FIN 451 Investments and Portfolio Management All Weeks Problem Set

Question

Grand Canyon FIN451 week 1 Problem Set

Complete the following:

- Chapter 3: problem sets, numbers 12, 13, 14, 15, 16, and 17
- Chapter 4: problem sets, numbers 11, 13, 15, 16, 22, 24, 27, and 28

APA format is not required, but solid academic writing is expected.

Answers should be submitted using an Excel spreadsheet in order to show all calculations, where applicable.

You are not required to submit this assignment to Turnitin.

Grand Canyon FIN451 week 2 Problem SET

- Chapter 5: problem sets, numbers 5, 6, and 11, and CFA problems, numbers 1 and 10
- Chapter 6: problem sets, number 21, and CFA problems, number 2

APA format is not required, but solid academic writing is expected.

Answers should be submitted using an Excel spreadsheet in order to show all calculations, where applicable.

You are not required to submit this assignment to Turnitin.

Answers should be submitted using an Excel spreadsheet in order to show all calculations, where applicable.

5. Suppose your expectations regarding the stock market are as follows:

State of the Economy Probability HPR

Boom 0.3 44%

Normal growth 0.4 14

Recession 0.3 216

Use Equations 5.6–5.8 to compute the mean and standard deviation of the HPR on

stocks. (LO 5-4)

6. The stock of Business Adventures sells for $40 a share. Its likely dividend payout

and end-of-year price depend on the state of the economy by the end of the year as

follows: (LO 5-2)

Dividend Stock Price

Boom $2.00 $50

Normal economy 1.00 43

Recession .50 34

a. Calculate the expected holding-period return and standard deviation of the holdingperiod

return. All three scenarios are equally likely.

b. Calculate the expected return and standard deviation of a portfolio invested half in

Business Adventures and half in Treasury bills. The return on bills is 4%.

11. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be

either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless

investment in T-bills pays 5%. (LO 5-3)

a. If you require a risk premium of 10%, how much will you be willing to pay for the

portfolio?

b. Suppose the portfolio can be purchased for the amount you found in ( a ). What will

the expected rate of return on the portfolio be?

c. Now suppose you require a risk premium of 15%. What is the price you will be willing

to pay now?

d. Comparing your answers to ( a ) and ( c ), what do you conclude about the relationship

between the required risk premium on a portfolio and the price at which the portfolio

will sell?

1. A portfolio of nondividend-paying stocks earned a geometric mean return of 5%

between January 1, 2005, and December 31, 2011. The arithmetic mean return for

the same period was 6%. If the market value of the portfolio at the beginning of

2005 was $100,000, what was the market value of the portfolio at the end of

2011?

10. Probabilities for three states of the economy and probabilities for the returns on a

particular stock in each state are shown in the table below.

State of Economy

Probability of

Economic State

Stock

Performance

Probability of Stock

Performance in Given

Economic State

Good .3 Good .6

Neutral .3

Poor .1

Neutral .5 Good .4

Neutral .3

Poor .3

Poor .2 Good .2

Neutral .3

Poor .5

What is the probability that the economy will be neutral and the stock will experience

poor performance?

Chapter 6

21. The following figure shows plots of monthly rates of return and the stock market for

two stocks. (LO 6-5)

a. Which stock is riskier to an investor currently holding her portfolio in a diversified

portfolio of common stock?

b. Which stock is riskier to an undiversified investor who puts all of his funds in only

one of these stocks?

2. George Stephenson’s current portfolio of $2 million is invested as follows:

Summary of Stephenson’s Current Portfolio

Value

Percent of

Total

Expected

Annual

Return

Annual

Standard

Deviation

Short-term bonds $ 200,000 10% 4.6% 1.6%

Domestic large-cap equities 600,000 30 12.4 19.5

Domestic small-cap equities 1,200,000 60 16.0 29.9

Total portfolio $2,000,000 100% 13.8% 23.1%

Stephenson soon expects to receive an additional $2 million and plans to invest the entire

amount in an index fund that best complements the current portfolio. Stephanie Coppa,

CFA, is evaluating the four index funds shown in the following table for their ability to

produce a portfolio that will meet two criteria relative to the current portfolio: (1) maintain

or enhance expected return and (2) maintain or reduce volatility

Each fund is invested in an asset class that is not substantially represented in the

current portfolio.

