Exam 3 - Sample Solution
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Jan 9, 2024
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Solutions to Exam 3 (Sample) Section 1- Multiple Choice - Circle the single best answer
to each question
#1. The arbitrage pricing theory predicts that expected returns depend on ____________. The CAPM predicts that
expected returns depend on _________________.
(a) systematic risk, systematic risk
(b) unsystematic risk, systematic risk
(c) systematic risk, unsystematic risk
(d) unsystematic risk, unsystematic risk
#2. According to the Fama-French 3 factor model, a stock with a larger ___________ will have a greater ___________.
(a) ratio of book equity value to market equity value, realized return
(b) ratio of book equity value to market equity value, expected return
(c) beta coefficient on HML, expected return (d) beta coefficient on HML, realized return
#3. According to the Fama-French 3 factor model, a firm with a low value for market equity
will ___________ have a
higher beta coefficient on ___________ compared to a firm with a high value for market equity
(a)
always, SMB
(b) usually but not always, SMB
(c) always, HML
(d) usually but not always, HML
(e) always, UMD
(f) usually but not always, UMD
#4. The risk premium for exposure to factor 1 is 5%, the risk premium for exposure to factor 2 is 10%, and the risk
premium for exposure to factor 3 is 4%. The risk-free rate is 2%. According to the APT, if a stock has a beta with
respect to factor 1 of 1, a beta with respect to factor 2 of .5, and a beta with respect to factor 3 of -1. The expected
return on the stock will be ________.
(a) 6%
(b) 8%
(c) 10%
(d) 12%
(e) 14%
(f) 16%
(g) none of the above
#5. The risk premium for exposure to factor 1 is 4% and the risk premium for exposure to factor 2 is 3%. A stock has
a beta with respect to factor 1 of 1.5. The expected return on the stock is 13%. The risk-free rate is 3%. Given this
data, according to the APT, the beta of the stock with respect to risk factor 2 must be ________.
(a) less than 1
(b) between 1 and 1.5
(c) between 1.5 and 2
(d) above 2
#6. Suppose all stocks obey an APT three-factor model. The risk-free interest rate is 4%. Stock A has a beta of 1 with
respect to factor 1, a beta of 1 with respect to factor 2, and a beta of 1 with respect to factor 3. Stock B has a beta of 1
with respect to factor 1, a beta of 2 with respect to factor 2, and a beta of 3 with respect to factor 3. An investor has a
portfolio with $8,000 invested in stock A and $2,000 invested in stock B. What is the beta on the third risk factor for
the investor's portfolio?
(a) less than 1
(b) between 1 and 1.5
(c) between 1.5 and 2
(d) between 2 and 2.5
(e) above 2.5
#7. Fund A is a fund that invests in small value stocks. Fund B is a fund that invests in small growth stocks. Fund C is
a fund that invests in large value stocks. Fund D is a fund that invests in large growth stocks. Which fund would you
expect to have a negative beta coefficient on SMB, a positive beta coefficient on HML, and a positive beta coefficient
on the market return?
(a) Fund A
(b) Fund B
(c) Fund C
(d) Fund D
#8. Suppose all stocks obey an APT two-factor model. A given stock has a beta of 1 with respect to factor 1 and a beta
of -1 with respect to factor 2. According to the APT, the expected return on this stock as of the start of last year was
10%. If last year the actual value of Factor 1 was 4% higher than expected and the actual value of Factor 2 was 4%
lower than expected, what is your best guess of the return that the stock experienced last year?
(a) less than 10.5%
(b) between 10.5% and 13.5%
(c) between 13.5% and 17.5%
(d) between 17.5% and 20.5%
(e) more than 20.5%
#9. Evidence on the performance of professional mutual fund managers generally supports the notion of
________________.
(a) Convex market efficiency (b) Semistrong form market efficiency
(c) Gamma market efficiency
(d) a and b
(e) a and c
(f) b and c (g) a and b and c
#10. A study shows that starting one week after a firm announces a sharp increase in quarterly earnings a firm's stock tends to earn an abnormally high risk-adjusted return for the subsequent 6-month period. Is this evidence consistent with semi-strong market efficiency?
