Module 7 Measures of Investment Returns

Question 1

Assuming Von made a $10,000 investment four years ago that presently has a value of $31,500, calculate the geometric mean return over the four-year investment period.

A)
57.50%
B)
33.22%
C)
53.75%
D)
78.75%

Answer 1

b The answer is 33.22%. An investment growing from $10,000 to $31,500 over a four-year period has a geometric mean return equal to 33.22%, calculated as follows:

PV = −10,000

FV = 31,500

N = 4

Solve for I/YR = 33.2225, or 33.22%

LO 7.1.1

Question 2

An investor who owns a sector fund that has substantial unsystematic risk and would like to know how a portfolio manager performed on a risk-adjusted basis would use which of the following indicators?

A)
Sharpe ratio
B)
Treynor ratio
C)
Jensen’s alpha
D)
Beta

Answer 2

a Sharpe uses standard deviation and assumes the portfolio is not well diversified and measures total risk.

LO 7.2.1

Question 3

Cindy has been an active investor for many years. She currently has a money market mutual fund and several equity mutual funds. She wants to maximize her return on an intermediate-term bond and plans to hold the bond to maturity.

Which of these two bonds would be more appropriate for Cindy, and why?

Bond 1: callable at par value; BBB rated; coupon = 6%; matures in six years; selling for $863; duration = 5.16
Bond 2: callable at par value; A rated; coupon = 10%; matures in four years; selling for $1,103; duration = 3.5
Bond 1, because it is selling for a discount and is less likely to be called.
Bond 1, because it has a higher yield to maturity than Bond 2.
Bond 2, because its higher coupon gives it a better total return.
Bond 2, because it has a higher yield to maturity than Bond 1.
A)
II only
B)
I and II
C)
III and IV
D)
I only

Answer 3

b Explanation
The answer is I and II. Below are the TVM inputs used on the financial calculator for each bond.

YTM for Bond 1:

PV = -$863

FV = $1,000

PMT = $1,000 x 6% = $60 / 2 = $30

N = 12 (6 x 2 periods per year)

Solve for I/YR = 9%

YTM for Bond 2:

PV = -$1,103

FV = $1,000

PMT = $1,000 x 10% = $100 / 2 = $50

N = 8 (4 x 2 periods per year)

Solve for I/YR =7%

In addition, Bond 1 is selling at a discount—unlike Bond 2 selling at a premium—so it is not likely to be called.

LO 7.4.1

Question 4

Myles purchased 1,000 shares of XYZ growth fund for $15 per share. At the end of the two years, he sold all of the shares for $22 per share. At the end of each year, the fund paid a dividend of $0.50 per share. Calculate the fund’s time-weighted return over the two-year period.

A)
24.15%
B)
18.07%
C)
13.62%
D)
20.82%

Answer 4

a Explanation
The answer is 24.15%. The fund produced a 24.15% time-weighted rate of return over the two-year period, calculated as follows:

CF0 = -15 × 1,000 = −15,000

CF1 = 0.50 × 1,000 = 500

CF2 = (0.50 × 1,000) + (22 × 1,000) = 22,500

Solve for the internal rate of return (IRR/YR) = 24.1525% (rounded to 24.15%)

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Question 4

Janice, who is in the 35% marginal income tax bracket, would like to purchase a bond for her investment portfolio. Assuming all of the bonds are of similar investment quality, which would produce the highest after-tax yield?

A)
2.75% U.S. Treasury bond
B)
2.25% U.S. Treasury note
C)
3.55% municipal bond
D)
5.25% corporate bond

Answer 4

c Janice should purchase the municipal bond based on the following after-tax yield calculations:

U.S. Treasury bond [2.75% × (1 − 0.35)]

1.79%

Corporate bond [5.25% × (1 − 0.35)]

3.41%

Municipal bond (tax-free)

3.55%

U.S Treasury note [2.25% × (1 − 0.35)]

1.46%

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Question 5

You own a small-cap fund and are trying to compare its performance to an appropriate benchmark. Which of the following benchmarks would be the best to use?

A)
The S&P 500 Index
B)
Russell 2000
C)
CS First Boston High Yield
D)
Treasury bills

Answer 5

nb The Russell 2000 is generally considered the benchmark for small-cap funds.

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Question 5

Michael purchased 800 shares of ABC stock for $75 per share. The stock paid a $1.20 dividend per share at the end of the year, and there was a 2-for-1 stock split during the year. Assuming the value of his investment at the end of the year was $66,000, calculate the holding period return for the investment.

A)
14.0%
B)
12.0%
C)
8.3%
D)
13.2%

Answer 5

d The answer is 13.2%. The investment’s holding period return is calculated as [($66,000 − $60,000) + ($1.20 × 800 × 2)] ÷ $60,000 = 13.2%. The dividend is based on 1,600 shares because of the 2-for-1 stock split.

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Question 5

To measure the performance of an investment manager, which of the following methods of computing returns should be used?

A)
Time-weighted return
B)
Dollar-weighted return
C)
Arithmetic average
D)
Holding period return

Answer 5

a The answer is time-weighted return. The time-weighted return should be used to measure the performance of an investment manager.

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Question 5

Your client purchased a call of KLN Corp. for $800. The exercise price was $35, and the market price of KLN Corp. stock was $38. Six months later, the market price of KLN Corp. stock was $40 and the client sold the call for $1,250.

What was the holding period return on this investment?

A)
14.28%
B)
56.25%
C)
8.57%
D)
63.82%

Answer 5

b

HPR = (Sale price-purchase price)/purchase price
(1250-800)/800
56.25%

Question 5

A mutual fund with an investment objective of growth and income has an alpha of +4, a beta of 1.5, and a Sharpe ratio of 1.15. The fund

A)
should be purchased, because it has a relatively low level of risk in relation to return.
B)
should not be purchased, because it has a low level of return in relation to risk.
C)
should be purchased, because the rate of return is high in relation to risk.
D)
should not be purchased even though the rate of return compensates for the level of risk.

