Foundations of Finance, 7e (Keown/Martin/Petty)
Chapter 6 The Meaning and Measurement of Risk and Return
6.1 Learning Objective 1
1) Accounting profits is the most relevant variable the financial manager uses to measure returns.
2) Cash flows is the most relevant variable to measure the returns on debt instruments, while
GAAP net income is the most relevant variable to measure the returns on common stock.
3) The expected rate of return from an investment is equal to the expected cash flows divided by
the initial investment.
4) Actual returns are always less than expected returns because actual returns are determined at
the end of the period and must be discounted back to present value.
5) Another name for an asset’s expected rate of return is holding-period return.
6) The realized rate of return, or holding period return, is equal to the holding period dollar gain
divided by the price at the beginning of the period.
7) The risk-return tradeoff that investors face on a day-to-day basis is based on realized rates of
return because expected returns involve too much uncertainty.
8) Stock A has the following returns for various states of the economy:
State of
the Economy Probability Stock A’s Return
Recession 10% -30%
Below Average 20% -2%
Average 40% 10%
Above Average 20% 18%
Boom 10% 40%
Stock A’s expected return is
A) 5.4%.
B) 7.2%.
C) 8.2%.
D) 9.6%
9) Stock A has the following returns for various states of the economy:
State of
the Economy Probability Stock A’s Return
Recession 9% -72%
Below Average 16% -15%
Average 51% 16%
Above Average 14% 35%
Boom 10% 85%
Stock A’s expected return is
A) 9.9%.
B) 12.7%.
C) 13.8%.
D) 16.5%.
10) You are considering a sales job that pays you on a commission basis or a salaried position
that pays you $50,000 per year. Historical data suggests the following probability distribution for
your commission income. Which job has the higher expected income?
Probability of
Commission Occurrence
$15,000 .15
$35,000 .20
$48,000 .35
$67,000 .22
$80,000 .18
A) The salary of $50,000 is greater than the expected commission of $49,630.
B) The salary of $50,000 is greater than the expected commission of $48,400.
C) The salary of $50,000 is less than the expected commission of $50,050.
D) The salary of $50,000 is less than the expected commission of $52,720.
11) Use the following data:
Market risk premium = 10%
Risk free rate = 2%
Beta of XYZ stock = 1.6
Beta of PDQ stock = 2.4
Investment in XYZ stock = $15,000
Investment in PDQ stock = $60,000
You have no assets other than your investments in XYZ and PDQ stock.
What is the expected return of your portfolio? Show all work.
6.2 Learning Objective 2
1) Variation in the rate of return of an investment is a measure of the riskiness of that investment.
2) A rational investor will always prefer an investment with a lower standard deviation of
returns, because such investments are less risky.
3) For a well-diversified investor, an investment with an expected return of 10% with a standard
deviation of 3% dominates an investment with an expected return of 10% with a standard
deviation of 5%.
4) Due to strict stock market controls, the most a stock’s value can drop in one trading day is 5%.
5) Stock A has the following returns for various states of the economy:
State of the Economy Probability Stock A’s Return
Recession 10% -30%
Below Average 20% -2%
Average 40% 10%
Above Average 20% 18%
Boom 10% 40%
Stock A’s standard deviation of returns is
A) 10%.
B) 14%.
C) 17%.
D) 20%
6) Stock A has the following returns for various states of the economy:
State of the Economy Probability Stock A’s Return
Recession 9% -72%
Below Average 16% -15%
Average 51% 16%
Above Average 14% 35%
Boom 10% 85%
Stock A’s standard deviation of returns is
A) 12%.
B) 29%.
C) 37%.
D) 43%.
7) Stock A has an expected return of 12% with a standard deviation of 8%. If returns are
normally distributed, then approximately two-thirds of the time the return on stock A will be
A) between 12% and 20%.
B) between 8% and 12%.
C) between -4% and 28%.
D) between 4% and 20%.
8) Which of the following investments is clearly preferred to the others for an investor who is not
holding a well-diversified portfolio?
Investment
k
σ
A 18% 20%
B 20% 20%
C 20% 22%
A) Investment A
B) Investment B
C) Investment C
D) Cannot be determined without information regarding the risk-free rate of return.
9) Assume that you have $165,000 invested in a stock that is returning 11.50%, $85,000 invested
in a stock that is returning 22.75%, and $235,000 invested in a stock that is returning 10.25%.