(a) Yes, it is consistent
(b) No, it is not consistent
(c) Cannot determine without knowing the unsystematic risk level of these stocks
#11. Which type of market efficiency assumes that a stock price always includes all information known to a firm's management about a firm’s profitability?
(a) weak-form market efficiency
(b) semistrong-form market efficiency
(c) strong-form market efficiency
(d) a and b
(e) b and c
(f) a and b and c
#12. The market expects a firm's annual earnings are going to be 20% lower than last year's earnings. The firm
announces their actual annual earnings number and these earnings were actually 10% lower than last year's earnings.
According the semi-strong version of the efficient market hypothesis, when this news is released, we would expect the
firm's stock price to __________.
(a) decrease immediately after the news is released
(b) decrease gradually after the news is released
(c) increase immediately after the news is released
(d) increase gradually after the news is released
#13. According to our class discussion, academic evidence suggests that almost all investors trade in a completely
rational manner.
(a) True
(b) False
#14. If an investor believes in market efficiency, they should generally prefer to invest in _________.
(a) passive index funds
(b) actively managed funds
(c) risk arbitrage funds
#15. Suppose a stock is worth $10 under its current operating strategy. The firm agrees to be acquired for a price of
$20 a share pending regulatory approval in a deal that was not anticipated by the market. Upon news of this acquisition,
the stock price increases from $10 to $17. Assuming the market is efficient, the market must expect that the probability
that the deal is consummated is _________.
(a) between 0 and 40%
(b) between 40% and 60%
(c) between 60% and 80%
(d) over 80%
#16. DFA's investment strategies were heavily influenced by _________________. DFA was primarily concerned about negative __________ information when they purchased stocks.
(a) The CAPM model, public
(b) The CAPM model, private
(c) The Fama-French 3 factor model, public
(d) The Fama-French 3 factor model, private
#17. DFA often purchased __________ of stock at substantial _______.
(a) blocks, discounts
(b) blocks, premia
(c) exotic positions, discounts
(d) exotic position, premia
Note: For all remaining multiple-choice problems the word beta refers to the beta from the CAPM and you can
assume the CAPM is the appropriate model to be used to predict expected returns. #18. A firm currently operates in industry A and it is considering starting a division that operates in industry B. In calculating the NPV of entering this new industry, the firm should use _________ as the discount rate.
(a) the firm’s current r
wacc
(b) an estimate of r
wacc calculated using data from other firms operating in industry A (c) an estimate of r
wacc calculated using data from other firms operating in industry B
(d) the firm’s borrowing rate r
debt
#19. In using the formula for the weighted average cost of capital (r
wacc
), we argued that one should use _________.
(a) the book value of debt and the book value of equity (b) the market value of debt and the market value of equity
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#20. A firm has $600 million in stock and $600 million in bonds. The expected return on the firm’s stock is 20%. The expected return on the firm's debt is 5%. The corporate tax rate is 20%. What is this firm’s weighted average cost of capital?
(a)
Less than 10%
(b) 10.0%
(c)
10.5%
(d) 11.0%
(e)
11.5%
(f)
12.0%
(g)
More than 12.0%
(h)
None of the above
#21. A firm’s current debt-to-equity ratio is 1 (that is D/E=1). The beta on the firm’s stock is currently estimated to be 2.0. The corporate tax rate is 30%. What will the beta on the firm’s stock be if the firm changes its debt-equity ratio to 0.5?
(a)
Less than 1.5
(b)
Between 1.5 and 1.7
(c)
Between 1.7 and 2.0
(d)
More than 2.0
#22. A firm’s target debt-equity ratio is 2.0. The firm is currently unlevered and currently the firm’s stock has a beta of
1.0. The risk-free rate is 3%, the corporate tax rate is 20%, and the market risk premium is 5%. What will be the expected return on the firm’s stock at its target debt-to-equity ratio?
(a)
Less than 13%
(b)
Between 13% and 17%
(c)
Between 17% and 20%
(d)
More than 20%
#23. Firm A sells yachts and Firm B sells dog food. Both firms are entirely equity financed. Yacht sales tend to be much more sensitive than dog food sales to the macroeconomy and to the stock market. Which firm will have a greater weighted average cost of capital?