Answer 5

c The answer is should be purchased, because the rate of return is high in relation to risk. A positive alpha indicates the fund performed better than it should have on a risk-adjusted basis. Also, an alpha of +4, which is very high, means it performed 4% better than expected.

LO 7.2.1

Question 6

If the market interest rate is 7.27%, the current yield of a bond with a 9% coupon, $1,000 par, selling for $1,120, and maturing in 10 years is

A)
6.49%.
B)
7.27%.
C)
9.00%.
D)
8.04%.

Answer 6

d The answer is 8.04%. The current yield is the coupon payment divided by the market price of the bond:

($90 ÷ $1,120) x 100 = 8.04%.

LO 7.4.1

Question 6

Crowder made an investment that paid him an 8% nominal rate of return for the year in which he held the investment. During that year, the inflation rate was 3%. Based on this information, calculate Crowder’s inflation-adjusted return (real return).

A)
4.85%
B)
3.08%
C)
2.67%
D)
5.10%

Answer 6

a The answer is 4.85%. The inflation-adjusted return (IAR) is computed as:

IAR = [((1 + nominal rate of return) ÷ (1 + inflation rate)) − 1] × 100

= ((1.08 ÷ 1.03) − 1) × 100 = 4.8544, or 4.85%

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Question 6

Sammy owns a 7% corporate bond that is currently trading at $1,040. The bond matures in 22 years; however, it is callable in nine years at a 3% premium over par. What is the yield-to-call on Sammy’s bond?

A)
6.82%
B)
6.97%
C)
6.65%
D)
6.57%

Answer 6

c The call premium is 3%, which would be a price of $1,030. The inputs can be used on the financial calculator:

TVM Inputs
-$1,040 PV
$1,030 FV
$35 = $1,000 x 7% = $70 / 2 PMT
N = 18 (9 x 2 periods per year) N
Solve for I/YR = 6.65%
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Question 6

CDE Inc. bonds have these characteristics:

10% coupon
$1,000 par value
Current price of $1,136.92
Eight years to maturity
Callable in five years at $1,100
Calculate the bond’s yield to maturity (YTM) and yield to call (YTC).

A)
YTM: 7.65%; YTC: 8.24%
B)
YTM: 3.84%; YTC: 4.13%
C)
YTM: 7.97%; YTC: 8.54%
D)
YTM: 7.68%; YTC: 8.26%

Answer 6

d Explanation
The answer is YTM: 7.68%; YTC: 8.26%

Yield to maturity is calculated using the following TVM inputs on the financial calculator:

PMT = $1,000 x 10% = $100 / 2 = $50

FV = $1,000

PV = -$1,136.92

N = 16 (8 x 2 periods per year)

Solve for I/YR (YTM) = 7.68, or 7.68%

Yield to call is calculated using the following TVM inputs on the financial calculator:

PMT = $1,000 x 10% = $100 / 2 = $50

FV = $1,100

PV = -$1,136.92

N =10 (5 x 2 periods per year)

Solve for I/YR (YTC) = 8.26, or 8.26%

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Question 7

Zenith Mutual Fund has had the following annual returns: +12%, +18%, +22%, and –13%. What is the Zenith Fund’s geometric mean return?

A)
10.17%
B)
8.83%
C)
9.75%
D)
11.66%

Answer 7

b The simplest way to do this problem is to see how much $1 would have grown to over the four years, and then do a simple time value of money calculation. $1.00 × 1.12 × 1.18 × 1.22 × 0.87 = $1.4027. (1) PV, 1.4027 FV, 4 N, I/YR = 8.8281%.

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Question 8

Rose purchased TRM stock for $40. A year later the stock paid a dividend of $4. At the end of the second year, Rose sold her TRM stock for $60 per share. What is the time-weighted return for TRM stock for the two-year period?

A)
27.58%
B)
23.26%
C)
20.81%
D)
18.56%

Answer 8

a The answer is 27.58%. Time-weighted return is calculated as follows:

CF0 = (40)

CF1 = 4

CF2 = 60

IRR/YR = 27.58%

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Question 8

Jane considers herself to be a conservative investor. To generate additional income, she wants to add an investment-grade bond to her portfolio. She lives in a state that does not have an income tax and she is in the 35% federal income tax bracket. Select the best choice for her portfolio.

A)
Bond B, A rated corporate debenture with a 4.75% coupon rate
B)
Bond D, AAA rated Treasury bond with a 1.5% coupon rate
C)
Bond C, D rated corporate debenture with a 6% coupon rate
D)
Bond A, AA rated municipal bond with a 3.5% coupon rate

Answer 8

d The answer is Bond A, AA rated municipal bond with a 3.5% coupon rate. Even though Bond C has the highest after-tax rate of return, this bond would not be appropriate for Jane based on her desire for an investment-grade bond. Therefore, Bond A would be the best choice.

Calculations:

Bond A: 3.5%

Bond B: 4.75% × (1 – 0.35) = 3.0875%

Bond C: 6% × (1 – 0.35) = 3.90%

Bond D: 1.5% × (1 – 0.35) = 0.9750%

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Question 9

Mark owns a corporate bond with a coupon rate of 6.78%. Assume the annual inflation rate is 2.5% and he is in the 35% federal marginal income tax bracket. Calculate his after-tax, inflation-adjusted rate of return on this bond.

A)
1.86%
B)
2.04%
C)
1.50%
D)
4.17%

Answer 9

a The answer is 1.86%. First, calculate Mark’s after-tax rate of return on the corporate bond [0.0678 × (1 – 0.35)] = 0.04407, or 4.41%.