What is the expected return of your portfolio?
A) 15.6%
B) 12.9%
C) 18.3%
D) 14.8%
10) Assume that you have $200,000 invested in a stock that is returning 14%, $300,000 invested
in a stock that is returning 18%, and $400,000 invested in a stock that is returning 15%. What is
the expected return of your portfolio?
A) 13.25%
B) 14.97%
C) 15.67%
D) 15.78%
11) You are given the following probability distribution for XYZ common stock’s returns during
the next year, which are assumed to be normally distributed. Show all work below, and complete
the following:
Return
Probability
12%
20%
16%
60%
20%
20%
a. Calculate the standard deviation of the returns, and round to the nearest one-half percent.
b. Draw a graphical representation of XYZ’s normal distribution below (ye old bell-shaped
curve). LABEL THE AXES OF THE GRAPH OR THE FOLLOWING RESULTS WILL BE
MEANINGLESS. Using your result in part A for the standard deviation (rounded to the nearest
one-half percent) explain and indicate on the graph, the probability that XYZ will return more
than 13.5%, assuming a normal distribution.
12) Discuss whether the standard deviation of a portfolio is, or is not, a weighted average of the
standard deviations of the assets in the portfolio. Fully explain your answer.
13) Bay Land, Inc. has the following distribution of returns:
State
Return
Probability
Boom
0.3
0.25
Normal
0.4
0.15
Bust
0.3
0.30
Assuming that these returns are normally distributed, what is the probability that Bay Land, Inc.
will return less than 7.25%? Show all work, and clearly explain and state your answer.
6.3 Learning Objective 3
1) Historically, investments with the highest returns have the lowest standard deviations because
investors do not like risk.
2) An investor with a required return of 8% for stock A will purchase stock A if the expected
return for stock A is less than or equal to 8%.
3) In general, the required rate of return is a function of (1) the time value of money, (2) the risk
of an asset, and (3) the investor’s attitude toward risk.
4) As the required rate of return of an investment decreases, the market price of the investment
decreases.
5) In an efficient market, a stock with a standard deviation of returns of 12% could have a higher
expected return than a stock with a standard deviation of 10% because the beta for the higher
standard deviation stock could be lower than the beta for the lower standard deviation stock.
6) Small company stocks have historically had higher average annual returns than large company
stocks, and also a higher risk premium.
7) Investment A and Investment B both have the same expected return, but Investment A is more
risky than Investment B. In the technical jargon of modern portfolio theory, Investment A is said
to “dominate” Investment B.
8) Negative historical returns are not possible during periods of high volatility (high standard
deviations of returns) due to the risk-return tradeoff.
9) Investment A has an expected return of 15% per year, while investment B has an expected
return of 12% per year. A rational investor will choose
A) investment A because of the higher expected return.
B) investment B because a lower return means lower risk.
C) investment A if A and B are of equal risk.
D) investment A only if the standard deviation of returns for A is higher than the standard
deviation of returns for B.
10) Investment A has an expected return of 14% with a standard deviation of 4%, while
investment B has an expected return of 20% with a standard deviation of 9%. Therefore,
A) a risk averse investor will definitely select investment A because the standard deviation is
lower.
B) a rational investor will pick investment B because the return adjusted for risk (20% – 9%) is
higher than the return adjusted for risk for investment A ($14% – 4%).
C) it is irrational for a risk-averse investor to select investment B because its standard deviation
is more than twice as big as investment A’s, but the return is not twice as big.
D) rational investors could pick either A or B, depending on their level of risk aversion.
11) Which of the following investments is clearly preferred to the others for a risk-averse
investor:
Investment
k
σ
A 14% 12%
B 22% 20%
C 18% 16%
A) Investment A
B) Investment B
C) Investment C
D) Cannot be determined without additional information
12) Hole Con Shooz, Inc. has normally distributed returns with an expected return of 15% and a
standard deviation of 5%, while Ed Allenmunds Shooz, Inc. has normally distributed returns
with an expected return of 15% and a standard deviation of 15%. Which of the following is true?
A) Ed Allenmunds’ investors are not being adequately compensated for relevant risk.
B) Hole Con is likely to experience returns larger than those of Ed Allenmunds.
C) Ed Allenmunds is more likely to have negative returns than Hole Con.
D) Rational investors will prefer Ed Allenmunds, Inc. over Hole Con Shooz, Inc.
