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Chapter 9, Solutions

Cornett, 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.

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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.

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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.

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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.

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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.

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Chapter 9, Solutions

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Cornett, Adair, and Nofsinger

6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why? General Electric is a firm that has diversified business lines. It makes kitchen appliances, medical devices, and own the TV network NBC. Thus, much of GE’s firm specific risk is reduced. Coca-Cola does not have such business line diversification. So GE’s total risk is likely to be lower because its firm specific risk is lower.

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7. Can a company change its total risk level over time? How? A company can change is risk level over time. The company can change the mix of business lines it pursues. Some industries are riskier than others. For example, the airline industry has much risk while the utility industry has much less risk. Companies can also change their risk by changing the amount of money they have borrowed (more borrowing is riskier).

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8. 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. It is computed by dividing the standard deviation of return by the total return. Investors would prefer to achieve a high return with little risk. In other words, they would like a high return with little standard deviation. This is realized in the coefficient of variation measure by a lower number.

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9. You receive an investment newsletter advertisement in the mail. 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. It also claims that this stock is a surefire safe bet for the future. Explain how these two claims are inconsistent with finance theory. A stock that can earn a large return quickly versus the market is a very volatile stock. Thus, it is a high risk stock. The stock may indeed increase in the future. However, high risk means that it could also decrease much in price in the future. It is not a surefire safe bet.

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10. What does diversification do to the risk and return characteristics of a portfolio? Diversifying does little for the return of the portfolio. The portfolio return is the weighted average of the investment returns in the portfolio. However, diversification can do much for reducing the total risk of the portfolio as measured by the standard deviation. By combining assets that perform differently in different economic environments, the overall level of the risk in the portfolio is reduced. In addition, diversifying reduces the firm specific portion of each asset’s total risk.

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Chapter 9, Solutions

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Cornett, Adair, and Nofsinger

11. Describe the diversification potential of two assets with a −0.8 correlation. What’s the potential if the correlation is +0.8? The diversification potential is very good with two assets that have a −0.8 correlation. Since these two assets tend to move in opposite directions, the combination will greatly reduce the risk or volatility an investor would experience with only one of the assets. There is not much diversification potential for two assets with a correlation close to one, like +0.8.

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12. You are a risk adverse investor with a low-risk portfolio of bonds. 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 9.6). In some economic environments, stocks do well and bonds do not. During other times, bonds do better. Adding a small portion of stocks to a bond portfolio can actually decrease the volatility of the portfolio.

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13. You own only two stocks in your portfolio but want to add more. When you add a third stock, the total risk of your portfolio declines. When you add a tenth stock to the portfolio, the total risk declines. Adding which stock, the third or the tenth, likely reduced the total risk more? Why? A portfolio of two stocks likely still has much firm specific risk left. Assuming that the stocks are not highly correlated, a nine stock portfolio should already have much of its firm specific risk diversified away. Therefore, the third stock added has much more potential for reducing the risk of the portfolio than the tenth stock added.

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14. Many employees believe that their employer’s stock is less likely to lose half of its value than a well diversified portfolio of stocks. Explain why this belief is erroneous. A single firm has a lot of firm specific risk. This means that it has more volatility in its returns than the overall stock market. Remember, high volatility means large price changes. Also consider that if a well diversified stock portfolio falls by half, this means large declines for the overall stock market and all firms, including the employer’s stock (known as market risk). But a large decline in the employer’s stock does not mean a large decline occurs in the overall market (firm specific risk).

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15. Explain what we mean when we say that one portfolio dominates another portfolio? A dominate portfolio has a better risk return relationship. This means that it either has high return for the level of risk taken or lower risk for the level of return achieved. No investor should want a dominated portfolio.

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16. Explain what the efficient frontier is and why it is important to investors.

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Chapter 9, Solutions

Cornett, Adair, and Nofsinger

The efficient frontier is the set of efficient, or dominating, portfolios. These portfolios have the highest return for each level of risk desired. Since all other portfolios are dominated by the efficient frontier portfolios, all investors should and these efficient portfolios. LG6

17. If an investor’s desired risk level changes over time, should the investor change the composition of his or her portfolio? How? Yes, investors should modify their portfolios to be consistent with their level of risk. For example, many people want to reduce their level of risk as they approach their retirement years. One way to change the level of risk in a portfolio is to change the allocation of stocks and bonds. An increase in bonds would cause a decrease in the risk of the portfolio.

