Deck 7: Investor Preferences and Portfolio Concepts

Question 1

The slope coefficient from the market model can be used as an estimate of the risk-free rate.

Answer 1

False
Explanation: Due to the linear relationship between expected return and standard deviation,the efficient set is now a range of possible combinations of the risk-free asset and a particular risky portfolio.It is the choice of the risky asset that determines the slope of this line.

Question 2

Which of the following is typically used as a proxy for a risk-free asset?

Answer 2

D
Explanation: A risky asset is defined as one whose cash flows are not certain across all possible states of the world,compared with a risk-free asset,which is an asset that returns a certain pay-off no matter what occurs in the future.There is generally little chance of a government collapsing and failing to meet its obligations,and so a government security is often viewed as a risk-free asset.For example,a $100 000 Treasury note will return $100 000 at maturity regardless of whether the economy is depressed or booming.

Question 3

Given the above information,what is the expected utility for investment B?

Answer 3

B
Explanation: According to equation 7.1,we can compute the expected utility for investment B as follows: 0.90  ln(110)+ 0.1  ln(70)= 4.9987.

Question 4

As the number of assets increases,the variance of an equally weighted portfolio approaches the average covariance.

Question 5

Given a log utility function,a risk-averse investor will favour an asset that pays $100 with certainty over an asset that pays $90 with certainty.

Question 6

Given the above information,what is the expected utility for investment A?

Question 7

Transitivity is one of the five important assumptions of the expected utility model.

Question 8

A feature of indifference curves is a positive slope.

Question 9

Which of the following are properties required to define Von Neumann-Morgenstern utility?

Question 10

The typical Von Neumann-Morgenstern utility is convex.

Question 11

Individual portfolios can consist of human capital,furniture,the family home,car,bank deposits,shares,bonds and other financial assets.The bank deposits are always considered as risk free assets.

Question 12

Under a concave quadratic utility preference function with a constant term of 0.0001,a wealth level of 100 will have a utility of:

Question 13

Which of the following measures the spread or volatility of uncertain future returns?

Question 14

Arbitrage profits are generally defined to exist in situations where there are positive returns to be made from investments that have:

Question 15

Indifference curves are curves drawn where expected utility is held constant,and characteristics of the portfolios such as expected return and standard deviation are allowed to change.The emphasis on expected return and standard deviation simplifies the drawing of indifference curves that are often used in solving the investment choice problem.Indifference curves,as plotted in figure 7.1,exhibit positive slope.
The variance of a portfolio is a non- linear function of the weight invested in the risky asset.

Question 16

Figure 7.8,page 213,provides an important insight into the relationship between curvature of the two-asset opportunity set and the correlation between two assets.For perfectly positive correlation,correlation coefficient of +1,the opportunity set is a straight line including both the risky portfolios.For perfectly negative correlation,correlation coefficient of -1,the opportunity set consists of two lines intersecting at the zero variance axis.All other possible opportunity sets lie between these two extremes.
Which of the following is an input into the Markowitz (1959)optimal portfolio determination?

Question 17

Investors are generally assumed to be:

Question 18

Once a portfolio becomes sufficiently large,the __________ is of greatest importance with respect to risk.

Question 19

The opportunity set between two assets will be a curve rather than a straight line when the correlation is between -1 and 1.

Question 20

A risk-free asset is defined as one whose cash flows are not certain across all possible states of the world.

Question 21

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
Calculate the return on an optimal portfolio where the return on the risky asset is 5%,the return on the risk-free asset is 4%,and where the investor invests has a weight of 75% in the risky asset.

Question 22

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
Given a portfolio of 95 shares,what is the total number (variances and covariances)of estimates using the Sharpe's (1963)simple model of asset returns?

Question 23

The share market is currently returning 14% p.a. ,while the risk-free asset return is 6%.If an investor wishes to earn a return of 10%,what weight should the investor hold in the risk-free asset?

Question 24

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
In estimating the covariance matrix,the Markowitz approach for ten assets involves how many calculations?

Question 25

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What is the expected utility of asset B?

Question 26

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
An investor wishes to earn a portfolio with a standard deviation of 5%,by placing funds in the risk-free and risky asset portfolios.If the risky asset portfolio has a standard deviation and return of 10% and 5% respectively,calculate the weight that needs to be invested in the risky asset to achieve a standard deviation of 5%.

Question 27

Assume an investor has log utility.The investor faces a choice between an asset with a utility of 6.250 and an investment that will pay $500 in a bad state and $525 in a good state (as there are only two possible future states).What does the probability of the good state need to be for the investor to be indifferent between the assets?

Question 28

The share market is currently returning 18% p.a. ,while the risk-free asset return is 6%.If an investor wishes to earn a return of 22%,what weight should the investor hold in the risk-free asset?

Question 29

The share market is currently returning 18% p.a. ,while the risk-free asset return is 6%.If an investor wishes to earn a return of 10%,what weight should the investor hold in the risk-free asset?

Question 30

A portfolio comprising two assets can be formed with zero variance,provided the correlation between the securities is:

Question 31

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
In estimating the covariance matrix,the Sharpe diagonal approach for 10 assets involves how many calculations?

Question 32

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What is the expected utility of asset A?

Question 33

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.By how much will the utility of asset B exceed that of asset A for this investor?

Question 34

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Question 35

The key factor in asset choice is the effect of the additional asset on the existing portfolio.To calculate the change in portfolio variance and expected return with an additional asset,what does the investor require?

Question 36

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor that has a log utility function.By how much will the utility of asset B exceed that of asset A for this investor?

Question 37

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
Given a portfolio of 50 shares,how many variance and unique covariance terms can be estimated using the Markowitz approach?

Question 38

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Question 39

As per figure 7.8,the relationship between securities with various correlation coefficients is depicted.We can see from this that it is possible to create a portfolio that is risk-free where the correlation between two securities is -1.
According to Markowitz (1959),if all of the portfolios that satisfy the mean-variance criterion are identified,and investor preferences can be modelled,then the portfolio chosen by an investor is that combination of __________ that maximises expected utility.

Question 40

Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?