13) You are considering investing in a project with the following possible outcomes:
Probability of Investment
States Occurrence Returns
State 1: Economic boom 18% 20%
State 2: Economic growth 42% 16%
State 3: Economic decline 30% 3%
State 4: Depression 10% -25%
Calculate the expected rate of return and standard deviation of returns for this investment,
respectively.
A) 8.72%, 12.99%
B) 7.35%, 12.99%
C) 3.50%, 1.69%
D) 2.18%, 1.69%
14) Changes in the general economy, like changes in interest rates or tax laws represent what
type of risk?
A) Company-unique risk
B) Market risk
C) Unsystematic risk
D) Diversifiable risk
15) The minimum rate of return necessary to attract an investor to purchase or hold a security is
referred to as the
A) stock’s beta.
B) investor’s risk premium.
C) investor’s required rate of return.
D) risk-free rate.
16) The relevant variable a financial manager uses to measure returns is:
A) net income determined using generally accepted accounting principles.
B) earnings per share minus dividends per share.
C) cash flows.
D) dividends.
17) Of the following different types of securities, which is typically considered most risky?
A) Long term corporate bonds
B) Long term government bonds
C) Common stocks of large companies
D) Common stocks of small companies
18) Assume that an investment is forecasted to produce the following returns: a 10% probability
of a $1,400 return; a 50% probability of a $6,600 return; and a 40% probability of a $10,500
return. What is the expected amount of return this investment will produce?
A) $6,167
B) $7,640
C) $12,890
D) $18,500
19) Assume that an investment is forecasted to produce the following returns: a 20% probability
of a 12% return; a 50% probability of a 16% return; and a 30% probability of a 19% return. What
is the expected percentage return this investment will produce?
A) 33.3%
B) 16.1%
C) 9.3%
D) 15.7%
20) Assume that an investment is forecasted to produce the following returns: a 20% probability
of a 12% return; a 50% probability of a 16% return; and a 30% probability of a 19% return. What
is the standard deviation of return for this investment?
A) 5.89%
B) 16.1%
C) 2.43%
D) 15.7%
13
21) The category of securities with the highest historical risk premium is
A) large company stocks.
B) small company stocks.
C) government bonds.
D) small company corporate bonds.
22) If you were to use the standard deviation as a measure of investment risk, which of the
following has historically been the least risky investment?
A) Common stock of large firms
B) U.S. Treasury bills
C) Common stock of small firms
D) Long-term government bonds
23) If you were to use the standard deviation as a measure of investment risk, which of the
following has historically been the highest risk investment?
A) Common stock of large firms
B) U.S. Treasury bills
C) Common stock of small firms
D) Long-term government bonds
24) You are considering a security with the following possible rates of return:
Probabilit
y
Return
(%)
0.15
9.5
0.25
13.6
0.50
14.9
0.10
25.3
a. Calculate the expected rate of return.
b. Calculate the standard deviation of the returns.
25) You are considering the three securities listed below.
Returns
Probability
Stock A
Stock B
Stock C
20%
2%
-3%
5%
50%
10%
8%
8%
30%
15%
20%
12%
a. Calculate the expected return for each security.
b. Calculate the standard deviation of returns for each security.
c. Compare Stock A with Stocks B and C. Is Stock A preferred over the others?
6.4 Learning Objective 4
1) The benefits of diversification occur as long as the investments in a portfolio are not perfectly
positively correlated.
2) Proper diversification generally results in the elimination of risk.
3) A stock with a beta of 1 has systematic or market risk equal to the “typical” stock in the
marketplace.
4) Diversifying among different kinds of assets is called asset allocation.
5) Asset allocation is not recommended by financial planners because mixing different types of
assets, such as stocks with bonds, makes it more difficult to track performance and adjust
portfolios to changing market conditions.
6) A stock with a beta of 1.4 has 40% more variability in returns than the average stock.
7) Adding stocks to a bond portfolio will increase the riskiness of the portfolio because stocks
have higher standard deviations of returns than bonds.
8) An all-stock portfolio is more risky than a portfolio consisting of all bonds.
9) Company unique risk can be virtually eliminated with a portfolio consisting of approximately
20 securities.
10) Total risk equals systematic risk plus unsystematic risk.
11) A well-diversified portfolio typically has systematic risk equal to about 40% of the
portfolio’s total risk.
12) A security with a beta of one has a required rate of return equal to the overall market rate of
return.