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18. Say you own 200 shares of Mattel and 100 shares of RadioShack. 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. The weights are determined by the proportion of money invested in each firm. The portfolio’s return in these two cases would be different because the proportions of money invested in each stock are different.

Problems Basic Problems LG1

9-1 Investment Return FedEx Corp stock ended the previous year at $103.39 per share. It paid a $0.35 per share dividend last year. It ended last year at $106.69. If you owned 300 shares of FedEx, what was your dollar return and percent return? Dollar Return  Ending Value  Beginning Value  Income $106.69300 - $103.39300 $0.35 300

Percentage Return = $1,095 ÷ ($103.39×300) = 0.0353 = 3.53% LG1

9-2 Investment Return Sprint Nextel Corp stock ended the previous year at $23.36 per share. It paid a $2.37 per share dividend last year. It ended last year at $18.89. If you owned 500 shares of Sprint, what was your dollar return and percent return?

 EndingValue  BeginningValue Income $18.89  Dollar Return  500 - $23.36  500 $2.37  500 Percentage Return = -$1,050 ÷ ($23.36×500) = -0.0899 = -8.99% LG3

9-3 Total Risk Rank the following three stocks by their level of total risk, highest to lowest. Rail Haul has an average return of 12 percent and standard deviation of 25

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Chapter 9, Solutions

Cornett, Adair, and Nofsinger

percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. Rank by standard deviation: Idol Staff, Rail Haul, and then Poker-R-Us LG3

9-4 Total Risk Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has an average return of 13 percent and standard deviation of 29 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. Rank by standard deviation: Fruit Fly, Night Ryder, and then WholeMart

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9-5 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. Rank by coefficient of variation: Rail Haul CoV=20/9=2.22, and Idol Staff CoV=35/15=2.33.

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CoV=25/12=2.08,

Poker-R-Us

9-6 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Night Ryder has an average return of 13 percent and standard deviation of 29 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. Rank by coefficient of variation: Night Ryder CoV=29/13=2.23, WholeMart CoV=25/11=2.27, and Fruit Fly CoV=40/16=2.5.

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9-7 Dominant Portfolios Determine which one of these three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Blue has an expected return of 12 percent and risk of 18 percent. The expected return and risk of portfolio Yellow are 13 percent and 17 percent, and for the Purple portfolio are 14 percent and 20 percent. Portfolio Yellow dominates Portfolios Blue and Purple because it has both a higher expected return and a lower risk level.

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9-8 Dominant Portfolios Determine which one of the three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Green has an expected return of 15 percent and risk of 21 percent. The expected return and risk of portfolio Red are 13 percent and 17 percent, and for the Orange portfolio are 13 percent and 16 percent.

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Chapter 9, Solutions

Cornett, Adair, and Nofsinger

Portfolio Orange dominates Portfolios Red and Green because it has the same or lower expected return with a lower risk level. LG7

9-9 Portfolio Weights An investor owns $4,000 of Adobe Systems stock, $5,000 of Dow Chemical, and $6,000 of Office Depot. What are the portfolio weights of each stock? Total portfolio is $4,000 + $5,000 + $6,000 = $15,000 Adobe System weight = $4,000 / $15,000 = 0.2667 Dow Chemical weight = $5,000 / 15,000 = 0.3333 Office Depot weight = $6,000 / $15,000 = 0.4

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9-10 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of Dow Chemical, and $7,000 of Office Depot. What are the portfolio weights of each stock? Total portfolio is $3,000 + $6,000 + $7,000 = $16,000 Adobe System weight = $3,000 / $16,000 = 0.1875 Dow Chemical weight = $6,000 / 16,000 = 0.375 Office Depot weight = $7,000 / $16,000 = 0.4375

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9-11 Portfolio Return Year-to-date, Oracle had earned a −1.34 percent return. During the same time period, Valero Energy earned 7.96 percent and McDonalds earned 0.88 percent. If you have a portfolio made up of 30 percent Oracle, 20 percent Valero Energy, and 50 percent McDonalds, what is your portfolio return? Portfolio Return is 0.3×−1.34% + 0.2×7.96% + 0.5×0.88% = 1.63%

