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apma module 2 Questions and Correct
Answers
What is modern portfolio theory (MPT)? Ans: A development by
Harry Markowitz that showed how to derive the expected return
and risk for a portfolio and how to achieve an effective
diversification effect
In Harry Markowitz' MPT model, what is the measure for portfolio
risk? Ans: Standard deviation
What is mean-variance optimization? Ans: The goal of putting
together optimal portfolios that acknowledge not only the
importance of return and risk but how the various investments
perform relative to each other. It requires looking at the return
(mean) and standard deviation (variance) of each asset, as well as
the correlation with every other asset. These investment portfolios
lie on the efficient frontier. When using this approach, investors
are striving to optimize their amount of return (mean) for any
given level of risk (variance, and our measure of risk is standard
deviation). Investors are trying to take only as much risk as
necessary to achieve a given level of return.
What did Markowitz do to make standard deviation a meaningful
measure of portfolio risk? Ans: He relied on a set of assumptions
that implied a theoretical perfect financial market. Investors are
trying to obtain the optimal amount of return they can for the
level of risk they are taking.
What assumptions did Markowitz rely on to make standard
deviation a meaningful measure of portfolio risk? Ans: Investors
are risk averse, investors make investment decisions based on
expected return and risk only, investors have homogeneous
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, 2 | Page
expectations regarding return and risk for all the investment
opportunities available in the market, investors have a common
one-period investment horizon, investors have free access to all
information relevant to investment decision making, there are no
transaction costs, and the capital market is perfectly competitive
Describe the assumption: Investors are risk averse Ans: Investors
prefer higher returns to lower returns given the same level of risk.
Likewise, investors prefer less risk to more risk, given the same
level of expected return.
Describe the assumption: Investors make investment decisions
based on expected return and risk only Ans: Their utility function
(satisfaction level) is set in the dimension of expected return and
risk, with risk being measured by standard deviation
Describe the assumption: Investors have homogenous expectations
regarding return and risk for all the investment opportunities
available in the market Ans: The investment opportunity, set in
the dimension of risk and return, is identical for all investors.
Thus, an investor's investment choice depends on his or her
indifference curve, which reflects the risk/return trade-off of that
investor
Describe the assumption: Investors have a common one-period
investment horizon Ans: The period can cover any length of time.
For example, it can be as short as a day or as long as a year. An
investor tries to make an optimal investment decision to maximize
expected utility. While investors prefer more wealth to less wealth,
the utility increases at a diminishing rate as wealth increases.
Describe the assumption: Investors have free access to all
information relevant to investment decision making Ans: Thus,
there is no privileged access to inside information
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, 3 | Page
Describe the assumption: There are no transaction costs Ans:
Thus, commissions, fees, and taxes are nonexistent. Moreover,
every investment is perfectly divisible. Therefore, investors can
trades securities on a fractional basis.
Describe the assumption: The capital market is perfectly
competitve Ans: As a result, no one is able to manipulate the
market
What is the minimum variance frontier? Ans: It traces the outside
of all the portfolio combinations that an investor could choose
from, including every publicly and non-publicly traded asset
around the world; portfolios outside this cannot exist. Portfolios
that lie within this parabola, instead of the efficient frontier, are
inefficient with more risk being taken that should be for the
amount of return achieved (not enough return achieved for the
amount of risk taken).
What is the investment opportunity set? Ans: The set of asset
combinations inside of the minimum variance frontier, which is
the set of all investable portfolios
What is the efficient frontier? Ans: As good as it gets. The top part
of the minimum variance frontier. A risk-averse investor would
limit her or his portfolio choices to that upper boundary of the
investment opportunity set. It provides an investor the highest
return at any given level of risk, as well as the lowest risk at any
given level of return. Investors should choose portfolios along the
efficient frontier that are most aligned with their preferences
regarding risk and return.