(a) Firm A
(b) Firm B
(c) Cannot determine without knowing the risk-free interest rate
#24. A firm currently has $50 million in bonds outstanding and the beta on the firm’s stock is currently estimated to be 1.0. The book value of equity on the firm's balance sheet is $10 million and the firm has 1 million shares outstanding trading at a price of $50 a share. If the firm changes its capital structure so that the firm adopts a debt to equity ratio of .25, what will be the new beta on the firm’s stock be? There are no taxes.
(a) Less than 0.5
(b) Between 0.5 and 0.8
(c) Between 0.8 and 1.0
(d) Between 1.0 and 1.3
(e) More than 1.3
#25. A firm currently has no debt and its equity beta is currently 1.0. The risk-free interest rate is 3% and the market risk premium is 6%. There are no corporate taxes (i.e., the corporate tax rate is 0%). The firm considers switching its debt equity ratio to .5 (i.e., they will set D/E = .5). The debt they issue will pay 3% interest. If they make this change, what will the firm's weighted average cost of capital be after the change? (a) Less than 7.5%
(b) Between 7.5% and 8.5%
(c) Between 8.5% and 9.5%
(d) Between 9.5% and 10.5%
(e) Between 10.5% and 12.5%
(f) More than 12.5%
Section 2- Long Answer Problems - Show your work clearly as partial credit will be awarded.
#1. Suppose all stocks obey an APT three-factor model. The risk-free interest rate is 5%. Stock A has a beta of 0.5
with respect to factor 1, a beta of 1.0 with respect to factor 2, and a beta of -1.5 with respect to factor 3. Stock B has a
beta of 2.0 with respect to factor 1, a beta of -1.5 with respect to factor 2, and a beta of 3.0 with respect to factor 3. The
risk-premium on factor 1 is 3%, the risk-premium on factor 2 is 4%, and the risk premium on factor 3 is 3%. (a) Which stock has a greater expected return?
Expected return of A = 5% + .5 x 3% + 1.0 x 4% + -1.5 x 3% = 5 + 1.5 + 4 - 4.5
= 6.0%
Expected return of B = 5% + 2.0 x 3% - 1.5 x 4% + 3 x 3% = 5 + 6 - 6 + 9 =
14.0%
Since 14.0% > 6.0%
stock B has the higher expected return.
(b) Given your answer to (a), will all investors agree on which stock they prefer if they can choose to invest 1% of their
retirement portfolio in only one of these two stocks?
No. While B has a higher expected return, it also has more systematic risk as
measured by the betas on all of the risk factors. Thus, it is both systematically
risker and offers a higher expected return. Thus, the decision of which of these
two stocks to hold will depend on an investor's attitude towards risk.
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#2. Here is some data for two firms in the restaurant industry:
Restaurant Firm #1: $150 million in debt, $300 million in equity, current estimated equity beta of 1.50 Restaurant Firm #2: $50 million in debt, $200 million in equity, current estimated equity beta of 2.50.
These firms operate in a world with no taxes (i.e., T
c
=0 for all firms). Firm XYZ is a conglomerate firm with many different divisions and an overall beta for the firm of 1.0. The firm’s restaurant division is contemplating building a new restaurant. The risk-free interest rate is 4% and the market risk premium is 6%. The firm uses only equity finance for its restaurant division and thus it would finance the new restaurant entirely with equity (i.e., $0 in debt and $20 million in equity). If the firm did borrow to finance its restaurants, it would pay 5% interest on the borrowings. Given all of these data, what cost of capital should be used when calculating the NPV of the restaurant project? For each firm we can use the equation: β
E = [1+ D/E]* β
U
For firm 1:
β
U = 1.50 / 1.50 = 1.0
For firm 2:
β
U = 2.50 / 1.25 = 2.0
Averaging these we get: (1.0 + 2.0) / 2 = 1.50
Given our class discussion this is our most reasonable estimate of the unlevered industry beta.
Since the firm only uses equity, its cost of capital will be r
U
. We can derive r
U from the CAPM. r
U
= r
f
+ β
U
*(r
m
– r
f
) r
U
= 4% + 1.5*(6%) = 13.00%.
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