Index Fund Characteristics

Index Fund

Expected Annual

Return

Expected Annual

Standard Deviation

Correlation of Returns

with Current Portfolio

Fund A 15% 25% 10.80

Fund B 11 22 10.60

Fund C 16 25 10.90

Fund D 14 22 10.65

State which fund Coppa should recommend to Stephenson. Justify your choice by

describing how your chosen fund best meets both of Stephenson’s criteria. No calculations

are required.

Grand Canyon FIN451 week 3 Problem SET

- Chapter 7: problem sets, numbers 8a, 8b, 24, and 28, and CFA problems, number 2>APA format is not required, but solid academic writing is expected.

Chapter 8: problem sets, number 18, and CFA problems, numbers 7, 8, and 10

- APA format is not required, but solid academic writing is expected.
- A title page is expected.

Answers should be submitted using a Word document.

You are not required to submit this assignment to Turnitin.

APA format is not required, but solid academic writing is expected.

15. Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par

value. What coupon rate would they have to pay in order to sell at par if they paid their

coupons annually?

20. Fill in the table below for the following zero-coupon bonds, all of which have par values

of $1,000. (LO 10-2)

Price Maturity (years) Yield to Maturity

$400 20 ?

$500 20 ?

$500 10 ?

? 10 10%

? 10 8%

$400 ? 8%

37. The yield curve is upward-sloping. Can you conclude that investors expect short-term

interest rates to rise? Why or why not?

42. The following table contains spot rates and forward rates for three years. However, the

labels got mixed up. Can you identify which row of the interest rates represents spot

rates and which one the forward rates?

3. A convertible bond has the following features:

Coupon 5.25%

Maturity June 15, 2020

Market price of bond $77.50

Market price of underlying common stock $28.00

Annual dividend $1.20

Conversion ratio 20.83 shares

Calculate the conversion premium for this bond.

5. Bonds of Zello Corporation with a par value of $1,000 sell for $960, mature in five years,

and have a 7% annual coupon rate paid semiannually. (LO 10-6)

a. Calculate the:

(1) Current yield.

(2) Yield to maturity.

(3) Horizon yield (also called realized compound return) for an investor with a threeyear

holding period and a reinvestment rate of 6% over the period. At the end of

three years the 7% coupon bonds with two years remaining will sell to yield 7%.

b. Cite one major shortcoming for each of the following fixed-income yield measures:

(1) Current yield.

(2) Yield to maturity.

(3) Horizon yield (also called realized compound return).

CHAPTER 11

9. A nine-year bond has a yield of 10% and a duration of 7.194 years. If the bond’s yield

changes by 50 basis points, what is the percentage change in the bond’s price?

15. You will be paying $10,000 a year in tuition expenses at the end of the next two years.

Bonds currently yield 8%. (LO 11-2)

a. What is the present value and duration of your obligation?

b. What maturity zero-coupon bond would immunize your obligation?

c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation.

Now suppose that rates immediately increase to 9%. What happens to your net

position, that is, to the difference between the value of the bond and that of your

tuition obligation? What if rates fall to 7%?

1. Rank the following bonds in order of descending duration. (LO 11-2)

Bond Coupon Time to Maturity Yield to Maturity

A 15% 20 years 10%

B 15 15 10

C 0 20 10

D 8 20 10

E 15 15 15

3. As part of your analysis of debt issued by Monticello Corporation, you are asked to evaluate

two specific bond issues, shown in the table below.MONTICELLO CORPORATION BOND INFORMATION

Bond A (callable) Bond B (noncallable)

Maturity 2019 2019

Coupon 11.50% 7.25%

Current price 125.75 100.00

Yield to maturity 7.70% 7.25%

Modified duration to maturity 6.20 6.80

Call date 2013 —

Call price 105 —

Yield to call 5.10% —

Modified duration to call 3.10 —

a. Using the duration and yield information in the table, compare the price and yield

behavior of the two bonds under each of the following two scenarios:

i. Strong economic recovery with rising inflation expectations.

ii. Economic recession with reduced inflation expectations.

b. Using the information in the table, calculate the projected price change for bond B if

the yield-to-maturity for this bond falls by 75 basis points.

c. Describe the shortcoming of analyzing bond A strictly to call or to maturity.