Next, calculate the after-tax, inflation-adjusted rate of return {[(1 + 0.0441) ÷ (1 + 0.025)] – 1} × 100 = 1.8634, or 1.86%.

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Question 10

Harry has an investment that has produced the following returns: Year 1: 10%, Year 2: 5%, Year 3: –7%, Year 4: –3%, Year 5: 12%. Calculate the arithmetic mean return on this investment.

A)
6.75%
B)
3.40%
C)
8.50%
D)
17.00%

Answer 10

b The answer is 3.40%. The arithmetic mean is calculated by dividing the sum of the periodic returns by the total number of periods being evaluated. Therefore, Harry earned an average of 3.40% [(10% + 5% – 7% – 3% + 12%) ÷ 5] per year on his investment.

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Question 10

Al Jenkins owns a corporate bond that currently sells for $1,175. The coupon rate is 9%, interest is paid semiannually, and the bond matures in 20 years. The bond is callable in 11 years at $1,050.

What is the yield to call on this bond?

A)
7.32%
B)
7.00%
C)
6.72%
D)
7.42%

Answer 10

b The answer is 7.00%. The yield to call is calculated using the following TVM inputs in the financial calculator:

N = 22 (11 x 2 periods per year)

PV = -$1,175

FV= $1,000

PMT = 9% x $1,000 = $90 / 2 = $45

Solve for I/YR = 7.00%

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Question 11

Your client purchased the Zenith Fund three years ago at $13.16. Here are the year-end prices of the fund up until today:

20X7

$14.21

20X8

$15.86

20X9

$14.78

What is the geometric return of Zenith Fund for this three-year period?

A)
5.88%
B)
4.61%
C)
3.95%
D)
5.26%

Answer 11

c The $13.16 has grown to $14.78 over a three-year period, so ($13.16) is the PV: $14.78 FV, 3 N, and solve for I/YR, which equals 3.95%.

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Question 12

Lauren invested $15,000 in a growth and income fund four years ago. She received a dividend of $800 the first year and $900 each in the second, third, and fourth years. Today, her investment has a total value of $27,234.56. Calculate the approximate internal rate of return (IRR) on Lauren’s investment. (Round to the nearest percent.)

A)
13%
B)
12%
C)
21%
D)
18%

Answer 12

c The answer is 21%. IRR is the discount rate that equates the present value of all the cash inflows with the present value of the cash outflows. The cash flow inputs for the financial calculator are as follows:

• 15,000 CF0,

800 CF1,

900 CF2,

900 CF3,

27,234.56 + 900 = 28,134.56 CF4,

Solve for IRR/YR = 20.80 (rounded to 21%).

Note the final cash flow consists of both the dividend ($900) and the ending value ($27,234.56).

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Question 12

Bond ABC is selling at par, offers an 8% coupon, and matures in 20 years. The bond has a call feature that allows the issuer to call the bond after 10 years at a price of $1,050. Which of these statements explains the relationship between the bond’s yield to call (YTC) and yield to maturity (YTM)?

A)
The YTC for Bond ABC is 8.33%, which is more than Bond ABC’s YTM.
B)
The YTC for Bond ABC is 8.00%, which is more than Bond ABC’s YTM.
C)
The YTC for Bond ABC is 8.33%, which is less than Bond ABC’s YTM.
D)
The YTC for Bond ABC is 8.00%, which is equal to Bond ABC’s YTM.

Answer 12

a The answer is the YTC for Bond ABC is 8.33%, which is more than Bond ABC’s YTM.

Because Bond ABC is selling at par, the YTM is equal to the coupon rate of 8%. Use the following TVM inputs in the financial calculator:

PV = –$1,000

FV = $1,050

N = 20 (10 x 2 periods per year)

PMT = 8% × $1,000 = $80 ÷ 2 = $40

Solve for I/YR = 8.33%

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Question 12

Ellen is an aggressive investor who is willing to take above-average risk to maximize capital appreciation. She is not interested in current income. The two mutual funds that she has under consideration are the following:

Small-Cap Value Fund

Small-Cap Growth Fund

Current yield

1.1%v

0.6%g

Five-year total return

14.2%v

16.7%g

Beta

0.89v

1.14g

Sharpe ratio

1.12v

0.93g

Standard deviation

8.20v

12.60g

Alpha

+2.70v

+0.40g

Which mutual fund is more appropriate for Ellen and why?

A)
Small-cap value fund, because its risk-adjusted performance statistics are superior
B)
Small-cap value fund, because its coefficient of variation is higher
C)
Small-cap growth fund, because its total return is higher
D)
Small-cap growth fund, because growth stocks fit her goal of maximum capital appreciation

Answer 12

a Perhaps a fund other than one with a lower-than-market beta fund should have been considered since she is an aggressive investor. However, no such alternative is shown. Total return alone is insufficient reason to select one fund over another. Risk-adjusted return is the appropriate measure. The value fund has a higher alpha, a higher Sharpe ratio, and a higher risk-adjusted performance when the total return is divided by beta. The current yield is relatively low for both funds.

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Question 13

The answer is 10.00%. Solve for yield to maturity using the following TVM inputs in the financial calculator:

PV = −$677

FV = $1,000

PMT = 0

N = 8 (4 x 2 periods per year)

Solve for I/YR = 10% (rounded)

LO 7.4.1

Answer 13

a This is a false statement. A bond is selling at par when the current yield equals the YTM.

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Question 13

The yield to maturity on a zero-coupon bond ($1,000 par value) currently selling at $677 and maturing in four years is approximately

A)
15.00%.
B)
37.48%.
C)
10.00%.
D)
4.00%.

