Calculate the Sharpe ratio of each of the three portfolios in Problem 41. What portfolio weight in Hannah stock maximizes the Sharpe ratio? Data from Problem 41: You are currently only invested in the Natasha Fund (aside from risk-free securities). It has an expected return of 14% with a volatility of 20%. Currently, the risk-free rate of interest is 3.8%. Your broker suggests that you add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of 20%, a volatility of 60%, and a correlation of 0 with the Natasha Fund. a. Is your broker right? b. You follow your broker’s advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 60% is in the Natasha Fund and 40% is in Hannah stock. When you tell your finance professor about your investment, he says that you made a mistake and should reduce your investment in Hannah. Is your finance professor right? c. You decide to follow your finance professor’s advice and reduce your exposure to Hannah. Now Hannah represents 15% of your risky portfolio, with the rest in the Natasha fund. Is this the correct amount of Hannah stock to hold?
> Suppose that all investors have the disposition effect. A new stock has just been issued at a price of $50, so all investors in this stock purchased the stock today. A year from now the stock will be taken over, for a price of $60 or $40 depending on the
> See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. By how much did Mydeco increase its debt from 2012 to 2016? b. What was Mydeco’s EBITDA/Interest coverage ratio in 2012 and 2016? Did its coverage ratio ever fall bel
> Consider the price paths of the following two stocks over six time periods: Neither stock pays dividends. Assume you are an investor with the disposition effect and you bought at time 1 and right now it is time 3. Assume throughout this question that y
> How does the disposition effect impact investors’ tax obligations?
> To put the turnover of Figure 13.3 into perspective, let’s do a back of the envelope calculation of what an investor’s average turnover per stock would be were he to follow a policy of investing in the S&P 500 port
> Assume that all investors have the same information and care only about expected return and volatility. If new information arrives about one stock, can this information affect the price and return of other stocks? If so, explain why?
> From the start of 1999 to the start of 2009, the S&P 500 had a negative return. Does this mean the market risk premium we should have used in the CAPM was negative?
> Suppose that in place of the S&P 500, you wanted to use a broader market portfolio of all U.S. stocks and bonds as the market proxy. Could you use the same estimate for the market risk premium when applying the CAPM? If not, how would you estimate the co
> Standard and Poor’s also publishes the S&P Equal Weight Index, which is an equally weighted version of the S&P 500. a. To maintain a portfolio that tracks this index, what trades would need to be made in response to daily price changes? b. Is this index
> Suppose Best Buy stock is trading for $30 per share for a total market cap of $9 billion, and Walt Disney has 1.65 billion shares outstanding. If you hold the market portfolio, and as part of it hold 100 shares of Best Buy, how many shares of Walt Disney
> Aluminum maker Alcoa has a beta of about 2.0, whereas Hormel Foods has a beta of 0.45. If the expected excess return of the marker portfolio is 5%, which of these firms has a higher equity cost of capital, and how much higher is it?
> You would like to estimate the weighted average cost of capital for a new airline business. Based on its industry asset beta, you have already estimated an unlevered cost of capital for the firm of 9%. However, the new business will be 25% debt financed,
> See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. Compare Mydeco’s accounts payable days in 2012 and 2016. b. Did this change in accounts payable days improve or worsen Mydeco’s ca
> Unida Systems has 40 million shares outstanding trading for $10 per share. In addition, Unida has $100 million in outstanding debt. Suppose Unida’s equity cost of capital is 15%, its debt cost of capital is 8%, and the corporate tax rate is 40%. a. What
> Your company operates a steel plant. On average, revenues from the plant are $30 million per year. All of the plants costs are variable costs and are consistently 80% of revenues, including energy costs associated with powering the plant, which represent
> Harrison Holdings, Inc. (HHI) is publicly traded, with a current share price of $32 per share. HHI has 20 million shares outstanding, as well as $64 million in debt. The founder of HHI, Harry Harrison, made his fortune in the fast food business. He sold
> Weston Enterprises is an all-equity firm with two divisions. The soft drink division has an asset beta of 0.60, expects to generate free cash flow of $50 million this year, and anticipates a 3% perpetual growth rate. The industrial chemicals division has
> Consider the following airline industry data from mid-2009: a. Use the estimates in Table 12.3 to estimate the debt beta for each firm (use an average if multiple ratings are listed). b. Estimate the asset beta for each firm. c. What is the average ass
> In mid-2015, Cisco Systems had a market capitalization of $130 billion. It had A-rated debt of $25 billion as well as cash and short-term investments of $60 billion, and its estimated equity beta at the time was 1.11. a. What is Cisco’s enterprise value?