12. The following bond swaps could have been made in recent years as investors attempted

to increase the total return on their portfolio.From the information presented below, identify possible reason(s) that investors

may have made each swap. (LO 11-5)

Action Call Price YTM (%)

a. Sell Baa1 Electric Pwr. 1st mtg. 63 8% due 2017 108.24 95 7.71

Buy Baa1 Electric Pwr. 1st mtg. 23 8% due 2018 105.20 79 7.39

b. Sell Aaa Phone Co. notes 51 2% due 2018 101.50 90 7.02

Buy U.S. Treasury notes 61 2% due 2018 NC 97.15 6.78

c. Sell Aa1 Apex Bank zero coupon due 2020 NC 45 7.51

Buy Aa1 Apex Bank float rate notes due 2033 103.90 90 —

d. Sell A1 Commonwealth Oil & Gas 1st mtg. 6% due 2023 105.75 72 8.09

Buy U.S. Treasury bond 51 2% due 2029 NC 80.60 7.40

e. Sell A1 Z mart convertible deb. 3% due 2023 103.90 62 6.92

Buy A2 Lucky Ducks deb. 73 4% due 2029 109.86 75 10.43

Grand Canyon FIN451 week 4 Problem SET

- Chapter 10: problem sets, numbers 15, 20, 37, 42, and CFA problems numbers 3 and 5
- Chapter 11: problem sets, numbers 9 and 15, and CFA problems numbers 1, 3, and 12

APA format is not required, but solid academic writing is expected.

You are not required to submit this assignment to Turnitin.

Grand Canyon FIN451 week 5 Problem SET

- Chapter 9: problem sets, numbers 11, 12, 18 and 20, and CFA problems, numbers 3 and 5
- Chapter 13: problem sets, numbers 10, 11, 16, 17, 19, and 20, and CFA problems, numbers 4 and 6

APA format is not required, but solid academic writing is expected.

You are not required to submit this assignment to Turnitin.

Grand Canyon FIN451 week 6 Problem SET

- Chapter 15: problem sets, numbers 10, 13, and 24, and CFA problems, number 4
- Chapter 16: problem sets, numbers 10, 11, 12, and 28

APA format is not required, but solid academic writing is expected.

You are not required to submit this assignment to Turnitin.

CHAPTER 15

10. An investor purchases a stock for $38 and a put for $.50 with a strike price of $35. The

investor sells a call for $.50 with a strike price of $40. What is the maximum profit and

loss for this position? Draw the profit and loss diagram for this strategy as a function of

the stock price at expiration.

13. The common stock of the P.U.T.T. Corporation has been trading in a narrow price range

for the past month, and you are convinced it is going to break far out of that range in the

next three months. You do not know whether it will go up or down, however. The current

price of the stock is $100 per share, the price of a three-month call option with an

exercise price of $100 is $10, and a put with the same expiration date and exercise price

costs $7. (L O 15-2)

a. What would be a simple options strategy to exploit your conviction about the stock

price’s future movements?

b. How far would the price have to move in either direction for you to make a profit on

your initial investment?

24. A put option with strike price $60 trading on the Acme options exchange sells for $2. To

your amazement, a put on the firm with the same expiration selling on the Apex options

exchange but with strike price $62 also sells for $2. If you plan to hold the options position

until expiration, devise a zero-net-investment arbitrage strategy to exploit the pricing

anomaly. Draw the profit diagram at expiration for your position.

4. Suresh Singh, CFA, is analyzing a convertible bond. The characteristics of the bond and

the underlying common stock are given in the following exhibit:

Convertible Bond Characteristics

Par value $1,000

Annual coupon rate (annual pay) 6.5%

Conversion ratio 22

Market price 105% of par value

Straight value 99% of par value

Underlying Stock Characteristics

Current market price $40 per share

Annual cash dividend $1.20 per share

Compute the bond’s: (LO 15-3)

a. Conversion value.

b. Market conversion price.