Answer 13

c The answer is 10.00%. Solve for yield to maturity using the following TVM inputs in the financial calculator:

PV = −$677

FV = $1,000

PMT = 0

N = 8 (4 x 2 periods per year)

Solve for I/YR = 10% (rounded)

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Question 13

Capitalization-weighted indexes are

A)
constructed by giving each investment equal weighting.
B)
the preferred type of index to use in modern portfolio theory applications.
C)
uncommon and not suitable for performance measurement.
D)
characterized by higher-priced stocks having more influence on the overall movement of the index than lower-priced stocks.

Answer 13

b Explanation
The answer is the preferred type of index to use in modern portfolio theory applications. Capitalization weighted indexes are the most prevalent type of index and are best suited for modern portfolio theory applications. In a price-weighted index, higher-priced stocks within this index have more influence on the overall movement of this index than lower-priced stocks.

LO 7.3.1

Question 14

Johnny owns a municipal bond with a coupon rate of 4.25%. Assuming the annual inflation rate is 1.65%, calculate Johnny’s real rate of return on his bond.

A)
1.58%
B)
2.60%
C)
4.25%
D)
2.56%

Answer 14

d The answer is 2.56%. Johnny realized a real rate of return of 2.56%.

Real rate of return = {[(1 + 0.0425) ÷ (1 + 0.0165)] – 1} × 100 = 2.5578, or 2.56%.

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Question 15

A(n) ______________________ average allows small companies to have as much influence as large companies in the average; a(n)_________________ average gives greater influence to large companies than to small companies in the average; and a(n) ______________________ average gives greater influence to high-priced stocks than to low-priced stocks in the average.

A)
capitalization-weighted; price-weighted; equally weighted
B)
price-weighted; capitalization-weighted; equally weighted
C)
price-weighted; equally weighted; capitalization-weighted
D)
equally weighted; capitalization-weighted; price-weighted

Answer 15

d For a price-weighted index, higher priced stocks have more influence on the overall movement of this index than lower priced stocks. For a market capitalization weighted index, such as the S&P 500, a stock with a market capitalization value of $25 million will have 10 times the impact of a stock with a market capitalization value of a $2.5 million company.

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Question 15

To design a market capitalization weighted index, which of the following approaches should be used?

A)
Weight the components by their intrinsic value
B)
Weight the components by the total fair market value of their outstanding shares
C)
Weight the components by their geometric mean return over the past year
D)
Weight the components by their per share market prices

Answer 15

b A stock with a market capitalization value of $50 million will have 10 times the impact of a stock with a market capitalization value of a $5 million company.

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Question 15

Mary owns a portfolio consisting of two stocks, FUR and STC. FUR stock has a beta of 0.90, a standard deviation of 5%, and an actual return of 10%. STC stock has a beta of 1.10, a standard deviation of 7%, and an actual return of 12%. Assume a risk-free rate of return of 3%. Using the Treynor ratio, evaluate which stock had the better risk-adjusted performance.

A)
FUR stock
B)
STC stock
C)
Cannot be determined with the information provided
D)
Both stocks exhibit the same performance

Answer 15

b The answer is STC stock. The formula for the Treynor ratio is:

Tp = (rp − rf ) ÷ βp

Treynor for FUR stock = (0.10 − 0.03) ÷ 0.90 = 0.0777

Treynor for STC stock = (0.12 − 0.03) ÷ 1.10 = 0.0818

As a result, the Treynor ratio for STC stock is higher than FUR stock, indicating that STC has outperformed FUR on a risk-adjusted basis.

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Question 16

Seven years ago, KLO Industries issued a 15-year bond with a 6% coupon rate. The bonds are currently rated BB+. Due a decline in interest rates, the company decided to call the bonds for 106% of par value. Calculate the rate of return for an investor who purchased the bond at issue for par and surrendered it today for the call price.

A)
6.25%
B)
6.00%
C)
6.69%
D)
5.74%

Answer 16

c The answer is 6.69%. The yield to call on this issue is calculated using the following TVM inputs on the financial calculator:

FV = $1,060

PV = −$1,000

PMT = $30 (6% x $1,000 = $60 ÷ 2)

N =14 (7 x 2 periods per year)

Solve for I/YR = 6.69%

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Question 16

ABC Corporation has issued a 30-year callable bond with a 5.75% coupon at par. The current market price of the bond is $989.50. Calculate the current yield of this bond.

A)
2.91%
B)
5.75%
C)
5.81%
D)
5.69%

Answer 16

c The answer is 5.81%. The current yield is calculated as follows:

$57.50 ÷ $989.50 = 0.05811, or 5.81%.

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Question 16

Ashley purchased a five-year corporate bond with a 6.25% coupon paid semiannually. The bond is callable after three years for a price of $1,025. Assuming the bond is currently trading at $1,045, calculate its yield to call.

A)
2.69%
B)
2.31%
C)
5.38%
D)
4.62%

Answer 16

c The answer is 5.38%.

Yield to call can be calculated using the following TVM inputs on the financial calculator:

PV = –$1,045

FV = $1,025

PMT = $31.25 (6.25% × $1,000 = $62.50 ÷ 2)

N = 6 (3 x 2 periods per year)

Solve for I/YR = 5.38%

The yield to call is 5.38%, which is lower than the coupon rate of 6.25%, further validating that the bond is trading at a premium.

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Question 17

Steve has an AA rated bond with an annual coupon rate of 4.35% that is currently trading for $965. Calculate the bond’s current yield.

A)
4.35%
B)
4.20%
C)
4.51%
D)
3.50%

Answer 17

c The answer is 4.51%. The bond’s current yield is calculated as $43.50 ÷ $965. Annual interest payment as a percent of par equals $43.50 ($1,000 × 4.35%) divided by the current market price of $965.

