投资学期末试题库答案和分析(一)
TUTORIAL – SESSION 01
CHAPTER 01
1.Discuss the agency problem.
2.Discuss the similarities and differences between real and financial assets.
3.Discuss the following ongoing trends as they relate to the field of investments:
globalization, financial engineering, securitization, and computer networks. CHAPTER 02
Use the following to answer questions 1 to 3:
Consider the following three stocks:
1. The price-weighted index constructed with the three stocks is
A) 30
B) 40
C) 50
D) 60
E) 70
Answer: B Difficulty: Easy
Rationale: ($40 + $70 + $10)/3 = $40.
2. The value-weighted index constructed with the three stocks using a divisor
of 100 is
A) 1.2
B) 1200
C) 490
D) 4900
E) 49
Answer: C Difficulty: Moderate
Rationale: The sum of the value of the three stocks divided by 100 is 490: [($40 x 200) + ($70 x 500) + ($10 x 600)] /100 = 490
3. Assume at these prices the value-weighted index constructed with the
three stocks is 490. What would the index be if stock B is split 2 for 1 and stock C 4 for 1?
A) 265
B) 430
C) 355
D) 490
E) 1000
Answer: D Difficulty: Moderate
Rationale: Value-weighted indexes are not affected by stock splits.
4. An investor purchases one municipal and one corporate bond that pay
rates of return of 8% and 10%, respectively. If the investor is in the 20% marginal tax bracket, his or her after tax rates of return on the municipal and corporate bonds would be ________ and ______, respectively.
A) 8% and 10%
B) 8% and 8%
C) 6.4% and 8%
D) 6.4% and 10%
E) 10% and 10%
Answer: B Difficulty: Moderate
Rationale: rc = 0.10(1 - 0.20) = 0.08, or 8%; rm = 0.08(1 - 0) = 8%.
5. A 5.5% 20-year municipal bond is currently priced to yield 7.2%. For a
taxpayer in the 33% marginal tax bracket, this bond would offer an equivalent taxable yield of:
A) 8.20%.
B) 10.75%.
C) 11.40%.
D) 4.82%.
E) none of the above.
Answer: B Difficulty: Moderate
Rationale: 0.072 = rm (1-t); 0.072 = rm / (0.67); rm = 0.1075 = 10.75%
6. In order for you to be indifferent between the after tax returns on a
corporate bond paying 8.5% and a tax-exempt municipal bond paying
6.12%, what would your tax bracket need to be?
A) 33%
B) 72%
C) 15%
D) 28%
E) Cannot tell from the information given
.0612 = .085(1-t); (1-t) = 0.72; t = .28
7. Suppose an investor is considering a corporate bond with a 7.17% before-
tax yield and a municipal bond with a 5.93% before-tax yield. At what marginal tax rate would the investor be indifferent between investing in the corporate and investing in the muni?
A) 15.4%
B) 23.7%
C) 39.5%
D) 17.3%
E) 12.4%
tm = 1 - (5.93%/7.17%) = 17.29%
Use the following to answer questions 8 to 9:
8. Based on the information given, for a price-weighted index of the three
stocks calculate:
A) the rate of return for the first period (t=0 to t=1).
B) the value of the divisor in the second period (t=2). Assume that Stock
A had a 2-1 split during this period.
C) the rate of return for the second period (t=1 to t=2).
A. The price-weighted index at time 0 is (70 + 85 + 105)/3 = 86.67. The price-
weighted index at time 1 is (72 + 81 + 98)/3 = 83.67. The return on the
index is 83.67/86.67 - 1 = -3.46%.
B. The divisor must change to reflect the stock split. Because nothing else
fundamentally changed, the value of the index should remain 83.67. So
the new divisor is (36 + 81 + 98)/83.67 = 2.57. The index value is (36 +
81 + 98)/2.57 = 83.67.
C. The rate of return for the second period is 83.67/83.67 - 1 = 0.00%
9. Based on the information given for the three stocks, calculate the first-
period rates of return (from t=0 to t=1) on
A) a market-value-weighted index.
B) an equally-weighted index.
C) a geometric index.
A. The total market value at time 0 is $70 * 200 + $85 * 500 + $105 * 300 =
$88,000. The total market value at time 1 is $72 * 200 + $81 * 500 +
$98 * 300 = $84,300. The return is $84,300/$88,000 - 1 = -4.20%.