CHAPTER 16

10. Which of the following best explains a delta-neutral portfolio? A delta-neutral portfolio

is perfectly hedged against: (LO 16-5)

a. Small price changes in the underlying asset.

b. Small price decreases in the underlying asset.

c. All price changes in the underlying asset.

11. After discussing the concept of a delta-neutral portfolio, Washington determines that he

needs to further explain the concept of delta. Washington draws the value of an option

as a function of the underlying stock price. Draw such a diagram, and indicate how delta

is interpreted. Delta is the: (LO 16-5)

a. Slope in the option price diagram.

b. Curvature of the option price graph.

c. Level in the option price diagram.

12. Washington considers a put option that has a delta of 2 .65. If the price of the underlying

asset decreases by $6, then what is the best estimate of the change in option

price?

28. According to the Black-Scholes formula, what will be the value of the hedge ratio of a

put option for a very small exercise price? (

Grand Canyon FIN451 week 7 Problem SET

- Chapter 18: problem sets, number 7, and CFA problems, numbers 2, 3, 4, and 6
- Chapter 19: problem sets, numbers 5 and 8, and CFA problems, numbers 2 and 3

APA format is not required, but solid academic writing is expected.

You are not required to submit this assignment to Turnitin.

APA format is not required, but solid academic writing is expected.

CHAPTER 18

7. Consider the following information regarding the performance of a money manager in a

recent month. The table presents the actual return of each sector of the manager’s portfolio

in column (1), the fraction of the portfolio allocated to each sector in column (2), the

benchmark or neutral sector allocations in column (3), and the returns of sector indexes in

column (4).

2. The chairman provides you with the following data, covering one year, concerning the

portfolios of two of the fund’s equity managers (manager A and manager B). Although

the portfolios consist primarily of common stocks, cash reserves are included in the calculation

of both portfolio betas and performance. By way of perspective, selected data for

the financial markets are included in the following table. (LO 18-1)

Total Return Beta

Manager A 24.0% 1.0

Manager B 30.0 1.5

S&P 500 21.0

Lehman Bond Index 31.0

91-day Treasury bills 12.0

a. Calculate and compare the alpha of the two managers relative to each other and to the

S&P 500.

b. Explain two reasons the conclusions drawn from this calculation may be misleading.

3. Carl Karl, a portfolio manager for the Alpine Trust Company, has been responsible since

2015 for the City of Alpine’s Employee Retirement Plan, a municipal pension fund.

Alpine is a growing community, and city services and employee payrolls have expanded in

each of the past 10 years. Contributions to the plan in fiscal 2020 exceeded benefit payments

by a three-to-one ratio.

Th e plan’s board of trustees directed Karl fi ve years ago to invest for total return over the

long term. However, as trustees of this highly visible public fund, they cautioned him that

volatile or erratic results could cause them embarrassment. Th ey also noted a state statute that

mandated that not more than 25% of the plan’s assets (at cost) be invested in common stocks.

At the annual meeting of the trustees in November 2020, Karl presented the following

portfolio and performance report to the board.ALPINE EMPLOYEE RETIREMENT PLAN

Asset Mix as of 9/30/20

At Cost

(millions)

At Market

(millions)

Fixed-income assets:

Short-term securities $ 4.5 11.0% $ 4.5 11.4%

Long-term bonds and mortgages 26.5 64.7 23.5 59.5

Common stocks 10.0 24.3 11.5 29.1

$41.0 100.0% $39.5 100.0%

INVESTMENT PERFORMANCE

Annual Rates of

Return for Periods

Ending 9/30/20

5 Years 1 Year

Total Alpine Fund:

Time-weighted 8.2% 5.2%

Dollar-weighted (Internal) 7.7% 4.8%

Assumed actuarial return 6.0% 6.0%

U.S. Treasury bills 7.5% 11.3%

Large sample of pension funds

(average 60% equities, 40% fixed income) 10.1% 14.3%

Common stocks—Alpine Fund 13.3% 14.3%

Average portfolio beta coefficient 0.90 0.89

Standard & Poor’s 500 Stock Index 13.8% 21.1%

Fixed-income securities—Alpine Fund 6.7% 1.0%

Salomon Brothers’ Bond Index 4.0% 211.4%

Karl was proud of his performance and was chagrined when a trustee made the following

critical observations:

a. “Our one-year results were terrible, and it’s what you’ve done for us lately that

counts most.”

b. “Our total fund performance was clearly inferior compared to the large sample of other

pension funds for the last five years. What else could this reflect except poor management

judgment?”

c. “Our common stock performance was especially poor for the five-year period.”

d. “Why bother to compare your returns to the return from Treasury bills and the actuarial

assumption rate? What your competition could have earned for us or how we would

have fared if invested in a passive index (which doesn’t charge a fee) are the only relevant

measures of performance.”

e. “Who cares about time-weighted return? If it can’t pay pensions, what good is it!”