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Question 18

You are about to choose a new mutual fund to add to client portfolios. As you review the Morningstar reports for the funds you are considering, you have focused on each fund’s alpha as reported by Morningstar. Alpha tells you

A)
a fund’s percentage return above the risk-free rate of return.
B)
by what percentage a fund’s capital appreciation exceeded the capital appreciation of the average fund in its asset class.
C)
each fund’s performance relative to the S&P 500.
D)
the difference between a fund’s realized return and its risk-adjusted expected return.

Answer 18

d The answer is the difference between a fund’s realized return and its risk-adjusted expected return. Alpha does not compare directly to the S&P 500, but rather to the fund’s expected return, which is risk-adjusted for the fund’s beta. The total return, not just the capital appreciation component, is used in the Jensen formula. The risk-adjusted required return is the risk-free rate plus the risk premium multiplied by the fund’s beta.

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Question 18

Which of the following statements regarding performance measures is CORRECT?

A)
The Sharpe ratio uses beta as its measure of risk.
B)
The reliability of their betas is important for the Jensen and Sharpe performance measures.
C)
A negative alpha indicates the investment lost money.
D)
Jensen’s alpha may be used by itself to judge an investment.

Answer 18

d Beta is the risk measure for alpha, but Sharpe uses standard deviation as its risk measure. Therefore, the reliability of beta is relevant for alpha. Jensen’s alpha can be used by itself to judge an investment; the Sharpe ratio must be used in comparison with another Sharpe ratio in judging an investment. A negative alpha indicates the investment did not perform as well as expected given the risk taken. For example, an alpha of –1 means the investment underperformed by 1% compared to what it was expected to return. Accordingly, a negative alpha does not necessarily mean the investment lost money.

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Question 18

Select the CORRECT statement regarding security market indexes and averages.

A)
The S&P 500 Index is used by most professionals as a benchmark for U.S. large-cap equity investments.
B)
The Russell 2000 Index is used to benchmark small capitalization companies.
C)
The Wilshire 5000 Index is often used as a measure of the overall market within the United States.
D)
All of these statements are correct.

Answer 18

d Explanation
The answer is all of these statements are correct. Averages and indexes are constructed to inform investors about changes in the market. They also serve as benchmarks for the performance of investors’ portfolios and the performance of money managers.

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Question 18

Assuming Mary earned a 3% return from dividend reinvestment, a 2% return from capital gain reinvestment, and a 9% return from share price appreciation on her mutual fund, calculate her total return.

A)
14%
B)
12%
C)
5%
D)
3%

Answer 18

a The answer is 14%. Total return on a stock or mutual fund may be thought of as the sum of the capital appreciation/depreciation on the underlying principal of the investment and any income or earnings generated from that investment. Therefore, Mary’s total return equals 14% (3% + 2% + 9%).

LO 7.1.1

Question 19

Seven years ago, KLO Industries issued a 15-year bond with a 6% coupon rate. The bonds are currently rated BB+. Due a decline in interest rates, the company decided to call the bonds for 106% of par value. Calculate the rate of return for an investor who purchased the bond at issue for par and surrendered it today for the call price.

A)
5.74%
B)
6.69%
C)
6.00%
D)
6.25%

Answer 19

b The answer is 6.69%. The yield to call on this issue is 6.69%, calculated using the following TVM inputs:

FV = $1,060

PV = −$1,000

PMT = $30 (6% x $1,000 = $60 ÷ 2)

N = 14 (7 x 2 periods per year)

Solve for I/YR = 6.69%

LO 7.2.1

Question 20

Mildred manages a mutual fund whose goal is to provide a return similar to the U.S. small capitalization market. Choose the index that would provide the best benchmark for Mildred’s fund.

A)
Dow Jones Industrial Average (DJIA)
B)
Wilshire 5000
C)
Russell 2000
D)
S&P 500

Answer 20

c The answer is Russell 2000. The Russell 2000 is an index of small capitalization U.S. stocks. The DJIA represents 30 major blue-chip stocks. The S&P 500 is an index of 500 large capitalization U.S. stocks. The Wilshire 5000 is a broad market index.

LO 7.3.1

Question 20

Tripp is an investor in the 32% marginal tax bracket. If he invests in a 4.75% municipal bond, his taxable equivalent yield (TEY) would be

A)
3.23%.
B)
6.27%.
C)
4.75%.
D)
6.99%.

Answer 20

d taxable equivalent yield = tax-exempt yield ÷ (1 − marginal tax rate) = 4.75% ÷ (1 − 0.32) = 6.99%

LO 7.4.1

Question 21

The answer is the difference between a fund’s realized return and its risk-adjusted expected return. Alpha does not compare directly to the S&P 500, but rather to the fund’s expected return, which is risk-adjusted for the fund’s beta. The total return, not just the capital appreciation component, is used in the Jensen formula. The risk-adjusted required return is the risk-free rate plus the risk premium multiplied by the fund’s beta.

LO 7.2.1

Answer 21

c The answer is I, II, III, and IV. All of these statements are correct pertaining to time-weighted and dollar-weighted returns.

LO 7.1.1

Question 22

JK Mutual Fund has a return of 15.5% and a beta of 1.1. If the market return is 14%, and the risk-free rate is 4%, what is the alpha for JK Mutual Fund?

A)
0.00
B)
+0.50
C)
+1.00
D)
–0.50

Answer 22

b The answer is +0.50. Calculate alpha: 15.5 – [4 + (14 – 4)1.1] = +0.50.

LO 7.2.1

Question 23

Your client, Trace, owns a portfolio that earned 12% during the current year. His portfolio has a beta of 1.3 and a standard deviation of 14%. During the current year, the market (as represented by the S&P 500 index) earned 9%. If the current risk-free rate is 5%, which of the following accurately illustrates the Treynor ratios for Trace’s portfolio and the market?