> IDX Tech is looking to expand its investment in advanced security systems. The project will be financed with equity. You are trying to assess the value of the investment, and must estimate its cost of capital. You find the following data for a publicly t
> Suppose the market portfolio has an expected return of 10% and a volatility of 20%, while Microsoft’s stock has a volatility of 30%. a. Given its higher volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10%? b.
> Consider the setting of Problem 18. You decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second firm, Thurbinar Design, which is also engaged in a similar line of business. Thurbinar has a stoc
> Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin’s equity beta is 0.85, the risk free rate is 4%, and the market risk premium is 5%. If your f
> See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. How did Mydeco’s accounts receivable days change over this period? b. How did Mydeco’s inventory days change over this period? c.
> The Dunley Corp. plans to issue 5-year bonds. It believes the bonds will have a BBB rating. Suppose AAA bonds with the same maturity have a 4% yield. Assume the market risk premium is 5% and use the data in Table 12.2 and Table 12.3. a. Estimate the yiel
> During the recession in mid-2009, homebuilder KB Home had outstanding 6-year bonds with a yield to maturity of 8.5% and a BB rating. If corresponding risk-free rates were 3%, and the market risk premium was 5%, estimate the expected return of KB Home’s d
> In mid-2009, Rite Aid had CCC-rated, 6-year bonds outstanding with a yield to maturity of 17.3%. At the time, similar maturity Treasuries had a yield of 3%. Suppose the market risk premium is 5% and you believe Rite Aid’s bonds have a beta of 0.31. The e
> In mid-2012, Ralston Purina had AA-rated, 10-year bonds outstanding with a yield to maturity of 2.05%. a. What is the highest expected return these bonds could have? b. At the time, similar maturity Treasuries have a yield of 1.5%. Could these bonds actu
> Using the same data as in Problem 11, estimate the 95% confidence interval for the alpha and beta of Nike and Dell stock using Excel’s regression tool (from the data analysis menu) or the linest() function. Data from Problem 11: Go to Chapter Resources
> Using the same data as in Problem 11, estimate the alpha of Nike and Dell stock, expressed as % per month. Data from Problem 11: Go to Chapter Resources on and use the data in the spreadsheet provided to estimate the beta of Nike and Dell stock based o
> Go to Chapter Resources on and use the data in the spreadsheet provided to estimate the beta of Nike and Dell stock based on their monthly returns from 2011–2015.
> You need to estimate the equity cost of capital for XYZ Corp. You have the following data available regarding past returns: a. What was XYZ’s average historical return? b. Compute the market’s and XYZâ€
> Suppose Pepsico’s stock has a beta of 0.57. If the risk-free rate is 3% and the expected return of the market portfolio is 8%, what is Pepsico’s equity cost of capital?
> Suppose two stocks have a correlation of 1. If the first stock has an above average return this year, what is the probability that the second stock will have an above average return?
> At the end of 2015, Apple had cash and short-term investments of $41.60 billion, accounts receivable of $35.89 billion, current assets of $89.38 billion, and current liabilities of $80.61 billion. a. What was Apple’s current ratio? b. What was Apple’s qu
> Which organizational forms give their owners limited liability?
> Using the data from Table 11.3, what is the covariance between the stocks of Alaska Air and Southwest Airlines? Table 11.3: Alaska Air Šouthwest Airlines Ford Motor General Mills Microsoft HP Kellogg Volatility (Standard Deviation) 33% 37% 37% 31%
> Using your estimates from Problem 5, calculate the volatility (standard deviation) of a portfolio that is 70% invested in stock A and 30% invested in stock B. Data from Problem 5: Using the data in the following table, estimate (a) the average return a
> Use the data in Problem 5, consider a portfolio that maintains a 50% weight on stock A and a 50% weight on stock B. a. What is the return each year of this portfolio? b. Based on your results from part a, compute the average return and volatility of the
> What is the risk premium of a zero-beta stock? Does this mean you can lower the volatility of a portfolio without changing the expected return by substituting out any zero-beta stock in a portfolio and replacing it with the risk-free asset?
