## GC FIN 451 Week 2 Problem Set Solution

**GC FIN 451 Week 2 Problem Set Solution**

- 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.

www.mhhe.com/bkm

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.