A)
0.0538; 0.0100
B)
0.0050; 0.0100
C)
0.0538; 0.0400
D)
0.0050; 0.0400

Answer 23

c The answer is 0.0538; 0.0400. Calculations are as follows.

Trace’s Treynor = (0.12 – 0.05) ÷ 1.3 = 0.0538

Market’s Treynor = (0.09 – 0.05) ÷ 1 = 0.0400. The market has a beta of 1.0.

LO 7.4.1

Question 24

Kellie purchased a five-year bond with a coupon rate of 2.50% paid semiannually. The bond has a current market price of $985. Calculate the yield to maturity (YTM) for Kellie’s bond.

A)
2.8259%
B)
2.8238%
C)
2.8990%
D)
2.5000%

Answer 24

b The answer is 2.8238%. The bond’s YTM is calculated using the following TVM inputs in the financial calculator:

PV = −$985

FV = $1,000

PMT = 2.50% × $1,000 = $25 / 2 = $12.50

N = 10 (5 x 2 periods per year)

Solve for I/YR = 2.8238%

The YTM for Kellie’s bond is higher than its coupon rate because the bond is trading at a discount.

LO 7.4.1

Question 25

Andy purchased a four-year bond with a coupon rate of 7.5% paid semiannually. The bond is trading for $1,025 in the secondary market. Calculate the bond’s yield to maturity (YTM).

A)
8.05%
B)
4.34%
C)
6.78%
D)
3.39%

Answer 25

c The answer is 6.78%. The bond’s YTM is calculated using the following TVM inputs on the financial calculator:

PV = –$1,025

FV = $1,000

PMT = $37.50 (1,000 × 7.5% = $75 ÷ 2)

N = 8 (4 x 2 periods per year)

Solve for I/YR = 6.78%.

LO 7.4.1

Question 25

Jensen’s alpha is an absolute measurement. What does it tell you?

A)
The percentage a manager over- or underperformed based on the amount of risk taken
B)
The percentage of return that can be attributed to unsystematic risk
C)
The percentage of return that can be attributed to systematic risk
D)
The percentage by which a manager beat the market

Answer 25

a The answer is the percentage a manager over- or underperformed based on the amount or risk taken. Jensen’s alpha is a measure of the risk-adjusted value added by a portfolio manager. Specifically, alpha is measured as the portfolio’s actual or realized return in excess of (or deficient to) the expected return calculated by the capital asset pricing model (CAPM).

LO 7.2.1

Question 26

Which of the following statements regarding security market indexes is CORRECT?

A)
Market indexes reflect the average price behavior of a group of stocks at a given point in time.
B)
The Wilshire 100 Index is used as a measure of the financial stock sector.
C)
The S&P 500 Index automatically adjusts for stock splits and dividends by focusing on market value instead of price.
D)
The Russell 2000 Index is a well-known index used to benchmark large capitalization companies.

Answer 26

c The answer is the S&P 500 Index automatically adjusts for stock splits and dividends by focusing on market value instead of price. The Russell 2000 Index is a well-known index used to benchmark small capitalization companies. A market average, not a market index, reflects the average price behavior of a group of stocks at a given point in time. An index measures the current price behavior of a group of stocks in relation to a base value. The Wilshire 5000 index is used as a measure of the U.S. broad market.

LO 7.3.1

Question 27

Anita bought ULA stock for $25,000 six years ago. Today, she sold the stock for $67,000. Calculate Anita’s holding period return on ULA.

A)
16.80%
B)
8.40%
C)
168.00%
D)
28.00%

Answer 27

c The answer is 168.00%. Anita’s holding period rate of return was 168% {[(67,000 – 25,000) ÷ 25,000] × 100}.

LO 7.1.1

Question 28

Billie purchased a 10-year U.S. Treasury bond with a 6.5% coupon paid semiannually. Assuming the bond is currently trading at $1,075, calculate its yield to maturity (YTM).

A)
2.76%
B)
6.50%
C)
5.51%
D)
3.25%

Answer 28

c The answer is 5.51%. Use the following TVM inputs in the financial calculator:

PV = –$1,075

FV = $1,000

PMT = $32.50 (6.5% × $1,000 = $65 ÷ 2)

N = 20 (10 x 2 periods per year)

Solve for I/YR = 5.51%.

The YTM on the bond is 5.51%, which is lower than the coupon rate of 6.5%, further validating that the bond is trading at a premium.

LO 7.4.1

Question 28

Quincy has narrowed his choice down to the following four mid-cap funds, which is a category he wants to add to his portfolio. Which fund should Quincy choose?

A Fund

J Fund

Q Fund

Z Fund

Return

12% a

9% j

13% q

11% z and so on

Alpha

0.52

–1.04

0.66

1.10

Treynor

0.68

0.21

0.58

0.62

Sharpe

0.44

0.32

0.21

0.37

R-squared

0.88

0.78

0.82

0.84

A)
Q Fund
B)
J Fund
C)
Z Fund
D)
A Fund

Answer 28

c The R-squared for all four funds is greater than 0.70, meaning beta is reliable. Alpha uses beta, and is a measure of absolute return, and the best measure to use if beta is reliable. The fund with the highest alpha is the Z fund.

LO 7.2.1

Question 28

Jill is in the 24% marginal tax bracket. She owns a $1,000 par value public purpose municipal bond that pays $35 interest semiannually.

What pretax yield on corporate bonds would be comparable to the yield on Jill’s current investment?

A)
5.32%
B)
9.21%
C)
6.28%
D)
8.96%

Answer 28

Explanation
pretax yield
=
after tax yield / (1 − marginal tax rate)
$35 × 2 = $70 annual interest = 7.0% coupon rate

taxable equivalent yield (TEY) = 7.0% ÷ (1 - .24) = 7.0% ÷ 0.76 = 9.21%

LO 7.4.1

Question 29

In general, rising interest rates result in which of the following combinations?