> Suppose Autodesk stock has a beta of 2.16, whereas Costco stock has a beta of 0.69. If the risk-free interest rate is 4% and the expected return of the market portfolio is 10%, what is the expected return of a portfolio that consists of 60% Autodesk stoc
> Using the data in the following table, estimate (a) the average return and volatility for each stock, (b) the covariance between the stocks, and (c) the correlation between these two stocks. Year 2010 2011 2012 2013 2014 2015 Stock A -10% 20% 5% -5%
> Consider a portfolio consisting of the following three stocks: The volatility of the market portfolio is 10% and it has an expected return of 8%. The risk-free rate is 3%. a. Compute the beta and expected return of each stock. b. Using your answer from
> Suppose you group all the stocks in the world into two mutually exclusive portfolios (each stock is in only one portfolio): growth stocks and value stocks. Suppose the two portfolios have equal size (in terms of total value), a correlation of 0.5, and th
> Your investment portfolio consists of $15,000 invested in only one stock—Microsoft. Suppose the risk-free rate is 5%, Microsoft stock has an expected return of 12% and a volatility of 40%, and the market portfolio has an expected return of 10% and a vola
> A big pharmaceutical company, DRIg, has just announced a potential cure for cancer. The stock price increased from $5 to $100 in one day. A friend calls to tell you that he owns DRIg. You proudly reply that you do, too. Since you have been friends for so
> For fiscal year end 2015, Wal-Mart Stores, Inc. (WMT, brand name Walmart) had revenues of $485.65 billion, gross profit of $120.57 billion, and net income of $16.36 billion. Costco Wholesale Corporation (COST) had revenue of $116.20 billion, gross profit
> When the CAPM correctly prices risk, the market portfolio is an efficient portfolio. Explain why.
> Returning to Problem 38, assume you follow your broker’s advice and put 50% of your money in the venture fund. a. What is the Sharpe ratio of the Tanglewood Fund? b. What is the Sharpe ratio of your new portfolio? c. What is the optimal fraction of your
> You are currently only invested in the Natasha Fund (aside from risk-free securities). It has an expected return of 14% with a volatility of 20%. Currently, the risk-free rate of interest is 3.8%. Your broker suggests that you add Hannah Corporation to y
> The Optima Mutual Fund has an expected return of 20%, and a volatility of 20%. Optima claims that no other portfolio offers a higher Sharpe ratio. Suppose this claim is true, and the risk-free interest rate is 5%. a. What is Optima’s Sharpe Ratio? b. If
> There are two ways to calculate the expected return of a portfolio: either calculate the expected return using the value and dividend stream of the portfolio as a whole, or calculate the weighted average of the expected returns of the individual stocks t
> You have noticed a market investment opportunity that, given your current portfolio, has an expected return that exceeds your required return. What can you conclude about your current portfolio?
> In addition to risk-free securities, you are currently invested in the Tanglewood Fund, a broad based fund of stocks and other securities with an expected return of 12% and a volatility of 25%. Currently, the risk-free rate of interest is 4%. Your broker
> Assume all investors want to hold a portfolio that, for a given level of volatility, has the maximum possible expected return. Explain why, when a risk-free asset exists, all investors will choose to hold the same portfolio of risky stocks.