What is a utility function? Ans: It reflects a given investor's trade-
off between risk and return
© 2025 All rights reserved
apma module 2 Questions and Correct
Answers
What is modern portfolio theory (MPT)? Ans: A development by
Harry Markowitz that showed how to derive the expected return
and risk for a portfolio and how to achieve an effective
diversification effect
In Harry Markowitz' MPT model, what is the measure for portfolio
risk? Ans: Standard deviation
What is mean-variance optimization? Ans: The goal of putting
together optimal portfolios that acknowledge not only the
importance of return and risk but how the various investments
perform relative to each other. It requires looking at the return
(mean) and standard deviation (variance) of each asset, as well as
the correlation with every other asset. These investment portfolios
lie on the efficient frontier. When using this approach, investors
are striving to optimize their amount of return (mean) for any
given level of risk (variance, and our measure of risk is standard
deviation). Investors are trying to take only as much risk as
necessary to achieve a given level of return.
What did Markowitz do to make standard deviation a meaningful
measure of portfolio risk? Ans: He relied on a set of assumptions
that implied a theoretical perfect financial market. Investors are
trying to obtain the optimal amount of return they can for the
level of risk they are taking.
What assumptions did Markowitz rely on to make standard
deviation a meaningful measure of portfolio risk? Ans: Investors
are risk averse, investors make investment decisions based on
expected return and risk only, investors have homogeneous
© 2025 All rights reserved
, 2 | Page
expectations regarding return and risk for all the investment
opportunities available in the market, investors have a common
one-period investment horizon, investors have free access to all
information relevant to investment decision making, there are no
transaction costs, and the capital market is perfectly competitive
Describe the assumption: Investors are risk averse Ans: Investors
prefer higher returns to lower returns given the same level of risk.
Likewise, investors prefer less risk to more risk, given the same
level of expected return.
Describe the assumption: Investors make investment decisions
based on expected return and risk only Ans: Their utility function
(satisfaction level) is set in the dimension of expected return and
risk, with risk being measured by standard deviation
Describe the assumption: Investors have homogenous expectations
regarding return and risk for all the investment opportunities
available in the market Ans: The investment opportunity, set in
the dimension of risk and return, is identical for all investors.
Thus, an investor's investment choice depends on his or her
indifference curve, which reflects the risk/return trade-off of that
investor
Describe the assumption: Investors have a common one-period
investment horizon Ans: The period can cover any length of time.
For example, it can be as short as a day or as long as a year. An
investor tries to make an optimal investment decision to maximize
expected utility. While investors prefer more wealth to less wealth,
the utility increases at a diminishing rate as wealth increases.
Describe the assumption: Investors have free access to all
information relevant to investment decision making Ans: Thus,
there is no privileged access to inside information
© 2025 All rights reserved
, 3 | Page
Describe the assumption: There are no transaction costs Ans:
Thus, commissions, fees, and taxes are nonexistent. Moreover,
every investment is perfectly divisible. Therefore, investors can
trades securities on a fractional basis.
Describe the assumption: The capital market is perfectly
competitve Ans: As a result, no one is able to manipulate the
market
What is the minimum variance frontier? Ans: It traces the outside
of all the portfolio combinations that an investor could choose
from, including every publicly and non-publicly traded asset
around the world; portfolios outside this cannot exist. Portfolios
that lie within this parabola, instead of the efficient frontier, are
inefficient with more risk being taken that should be for the
amount of return achieved (not enough return achieved for the
amount of risk taken).
What is the investment opportunity set? Ans: The set of asset
combinations inside of the minimum variance frontier, which is
the set of all investable portfolios
What is the efficient frontier? Ans: As good as it gets. The top part
of the minimum variance frontier. A risk-averse investor would
limit her or his portfolio choices to that upper boundary of the
investment opportunity set. It provides an investor the highest
return at any given level of risk, as well as the lowest risk at any
given level of return. Investors should choose portfolios along the
efficient frontier that are most aligned with their preferences
regarding risk and return.
What is a utility function? Ans: It reflects a given investor's trade-
off between risk and return
© 2025 All rights reserved
