&/E ð ï ì d ^ ] } v ô WD ^ } o µ ] } v · Title: Microsoft PowerPoint - TA Session 8...

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FINC 430 TA Session 8 CAPM Solutions Marco Sammon

Transcript of &/E ð ï ì d ^ ] } v ô WD ^ } o µ ] } v · Title: Microsoft PowerPoint - TA Session 8...

Page 1: &/E ð ï ì d ^ ] } v ô WD ^ } o µ ] } v · Title: Microsoft PowerPoint - TA Session 8 Solutionsv2 Author: mcsam Created Date: 9/4/2018 4:23:06 PM

FINC 430 TA Session 8CAPM

Solutions

Marco Sammon

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Question 1 (10-37 in the Textbook)Suppose the market risk premium is 6.5% and therisk-free interest rate is 5%. Calculate the cost ofcapital of investing in a project with a beta of 1.2.

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Steps

1. Determine the MRP and RF2. Apply the CAPM equation

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Cost of Capital

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Question 2 (12-2 in the Textbook)Suppose the market portfolio has an expectedreturn of 10% and a volatility of 20%, whileMicrosoft’s stock has a volatility of 30%.a. Given its higher volatility, should we expectMicrosoft to have an equity cost of capital that ishigher than 10%?b. What would have to be true for Microsoft’sequity cost of capital to be equal to 10%?

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Steps

• Write Down CAPM regression•

• Take variance of both sides

• Write Down CAPM equation•

• Put in data from the question

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a. No, volatility includes diversifiable risk, so itcannot be used to assess the equity cost ofcapital.b. Microsoft stock would need to have a beta of1.

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Question 3 (12-6 in the Textbook)Suppose Best Buy stock is trading for $30 pershare for a total market cap of $9 billion, andWalt Disney has 1.65 billion shares outstanding. Ifyou hold the market portfolio, and as part of ithold 100 shares of Best Buy, how many shares ofWalt Disney do you hold?

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Steps

• Remember: Market is like someone owning every stock. If you hold the market, you just scale this up or down

• Determine number of shares Best Buy has outstanding

• Determine the ratio of DIS shares to Best Buy shares

• Determine # of DIS shares you hold

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Best Buy has 9/30 = 0.3 billion sharesoutstanding.Therefore, you hold 100 (1.65/0.3) = 550shares of Disney.

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Question 4 (12-10 in the Textbook)You need to estimate the equity cost of capital for XYZ Corp. You have thefollowing data available regarding past returns:

a. What was XYZ’s average historical return?b. Compute the market’s and XYZ’s excess returns for each year. Estimate XYZ’sbeta.c. Estimate XYZ’s historical alpha.d. Suppose the current risk-free rate is 3%, and you expect the market’s returnto be 8%. Use the CAPM to estimate an expected return for XYZ Corp.’s stock.e. Would you base your estimate of XYZ’s equity cost of capital on your answerin part (a) or in part (d)? How does your answer to part (c) affect yourestimate? Explain.

Year Risk-free return Market Return XYZ Return

2007 3% 6% 10%

2008 1 -37% -45%

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Steps

• Excess Return = Return – Risk Free Return• Write down CAPM equation

–

• Solve the CAPM equation for beta• Once you have beta, you can back out alpha

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a. (10% – 45%)/2 = –17.5%

b. Excess returns:MKT 3%, –38%XYZ 7%, –46%

c.

d.

e. Use (d)—CAPM is more reliable than average past returns,which would imply a negative cost of capital in this case!Ignore (c), as alpha is not persistent.

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Question 5

Consider the following diagram, plotting the standard deviation and expectedreturn of various assets. Assume that the CAPM holds. Asset F is risk-freeTreasury bills. Asset M is the market portfolio. Assets W, X, Y and Z areindividual risky assets that are all uncorrelated with each other.

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a. Calculate the beta of asset W.

Imagine running two regressions. Regression 1 is a regression of the excessreturns of asset Y on the excess returns of asset M. Regression 2 is aregression of the excess returns of asset Z on the excess returns of asset M.

b. Which of the following is true?i. The beta coefficient in regression 1 is higher than the beta coefficient inregression 2.ii. The beta coefficient in regression 1 is lower than the beta coefficient inregression 2.iii. The beta coefficient in regression 1 is the same as the beta coefficientin regression 2.iv. You cannot predict the relative magnitudes of the beta coefficients inthese regressions.

Explain your answer.