B. The return on Stock A for the first period is $72/$70 - 1 = 2.86%. The return on
Stock B for the first period is $81/$85 - 1 = -4.71%. The return on Stock
C for the first period is $98/$105 - 1 = -6.67%. The return on an equally
weighted index of the three stocks is (2.86% - 4.71% - 6.67%)/3 = -2.84% C. The geometric average return is [(1+.0286)(1-.0471)(1-.0667)](1/3)-1 =
[(1.0286)(0.9529)(0.9333)]0.3333 -1 = -2.92%
10.Discuss the advantages and disadvantages of common stock ownership,
relative to other investment alternatives.
CHAPTER 03
1. Assume you purchased 200 shares of XYZ common stock on margin at $70
per share from your broker. If the initial margin is 55%, how much did you borrow from the broker?
A) $6,000
B) $4,000
C) $7,700
D) $7,000
E) $6,300
Answer: E Difficulty: Moderate
Rationale: 200 shares * $70/share * (1-0.55) = $14,000 * (0.45) = $6,300.
2. You sold short 200 shares of common stock at $60 per share. The initial
margin is 60%. Your initial investment was
A) $4,800.
B) $12,000.
C) $5,600.
D) $7,200.
E) none of the above.
Answer: D Difficulty: Moderate
Rationale: 200 shares * $60/share * 0.60 = $12,000 * 0.60 = $7,200
3. You purchased 100 shares of ABC common stock on margin at $70 per
share. Assume the initial margin is 50% and the maintenance margin is 30%. Below what stock price level would you get a margin call? Assume the stock pays no dividend; ignore interest on margin.
A) $21
B) $50
C) $49
D) $80
E) none of the above
Answer: B Difficulty: Difficult
Rationale: 100 shares * $70 * .5 = $7,000 * 0.5 = $3,500 (loan amount); 0.30 = (100P - $3,500)/100P; 30P = 100P - $3,500; -70P = -$3,500; P = $50.
4. You purchased 100 shares of common stock on margin at $45 per share.
Assume the initial margin is 50% and the stock pays no dividend. What would the maintenance margin be if a margin call is made at a stock price of $30? Ignore interest on margin.
A) 0.33
B) 0.55
C) 0.43
D) 0.23
E) 0.25
Answer: E Difficulty: Difficult
Rationale: 100 shares * $45/share * 0.5 = $4,500 * 0.5 = $2,250 (loan amount); X = [100($30) - $2,250]/100($30); X = 0.25.
5. You purchased 300 shares of common stock on margin for $60 per share.
The initial margin is 60% and the stock pays no dividend. What would your rate of return be if you sell the stock at $45 per share? Ignore interest on margin.
A) 25%
B) -33%
C) 44%
D) -42%
E) –54%
Answer: D Difficulty: Difficult
Rationale: 300($60)(0.60) = $10,800 investment; 300($60) = $18,000 *(0.40) = $7,200 loan; Proceeds after selling stock and repaying loan: $13,500 -
$7,200 = $6,300; Return = ($6,300 - $10,800)/$10,800 = - 41.67%.
6. Assume you sell short 100 shares of common stock at $45 per share, with
initial margin at 50%. What would be your rate of return if you repurchase the stock at $40/share? The stock paid no dividends during the period, and you did not remove any money from the account before making the offsetting transaction.
A) 20%
B) 25%
C) 22%
D) 77%
E) none of the above
Answer: C Difficulty: Moderate
Rationale: Profit on stock = ($45 - $40) * 100 = $500, $500/$2,250 (initial investment) = 22.22%
7. You want to purchase XYZ stock at $60 from your broker using as little of
your own money as possible. If initial margin is 50% and you have $3000 to invest, how many shares can you buy?
A) 100 shares
B) 200 shares
C) 50 shares
D) 500 shares
E) 25 shares
Answer: A Difficulty: Moderate
Rationale: .5 = [(Q * $60)-$3,000] / (Q * $60); $30Q = $60Q-$3,000; $30Q = $3,000; Q=100.
8. You buy 300 shares of Qualitycorp for $30 per share and deposit initial
margin of 50%. The next day Qualitycorp's price drops to $25 per share.
What is your actual margin?
A) 50%
B) 40%
C) 33%
D) 60%
E) 25%
Answer: B Difficulty: Moderate
Rationale: AM = [300 ($25) - .5 (300) ($30) ] / [300 ($25)] = .40
9. You sold short 100 shares of common stock at $45 per share. The initial
margin is 50%. Your initial investment was
A) $4,800.
B) $12,000.
C) $2,250.
D) $7,200.
E) none of the above.
Answer: C Difficulty: Moderate
Rationale: 100 shares * $45/share * 0.50 = $4,500 * 0.50 = $2,250
10. List three factors that are listing requirements for the New York Stock
Exchange. Why does the exchange have such requirements? CHAPTER 04
1. Multiple Mutual Funds had year-end assets of $457,000,000 and liabilities
of $17,000,000. There were 24,300,000 shares in the fund at year-end.