> Assume the risk-free rate is 4%. You are a financial advisor, and must choose one of the funds below to recommend to each of your clients. Whichever fund you recommend, your clients will then combine it with risk-free borrowing and lending depending on t
> See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. What were Mydeco’s gross margins each year? b. Comparing Mydeco’s gross margin, EBIT margin, and net profit margin in 2012 to 2016
> You currently have $100,000 invested in a portfolio that has an expected return of 12% and a volatility of 8%. Suppose the risk-free rate is 5%, and there is another portfolio that has an expected return of 20% and a volatility of 12%. a. What portfolio
> You have $100,000 to invest. You choose to put $150,000 into the market by borrowing $50,000. a. If the risk-free interest rate is 5% and the market expected return is 10%, what is the expected return of your investment? b. If the market volatility is 15
> Suppose you have $100,000 in cash, and you decide to borrow another $15,000 at a 4% interest rate to invest in the stock market. You invest the entire $115,000 in a portfolio J with a 15% expected return and a 25% volatility. a. What is the expected retu
> You expect HGH stock to have a 20% return next year and a 30% volatility. You have $25,000 to invest, but plan to invest a total of $50,000 in HGH, raising the additional $25,000 by shorting either KBH or LWI stock. Both KBH and LWI have an expected retu
> You have $10,000 to invest. You decide to invest $20,000 in Google and short sell $10,000 worth of Yahoo! Google’s expected return is 15% with a volatility of 30% and Yahoo!’s expected return is 12% with a volatility of 25%. The stocks have a correlation
> Suppose Target’s stock has an expected return of 20% and a volatility of 40%, Hershey’s stock has an expected return of 12% and a volatility of 30%, and these two stocks are uncorrelated. a. What is the expected return and volatility of an equally weight
> Consider a world that only consists of the three stocks shown in the following table: a. Calculate the total value of all shares outstanding currently. b. What fraction of the total value outstanding does each stock make up? c. You hold the market port
> Fred holds a portfolio with a 30% volatility. He decides to short sell a small amount of stock with a 40% volatility and use the proceeds to invest more in his portfolio. If this transaction reduces the risk of his portfolio, what is the minimum possible
> Consider the portfolio in Problem 27. Suppose the correlation between Intel and Oracle’s stock increases, but nothing else changes. Would the portfolio be more or less risky with this change? Data from Problem 27: A hedge fund has cre
> A hedge fund has created a portfolio using just two stocks. It has shorted $35,000,000 worth of Oracle stock and has purchased $85,000,000 of Intel stock. The correlation between Oracle’s and Intel’s returns is 0.65. T
> Find online the annual 10-K report for Costco Wholesale Corporation (COST) for fiscal year 2015 (filed in October 2015). Answer the following questions from the notes to their financial statements: a. How many stores did Costco open outside of the U.S. i
> Using the same data as for Problem 23, calculate the expected return and the volatility (standard deviation) of a portfolio consisting of Johnson & Johnson’s and Walgreens’ stocks using a wide range of portfolio we
> Calculate (a) the expected return and (b) the volatility (standard deviation) of a portfolio that consists of a long position of $10,000 in Johnson & Johnson and a short position of $2000 in Walgreens. Data for Problem 25: Expected Return Stand
> For the portfolio in Problem 23, if the correlation between Johnson & Johnson’s and Walgreens’ stock were to increase, a. Would the expected return of the portfolio rise or fall? b. Would the volatility of the port
> Calculate (a) the expected return and (b) the volatility (standard deviation) of a portfolio that is equally invested in Johnson & Johnson’s and Walgreens’ stock. Data for Problem 23: Expected Return Standard
> Suppose Intel’s stock has an expected return of 26% and a volatility of 50%, while Coca-Cola’s has an expected return of 6% and volatility of 25%. If these two stocks were perfectly negatively correlated (i.e., their correlation coefficient is -1), a. Ca
> Suppose Ford Motor stock has an expected return of 20% and a volatility of 40%, and Molson Coors Brewing has an expected return of 10% and a volatility of 30%. If the two stocks are uncorrelated, a. What is the expected return and volatility of an equall
> You currently hold a portfolio of three stocks, Delta, Gamma, and Omega. Delta has a volatility of 60%, Gamma has a volatility of 30%, and Omega has a volatility of 20%. Suppose you invest 50% of your money in Delta, and 25% each in Gamma and Omega. a. W
> You own three stocks: 600 shares of Apple Computer, 10,000 shares of Cisco Systems, and 5000 shares of Colgate-Palmolive. The current share prices and expected returns of Apple, Cisco, and Colgate-Palmolive are, respectively, $500, $20, $100 and 12%, 10%
> Stock A has a volatility of 65% and a correlation of 10% with your current portfolio. Stock B has a volatility of 30% and a correlation of 25% with your current portfolio. You currently hold both stocks. Which will increase the volatility of your portfol
> Consider an equally weighted portfolio of stocks in which each stock has a volatility of 40%, and the correlation between each pair of stocks is 20%. a. What is the volatility of the portfolio as the number of stocks becomes arbitrarily large? b. What is
> See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. What were Mydeco’s retained earnings each year? b. Using the data from 2012, what was Mydeco’s total stockholdersâ€
> What is the volatility (standard deviation) of an equally weighted portfolio of stocks within an industry in which the stocks have a volatility of 50% and a correlation of 40% as the portfolio becomes arbitrarily large?
