Chapter 6
Risk and Return: The Basics
ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS
6-1 a. Stand-alone risk is only a part of total risk and pertains to the
risk an investor takes by holding only one asset. Risk is the
chance that some unfavorable event will occur. For instance, the
risk of an asset is essentially the chance that the asset’s cash
flows will be unfavorable or less than expected. A probability
distribution is a listing, chart or graph of all possible outcomes,
such as expected rates of return, with a probability assigned to
each outcome. When in graph form, the tighter the probability
distribution, the less uncertain the outcome.
b. The expected rate of return (k̂ ) is the expected value of a
probability distribution of expected returns.
c. A continuous probability distribution contains an infinite number of
outcomes and is graphed from -∞ and +∞.
d. The standard deviation (σ) is a statistical measure of the
variability of a set of observations. The variance (σ2) of the
probability distribution is the sum of the squared deviations about
the expected value adjusted for deviation. The coefficient of
variation (CV) is equal to the standard deviation divided by the
expected return; it is a standardized risk measure which allows
comparisons between investments having different expected returns
and standard deviations.
e. A risk averse investor dislikes risk and requires a higher rate of
return as an inducement to buy riskier securities. A realized
return is the actual return an investor receives on their
investment. It can be quite different than their expected return.
f. A risk premium is the difference between the rate of return on a
risk-free asset and the expected return on Stock I which has higher
risk. The market risk premium is the difference between the expected
return on the market and the risk-free rate.
g. CAPM is a model based upon the proposition that any stock’s required
rate of return is equal to the risk free rate of return plus a risk
premium reflecting only the risk remaining after diversification.
Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Answers and Solutions: 6 - 1
, h. The expected return on a portfolio. k̂ p, is simply the weighted-
average expected return of the individual stocks in the portfolio,
with the weights being the fraction of total portfolio value
invested in each stock. The market portfolio is a portfolio
consisting of all stocks.
i. Correlation is the tendency of two variables to move together. A
correlation coefficient (r) of +1.0 means that the two variables
move up and down in perfect synchronization, while a coefficient of
-1.0 means the variables always move in opposite directions. A
correlation coefficient of zero suggests that the two variables are
not related to one another; that is, they are independent.
j. Market risk is that part of a security’s total risk that cannot be
eliminated by diversification. It is measured by the beta
coefficient. Diversifiable risk is also known as company specific
risk, that part of a security’s total risk associated with random
events not affecting the market as a whole. This risk can be
eliminated by proper diversification. The relevant risk of a stock
is its contribution to the riskiness of a well-diversified
portfolio.
k. The beta coefficient is a measure of a stock’s market risk, or the
extent to which the returns on a given stock move with the stock
market. The average stock’s beta would move on average with the
market so it would have a beta of 1.0.
l. The security market line (SML) represents in a graphical form, the
relationship between the risk of an asset as measured by its beta
and the required rates of return for individual securities. The SML
equation is essentially the CAPM, ki = kRF + bi(kM - kRF).
m. The slope of the SML equation is (kM - kRF), the market risk premium.
The slope of the SML reflects the degree of risk aversion in the
economy. The greater the average investors aversion to risk, then
the steeper the slope, the higher the risk premium for all stocks,
and the higher the required return.
6-2 a. The probability distribution for complete certainty is a vertical
line.
b. The probability distribution for total uncertainty is the X axis
from -∞ to +∞.
6-3 Security A is less risky if held in a diversified portfolio because of
its lower beta and negative correlation with other stocks. In a
single-asset portfolio, Security A would be more risky because σA > σB
and CVA > CVB.
6-4 a. No, it is not riskless. The portfolio would be free of default risk
and liquidity risk, but inflation could erode the portfolio’s
purchasing power. If the actual inflation rate is greater than that
Answers and Solutions: 6 - 2 Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.
Risk and Return: The Basics
ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS
6-1 a. Stand-alone risk is only a part of total risk and pertains to the
risk an investor takes by holding only one asset. Risk is the
chance that some unfavorable event will occur. For instance, the
risk of an asset is essentially the chance that the asset’s cash
flows will be unfavorable or less than expected. A probability
distribution is a listing, chart or graph of all possible outcomes,
such as expected rates of return, with a probability assigned to
each outcome. When in graph form, the tighter the probability
distribution, the less uncertain the outcome.
b. The expected rate of return (k̂ ) is the expected value of a
probability distribution of expected returns.
c. A continuous probability distribution contains an infinite number of
outcomes and is graphed from -∞ and +∞.
d. The standard deviation (σ) is a statistical measure of the
variability of a set of observations. The variance (σ2) of the
probability distribution is the sum of the squared deviations about
the expected value adjusted for deviation. The coefficient of
variation (CV) is equal to the standard deviation divided by the
expected return; it is a standardized risk measure which allows
comparisons between investments having different expected returns
and standard deviations.
e. A risk averse investor dislikes risk and requires a higher rate of
return as an inducement to buy riskier securities. A realized
return is the actual return an investor receives on their
investment. It can be quite different than their expected return.
f. A risk premium is the difference between the rate of return on a
risk-free asset and the expected return on Stock I which has higher
risk. The market risk premium is the difference between the expected
return on the market and the risk-free rate.
g. CAPM is a model based upon the proposition that any stock’s required
rate of return is equal to the risk free rate of return plus a risk
premium reflecting only the risk remaining after diversification.
Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Answers and Solutions: 6 - 1
, h. The expected return on a portfolio. k̂ p, is simply the weighted-
average expected return of the individual stocks in the portfolio,
with the weights being the fraction of total portfolio value
invested in each stock. The market portfolio is a portfolio
consisting of all stocks.
i. Correlation is the tendency of two variables to move together. A
correlation coefficient (r) of +1.0 means that the two variables
move up and down in perfect synchronization, while a coefficient of
-1.0 means the variables always move in opposite directions. A
correlation coefficient of zero suggests that the two variables are
not related to one another; that is, they are independent.
j. Market risk is that part of a security’s total risk that cannot be
eliminated by diversification. It is measured by the beta
coefficient. Diversifiable risk is also known as company specific
risk, that part of a security’s total risk associated with random
events not affecting the market as a whole. This risk can be
eliminated by proper diversification. The relevant risk of a stock
is its contribution to the riskiness of a well-diversified
portfolio.
k. The beta coefficient is a measure of a stock’s market risk, or the
extent to which the returns on a given stock move with the stock
market. The average stock’s beta would move on average with the
market so it would have a beta of 1.0.
l. The security market line (SML) represents in a graphical form, the
relationship between the risk of an asset as measured by its beta
and the required rates of return for individual securities. The SML
equation is essentially the CAPM, ki = kRF + bi(kM - kRF).
m. The slope of the SML equation is (kM - kRF), the market risk premium.
The slope of the SML reflects the degree of risk aversion in the
economy. The greater the average investors aversion to risk, then
the steeper the slope, the higher the risk premium for all stocks,
and the higher the required return.
6-2 a. The probability distribution for complete certainty is a vertical
line.
b. The probability distribution for total uncertainty is the X axis
from -∞ to +∞.
6-3 Security A is less risky if held in a diversified portfolio because of
its lower beta and negative correlation with other stocks. In a
single-asset portfolio, Security A would be more risky because σA > σB
and CVA > CVB.
6-4 a. No, it is not riskless. The portfolio would be free of default risk
and liquidity risk, but inflation could erode the portfolio’s
purchasing power. If the actual inflation rate is greater than that
Answers and Solutions: 6 - 2 Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.