What was Multiple Mutual's Net Asset Value?
A) $18.11
B) $18.81
C) $69.96
D) $7.00
E) $181.07
Answer: A Difficulty: Moderate
Rationale: (457,000,000 - 17,000,000) / 24,300,000 = $18.11
2. Diversified Portfolios had year-end assets of $279,000,000 and liabilities of
$43,000,000. If Diversified's NAV was $42.13, how many shares must have
been held in the fund?
A) 43,000,000
B) 6,488,372
C) 5,601,709
D) 1,182,203
E) None of the above.
Answer: C Difficulty: Moderate
Rationale: ($279,000,000 - 43,000,000) / $42.13 = 5,601,708.996.
3. Pinnacle Fund had year-end assets of $825,000,000 and liabilities of
$25,000,000. If Pinnacle's NAV was $32.18, how many shares must have
been held in the fund?
A) 21,619,346,92
B) 22,930,546.28
C) 24,860,161.59
D) 25,693,645.25
E) None of the above.
Answer: C Difficulty: Moderate
Rationale: ($825,000,000 - 25,000,000) / $32.18 = 24,860,161.59.
4. The Profitability Fund had NAV per share of $17.50 on January 1, 200
5. On
December 31 of the same year the fund's NAV was $19.47. Income
distributions were $0.75 and the fund had capital gain distributions of
$1.00. Without considering taxes and transactions costs, what rate of
return did an investor receive on the Profitability fund last year?
A) 11.26%
B) 15.54%
C) 16.97%
D) 21.26%
E) 9.83%
Answer: D Difficulty: Moderate
Rationale: R = ($19.47 - 17.50 + .75 + 1.00) / $17.50 = 21.26%
5. Patty O'Furniture purchased 100 shares of Green Isle mutual fund at a net
asset value of $42 per share. During the year Patty received dividend
income distributions of $2.00 per share and capital gains distributions of
$4.30 per share. At the end of the year the shares had a net asset value of $40 per share. What was Patty's rate of return on this investment?
A) 5.43%
B) 10.24%
C) 7.19%
D) 12.44%
E) 9.18%
（40-42+2+4.3）/42=10.24%
6. A mutual fund had year-end assets of $560,000,000 and liabilities of
$26,000,000. There were 23,850,000 shares in the fund at year end. What was the mutual fund's Net Asset Value?
A) $22.87
B) $22.39
C) $22.24
D) $17.61
E) $19.25
Answer: B Difficulty: Moderate
Rationale: (560,000,000 - 26,000,000) / 23,850,000 = $22.389
7. A mutual fund had year-end assets of $465,000,000 and liabilities of
$37,000,000. If the fund NAV was $56.12, how many shares must have
been held in the fund?
A) 4,300,000
B) 6,488,372
C) 8,601,709
D) 7,626,515
E) None of the above.
Answer: D Difficulty: Moderate
Rationale: ($465,000,000 37,000,000) / $56.12 = 7,626,515
8. A mutual fund had NAV per share of $26.25 on January 1, 2005. On
December 31 of the same year the fund's rate of return for the year was
16.4%. Income distributions were $1.27 and the fund had capital gain
distributions of $1.85. Without considering taxes and transactions costs,
what ending NAV would you calculate?
A) $27.44
B) $33.88
C) $24.69
D) $42.03
E) $16.62
Answer: A Difficulty: Moderate
Rationale: .164 = (P - $26.25 + 1.27 + 1.85) / $26.25; P = $27.435
9. A mutual funds had average daily assets of $2.0 billion on 2005. The fund
sold $500 million worth of stock and purchased $600 million worth of stock during the year. The funds turnover ratio is ___.
A) 27.5%
B) 12%
C) 15%
D) 25%
E) 20%
Answer: D Difficulty: Moderate
Rationale: 500,000,000 / 2,000,000,000 = 25%
10. You purchased shares of a mutual fund at a price of $20 per share at the
beginning of the year and paid a front-end load of 5.75%. If the securities in which the find invested increased in value by 11% during the year, and
the funds expense ratio was 1.25%, your return if you sold the fund at the end of the year would be ____________.
A) 4.33
B) 3.44
C) 2.45
D) 6.87
E) None of the above
[20*(1-5.75%)*(1+11%-1.25%)-20]/20=0.0343
11. List and describe the more important types of mutual funds according to
their investment policy and use.