> Suppose the average stock has a volatility of 50%, and the correlation between pairs of stocks is 20%. Estimate the volatility of an equally weighted portfolio with (a) 1 stock, (b) 30 stocks, (c) 1000 stocks.
> Using the data from Table 11.3, what is the volatility of an equally weighted portfolio of Microsoft, Alaska Air, and Ford Motor stock? Table 11.3: Alaska Air Southwest Airlines Ford Motor General Mills Microsoft HP Kellogg Volatility (Standard Dev
> Using the data in Table 11.1, a. Compute the annual returns for a portfolio with 25% invested in North Air, 25% invested in West Air, and 50% invested in Tex Oil. b. What is the lowest annual return for your portfolio in part a? How does it compare with
> Suppose Tex stock has a volatility of 40%, and Mex stock has a volatility of 20%. If Tex and Mex are uncorrelated, a. What portfolio of the two stocks has the same volatility as Mex alone? b. What portfolio of the two stocks has the smallest possible vol
> Suppose Avon and Nova stocks have volatilities of 50% and 25%, respectively, and they are perfectly negatively correlated. What portfolio of these two stocks has zero risk?
> Suppose Wesley Publishing’s stock has a volatility of 60%, while Addison Printing’s stock has a volatility of 30%. If the correlation between these stocks is 25%, what is the volatility of the following portfolios of Addison and Wesley: (a) 100% Addison,
> Arbor Systems and Gencore stocks both have a volatility of 40%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) +1, (b) 0.50, (c) 0, (d) -0.50, and (e) -1.0. In which cases is the volatil
> Using the data in Table 10.2, a. What was the average annual return of Microsoft stock from 2002–2014? b. What was the annual volatility for Microsoft stock from 2002–2014? Table 10.2: S&P 500 Index Dividends Pai
> Assume that historical returns and future returns are independently and identically distributed and drawn from the same distribution. a. Calculate the 95% confidence intervals for the expected annual return of four different investments included in Table
> Nokela Industries purchases a $40 million cyclo-converter. The cyclo-converter will be depreciated by $10 million per year over four years, starting this year. Suppose Nokela’s tax rate is 40%. a. What impact will the cost of the purchase have on earning
> Using the data in the following table, calculate the return for investing in Boeing stock (BA) from January 2, 2008, to January 2, 2009, and also from January 3, 2011, to January 3, 2012, assuming all dividends are reinvested in the stock immediately.
> Repeat Problem 4 assuming that the stock fell $5 to $45 instead. a. Is your capital gain different? Why or why not? b. Is your dividend yield different? Why or why not? Data from Problem 4: You bought a stock one year ago for $50 per share and sold it
> You bought a stock one year ago for $50 per share and sold it today for $55 per share. It paid a $1 per share dividend today. a. What was your realized return? b. How much of the return came from dividend yield and how much came from capital gain?
> State whether each of the following is inconsistent with an efficient capital market, the CAPM, or both: a. A security with only diversifiable risk has an expected return that exceeds the risk-free interest rate. b. A security with a beta of 1 had a retu
> Suppose the market risk premium is 6.5% and the risk-free interest rate is 5%. Calculate the cost of capital of investing in a project with a beta of 1.2.
> Given the results to Problem 35, why don’t all investors hold Autodesk’s stock rather than Hershey’s stock? Data from Problem 35: Suppose the market risk premium is 5% and the risk-free interest rate is 4%. Using the data in Table 10.6, calculate the e
> Suppose the market risk premium is 5% and the risk-free interest rate is 4%. Using the data in Table 10.6, calculate the expected return of investing in a. Starbucks’ stock. b. Hershey’s stock. c. Autodeskâ€
> Suppose the risk-free interest rate is 4%. a. i. Use the beta you calculated for the stock in Problem 33(a) to estimate its expected return. ii. How does this compare with the stock’s actual expected return? b. i. Use the beta you calculated for the stoc
> Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%. a. Calculate the beta of a firm that goes up on average by 43% when the market goes up and goes down by 17% when the market goes down. b. Calculate the beta of a firm t
> Based on the data in Table 10.6, estimate which of the following investments you expect to lose the most in the event of a severe market down turn: (1) A $2000 investment in Hershey, (2) a $1500 investment in Macy’s, or (3) a $1000 inve