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9-12 Portfolio Return Year to date, Yum Brands had earned a 3.80 percent return. During the same time period, Raytheon earned 4.26 percent and Coca-Cola earned −0.46 percent. If you have a portfolio made up of 30 percent Yum Brands, 30 percent Raytheon, and 40 percent Coca-Cola, what is your portfolio return? Portfolio Return is 0.3×3.80% + 0.3×4.26% + 0.4×−0.46% = 2.23%

Intermediate Problems 9-13 Average Return The past five monthly returns for Kohl’s are 3.54 percent, 3.62 percent, −1.68 percent, −1.42 percent, and 8.75 percent. What is the average monthly LG1 return? Average Return = (3.54%+3.62%−1.68%−1.42%+8.75%) / 5 = 2.562% LG1

9-14 Average Return The past five monthly returns for PG&E are 2.14 percent, −1.37 percent, 3.77 percent, 6.47 percent, and 3.58 percent. What is the average monthly return? Average Return = (2.14%−1.37%+3.77%+6.47%+3.58%) / 5 = 2.918%

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Chapter 9, Solutions

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9-15 Standard Deviation Compute the standard deviation of Kohls’ monthly returns shown in Problem 9-13.

 3.54%  LG3

Cornett, Adair, and Nofsinger

2

2

2

2

2.562%    3.62%  2.562%     1.68%  2.562%     1.42%  2.562%   8.75%  2.5 5 1

9-16 Standard Deviation Compute the standard deviation of PG&E’s monthly returns shown in Problem 9-14.

 2.14% 

2

2

2

2

2.918%     1.37%  2.918%   3.77%  2.918%   6.47%  2.918%   3.58%  2.918 5 1

LG2&4 9-17 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.2 and 9.4) during each decade since 1950. Compute the coefficient of variation for each decade using the standard deviation and average return: Decade CoV 1950s NA 1960s 3.85 1970s 1.19 1980s 1.12 1990s 1.35 2000s 0.77 The lower the coefficient of variation, the better the risk-return relationship. The early two decades, 1950s and 1960s, have a poor risk return relationship for bonds. The 1950s coefficient of variation is not defined because the average is zero. The poor relationship in the 1950s is caused by the very low return in that decade. The three full decades since 1970 have had good risk-return relationship. LG2&4 9-18 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9.2 and 9.4) during each decade since 1950. Compute the coefficient of variation for each decade using the standard deviation and average return: Decade 1950s 1960s 1970s 1980s

CoV 0.40 0.33 0.29 0.29

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Chapter 9, Solutions

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1990s 0.24 2000s 0.55 The lower the coefficient of variation, the better the risk-return relationship. All these CoVs are very low. While they appear to have great risk-return relationships, it is because the risk is very low. T-bills are very safe instruments. However, they offer very low returns. 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 −0.12. The correlation between Thumb Devices and Sport Garb is −0.13. The correlation between Air Comfort and Sport Garb is 0.85. If you can pick only two stocks for your portfolio, which would you pick? Why? Air Comfort and Sport Garb have similar expected returns and standard deviations. Since their correlation is very high, not much risk will be reduced when combined. Combining either stock with Thumb Devices has good potential because it has higher return and they have low (negative) correlation it. Since Sport Garb has both lower risk (standard deviation) and lower correlation with Thumb Devices than does Air Comfort, combine Sport Garb and Thumb Devices. 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 0.88. The correlation between Pic Image and Warm Wear is −0.21. The correlation between Tax Help and Warm Wear is −0.19. If you can pick only two stocks for your portfolio, which would you pick? Why? Pic Image and Tax Help have similar expected returns and standard deviations. Since their correlation is very high, 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. Since Pic Image has both higher expected return and lower correlation with Warm Wear than does Tax Help, combine Pic Image and Warm Wear.

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Chapter 9, Solutions

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Cornett, Adair, and Nofsinger

9-21 Portfolio Weights If you own 300 shares of Alaska Air at $42.88, 350 shares of Best Buy at $51.32, and 250 shares of Ford Motor at $8.51, what are the portfolio weights of each stock? Total portfolio is 300×$42.88 + 350×$51.32 + 250×$8.51 = $32,953.50 Alaska Air weight = 300×$42.88 / $32,953.50 = 0.390 Best Buy weight = 350×$51.32 / $32,953.50 = 0.545 Ford Motor weight = 250×$8.51 / $32,953.50 = 0.065

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9-22 Portfolio Weights If you own 400 shares of Xerox at $17.34, 500 shares of Qwest at $8.15, and 350 shares of Liz Cl...