13) Unique security risk can be eliminated from an investor’s portfolio through diversification.
14) The Beta of a T-bill is zero.
15) The Beta of a T-bill is one.
16) Portfolio performance is determined mainly by stock selection and market timing, with less
emphasis on asset allocation.
17) Beta is a measurement of the relationship between a security’s returns and the general
market’s returns.
18) The relevant risk to an investor is that portion of the variability of returns that cannot be
diversified away.
19) The characteristic line for any well-diversified portfolio is horizontal.
20) The slope of the characteristic line of a security is that security’s Beta.
21) Beta represents the average movement of a company’s stock returns in response to a
movement in the market’s returns.
22) Because risk is measured by variability of returns, how long we hold our investments does
not matter very much when it comes to reducing risk.
23) The market rewards the patient investor, for between 1926 and 2008, there has never been a
time when an investor lost money if she held an all-stock portfolio for ten years.
24) The portfolio beta is simply the sum of the betas of the individual stocks in the portfolio.
25) Which of the following statements is most correct concerning diversification and risk?
A) Risk-averse investors often choose companies from different industries for their portfolios
because the correlation of returns is less than if all the companies came from the same industry.
B) Risk-averse investors often select portfolios that include only companies from the same
industry group because the familiarity reduces the risk.
C) Only wealthy investors can diversify their portfolios because a portfolio must contain at least
50 stocks to gain the benefits of diversification.
D) Proper diversification generally results in the elimination of risk.
26) Which of the following statements is most correct concerning diversification and risk?
A) Diversification is mainly achieved by the selection of individual securities for each type of
asset held in a portfolio.
B) Diversification is mainly achieved by the asset allocation decision, not the selection of
individual securities within each asset category.
C) Large company stocks and small company stocks together in a portfolio lead to dramatic
reductions in risk because their returns are negatively correlated.
D) Asset allocation is important for pension funds but not for individual investors.
27) An investor currently holds the following portfolio:
Amount
Invested
8,000 shares of Stock A$16,000 Beta = 1.3
15,000 shares of Stock B$48,000 Beta = 1.8
25,000 shares of Stock C $96,000 Beta = 2.2
The investor is worried that the beta of his portfolio is too high, so he wants to sell some stock C
and add stock D, which has a beta of 1.0, to his portfolio. If the investor wants his portfolio to
have a beta of 1.72, how much stock C must he replace with stock D?
A) $18,000
B) $24,000
C) $31,000
D) $36,000
28) Joe purchased 800 shares of Robotics Stock at $3 per share on 1/1/09. Bill sold the shares on
12/31/09 for $3.45. Robotics stock has a beta of 1.9, the risk-free rate of return is 4%, and the
market risk premium is 9%. Joe’s holding period return is:
A) 15.0%.
B) 16.5%.
C) 17.6%.
D) 21.1%.
29) You are thinking of adding one of two investments to an already well- diversified portfolio.
Security A Security B
Expected Return = 14% Expected Return = 16%
Standard Deviation of Standard Deviation of
Returns = 16% Returns = -20%
Beta = 1.2 Beta = 1.2
If you are a risk-averse investor, which one is the better choice?
A) Security A
B) Security B
C) Either security would be acceptable because they have the same beta.
D) Security B, but only if Security B’s required return is greater than 12%.
30) You are going to invest all of your funds in one of three projects with the following
distribution of possible returns:
PROJECT 1 PROJECT 2
Standard Standard
Probability Return Deviation Beta Probability Return Deviation Beta
50% Chance 22% 12% 1.1 30% Chance 36% 19.5% 1.0
50% Chance -4% 40% Chance 10.5%
30% Chance -20%
PROJECT 3
Standard
Probability Return Deviation Beta
10% Chance 28% 12% 1.2
70% Chance 18%
20% Chance -8%
If you are a risk averse investor, which one should you choose?
A) Project 1
B) Project 2
C) Project 3
D) Either Project 1 or Project 2 because they have the same expected return.
31) You are considering investing in Ford Motor Company. Which of the following are
examples of diversifiable risk?
I. Risk resulting from possibility of a stock market crash.
II. Risk resulting from uncertainty regarding a possible strike against Ford.
III. Risk resulting from an expensive recall of a Ford product.
IV. Risk resulting from interest rates decreasing.
A) I only
B) I and IV
C) I, II, III, IV
D) II, III