9-32 Risk.69% 15.1% Compute each stock’s average return. and Their Relationship Consider the following annual returns of Molson Coors and International Paper: Molson Coors International Paper 2006 16. Solutions Cornett. Date All Ordinaries Nikkei 225 FTSE 100 Date 9-13 All Ordinaries Nikkei 225 FTSE 100 . 9-33 Excel Problem Below are the monthly returns for May 2002 to June 2007 of three international stock indices.568318 0.3% 4.22% 22.7% −17. Estee Lauder was better. standard deviation. and FTSE 100 of England.00% 15. All Ordinaries of Australia.55% StDev= 11. Return.Chapter 9. Molson Coors was better. it is not a surprise that Estee Lauder has a better (lower) coefficient of variation.65% CoV = 0.994799 Estee Lauder has experienced a higher average return then Lowe’s with a lower risk (standard deviation).30% 22. Which stock appears better? Why? Solution by spreadsheet: Molson International Coors Paper Ave = 23.9% 26.5% 2005 −9. and coefficient of variation.2% 2003 −6.63% CoV = 0. it is not a surprise that Molson Coors has a better (lower) coefficient of variation.508324 1. Thus.004956 Molson Coors has experienced a higher average return then IP with a lower risk (standard deviation). Thus. 36% 4.01% 0.67% 3.51% -4.33% 4.72% 3.69% 1.68% 1.54% .35% 3.65% -0.71% 2.45% -4.38% (Australia) Nov 2004 Oct 2004 Sep 2004 Aug 2004 Jul 2004 Jun 2004 May 2004 Apr 2004 Mar 2004 Feb 2004 Jan 2004 Dec 2003 Nov 2003 Oct 2003 Sep 2003 Aug 2003 Jul 2003 Jun 2003 May 2003 Apr 2003 Mar 2003 Feb 2003 Jan 2003 Dec 2002 Nov 2002 Oct 2002 Sep 2002 9-14 (Japan) (England) 2.35% 4.24% 1.65% -1.77% 8.00% 2.01% 3.31% 1.15% 2.42% 0.93% 3.83% 3.57% 3.54% 3.70% 3.65% 2.49% 1.03% -0.92% 8.93% 4.71% 3. Solutions (Australia) Jun 2007 May 2007 Apr 2007 Mar 2007 Feb 2007 Cornett.20% 2.16% -5.55% 1.73% 2.04% -0.47% -1.10% -2.82% -0.10% 3.27% 0.24% 2.09% -2.65% -0.85% 2.76% -1.47% -1.54% 0.34% 2.28% -7.21% Jan 2007 Dec 2006 Nov 2006 1.44% -4.41% Jul 2005 1.31% -0.68% 0.02% 1.37% 1.42% -0.93% Jul 2006 2.67% 0.30% 7.24% 0.73% 8.33% -2.48% 1.79% 0.83% 0.11% 4.97% 2.43% 3.08% 0.19% 1.10% -1.33% 3.90% 5.14% 2.84% Oct 2006 2.06% 9.61% Oct 2005 3.21% 2.31% -0.28% 2.35% 1.28% 3.92% 0.40% 2.01% 6.98% 2.64% -4.75% 1.28% Jun 2005 May 2005 Apr 2005 2.23% 2.13% 1.52% 2.31% 3.59% 5.25% 0.87% 9. Adair.37% 2.92% 2.54% 4.12% 5.99% Jan 2006 Dec 2005 Nov 2005 -0.04% -2.51% 2.05% 0.64% 7.16% -1.91% -5.64% -6.80% -0.31% Sep 2006 Aug 2006 4.45% 5.27% -0.28% -0.30% 1.37% Jun 2006 May 2006 Apr 2006 Mar 2006 Feb 2006 -1.50% 1.82% 0.45% -2.91% -0.50% -1.29% 3.53% -4.40% 2.53% -0.73% 3.24% -2.32% 0.17% 3.80% 2.28% 3.67% -1.80% 5.79% -9.64% 3.12% 0.48% 4.66% 3.47% -1.35% 5.69% 2.91% -4.34% 3.47% -0.30% 6. and Nofsinger (Japan) (England) 1.63% 1.41% 2.51% -8.17% 0.Chapter 9.00% -1.29% -1.35% 0.35% -2.98% 2.76% 2.99% Sep 2005 Aug 2005 -3.20% 8.49% 1. and compare them. A.62% -11.53% 3.45% -4.71% -8.81% 3.39% 1. Solutions Mar 2005 Feb 2005 Jan 2005 Dec 2004 Cornett.559 0. Adair.73% 1. ii) All Ordinaries and FTSE 100.88% 0.36% -2.10% Nikkei 225 (Japan) 0.66% -0. and iii) Nikkei 225 and FTSE 100. Correlations All Ordinaries (Australia) All Ordinaries (Australia) Nikkei 225 (Japan) FTSE 100 (England) 1 0.692 Nikkei 225 (Japan) 1 0. All Ordinaries (Australia) 1.21% 3.13% -7.52% Ave = StDev = 2. Form a portfolio consisting of one third of each of the indices and show the portfolio return each year. Portfolio 0.10% 2.87% -9.79% Aug 2002 Jul 2002 Jun 2002 May 2002 -4.49% 1.43% A.89% -1.32% -0. Compute the correlation between i) All Ordinaries and Nikkei 225. C.61% -1. The FTSE 100 had the lowest return and had the middle level of risk. B. C.00% -8. Compute and compare each indices’ monthly average return and standard deviation.02% Research It! 9-15 .Chapter 9.81% -4. B.62% 4. and the portfolio’s return and standard deviation.96% -0.442 FTSE 100 (England) 1 The Nikkei and the FTSE are the least correlated. The All Ordinaries and the FTSE have the highest correlation. and Nofsinger -3.69% The All Ordinaries index had the highest monthly return with the lowest risk.81% FTSE 100 (England) 0.34% -5.84% -1.45% -2. the number of shares. minute to minute. Just enter your stocks. The table below shows the annual returns for the All REITs Index along side the returns of the S&P 500 Index. One of the easiest