Appraise the merits of each of these statements and give counterarguments that Karl

can use. (LO 18-2)

4. A portfolio manager summarizes the input from the macro and micro forecasts in the following

table: MICRO FORECASTS

Asset Expected Return (%) Beta

Residual Standard

Deviation (%)

Stock A 20 1.3 58

Stock B 18 1.8 71

Stock C 17 0.7 60

Stock D 12 1.0 55

MACRO FORECASTS

Asset Expected Return (%) Standard Deviation (%)

T-bills 8 0

Passive equity portfolio 16 23

a. Calculate expected excess returns, alpha values, and residual variances for these stocks.

b. Construct the optimal risky portfolio.

c. What is Sharpe’s measure for the optimal portfolio and how much of it is contributed

by the active portfolio? What is the M 2 ?

CHAPTER 19

5. Suppose a U.S. investor wishes to invest in a British firm currently selling for £40 per share.

The investor has $10,000 to invest, and the current exchange rate is $2/£. (LO 19-2)

a. How many shares can the investor purchase?

b. Fill in the table below for rates of return after one year in each of the nine scenarios

(three possible prices per share in pounds times three possible exchange rates).

Price per

Share (£)

Pound-Denominated

Return (%)

Dollar-Denominated Return for

Year-End Exchange Rate

$1.80/£ $2/£ $2.20/£

£35

£40

£45

c. When is the dollar-denominated return equal to the pound-denominated return?

8. Calculate the contribution to total performance from currency, country, and stock selection

for the manager in the following table. All exchange rates are expressed as units of

foreign currency that can be purchased with one U.S. dollar. (LO 19-4)

EAFE

Weight

Return on

Equity Index E1/ E0

Manager’s

Weight

Manager’s

Return

Europe .30 20% 0.9 .35 18%

Australia .10 15 1.0 .15 20

Far East .60 25 1.1 .50 20

2. John Irish, CFA, is an independent investment adviser who is assisting Alfred Darwin, the

head of the Investment Committee of General Technology Corporation, to establish a new pension fund. Darwin asks Irish about international equities and whether the Investment

Committee should consider them as an additional asset for the pension fund. (LO 19-3)

a. Explain the rationale for including international equities in General’s equity portfolio.

Identify and describe three relevant considerations in formulating your answer.

b. List three possible arguments against international equity investment, and briefly discuss

the significance of each.

c. To illustrate several aspects of the performance of international securities over time, Irish

shows Darwin the accompanying graph of investment results experienced by a U.S. pension

fund in the recent past. Compare the performance of the U.S.-dollar and non-U.S.-dollar

equity and fixed-income asset categories, and explain the significance of the result of the

account performance index relative to the results of the four individual asset class indexes.

performance index relative to the results of the four individual asset class indexes.

10 20 30 40

6

5

4

3

2

1

0

Annualized historical performance data

(percent)

Variability

(standard

deviation)

Real returns (%)

U.S.-$ bonds

Non-U.S.-$ bonds

EAFE index

Account performance index

S&P index

3. You are a U.S. investor considering purchase of one of the following securities. Assume

that the currency risk of the Canadian government bond will be hedged, and the sixmonth

discount on Canadian-dollar forward contracts is 2 .75% versus the U.S. dollar.

Bond Maturity Coupon Price

U.S. government 6 months 6.50% 100.00

Canadian government 6 months 7.50% 100.00

Calculate the expected price change required in the Canadian government bond that would

result in the two bonds having equal total returns in U.S. dollars over a six-month horizon.

Assume that the yield on the U.S. bond is expected to remain unchanged.