A)
Rising bond prices and falling stock prices
B)
Falling bond prices and rising stock prices
C)
Falling stock and bond prices
D)
Rising stock and bond prices

Answer 29

c In general, rising interest rates result in falling stock and bond prices.

LO 7.2.1

Question 29

Which of the following statements regarding the various performance measures are CORRECT?

A positive alpha indicates that the manager consistently underperformed the market on a risk-adjusted basis.
Jensen’s alpha indicates how much the realized return differs from the expected return, as per the capital asset pricing model (CAPM).
The Sharpe ratio is not useful for evaluating the performance of nondiversified portfolios.
The Treynor ratio does not indicate whether a portfolio manager outperformed or underperformed the market portfolio.
A)
I and III
B)
II and IV
C)
I and II
D)
II, III, and IV

Answer 29

b The answer is II and IV. Statements I and III are incorrect. A positive alpha indicates that the manager outperformed the market on a risk-adjusted basis. The Sharpe ratio uses total risk, as measured by standard deviation, and is useful for evaluating the performance of both nondiversified and well-diversified portfolios.

LO 7.2.1

Question 29

If a mutual fund’s beta and standard deviation are expected to decrease in the future, its average annual return and the market average annual return are expected to remain the same, and the risk-free rate is expected to remain constant, which of the following shows the real effect this would have on the following performance measures?

Option Alpha Sharpe Ratio
A increase decrease
B decrease decrease
C decrease increase
D increase increase
A)
Option D
B)
Option B
C)
Option C
D)
Option A

Answer 29

a The answer is Option D. A decrease in the risk level decreases the denominator of the Sharpe ratio, while the numerator stays constant, thereby increasing the Sharpe ratio. The decreased risk level, as measured by beta, decreases the expected return for the fund, while the actual portfolio return remains constant, thereby increasing the alpha.

LO 7.2.1

Question 30

Five years ago, XYZ Company issued a 20-year bond with a 4.75% coupon paid semiannually. The bond may be called at 104% of par, 10 years after issue. Assuming the bond is currently selling for $990, calculate the bond’s yield to call.

A)
4.95%
B)
5.68%
C)
2.84%
D)
5.18%

Answer 30

b The answer is 5.68%. The bond’s yield to call is calculated using the following TVM inputs on the financial calculator:

Note: XYZ Company has the option to call the issue in five years.

PV = -$990

N = 10 (5 x 2 periods per year)

PMT = $23.75 (4.75% x $1,000 = $47.50 ÷ 2)

FV = $1,040 ($1,000 × 1.04)

Solve for I/YR = 5.68%

LO 7.4.1

Question 30

Mutual fund QUE has a correlation coefficient with the market of 0.82, a beta of 1.05, and a standard deviation of 4%. The risk-free rate of return is 3.5%, and the return on the market is 12%. Mutual fund POI has a Sharpe ratio of 2.05, a Treynor ratio of 0.11, and an alpha of 0.70%. Decide which of the following a rational investor would select if the market’s standard deviation is 2% and QUE realized a 13% return.

A)
POI over QUE because QUE’s alpha is 0.58%.
B)
QUE over POI because QUE’s Sharpe ratio is 2.38.
C)
QUE over POI because QUE’s coefficient of variation is 0.31.
D)
POI over QUE because QUE’s Treynor ratio is 0.09.

Answer 30

b The answer is QUE over POI because QUE’s Sharpe ratio is 2.38.

QUE’s alpha = 13% – [3.5% + (12% – 3.5%) 1.05] = 0.58%

QUE’s Treynor ratio = (0.13 – 0.035) ÷ 1.05 = 0.09

QUE’s Sharpe ratio = (0.13 – 0.035) ÷ 0.04 = 2.38

QUE’s coefficient of variation = 4% ÷ 13% = 0.31

Because QUE’s R2 equals 67% (0.82 × 0.82), alpha and Treynor are not appropriate performance measures for comparison purposes. Because we do not know POI’s coefficient of variation, we must use the Sharpe ratio to select the better risk-adjusted return.

LO 7.2.1

Question 30

The performance of two growth and income mutual funds is displayed below:

ABC Fund XYZ Fund
Average annual rate of return 8.65% 6.78%
Standard deviation of returns 5.86% 9.98%
Beta 0.75 1.00
Assuming a risk-free rate of return of 5%, which of these statements is CORRECT?

A)
The Sharpe ratio for XYZ Fund is 0.1784 and 0.6229 for ABC Fund.
B)
All of these statements are correct.
C)
XYZ Fund has a higher level of systematic risk than ABC Fund.
D)
Based on the Treynor ratio, ABC Fund has a better risk-adjusted performance than XYZ Fund.

Answer 30

b The answer is all of the statements are correct. When compared with another investment, the higher the Treynor ratio, the better the risk-adjusted performance of the asset. Therefore, ABC Fund with a Treynor ratio of 0.0487 has a better risk-adjusted performance than XYZ Fund. XYZ Fund has a beta greater than ABC Fund, indicating a higher level of systematic risk.

Calculations:

Treynor ratio for ABC Fund is 0.0487 [(0.0865 – 0.05) ÷ 0.75]

Treynor ratio for XYZ Fund is 0.0178 [(0.0678 – 0.05) ÷ 1.00]

Sharpe ratio for ABC Fund is 0.6229 [(0.0865 – 0.05) ÷ 0.0586]

Sharpe ratio for XYZ Fund is 0.1784 [(0.0678 – 0.05) ÷ 0.0998]

LO 7.4.1

Question 30

Allison purchases 200 shares of ADM stock for $23 per share and makes subsequent purchases at the end of the following years:

Year 1: 50 shares at $26/share
Year 2: 75 shares at $29/share
Year 3: 25 shares at $36/share
At the end of Year 4, ADM is trading for $41 per share. There have been no dividends paid during the holding period. Calculate the annualized dollar-weighted return on Allison’s investment for this four-year period.

