9.1 Portfolio Risk and Return: Part 1

Question 1

Historical returns

Answer 1

document past performance

Question 2

expected returns

Answer 2

reflect anticipated future performance

An asset’s expected return is a function of the real risk-free rate, expected inflation, and any risk premiums that investors require as compensation

Question 3

Using a mean and variance approach assumes that

Answer 3

assumes that returns are normally distributed and that markets are informationally and operationally efficient.

However, these assumptions do not necessarily hold.

Question 4

A normal distributions has three characteristics:

Answer 4

1. Its mean and median are equal.
2. It is completely defined by its mean and variance
3. It is symmetric around its mean.

Question 5

Utility

Answer 5

measures the relative satisfaction gained from a particular portfolio

The utility that investors derive from an asset or portfolio is a function of their degree of risk aversion, which is the marginal reward that they require as compensation for taking an additional unit of risk

Question 6

The key conclusions from utility functions are:

Answer 6

1. Utility has no maximum or minimum
2. A higher return contributes to higher utility
3. Higher variance reduces utility (for risk-averse investors)
4. Utility is only useful in ranking investment options

Question 7

Indifference curves

Answer 7

plot the risk-return pairs that have the same utility.

For risk-averse investors, the slope will be positive.

All the points on a particular indifference curve have the same utility.

Greater utility is present on higher indifference curves, as shown in the diagram below.

Question 8

Indifference curves are steeper for investors that are

Answer 8

more risk-averse

Question 9

The capital allocation line (CAL)

Answer 9

represents the investment options for this portfolio of two securities.

It is the plot of different risk-return combinations derived by changing the weights of the two securities.

The CAL represents all the investment options. An investor must be somewhere on the line

Question 10

what does the slope of the capital allocation line (CAL) represent?

Answer 10

the additional return required for every increment in risk, which is the market price of risk

The slope is equivalent to the Sharpe ratio.

Question 11

The covariance between the returns on two assets is calculated as:

Answer 11

the product of their correlation and the individual standard deviations

Question 12

The minimum-variance frontier

Answer 12

the left edge of the possibilities in the graph below

It represents the least portfolio risk that can be obtained for a given expected return

Question 13

The global minimum-variance portfolio

Answer 13

located on the far left of the curve, is the least risky of the minimum variance portfolios.

Question 14

the Markowitz efficient frontier

Answer 14

The section of the minimum-variance frontier that lies above the global minimum-variance portfolio

Risk-averse investors will not consider portfolios on the lower half of the minimum-variance frontier because, for any portfolio that plots in this section, there is a Markowitz efficient frontier that offers a higher expected return for the same level of risk.

Question 15

According to the two-fund separation theorem

Answer 15

all investors will use the risky portfolio P to a greater or lesser extent depending on their level of risk aversion

Investors will have different allocations to the risk-free asset, but they will all create portfolios that use the optimal portfolio, P, and plot on the CAL according to their risk tolerance

Question 16

Optimal Investor Portfolio

Answer 16

The location of an investor’s optimal portfolio on the CAL will be at its point of tangency with their indifference curve

Question 17

With respect to the mean–variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:

a) risky assets.

b) equity securities.

c) feasible investments.

Answer 17

a) risky assets.

Question 18

Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:

a) highest expected return for a given level of risk.

b) lowest amount of risk for a given level of return.

c) highest expected return relative to the risk-free rate.

Answer 18

c) highest expected return relative to the risk-free rate.

Question 19

Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor’s ability to:

a) lend at the risk-free rate.

b) borrow at the risk-free rate.

c) purchase the risk-free asset.

Answer 19

b) borrow at the risk-free rate.

The CAL dominates the efficient frontier at all points except for the optimal risky portfolio. The ability of the investor to purchase additional amounts of the optimal risky portfolio by borrowing (i.e., buying on margin) at the risk-free rate makes higher rates of return for levels of risk greater than the optimal risky asset possible.

Question 20

Which of the following is least likely an assumption underlying the capital asset pricing model (CAPM)?

a) Investors analyze securities according to their own future cash flow estimates and probability distributions.

b) There are no restrictions on short selling assets.

c) The amount invested in an asset can be as much or as little as the investor wants.

Answer 20

a) Investors analyze securities according to their own future cash flow estimates and probability distributions.

Question 21

When constructing the optimal portfolios for investors with different risk preferences, the investor with the higher risk aversion is most likely to have a:

a) lower expected return.

b) steeper capital allocation line.

c) flatter indifference curve.

Answer 21

a) lower expected return.