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c. Consider the same two regressions. Which of the following is true?

v. The R2 in regression 1 is higher than the R2 in regression 2.vi. The R2 in regression 1 is lower than the R2 in regression 2.vii. The R2 in regression 1 is the same as the R2 in regression 2.viii. You cannot predict the relative magnitudes of the R2 in these regressions.

Explain your answer.

d. Suppose you formed a portfolio P by holding 40% of your wealth in W and therest of your wealth in Z. Calculate the expected return and the standarddeviation of P.

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a. Calculate the beta of asset W.

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b. Which of the following is true? i. The beta coefficient in regression 1 is higher than the beta coefficient in regression 2.ii. The beta coefficient in regression 1 is lower than the beta coefficient in regression 2.iii. The beta coefficient in regression 1 is the same as the beta coefficient in regression 2.iv. You cannot predict the relative magnitudes of the beta coefficients in these regressions.

Explain your answer.

Since asset Y has the same expected return as asset Z, they must have the same beta. (Answer iii.)

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c. Consider the same two regressions. Which of the following istrue?

v. The R2 in regression 1 is higher than the R2 in regression 2.vi. The R2 in regression 1 is lower than the R2 in regression 2.vii. The R2 in regression 1 is the same as the R2 in regression 2.viii. You cannot predict the relative magnitudes of the R2 inthese regressions.

Explain your answer.

Y and Z have the same systematic risk (because of same betas).However, Z has more overall risk and therefore has moreidiosyncratic risk. Therefore, the R2 in regression 1 will be higher,since more of the total risk of Y will be explained by M.(Answer v.)

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d. Suppose you formed a portfolio P by holding 40% of your wealth in W and the rest of your wealth in Z. Calculate the expected return and the standard deviation of P.

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Question 6

Answer the following questions using the data from theExcel file. The returns data provided are monthlyreturns.

a. What is XYZ’s beta?b. According to the CAPM, what percentage of XYZ’sreturn movements is due to firm specific risk?c. Does the level of firm specific risk of a stockindicate whether the CAPM is a valid theory?

See Excel file for the solutions

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Firm Specific Risk

• Write Down CAPM regression•

• Take variance of both sides

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EXTRA QUESTIONS

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Question 7On Sunday, March 5, 2006, AT&T announced that it would be acquiring BellSouth. You have the following information:

You also know that the return on the market portfolio of stocks was -0.70 %(-0.007) on March 6 (calculated based on the closing values of the S&P 500index on March 3 and March 6). Assume that the riskless rate is zero and thatno dividends were paid on March 3 or March 6.

AT&T BellSouth

Number of shares outstanding 3.88 billion 1.80 billion

Beta (β) 0.80 0.83

Alpha (α) 0.00 0.00

Closing price per share on Friday, March 3 $27.99 $31.46

Closing price per share on Monday, March 6 $27.02 $34.50

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a. What was the firm-specific return for AT&T on March 6, & , (inpercent)? What was the firm-specific return for BellSouth on March 6,

, (in percent)?

b. Assume that for both AT&T and for BellSouth, the only firm-specificnews that arrived between the end of trading on Friday March 3 and theend of trading on March 6 was the news about AT&T's acquisition ofBellSouth. How much value (in dollars) did the announcement of theacquisition create/destroy for AT&T shareholders? How much value (indollars) did the announcement of the acquisition create/destroy forBellSouth shareholders? Does the proposed acquisition seem to create ordestroy value overall?

(End of question)

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a. To compute the firm-specific return, solve the CAPM regression

𝑟 , − 𝑟 , = 𝛼 + 𝛽 (𝑟 , − 𝑟 , ) + 𝜀 ,

for 𝜀 , using the return on the firm

𝑟 , =𝑃 , − 𝑃 ,

𝑃 ,

(since there are no dividends here). Hence:

𝜀 & , = 𝑟 & , − α & + 𝛽 & (𝑟 , − 𝑟 , )

=27.02 − 27.99

27.02− 0 + 0.8 −0.0070 − 0

= −0.0291 , 𝑜𝑟 2.91%

𝜀 , = 𝑟 , − α + 𝛽 (𝑟 , − 𝑟 , )

=34.50 − 31.46

31.46− 0 + 0.83 −0.0070 − 0

= 0.1024 , 𝑜𝑟 10.24%

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b. The value created or destroyed is the firm-specific return times the initial total market value of the firm. Thus:

& ,

,

Since the deal is creating value overall (i.e. for AT&T and BellSouth overall).


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