A)
16.05%
B)
14.55%
C)
15.05%
D)
15.55%

Answer 30

a The answer is 16.05%. To use the uneven cash flow method to solve for the internal rate of return:

CF0 (4,600) (200 × 23)

CF1 (1,300) (50 × 26)

CF2 (2,175) (75 × 29)

CF3 (900) (25 × 36)

CF4 14,350 (350 × 41)

Solve for IRR/YR = 16.0531, or 16.05%

LO 7.4.1

Question 30

What is the internal rate of return (IRR) on an investment that was purchased for $10,000, generated income at the end of Year 1 of $600, required an additional expenditure at the end of Year 2 of $300, and was sold at the end of Year 3 for $13,000?

A)
9.50%
B)
6.28%
C)
10.24%
D)
12.11%

Answer 30

c The answer is 10.24%. The following cash flows are used on the financial calculator:

CF0 = (10,000)

CF1 = 600

CF2 = (300)

CF3 = 13,000

Solve for IRR/YR = 10.2432, or 10.24%.

LO 7.1.1

Question 31

Frank purchased 100 shares of ABC common stock five years ago at a cost of $5,000. The stock paid these dividends:

Year Amount
1 $200.00
2 $200.00
3 $250.00
4 $275.00
5 $300.00
At the time the fifth-year dividend was paid, Frank sold the stock for $8,500.

What is the dollar-weighted return on ABC stock?

A)
15.51%
B)
12.67%
C)
15.11%
D)
18.15%

Answer 31

c The answer is 15.11%. This problem involves calculating the IRR/YR for uneven cash flows per the following inputs. Using the HP 10bII+:

• 5000, CF0

200, CF1

200, CF2

250, CF3

275, CF4

8800 ($300 + $8,500), CF5

Solve for IRR/YR = 15.1076 = 15.11%

LO 7.1.1

Question 31

Harry purchased 100 shares of MNL common stock five years ago at a cost of $4,300. The stock paid these dividends:

Year Amount
1 $180
2 $180
3 $200
4 $225
5 $230
At the time the fifth-year dividend was paid, Harry sold the stock for $8,900.

What was Harry’s average annual compound rate of return (IRR) on MNL stock?

A)
12.68%
B)
9.35%
C)
19.21%
D)
15.66%

Answer 31

c The answer is 19.21%. Calculation follows:

Financial Calculator Inputs
4,300 (+/–) CF0
180 CF1
180 CF2
200 CF3
225 CF4
230 +
8,900 =, CF5
Solve for IRR/YR
(Answer = 19.21%)
LO 7.1.1

Question 32

Nancy bought $4,000 worth of common stock two years ago. She received dividends of $30 each quarter for the first year and $35 each quarter for the second year. The stock currently is worth $4,100. The graph below summarizes inflows and outflows.

0 -4000
1 30
2 30
3 30
4 30
5 35
6 35
7 35
8 35 4100

What is the internal rate of return that the stock has earned?

A)
0.99%
B)
4.45%
C)
1.11%
D)
3.61%

Answer 32

b The answer is 4.45%. Below are the keystrokes for the HP 10BII+; refer to the Financial Calculator Workbook to figure inputs for the TI BAII+:

HP 10bII+
(set for 4 P/YR)
4000, +/–, CFj
30, CFj, 4, SHIFT, Nj
35, CFj, 3, SHIFT, Nj
4100, +, 35, =, CFj
SHIFT, IRR/YR
LO 7.1.1

Question 32

What is the taxable equivalent yield on a municipal bond with an 8.75% return for an investor in the 24% marginal tax bracket?

A)
6.65%
B)
11.51%
C)
8.75%
D)
2.10%

Answer 32

b The formula for solving this problem is 8.75% ÷ (1 – 0.24) = 8.75% ÷ 0.76 = 11.51%.

LO 7.4.1

Question 32

An investor who would like to know how a portfolio manager performed relative to how the manager was expected to perform on a risk-adjusted basis would use which one of the following indicators?

A)
Jensen’s alpha
B)
Beta
C)
Sharpe ratio
D)
Treynor ratio

Answer 32

a The answer is Jensen’s alpha. The indicator that measures performance in relation to what was expected on a risk-adjusted basis is Jensen’s alpha. A positive number (alpha) indicates that the manager performed better than expected on a risk-adjusted basis.

LO 7.2.1

Question 32

Kumar purchased 100 shares of YTR stock from his broker. He earned returns of 7%, –3%, 8%, –10%, and 12% in years 1 through 5 respectively. Calculate Kumar’s geometric mean return on his investment over the five-year period.

A)
2.26%
B)
2.80%
C)
2.47%
D)
1.40%

Answer 32

c The answer is 2.47%.

First, calculate the future value per $1 of Kumar’s investment: (1.07)(0.97)(1.08)(0.90)(1.12) = 1.13.

Next, calculate the geometric mean: PV = –1, FV = 1.13, N = 5, solve for I/YR = 2.4745, or 2.47%.

LO 7.4.1

Question 32

Robinson owns a municipal bond with a coupon rate of 2.75%. He is currently in the 32% federal marginal income tax bracket and resides in a state that does not impose a state income tax. Calculate his municipal bond’s taxable equivalent yield (TEY).

A)
3.66%
B)
4.04%
C)
6.75%
D)
2.75%

Answer 32

b The answer is 4.04%. The bond’s TEY is calculated as follows:

2.75% ÷ (1 – 0.32).

LO 7.4.1