CHAPTER 05
1. Over the past year you earned a nominal rate of interest of 10 percent on
your money. The inflation rate was 5 percent over the same period. The
exact actual growth rate of your purchasing power was
A) 15.5%.
B) 10.0%.
C) 5.0%.
D) 4.8%.
E) 15.0%
Answer: D Difficulty: Moderate
Rationale: r = (1+R) / (1+I) - 1; 1.10% / 1.5% - 1 = 4.8%.
2. You purchased a share of stock for $20. One year later you received $1 as
dividend and sold the share for $29. What was your holding period return?
A) 45%
B) 50%
C) 5%
D) 40%
E) none of the above
Answer: B Difficulty: Moderate
Rationale: ($1 + $29 - $20)/$20 = 0.5000, or 50%.
Use the following to answer questions 3-5:
You have been given this probability distribution for the holding period return for KMP stock:
3. What is the expected holding period return for KMP stock?
A) 10.40%
B) 9.32%
C) 11.63%
D) 11.54%
E) 10.88%
Answer: A Difficulty: Moderate
Rationale: HPR = .30 (18%) + .50 (12%) + .20 (-5%) = 10.4%
4. What is the expected standard deviation for KMP stock?
A) 6.91%
B) 8.13%
C) 7.79%
D) 7.25%
E) 8.85%
Answer: B Difficulty: Difficult
Rationale: s = [.30 (18 - 10.4)2 + .50 (12 - 10.4)2 + .20 (-5 - 10.4)2]1/2 = 8.13%
5. What is the expected variance for KMP stock?
A) 66.04%
B) 69.96%
C) 77.04%
D) 63.72%
E) 78.45%
A Difficulty: Difficult
Rationale: s = [.30 (18 - 10.4)2 + .50 (12 - 10.4)2 + .20 (5 - 10.4)2] = 66.04%
6. You purchase a share of Boeing stock for $90. One year later, after
receiving a dividend of $3, you sell the stock for $92. What was your
holding period return?
A) 4.44%
B) 2.22%
C) 3.33%
D) 5.56%
E) none of the above
Answer: D Difficulty: Moderate
Rationale: HPR = (92 - 90 + 3) / 90 = 5.56%
7. An investor purchased a bond 45 days ago for $985. He received $15 in
interest and sold the bond for $980. What is the holding period return on his investment?
A) 1.52%
B) 0.50%
C) 1.02%
D) 0.01%
E) None of the above
Answer: C Difficulty: Easy
Rationale: HPR = ($15+980-985)/$985 = .010152284 = approximately 1.02%.
8. Over the past year you earned a nominal rate of interest of 8 percent on
your money. The inflation rate was 3.5 percent over the same period. The exact actual growth rate of your purchasing power was
A) 15.55%.
B) 4.35%.
C) 5.02%.
D) 4.81%.
E) 15.04%
Answer: B Difficulty: Moderate
Rationale: r = (1+R) / (1+I) - 1 ; 1.08 / 1.035 - 1 = 4.35%.
9. Over the past year you earned a nominal rate of interest of 14 percent on
your money. The inflation rate was 2 percent over the same period. The
exact actual growth rate of your purchasing power was
A) 11.76%.
B) 16.00%.
C) 15.02%.
D) 14.32%.
E) none of the above.
10. An investment provides a 2% return semi-annually, its effective annual rate is
A) 2%.
B) 4%.
C) 4.02%
D) 4.04%
E) none of the above
(1.02)2 -1 = 4.04%
11. Discuss the relationships between interest rates (both real and nominal),
expected inflation rates, and tax rates on investment returns.
12. Discuss why common stocks must earn a risk premium.
CHAPTER 07
1. Market risk is also referred to as
A) systematic risk, diversifiable risk.
B) systematic risk, nondiversifiable risk.
C) unique risk, nondiversifiable risk.
D) unique risk, diversifiable risk.
E) none of the above.
Answer: B Difficulty: Easy
Rationale: Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable,
unique, nonsystematic, and firm-specific risks are synonyms referring to
the risk that can be eliminated from the portfolio by diversification.
2. The variance of a portfolio of risky securities
A) is a weighted sum of the securities' variances.
B) is the sum of the securities' variances.
C) is the weighted sum of the securities' variances and covariances.
D) is the sum of the securities' covariances.
E) none of the above.
Answer: C Difficulty: Moderate
Rationale: The variance of a portfolio of risky securities is a weighted sum taking into account both the variance of the individual securities and the cova
riances between securities.
3. Other things equal, diversification is most effective when
A) securities' returns are uncorrelated.
B) securities' returns are positively correlated.
C) securities' returns are high.
D) securities' returns are negatively correlated.