ways to invest in real estate is through real estate investment trusts (REITs) that trade like stocks on the stock exchanges. Adair. and your commission cost and you can see how your portfolio is doing. own rental units.Chapter 9.com/) The portfolio might look something like this: Integrated Mini Case: Diversifying with Other Asset Classes Many more types of investments are available besides stocks. DUK. LMT. (http://finance. and cash securities. Try entering symbols EBAY. These portfolio managers will update your portfolio as stock prices change. assume you own 200 shares of each. You watch the value of the portfolio change and see how each stock is doing every day. A REIT represents ownership in a portfolio consisting of a pool of real estate assets. What is the risk and return characteristics of these investments and do they provide diversification opportunities to the typical stock investor? You can invest in real estate in many ways. your purchase price. You can build properties. Many financial websites have the capability to follow the stocks in your portfolio over time. Go to the site and start a portfolio to watch (which required free registration). Many people invest in real estate and in precious metals. S&P 500 Index All REITs Gold Price 9-16 . T. An index of all REITs is a good measure of the performance of the real estate market. primarily gold. and trade raw land. Yahoo! Finance has a portfolio management tool. These activities take enormous time and expertise. As a start. and GSK.yahoo. and Nofsinger Following a Portfolio Following stocks in a portfolio is easier than ever. bonds. Solutions Cornett. 7% 10. 9-17 .1% Gold has been a highly sought-after asset all over the world.1% 28.3% 34.S.9% 15.4% 0.5% 28.4% 28.0% -9.5% 0.6% 17.8% 18.3% -2.6% 7.3% 37. citizens to hand in all the gold they possessed.8% 0.7% -2.6% 19.5% 14.7% 12.5% 15.0% 8.8% 31.0% -4.0% 31.8% 5.9% -18. Americans have sought to “strike it rich” through gold rushes in North Carolina (early 1800s).7% 17.1% -1.4% 32.6% 21.5% 5. President Franklin D.6% 14.3% 35.0% 19.3% 32.9% 15.7% 25.0% 1.8% 18.8% -17. The United States has had a very chaotic history with gold. Roosevelt ordered U.Chapter 9.9% -4. The table also shows the return from gold prices.S.2% 18. and has retained at least some economic value over thousands of years.8% 24.4% -4.2% -10.6% -21.2% 38.4% -0.5% 6.7% 21.9% 4.5% -10. California and Nevada (mid-1800s).9% 19.6% 25.5% -3.. and Nofsinger Index 36.6% 31. Struggling in the Great Depression.3% -19.4% 23.3% 22.7% 11.4% -1.5% 5.3% 35.2% 18.8% -7.2% 16. and Alaska (late 1800s).4% -17.3% 49.9% -5.6% 37.8% -1.9% -16.4% 8.1% 33.2% -32.2% 6.2% 1.5% Cornett.2% 23.1% -5.2% 5.8% 3.9% 21. Adair.4% 22.2% -15.8% Changes -19.1% -11. Solutions 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 37.0% 126.1% 22. citizens owning gold was not lifted until the end of 1974. The ban on U.5% 30.6% 30.7% 10.8% -6.2% 30.5% 25.9% -22.9% 4.6% 18. Adair.3. during many years. Dev. Thus.2% B.2% 13.3% 15.5% 15. A. Dev. What is the average return and standard deviation of this portfolio? Also compute the average return and standard deviation of the following portfolios: 75%/20%/5% and 80%/5%/15%. Solutions Cornett. How do these portfolios perform compared to owning just stocks? C.0% The first two portfolios would have had similar returns as the all stock portfolio. these two portfolios performed better than the all stock portfolio. Compute the annual returns of a portfolio consisting of 50% stocks / 40% real estate / 10% gold. but both would have had lower risk. B.= 12.3% 13.3% Ave = Std. 9-18 . Using a spreadsheet. 50/40/10 75/20/5 80/5/15 14. real estate. Ave = Std. However.7% 27. Plot the average return and standard deviation of the three assets and the three portfolios on a risk-return graph like Figure 9.3% 7.= S&P 500 All REITs Gold Index Index Price 14.6% 17. SOLUTION: A. and gold are all volatile.0% 14. This looks promising for diversification opportunities. compute the average return and standard deviation of each of the three asset class. and Nofsinger The returns for stocks.Chapter 9. the return of one asset is up while the others are down.1% 13. and Nofsinger C.Chapter 9. 9-19 . Solutions Cornett. Adair.
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