E) B and C.
Answer: D Difficulty: Moderate
Rationale: Negative correlation among securities results in the greatest reduction of portfolio risk, which is the goal of diversification.
4. The Capital Allocation Line provided by a risk-free security and N risky
securities is
A) the line that connects the risk-free rate and the global minimum-
variance portfolio of the risky securities.
B) the line that connects the risk-free rate and the portfolio of the risky
securities that has the highest expected return on the efficient frontier.
C) the line tangent to the efficient frontier of risky securities drawn from
the risk-free rate.
D) the horizontal line drawn from the risk-free rate.
E) none of the above.
Answer: C Difficulty: Moderate
Rationale: The Capital Allocation Line represents the most efficient combinations of the risk-free asset and risky securities. Only C meets that definition.
5. Which of the following statements is (are) true regarding the variance of a
portfolio of two risky securities?
A) The higher the coefficient of correlation between securities, the greater
the reduction in the portfolio variance.
B) There is a linear relationship between the securities' coefficient of
correlation and the portfolio variance.
C) The degree to which the portfolio variance is reduced depends on the
degree of correlation between securities.
D) A and B.
E) A and C.
Answer: C Difficulty: Moderate
Rationale: The lower the correlation between the returns of the securities, the mo re portfolio risk is reduced.
Use the following to answer questions 6-11:
Consider the following probability distribution for stocks A and B:
6. The expected rates of return of stocks A and B are _____ and _____ ,
respectively.
A) 13.2%; 9%
B) 14%; 10%
C) 13.2%; 7.7%
D) 7.7%; 13.2%
E) none of the above
Answer: C Difficulty: Easy
Rationale: E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2
%;
E(RB) = 0.1(8%) + 0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.
7. The standard deviations of stocks A and B are _____ and _____, respectively.
A) 1.5%; 1.9%
B) 2.5%; 1.1%
C) 3.2%; 2.0%
D) 1.5%; 1.1%
E) none of the above
Answer: D Difficulty: Moderate
Rationale: sA = [0.1(10% - 13.2%)2 + 0.2(13% - 13.2%)2 + 0.2(12% - 13.2%)2 + 0.3(14% - 13.2%)2 + 0.2(15% - 13.2%)2]1/2 = 1.5%; sB = [0.1(8% - 7.7%)2 + 0.2(7% -
7.7%)2 + 0.2(6% - 7.7%)2 + 0.3(9% - 7.7%)2 + 0.2(8% - 7.7%)2]1/2 = 1.1%.
8. The coefficient of correlation between A and B is
A) 0.47.
B) 0.60.
C) 0.58
D) 1.20.
E) none of the above.
Answer: A Difficulty: Difficult
Rationale: covA,B = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% -
7.7%) +
0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) + 0.2(15% -
13.2%)(8% - 7.7%) = 0.76; rA,B = 0.76/[(1.1)(1.5)] = 0.47.
9. If you invest 40% of your money in A and 60% in B, what would be your
portfolio's expected rate of return and standard deviation?
A) 9.9%; 3%
B) 9.9%; 1.1%
C) 11%; 1.1%
D) 11%; 3%
E) none of the above
Answer: B Difficulty: Difficult
Rationale: E(RP) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; sP = [(0.4)2(1.5)2 + (0.6)2(1.1)2 +
2(0.4)(0.6)(1.5)(1.1)(0.46)]1/2 = 1.1%.
10. Let G be the global minimum variance portfolio. The weights of A and B in
G are __________ and __________, respectively.
A) 0.40; 0.60
B) 0.66; 0.34
C) 0.34; 0.66
D) 0.76; 0.24
E) 0.24; 0.76
Answer: E Difficulty: Difficult
Rationale: wA = [(1.1)2 - (1.5)(1.1)(0.46)]/[(1.5)2 + (1.1)2 -
(2)(1.5)(1.1)(0.46) = 0.23;
wB = 1-
0.23 = 0.77.Note that the above solution assumes the solutions obtaine
d in question 13 and 14.
11. The expected rate of return and standard deviation of the global minimum
variance portfolio, G, are __________ and __________, respectively.
A) 10.07%; 1.05%
B) 9.04%; 2.03%
C) 10.07%; 3.01%
D) 9.04%; 1.05%
E) none of the above
Answer: D Difficulty: Moderate
Rationale: E(RG) = 0.23(13.2%) + 0.77(7.7%) = 8.97% . 9%; sG = [(0.23)2(1.5)2 + (0.77)2(1.1)2 + (2)(0.23)(0.77)(1.5)(1.1)(0.46)]1/2 = 1.05%.